Structures in Response to Compartment Fires
Doctor of Philosophy, University of Edinburgh, 2001.
This thesis and the research described and reported within has been completed solely by Susan Lamont under the supervision of Dr A.S. Usmani, Prof. D.D. Drysdale, Dr B. Lane and Prof. J.M. Rotter.
Where other sources are quoted full references are given.
Susan Lamont, 29th September 2001.
http://www.civ.ed.ac.uk/research/fire/project/thesis/masterSL2.pdf (local copy here).
For many years the ability of highly redundant composite framed structures to resist the effects of fire has been undervalued and largely misunderstood. This was first realised when, after a number of real fires in multi-storey composite steel framed structures structural failure did not occur. The Broadgate Phase 8 fire is probably the most notable. This accidental fire happened during the Construction phase when the steel frame was only partially fire protected. Despite very high temperatures during the fully developed phase of the fire and considerable deflections in the composite slab there was no collapse. This initiated construction of an 8-storey composite steel frame at Building Research Establishment�s (BRE�s) large scale test facility in Cardington. Six fire tests were conducted, of varying size and configuration, to observe and ultimately explain why composite steel-framed structures adopt very large deflections during a fire but do not collapse.
Computer modelling of the tests by a number of research groups, including the University of Edinburgh, followed. Finite element modelling of these tests provided a wealth of information about the behaviour of whole frame structures in fire. However despite extensive dissemination of the available information, improvements in design guidance have been hindered by the wide scope it was required to cover and the large number of variables involved, when the new knowledge was based on analysis of only six tests all conducted on the same structure.
The purpose of this research has been to confirm and extend the conclusions of the Cardington frame fire tests and the subsequent numerical modelling. Two generic composite steel frames were designed in accordance with EC4 Part 1.1. Their shape and size in plan were chosen to be significantly different from the Cardington frame.
An investigation of the methods available to model compartment fires was carried Out. Comparisons were made between predicted natural fires and atmosphere temperatures measured during experimental compartment fires. Heat transfer models were also tested against steel and concrete temperatures recorded during the Cardington tests. Using these design tools, natural fire curves were assumed and heat transfer calculations were made, to obtain steel and concrete temperature histories as inputs to structural analyses.
A series of parametric studies was conducted on the two generic frames to investigate the response of the structure if the fire exposure or location changed. The fire scenarios included compartment fires on the whole floor, at the edge and corners of the structures. By altering the size and location of the compartment, the level of restraint to thermal expansion and thermal bowing of the structural elements changed.
A further set of studies varied the number of beam members with applied fire protection. Three scenarios were tested. Primary and edge beams protected, only edge beams protected and all beams unprotected. In all studies secondary beams were unprotected and columns were protected to their full height. The behaviour observed in the Cardington frame tests has been confirmed in both generic frames and new phenomena have been highlighted.
The temperature history of a natural fire depends upon the available ventilation, fire load, room geometry and thermal properties of the boundary wall materials. Many fire scenarios exist leading to a range of thermal responses in the structural elements, which are manifested in various combinations of deflections and forces. In composite floor slabs fires of short post-flashover duration result in low concrete temperatures but high temperatures in the steel beams. High gradients exist over the depth of the composite causing thermal bowing behaviour. Fires of longer duration allow the concrete to reach much greater temperatures therefore, thermal expansion of the composite is the more dominant behaviour.
Differences in compartment fire size and location provide various degrees of restraint to an expanding structure. The level and location of restraint is a contributing factor to the patterns of deflections and forces.
Removing applied fire protection from all steel beams leads to greater deflections of the composite floor. However, relative displacements between an unprotected edge beam and the centre of the fire compartment may be reduced causing a reduction in the tensions experienced by the slab at high deflections. Providing applied fire protection to steel beams in composite structures may not be necessary although the impact of large deflections on compartment breach should be considered.
Overall the generic frame structures behaved well under all scenarios tested.
The following papers and reports have heen produced as a result of this research:
S. Lamont, A.S. Usmani and Prof. D.D. Drysdale. Heat transfer analysis of the composite slab in the Cardington frame fire tests. Fire Safety Journal 2001.
A.M. Sanad, S. Lamont, A.S. Usmani and J.M. Rotter. Structural behaviour in fire compartment under different heating regimes - Part 1 (slab thermal gradients). Fire Safety Journal, Vol. 35, 2000.
A.M. Sanad, S. Lamont, A.S. Usmani and J.M. Rotter. Structural behaviour in fire compartment under different heating regimes - Part 2 (slab mean temperatures). Fire Safety Journal, Vol. 35, 2000.
A.S. Usmani, J.M. Rotter, S. Lamont, A.M. Sanad and M. Gillie. Fundamental principles of structural behaviour under thermal effects. Accepted by the Fire Safety Journal.
S. Lamont, B. Lane, AS. Usmani and D.D. Drysdale. The fire resistance test in the context of real beams. (submitted to AISC Engineering Journal June 2001).
S. Lamont, A.S. Usmani, J.M. Rotter and B. Lane. New concepts in structural strength assessment for large buildings in fire. In Proceedings of the 2001 Structures Congress and Exposition, ASCE, SEI.
S. Lamont, A.S. Usmani and D.D. Drysdale. Fire protection of steel beams in composite framed structures. In proceedings of the 9th Fire science and Engineering Conference, Interflam 2001.
Presentations to STIFF
S. Lamont and A. Usmani. A comparison of structural behaviour in response to a wellventilated and an under-ventilated fire. Presented at STIFF (STeel in Fire Forum) 23rd April 2001. www.shef.ac.uk/fire-research/steelinfire.
S. Lamont and A. Usmani. A comparison of structural behaviour in response to a "short-hot" and a "long-cool" fire. Presented at STIFF (STeel in Fire Forum) 12th September 2001. www.shef.ac.uk/fire-research/steelinfire.
S. Lamont and D.D. Drysdale. Evaluation of the software O Zone. In Development of the UK and European fire design codes-Natural fires and the response of structural steel. CORUS Publication, 2001.
A special thank you to my supervisors Dr A.S. Usmani, Prof. D.D. Drysdale and Dr B. Lane for their support and expert advice.
Thank you to my family, friends and most of all Max for their faith and support throughout the last three years.
This research was funded by an EPSRC Case award through Ove Arup and is gratefully acknowledged.
List of Figures xxv
List of Tables xxv
1 Introduction. 1
2 An overview of structural fire safety design and research. 7
2.1 Introduction. 8
2.2 Traditional Design. 8
2.2.1 The fire resistance test. 82.3 The Swedish Design Guide. 24
2.2.2 Critical steel temperature. 11
2.2.3 Fire protection. 11
2.2.4 Shortcomings of the fire resistance test. 13
2.2.5 Equivalent fire exposure. 14
2.2.6 Natural Fire method. 20
2.2.7 Fire resistance by calculation. 20
2.4 Performance based design. 25
2.5 Factors affecting the behaviour of structures in fire. 28
2.5.1 Mechanical properties of steel at elevated temperatures. 282.6 Research into the behaviour of single elements of structure in fire. 41
2.5.2 Mechanical properties of concrete at elevated temperature. 32
2.5.3 Thermal Bowing and Thermal Expansion. 36
2.5.4 Redundancy. 40
2.5.5 Loading. 40
2.7 Frame Analysis. 51
2.8 Conclusion. 54
3 Thermal response of structures to real fire. 55
3.1 Introduction. 56
3.2 Natural Fire Curves. 56
3.3 Compartment Fires. 57
3.4 The burning regime: Ventilation vs. Fuel controlled fires. 63
3.4.1 Opening factor. 643.5 CIB compartment fire experiments. 66
3.4.2 Differentiating between fuel and ventilation controlled fires. 64
3.4.3 Fuel controlled fire. 65
3.6 Compartment fire modelling. 67
3.6.1 Model types. 673.7 Parametric T-t curves. 77
3.6.2 Zone modelling. 68
3.6.3 Heat balance equation for an enclosure (Pettersson et al, 1976 ). 70
3.6.4 Empirical/Characteristic temperature curves. 74
3.8 The Natural Fire Safety Concept.  81
3.9 Other factors influencing the rate of heat release in a compartment fire. 84
3.9.1 Vent location. 843.10 Compartment fire models for computers. 88
3.9.2 Fuel load. 85
3.9.3 Compartment dimensions. 86
3.9.4 Thermal inertia of the compartment boundaries, kpc. 87
3.11 Heat Transfer. 91
3.12 Thermal properties of materials. 94
3.13 Predicting steel temperatures. 98
3.13.1 Hp/A Concept. 993.14 Modelling heat transfer in concrete. 102
3.13.2 Simple heat transfer models. 100
3.13.3 Uninsulated steel.  100
3.13.4 Insulated steel. 101
3.13.5 Nomograms. 102
3.15 Conclusions. 105
4 Composite steel frame structures in fire: Research and design developments. 107
4.1 Introduction. 108
4.2 Case studies. 108
4.3 Fire tests. 109
4.3.1 BHP William Street fire tests, Melbourne.  1094.4 The PIT Project. 118
4.3.2 Stuttgart-Vaihingen University fire tests, Germany. 110
4.3.3 Cardington frame fire tests. 111
4.4.1 The numerical models. 1214.5 Numerical Modelling at Sheffield University. 133
4.4.2 Theoretical analyses. 131
4.4.3 Parametric studies. 131
4.4.4 Analysis of the raw test data by British Steel. 132
4.4.5 Conclusions of the PIT project. 132
4.6 Developments in Europe. 134
4.6.1 ECSC Project.  1344.7 Design guidance. 135
4.8 Conclusion. 138
5 Heat transfer analysis of the Cardington frame fire tests using HADAPT. 140
5.1 Introduction. 141
5.2 Solving Transient Conduction using the Finite Element Method. 141
5.2.1 The Governing Differential Equations and Finite Element Formulation. 1425.3 Modelling Phase Change. 143
5.4 Interface Elements for modelling heat transfer between two materials. 144
5.5 The Models. 144
5.5.1 Material Properties. 1455.6 Modelling and Analysis. 146
5.6.1 Model 1: No Metal Deck. 1465.7 Model 2: Including the Metal Deck. 156
5.6.2 Hottest and Coolest slab. 147
5.6.3 Sensitivity Analyses. 149
5.6.4 Summary. 154
5.6.5 Correlation with measured temperatures. 156
5.7.1 Prediction of Test 4 Temperatures. 1605.8 Modelling Edge beams. 160
5.9 Conclusions. 169
6 Analytical and numerical analysis of simple beam models in fire. 173
6.1 Introduction. 174
6.2 Thermal expansion and thermal bowing Interaction. 174
6.2.1 The heating regime. 1756.3 Runaway in axially unrestrained and axially restrained beams. 193
6.2.2 Thermal expansion. 175
6.2.3 Thermal Bowing. 179
6.2.4 Combined thermal expansion and thermal bowing. 181
6.2.5 Numerical analysis of thermal expansion and thermal bowing in a restrained beam. 183
6.2.6 Summary. 191
6.4 Conclusions. 202
7 Structural behaviour in British Steel Test 1 under different heating regimes. 204
7.1 Introduction. 205
7.2 Effect of varying the slab thermal gradients in British Steel test 1. 205
7.2.1 Description of the fire compartment. 2057.3 Effect of varying the slab mean temperature in British Steel test 1. 219
7.2.2 The finite element model. 206
7.2.3 Slab gradient variation in longitudinal direction. 210
7.2.4 Slab gradient variation in transverse direction. 214
7.3.1 Slab mean temperature variation in longitudinal direction. 2197.4 Conclusions. 231
7.3.2 Mean temperature variation in transverse direction. 226
8 Parametric studies on a small generic composite steel frame. 232
8.1 Introduction. 233
8.2 Analysis. 234
8.2.1 The generic frame. 2348.3 Parametric Studies. 244
8.2.2 Design fires. 234
8.2.3 Heat transfer. 235
8.2.4 Temperature loading. 236
8.2.5 The structural model. 238
8.2.6 The numerical model. 243
8.4 Results. 244
8.4.1 Short versus long post-flashover fires in the 2x2 bay frame with edge beams protected. 2448.5 Conclusions. 317
8.4.2 Impact of imposed loading on primary beam instability. 280
8.4.3 Impact of secondary beams on primary beam instability. 281
8.4.4 Simple beam study. 282
8.4.5 Effect of applied fire protection in a "long" post-flashover fire. 286
8.4.6 Effect of applied fire protection in a "short" post-flashover fire. 301
8.4.7 Behaviour of the slab. 312
9 Parametric studies on a relatively large generic composite steel frame. 320
9.1 Introduction. 321
9.2 The generic frame. 321
9.3 Compartment fires. 322
9.4 Temperature loading. 323
9.5 Scenarios tested. 323
9.6 Results. 324
9.6.1 Short versus long post-flashover fires in the 9x9 bay frame with the Edge beams unprotected. 3249.7 Large versus small frames. 356
9.6.2 Corner and Edge compartment fires in the 9 x 9 frame. 339
9.6.3 Effect of protection level under a "long" post-flashover fire in a large frame. 350
9.6.4 Response of the beams. 352
9.6.5 Slab behaviour. 352
9.6.6 Summary. 356
9.8 Conclusions. 358
10 Conclusions and Further work. 360
10.1 Introduction. 361
10.2 Summary and Conclusions. 361
10.3 Further work. 366
A Review of the Parametric Temperature-time curve in EC 1 Part 2.2. 388
B Review of 0 Zone. 389
List of Figures
2.1 Standard Temperature-time curves. 10
2.2 Comparison of the standard fire curve and real temperature-time histories. The fire load is in kg/m2 and the ventilation is a fraction of one wall e.g 15(1/2) corresponds to a fire load of 15kg/m2 and ventilation equal to half of one wall.  15
2.3 Equivalent fire severity on a temperature basis.  16
2.4 Fire and structural response models.  21
2.5 The Hp/A concept. 22
2.6 Outline of the New Zealand fire engineering design procedure. 26
2.7 Thermal expansion of steel with increasing temperature.  29
2.8 Stress-strain curves for typical-hot rolled steel at elevated temperatures.  32
2.9 Stress-strain curves for steel illustrating yield strength and proof strength.  32
2.10 Reduction in yield strength and modulus of elasticity of steel with temperature (EC3 1995).  33
2.11 Thermal expansion of concretes.  34
2.12 Poisson ratio.  35
2.13 Concrete creep.  36
2.14 Stress strain relationships for concrete at elevated temperatures (EC2 1993).  37
2.15 Design values for reduction in compressive strength with temperature.  38
2.16 Design values for reduction of modulus of elasticity.  39
2.17 Column expansion in fire. 44
2.18 Complete load-deflection curve for a reinforced concrete slab.  49
2.19 Tensile membrane load carrying mechanism in a slab with clamped edges.  50
2.20 Tensile membrane load carrying mechanism in a simply supported slab.  51
3.1 The course of a well-ventilated compartment fire.  57
3.2 The effect of enclosure on the rate of burning of a slab of polymethylmethacrylate (Friedman 1975 as cited by Drysdale ). 58
3.3 t2 fire growth according to Equation 3.4.  61
3.4 Pressure profile over the opening in a compartment resulting in cold air flowing in and hot gases flowing out. 64
3.5 Determination of a weighted value of Aw√H for enclosures with more than one opening.  65
3.6 Schematic diagram showing the variation of mass burning rate with ventilation parameter AwH1/2 and fuel bed area Af.  66
3.7 Average compartment temperatures during the steady burning period for wood crib fires in model enclosures as a function of the "opening factor". Symbols refer to different compartment shapes.  67
3.8 2 zones in a compartment fire model. 68
3.9 Illustration of the heat balance in a fire compartment (Pettersson, 1976 ). 71
3.10 Theoretical temperature-time curves for compartment fires with different fire load densities and opening factors (Pettersson, 1976 ). 74
3.11 Gas temperature-time curves in full-scale fire. Solid lines represent experimental data for a fire load density of 96MJ/m2 and an opening factor, Aw√H/At = 0.068m1/2. The dashed line is the calculated temperature-time curve using the measured rate of burning (Pettersson, 1976 ). 75
3.12 Theoretical temperature-time curves for fully developed fires in compartments of different boundaries: A, materials with thermal properties corresponding to the average values for concrete, brick and lightweight concrete; B, concrete (500kg/m3); F, 80% uninsulated steel sheeting, 20% concrete. In all cases the fire load and ventilation factor were consistent (Pettersson, 1976 ). 76
3.13 A comparison of Temperature-time curves (Lie, 1974 ). 77
3.14 Comparison between T-t curves obtained by solving a heat balance and those described by an analytical expression for ventilation-controlled fires in enclosures bounded by dominantly heavy materials (ρ≥1600kg/m3) (Lie, 1995 ). 78
3.15 Comparison between T-t curves obtained by solving a heat balance and those described by an analytical expression for ventilation-controlled fires in enclosures bounded by dominantly light materials (ρ≤1600kg/m3) (Lie, 1995 ). 78
3.16 Scope of the Natural Fire Safety Concept Research.  82
3.17 Scope of the Natural Fire Safety Concept Research.  84
3.18 Plot of the recorded atmosphere temperatures in British Steel long compartment test 6. 87
3.19 Thermal properties of steel.  96
3.20 Density of structural concrete at high temperatures.  97
3.21 Thermal properties of different structural concretes.  98
3.22 Thermal properties of concrete.  99
3.23 Typical nomogram for estimating maximum steel temperatures using the "Element factor".  103
3.24 Temperature contours in concrete beams exposed to the standard fire from EC2.  104
3.25 A slab heated on one face showing the dry-wet interface. 104
4.1 Plan view of the Cardington 8-storey frame showing the 4 British Steel Tests. 111
4.2 Plan view of the Cardington 8-storey frame showing the 2 BRE Tests. 112
4.3 British Steel Test 1: Restrained beam test. 113
4.4 Column squashing in British Steel Test 2: Plane frame test. 114
4.5 Connection failure in British Steel Test 2: Plane frame test. 114
4.6 Local buckling of beams in British Steel Test 3: Corner test. 115
4.7 Compartment fire in progress in British Steel Test 4: Office demonstration test. 116
4.8 Aftermath of the British Steel Test 4: Office demonstration test. 117
4.9 Local buckling of the lower flange and folding of the webs in British Steel Test 4: Office demonstration test. 117
4.10 Average atmosphere temperatures recorded in the British Steel tests. 119
4.11 Average atmosphere temperatures recorded in the BRE corner test.  119
4.12 Average atmosphere temperatures recorded in the BRE large compartment test (1/2 floor).  120
4.13 Steel material behaviour in Eurocode 3 Part 1.2.  121
4.14 Compressive concrete material behaviour in Eurocode 2 Part 1.2.  122
4.15 Flowchart describing the program SRAS.  125
4.16 Flowchart describing the details of stress calculation within SRAS.  126
4.17 Deflection against beam lower flange temperature measured and predicted by the Edinburgh University grillage model of test 1. 129
4.18 Deflection against beam lower flange temperature measured and predicted by the Edinburgh University FEAST model of test 1. 130
4.19 Strains measured and predicted by the Edinburgh University Grillage model of British Steel test 1. 130
4.20 The floor plan of the ECSC Building. 134
4.21 The basis of the SCI design procedure.  137
5.1 Typical variation of enthalpy (H) and ceff with temperature. 143
5.2 Interface element with its nodal connectivity. 144
5.3 The concrete slab model. 145
5.4 The mesh. 146
Predicted and measured concrete temperatures in Test 3 at CS1:
5.5 No water evaporation, No metal deck. 147
5.6 Includes water evaporation, No metal deck. 148
5.7 Thermocouple locations through the depth of the slab at CS1 in test 3. 148
5.8 Upper bound solution (HOTTEST SLAB), No metal deck. 150
5.9 Lower bound solution (COOLEST SLAB), No metal deck. 150
5.10 Sensitivity of the predicted concrete temperatures to changes in conductivity. 151
5.11 Sensitivity of the predicted concrete temperatures to changes in density and specific heat. 152
5.12 Sensitivity of the predicted concrete temperatures to changes in moisture content. 152
5.13 Sensitivity of the predicted concrete temperatures to changes in the temperature range for water evaporation (5% moisture content). 153
5.14 Sensitivity of the predicted concrete temperatures to changes in resultant emissivity. 154
5.15 Sensitivity of the predicted concrete temperatures to changes in convection coefficient. 155
5.16 Sensitivity of the predicted concrete temperatures to changes in convection coefficient. 155
5.17 Sensitivity of the predicted concrete temperatures to changes in slab thickness. 156
5.18 Test 3 Predicted and measured temperatures at CS1, No metal deck. 157
5.19 Test 3 Predicted temperature profile (heating). 158
5.20 Test 3 Predicted temperature profile (heating). 158
5.21 Test 3 Predicted temperature profile (heating). 158
5.22 Test 3 Predicted temperature profile (cooling). 159
5.23 Test 3 Predicted temperature profile (cooling). 159
5.24 Test 3 Predicted and measured temperatures at CS1, includes metal deck. 160
5.25 Thermocouple locations in the depth of the slab in Test 1 and Test 2. 161
5.26 Test 1 Predicted and measured temperatures at B1, includes metal deck. 161
5.27 Test 2 Predicted and measured temperatures at CS2, includes metal deck. 162
5.28 Test 4 Predicted temperatures at CS1, includes metal deck. 162
5.29 Cross section through an unprotected edge beam in Test 4. 163
5.30 Cross section through a protected edge beam in Test 3. 164
5.31 Test 3: The mesh used to model protected edge beam. 165
5.32 Test 3: 2D HADAPT contour plot of the protected edge beam. 166
5.33 Test 3: Plan of test compartment showing location of thermocouples for measuring beam temperature profiles. 166
5.34 Test 3: Location of thermocouples in protected edge beam on gridline F. 167
5.35 Test 3: comparison between predicted and measured steel temperatures in the web and lower flange of the edge beam on gridline F at location G. 167
5.36 Test 3 comparison between predicted and measured steel temperatures in the top flange of the edge beam on gridline F at location G. 168
5.37 Test 3: comparison between predicted and measured steel temperatures in the web and lower flange of the edge beam on gridline F at location K. 168
5.38 Test 3 comparison between predicted and measured steel temperatures in the top flange of the edge beam on gridline F at location K. 169
5.39 Test 4: Plan of test compartment showing location of thermocouples for measuring beam temperature profiles. 170
5.40 Test 4: Location of thermocouples in the unprotected edge beams. 170
5.41 Test 4 comparison between predicted and measured temperatures in edge beam on gridline 4 position B3. 171
5.42 Test 4 comparison between predicted and measured temperatures in edge beam on gridline D position B11. 171
6.1 Uniform mean temperature and through depth thermal gradient over the cross-section of a beam. 175
6.2 Thermal expansion in simple beams with different restraint conditions. 177
6.3 Thermal expansion against finite lateral restraints. 178
6.4 Buckling temperatures for thermal expansion against finite lateral restraints (Usmani et al ). 179
6.5 Thermal bowing in simple beams with different restraint conditions. 180
6.6 Thermal bowing in a beam with rotational stiffness kr at its ends. 181
6.7 Thermal expansion and thermal bowing interaction in simple beam models. 182
6.8 Temperature deflection responses for combinations of ΔT and T,y. 183
6.9 Numerical Model:Deflection at mid-span of the fully fixed beam. 185
6.10 Numerical Model: Axial force at mid-span of the fully fixed beam. 186
6.11 Numerical Model: Moment at mid-span of the fully fixed beam. 186
6.12 Numerical Model: Deflections at mid-span of the pinned beam, ΔT=400°C. 187
6.13 Numerical Model: Deflections at mid-span of the pinned beam, T,y=1°C/mm. l87
6.14 Numerical Model: Deflections at mid-span of the pinned beam, T,y=5°C/mm. l87
6.15 Numerical Model: Axial force at mid-span of the pinned beam, ΔT=400°C. 188
6.16 Numerical Model: Axial force at mid-span of the pinned beam, T,y=1°C/mm. 188
6.17 Numerical Model: Axial force at mid-span of the pinned beam, T,y=5°C/mm. 188
6.18 Numerical Model: Moment at mid-span of the pinned beam, ΔT=400°C. 189
6.19 Numerical Model: Moment at mid-span of the pinned beam, T,y=1°C/mm. l9O
6.20 Numerical Model: Moment at mid-span of the pinned beam, T,y=5°C/mm. l9O
6.21 Deflections of the pinned beam at mid-span in response to thermal expansion and thermal bowing. 191
6.22 Axial forces in the pinned beam in response to thermal expansion and thermal bowing. 192
6.23 Moments in the pinned beam in response to thermal expansion and thermal bowing. 192
6.24 Runaway in an axially restrained and unrestrained beam. 195
6.25 The effect of loading on a simple restrained beam subject to heating. 196
6.26 Rates of deflection at mid-span against temperature for all load cases. 197
6.27 Catenary action coupled with flexural resistance. 197
6.28 Moment equilibrium for udl 0.5w. 199
6.29 Axial force for udl 0.5w. 200
6.30 Moment equilibrium for udl 1.0w. 200
6.31 Axial force for udl 1.0w. 201
6.32 Moment equlibrium for udl 2.0w. 201
6.33 Axial force for udl 2.0w. 202
7.1 Layout of the Cardington frame fire test. 206
7.2 Layout of the Cardington frame fire test. 207
7.3 Cross section of one rib showing the location of the geometric centroid and the temperature gradient through its depth. 208
7.4 Cross section of the composite beam showing the location of the slab geometric centroid and the temperature gradient through it. 208
7.5 Idealisation of the temperature regime acting on the slab. 209
7.6 Joist deflection: Varying the temperature gradient in the longitudinal slab. 211
7.7 Moments at mid-span: Varying the temperature gradient in the longitudinal slab. 211
7.8 Axial forces at mid-span: Varying the temperature gradient in the longitudinal slab. 212
7.9 Moment Differences: Varying the temperature gradient in the longitudinal slab. 212
7.10 Ribs axial force: Varying the temperature gradient in the longitudinal slab. 213
7.11 Ribs moment over the joist: Varying the temperature gradient in the longitudinal slab. 214
7.12 Joist Deflection: Varying the temperature gradient in the transverse slab. 215
7.13 Axial force at x/l=0.0: Varying the temperature gradient in the transverse slab. 216
7.14 Axial force at x/l=0.5: Varying the temperature gradient in the transverse slab. 216
7.15 Joist Moment at x/l=0.0 and 0.5: Varying the temperature gradient in the transverse slab. 217
7.16 Moment Differences: Varying the temperature gradient in the transverse slab. 218
7.17 Ribs Axial force: Varying the temperature gradient in the transverse slab. 218
7.18 Ribs Moment over the joist: Varying the temperature gradient in the transverse slab. 219
7.19 Joist Deflection: Varying the temperature at the centroid of the longitudinal slab. 220
7.20 Axial force at x/l=0.0: Varying the temperature at the centroid of the longitudinal slab. 221
7.21 Axial force at x/l=0.5: Varying the temperature at the centroid of the longitudinal slab. 222
7.22 Moment differences: Varying the temperature at the centroid of the longitudinal slab. 223
7.23 Joist Moment at x/l=0.0 and 0.5: Varying the temperature at the centroid of the longitudinal slab. 223
7.24 Ribs axial force : Varying the temperature at the centroid of the longitudinal slab. 225
7.25 Ribs Moment over the joist: Varying the temperature at the centroid of the longitudinal slab. 225
7.26 Joist deflection: Varying the temperature at the centroid of the transverse slab. 227
7.27 Axial force at x/l=0.0: Varying the temperature at the centroid of the transverse slab. 228
7.28 Axial force at x/l=0.5: Varying the temperature at the centroid of the transverse slab. 228
7.29 Moment Differences: Varying the temperature at the centroid of the transverse slab. 229
7.30 Joist Moment at x/l=0.0 and 0.5: Varying the temperature at the centroid of the transverse slab. 229
7.31 Ribs Axial force: Varying the temperature at the centroid of the transverse slab. 230
7.32 Ribs moment over the joist: Varying the temperature at the centroid of the transverse slab. 230
8.1 Schematic plan view of the 2x2 bay generic frame. 235
8.2 Compartment fire Temperature-time curves developed by Pettersson.  236
8.3 Mean steel and concrete temperatures against time used in the ABAQUS model. 238
8.4 Mean steel and concrete temperatures against secondary beam temperature used in the ABAQUS model. 239
8.5 Points of beam temperature data in ABAQUS. 239
8.6 Linear gradient history of the concrete slab. 240
8.7 Column temperature histories. 240
8.8 Idealisation of the temperature regime acting over the slab. 241
8.9 Non-linear gradients through the depth of the slab for the "short-hot" fire, OF=0.02. 241
8.10 Non-linear gradients through the depth of the slab for the "short-hot" fire, OF=0.08. 243
8.11 ABAQUS mesh of the 2x2 frame. 243
8.12 Deflection history of the unprotected secondary beams against secondary beam temperature. 246
8.13 Deflection history of the unprotected primary beams against secondary beam temperature. 246
8.14 Deflection history of the unprotected secondary beams against time. 247
8.15 Deflection history of the protected edge beams parallel to the primary beams against secondary beam temperature. 247
8.16 Deflection history of the protected edge beams parallel to the secondary beams against secondary beam temperature. 248
8.17 Rates of deflection at mid-span of the edge and primary beams against secondary beam temperature, OF=0.02. 248
8.18 Rates of deflection at mid-span of the edge and primary beams against secondary beam temperature, OF=0.08. 249
8.19 Deflection contours in the slab at the end of heating. 250
8.20 Variation of axial force along secondary beam AC2 at various secondary beam temperatures, OF=0.02. 251
8.21 Variation of axial force along secondary beam AC2 at various secondary beam temperatures, OF=0.08. 251
8.22 Secondary beam AB2: Axial force against secondary beam temperature, OF=0.02. 252
8.23 Secondary beam AB2: Axial force against secondary beam temperature, OF=0.08. 253
8.24 Secondary beam AB4: Axial force against secondary beam temperature, OF=0.02. 253
8.25 Secondary beam AB4: Axial force against secondary beam temperature, OF=0.08. 254
8.26 Primary beam B14: Axial force against secondary beam temperatures, OF=0.02. 256
8.27 Primary beam B14: Axial force against secondary beam temperatures, OF=0.08. 256
8.28 Primary beam B46: Axial force against secondary beam temperatures, OF=0.02. 257
8.29 Primary beam B46: Axial force against secondary beam temperatures, OF=0.08. 257
8.30 Moment resisting connection. 258
8.31 Rotations near the ends of the primary beam B14. 258
8.32 Material yield limits of the primary beam. 259
8.33 Movement of column B1, OF=0.02. 260
8.34 Movement of column B1, OF=0.08. 261
8.35 Vertical displacement history of column B4 at slab level. 262
8.36 Reaction forces recorded in the columns against secondary beam temperature. 262
8.37 Primary beam B14: Shear force against secondary beam temperatures, OF=0.02. 263
8.38 Primary beam B14: Shear force against secondary beam temperatures, OF=0.08. 263
8.39 Edge beam ABi: Axial force against secondary beam temperature, OF=O.0226
8.40 Edge beam BC1: Axial force against secondary beam temperature, OF=0.0226
8.41 Edge beam ABi: Axial force against secondary beam temperature, OF=O.0826
8.42 Edge beam BC1: Axial force against secondary beam temperature, OF=0.0826
8.43 Horizontal displacement of all the columns at slab level, OF=0.08. 266
8.44 Composite axial forces along secondary beam AC2. 267
8.45 Composite axial forces along secondary beam AC4. 267
8.46 Composite moments along secondary beam AC2. 268
8.47 Axial force in the ribs of the slab, 1200mm from gridline A, OF=0.02. 269
8.48 Axial force in the ribs of the slab, 1200mm from gridline A, OF=0.08. 269
8.49 Axial force in the thin direction of the slab 600mm from gridline 1, OF=0.02. 270
8.50 Axial force in the thin direction of the slab 600mm from gridline 1, OF=0.08. 270
8.51 Axial force in the thin direction of the slab 4200mm from gridline 1, OF=0.02. 271
8.52 Axial force in the thin direction of the slab 4200mm from gridline 1, OF=0.08. 272
8.53 Axial force contours in the slabs x (1) direction at the end of heating. 273
8.54 Axial force contours in the slabs y (3) direction at the end of heating. 274
8.55 Mechanical strains in the reinforcement OF=0.02, whole floor fire at. 600°C. 275
8.56 Mechanical strains in the reinforcement OF=0.02, whole floor fire at 750°C 276
8.57 Mechanical strains in the reinforcement OF=0.08, whole floor fire, at 600°C. 277
8.58 Mechanical strains in the reinforcement OF=0.08, whole floor fire at 750°C. 278
8.59 Mechanical strains in the reinforcement OF=0.08, whole floor fire at. 950°C. 279
8.60 Deflection history of the secondary beams at mid-span. A comparison between Cardington live load and the reference case. 281
8.61 Primary beam B14: Axial force in response to the Cardington live load against secondary beam temperature. 282
8.62 Schematic plan view of the 2x2 bay generic frame with all the secondary beams removed. 283
8.63 Deflection history of the primary beams at mid-span with no secondary beams in the frame. 284
8.64 Axial force in Primary beam B14 with no secondary beams in the frame. 284
8.65 Deflection contours in the slab at 950°C. 285
8.66 The simple ABAQUS "cross" beams model. 287
8.67 Axial force in the primary beam of the simple ABAQUS "cross" beams model. 288
8.68 Deflection contours in the slab at 750°C. 289
8.69 Deflections of the secondary beams, OF=0.02. 290
8.70 Deflections of the primary beams, OF=0.02. 291
8.71 Deflections of the edge beams parallel to the secondary beams, OF=0.02. 291
8.72 Deflections of the edge beams parallel to the primary beams, OF=0.02. 292
8.73 Rates of deflection at mid-span of the edge and primary beams against secondary beam temperature, OF=0.02, primary and edge beams protected. 292
8.74 Rates of deflection at mid-span of the edge and primary beams against secondary beam temperature, OF=0.02, edge beams protected. 293
8.75 Rates of deflection at mid-span of the edge and primary beams against secondary beam temperature, OF=0.02, all beams unprotected. 293
8.76 Variation of axial force against secondary beam temperatures, primary and edge beams protected. 294
8.77 Variation of axial force against secondary beam temperatures, only edge beams protected. 294
8.78 Variation of axial force against secondary beam temperatures, all beams unprotected. 295
8.79 Horizontal movement of column B1, OF=0.02, primary and edge beams protected. 296
8.80 Horizontal movement of column B1, OF=0.02, edge beams protected. 296
8.81 Horizontal movement of column B1, OF=0.02, all beams unprotected. 297
8.82 Variation of axial force at the mid-span of edge beam AB1 and BC1 against temperature, primary and edge beams protected. 297
8.83 Variation of axial force at the mid-span of edge beam AB1 and BC1 against temperature, edge beams protected only. 298
8.84 Variation of axial force at the mid-span of edge beam AB1 and BC1 against temperature, all beams unprotected. 298
8.85 Mechanical strains in the reinforcement OF=0.02, whole floor fire at 750°C, edge beams protected. 299
8.86 Mechanical strains in the reinforcement OF=0.02, whole floor fire at 750°C, all beams unprotected. 300
8.87 Deflection contours in the slab at 950°C. 302
8.88 Deflections of the secondary beams, OF=0.08. 303
8.89 Deflections of the primary beams, OF=0.08. 304
8.90 Deflections of the edge beams parallel to the secondary beams, OF=0.08. 304
8.91 Deflections of the edge beams parallel to the primary beams, OF=0.08. 305
8.92 Rates of deflection at mid-span of the edge and primary beams against secondary beam temperature, OF=0.08. 305
8.93 Rates of deflection at mid-span of the edge and primary beams against secondary beam temperature, OF=0.08. 306
8.94 Secondary beam AB2: Axial force against secondary beam temperatures, OF=0.08, edge beams protected. 307
8.95 Secondary beam AB2: Axial force against secondary beam temperatures, OF=0.08, all beams unprotected. 307
8.96 Primary beam B14: Axial force against secondary beam temperatures, OF=0.08, edge beams protected. 308
8.97 Primary beam B14: Axial force against secondary beam temperatures, OF=0.08, all beams unprotected. 308
8.98 Movement of column B1, edge beams protected. 309
8.99 Movement of column B1, all beams unprotected. 309
8.100 Variation of axial force against secondary beam temperatures, only edge beams protected. 310
8.101 Variation of axial force against secondary beam temperatures, all beams unprotected. 310
8.102 Variation of axial force at the mid-span of edge beam AB1 and BC1 against temperature, edge beams protected only. 311
8.103 Variation of axial force at the mid-span of edge beam AB1 and BC1 against temperature, all beams unprotected. 311
8.104 Axial force in the thin direction of the slab 600mm from gridline 1, edge beams protected. 312
8.105 Axial force in the thin direction of the slab 600mm from gridline 1, edge beams unprotected. 313
8.106 Force in the thin direction of the slab 4200mm from gridline 1, edge beams protected. 313
8.107 Force in the thin direction of the slab 4200mm from gridline 1, edge beams unprotected. 314
8.108 Mechanical strains in the reinforcement OF=0.08, whole floor fire at 950oC, edge beams protected. 315
8.109 Mechanical strains in the reinforcement OF=0.08, whole floor fire at 950oC, edge beams unprotected. 316
9.1 Schematic plan view of the 9x9 bay generic frame. 321
9.2 Schematic plan view of the 9x9 bay generic frame numerical model. 322
9.3 The finite element mesh of the 9x9 frame created in ABAQUS. 322
9.4 Schematic plan view of the 9x9 bay generic frame showing the location of the compartment fires. 323
9.5 Mean steel and concrete temperatures against secondary beam temperature used in the ABAQUS model. 324
9.6 Deflection history of the unprotected secondary beams against secondary beam temperature. 326
9.7 Deflection history of the unprotected primary beams against secondary beam temperature. 326
9.8 Deflection history of the protected edge beams parallel to the secondary beams against secondary beam temperature. 327
9.9 Deflection history of the protected edge beams parallel to the primary beams against secondary beam temperature. 327
9.10 Deflection contours in the slab at a reference temperature of 600°C. 328
9.11 Deflection contours in the slab at the end of heating. 329
9.12 Variation of axial force along secondary beam AD2 at various secondary beam temperatures, OF=0.02. 330
9.13 Variation of axial force along secondary beam AD2 at various secondary beam temperatures, OF=0.08. 330
9.14 Secondary beam AB2: Axial force against secondary beam temperature, OF=0.02. 331
9.15 Secondary beam AB2: Axial force against secondary beam temperature, OF=0.08. 331
9.16 Primary beam B14: Axial force against secondary beam temperature, OF=0.02. 332
9.17 Primary beam B14: Axial force against secondary beam temperature, OF=0.08. 333
9.18 Rotations near the ends of the primary beam B14, OF=0.08. 333
9.19 Material yield limits of the primary beam. 334
9.20 Edge beam AB1: Axial force against secondary beam temperature, OF=0.02. 335
9.21 Edge beam AB1: Axial force against secondary beam temperature, OF=0.08. 335
9.22 Edge beam BC1: Axial force against secondary beam temperature, OF=0.02. 336
9.23 Edge beam BC1: Axial force against secondary beam temperature, OF=0.08. 336
9.24 Edge beam A14: Axial force against secondary beam temperature, OF=0.02. 337
9.25 Edge beam A14: Axial force against secondary beam temperature, OF=0.08. 337
9.26 Edge beam A47: Axial force against secondary beam temperature, OF=0.02. 338
9.27 Edge beam A47: Axial force against secondary beam temperature, OF=0.08. 339
9.28 Mechanical strains in the reinforcement OF=0.02, corner compartment fire at 750°C. 340
9.29 Mechanical strains in the reinforcement OF=0.08, corner compartment fire at 950°C. 341
9.30 Deflection history of the unprotected secondary beams against secondary beam temperature. 342
9.31 Deflection history of the unprotected secondary beams against secondary beam temperature. 343
9.32 Deflection contours in the slab at the end of heating. 344
9.33 Secondary beam AB1l: Axial force against secondary beam temperature, Edge compartment. 345
9.34 Secondary beam AB2: Axial force against secondary beam temperature, Corner compartment. 345
9.35 Secondary beam BC11: Axial force against secondary beam temperature, Edge compartment. 346
9.36 Secondary beam BC2: Axial force against secondary beam temperature, Corner compartment. 346
9.37 Primary beam B1013: Axial force against secondary beam temperature, Edge compartment. 347
9.38 Primary beam B14: Axial force against secondary beam temperature, Corner compartment. 347
9.39 Mechanical strains in the reinforcement OF=0.02, corner compartment fire at 750°C. 348
9.40 Mechanical strains in the reinforcement OF=0.02, edge compartment fire at 750°C. 349
9.41 Mid-span deflection of the secondary beams. 350
9.42 Mid-span deflection of the primary beams. 351
9.43 Mid-span deflection of the edge beams along gridline 1. 351
9.44 Mid-span deflection of the edge beams along gridline A. 352
9.45 Deflection contours in the slab at 750°C. 353
9.46 Edge beam AB1: Variation of axial force against secondary beam temperature, edge beams protected. 354
9.47 Edge beam AB1: Variation of axial force against secondary beam temperature, edge beams unprotected. 354
9.48 Mechanical strains in the reinforcement OF=0.02, edge beams protected at 750°C. 355
9.49 Mechanical strains in the reinforcement OF=0.02, edge beams unprotected at 750°C. 357
10.1 Matrix of possible parametric studies. 368
List of Tables
2.1 Ingberg�s fuel load fire severity relationship.  15
2.2 Extracts from a typical table in the "Yellow Book" for Fendolite Mu. 22
2.3 Load factors for fire limit state.    41
3.1 Parameters used for t2 fires (Evans 1995 as cited by Drysdale 1998)  60
3.2 Fire growth parameters and time to reach the rate of heat release Qg =1000kW for t2 fires in DD 240 . 60
3.3 List of major deterministic post-flashover models.  69
3.4 The thermal properties of compartment boundary materials. 77
5.1 Material Properties. 146
5.2 Variables associated with the hottest and coolest slab. 149
5.3 Material Properties in the Edge beam and Column models. 163
5.4 Properties of Vicuclad at elevated temperatures. Provided by Promat Technical Department 7/6/2000.  164
6.1 Conditions in each run on Model 1. 185
6.2 Conditions in each run on Model 2. 187
6.3 Conditions in each run on Model 3. 190
7.1 Reference thermal loading on the structure. 207
7.2 Four Parts to the parametric analysis. 210
8.1 Mean temperature ΔT and gradient T,y in the concrete slab. 238
8.2 Loads on the Cardington frame.  242
8.3 Loads applied to the generic frames. 242
8.4 Load ratio. 242
8.5 Scenarios conducted on the generic frames (*No secondary beams in the frame of scenario 7). 244
8.6 Cases studied on the simple ABAQUS "cross" beam model. 286
8.7 Reference temperature at the primary beam instability in each scenario. 317
9.1 Scenarios conducted on the generic frames. 324
1.1 Background to the project.
Fire safety engineers are concerned first and foremost with life safety not only of the occupants of a building but also the fire service. The aim of structural fire engineering design is to ensure that structures do not collapse when subjected to high temperatures in fire. Traditional prescriptive methods of design based on fire resistance testing, require steel elements of construction to stay below a critical temperature, typically 550°C, for the fire resistance period of the structure. This has led to extensive use of passive fire protection to limit the heating of the structural elements (boards, sprays and intumescents) at considerable cost (up to 20% of the total construction cost).
It has been acknowledged for many years that the failure of determinate structures in the fire resistance furnace bears little resemblance to the failure of similar elements as part of a highly redundant frame. However the fire resistance test has a history of safety albeit not based on scientific reasoning.
Design of structures for fire still relies on single element behaviour in the fire resistance test. The future of structural fire design has to be evaluated in terms of the whole performance based design of structures for fire. This should include natural fire exposures, heat transfer calculations and whole frame structural behaviour, recognising the interaction of all elements of the structure in the region of the fire and any cooler elements outside the boundary of the compartment.
The beginnings of change started after evidence from real fires suggested that the contributions of modern steel deck composite floor systems were under utilised when designing for the fire limit state.
On the 23rd June 1990 a fire developed in the partly completed fourteen storey building in the Broadgate development.  The fire began in a large contractors hut on the first floor and smoke spread undetected throughout the building. The fire detection and sprinkler system were not yet operational out of working hours.
The fire lasted 4.5 hours including 2 hours where the fire exceeded 1000°C. The direct fire loss was in excess of �25 million however, only a fraction of the cost (�2 million) represented structural frame and floor damage. The major damage was to the building fabric as a result of smoke. Moreover, the structural repairs after the fire took only 30 days. The structure of the building was a steel frame with composite steel deck concrete floors and was only partially protected at this stage of construction. During and after the fire, despite large deflections in the elements exposed to fire, the structure behaved well and there was no collapse of any of the columns, beams or floors.  The Broadgate phase 8 fire was the first opportunity to examine the influence of fire on the structural behaviour of a modern fast track steel framed building with composite construction.
Prompted by the evidence from Broadgate, Building Research Establishment (BRE) built an 8-storey composite steel and lightweight concrete frame at their large scale test facility at Cardington. The frame was subjected to six full-scale fire tests (2 by BRE and 4 by British Steel (now CORUS)) enabling the behaviour of the structure during fire to be observed and recorded. The outputs from these tests were introduced to the public domain. Edinburgh University in collaboration with British Steel and Imperial College carried out a research project (funded by the Department of Environment, Transport and Regions "Partners in Technology" scheme) to model the structural behaviour of the 4 British Steel tests using finite element codes. One aim of the research programme was to develop numerical models capable of predicting the structural behaviour of a modern, multi-storey composite steel frame building during a real compartment fire. The most important outcome however was the explanation and understanding of the structural behaviour in response to fire.
The computer package ABAQUS  was used by Edinburgh University and British Steel to develop numerical models of the four tests. ABAQUS is a powerful commercial code capable of modelling the geometric and material nonlinear behaviour of a structure during fire. The models have captured the global structural behaviour and agree with measured data from the tests. The results and understanding gained through the models have highlighted complex behaviour.
1.2 Aims of this research.
This PhD project has evolved as a direct result of the modelling of the Cardington frame fire tests. Both the test data and the modelling provided a wealth of new information about whole frame structural behaviour in fire. However the tests were carried out on one building. As a result of the Cardington frame tests and theoretical work by Bailey  SCI (Steel Construction Institute) have produced a simple conservative design guide in the form of look-up tables for composite frame structures in fire. The tables are applicable to common buildings. This level one design guide is as a major step forward for structural fire engineering in the UK. However, for detailed design guidance to be produced different buildings of various sizes and configurations should be investigated under contrasting fire scenarios. The primary aim of this project was to use the modelling approach developed and checked against real test data to create generic composite steel frames and fire scenarios. Parametric studies and sensitivity analyses were conducted on the generic frames. "What-if," scenarios considered included, what-if,
- there is a fire in a corner or edge compartment or over a whole floor level?
- only the columns are protected?
- the fire severity changes?
Output from these analyses adds to the information collected as a result of modelling the Cardington frame tests and will help the development of performance based design guidance for fire.
1.3 Outline of thesis chapters
Chapter 2. An overview of structural fire safety design and research.
Traditional and performance based design methods and the history of this field of research will be outlined. Research into the behaviour of single elements of construction in fire and studies of steel frames before the Cardington frame tests will be presented. A summary of the factors affecting structures in fire, for instance degradation of mechanical properties and restraint conditions, will also be given.
Chapter 3. Thermal response of structures to real fires.
Prescriptive fire gradings and design methods based on heating single elements in the fire resistance test over-simplify the whole fire design process. The real problem can be addressed by performance based design methods where possible fire scenarios are investigated and fire temperatures are calculated based on the compartment size, shape, ventilation, assumed fire load and thermal properties of the compartment boundaries. The temperatures achieved by the connected structure can then be determined by heat transfer analysis. This chapter describes and tests some of the methods available to engineers and designers to predict fire temperatures and heat transfer to the structure.
Chapter 4. Whole frame composite steel structures in fire: Research and design developments.
This chapter will review recent experimental work and numerical modelling of whole frame composite steel structures in fire. Design methods developed as a direct result of this research will also be discussed.
Chapter 5. Heat transfer analysis of the Cardington frame fire tests using HADAPT.
This chapter describes heat transfer analysis of the Cardington frame tests. Using the finite element code HADAPT the temperatures achieved by the composite slab and the edge beams were predicted. The results of these analyses are given and discussed. This work was carried out for two reasons. One to supplement the existing Cardington frame data and two to have a reliable method of modelling heat transfer to structural elements for any compartment fire scenario.
Chapter 6. Analytical and numerical analysis of simple beam models in fire.
This chapter describes analytical and numerical analyses on a simple beam to aid our understanding of the behaviour of structures in fire. Thermal bowing and thermal expansion effects were analysed on a simple beam, first individually and then combined. The effect of the beam end restraint conditions were also studied to explain why runaway occurs much earlier in axially unrestrained beams, as tested in the fire resistance test, when compared with axially restrained beams, typical of beams in real structures.
Chapter 7. Structural behaviour in British Steel Test 1 under different heating regimes.
Following the simple studies and understanding of thermal bowing and thermal expansion effects in Chapter 6. A parametric study was conducted on an ABAQUS grillage model of British Steel Test 1 (restrained beam test) to understand the effects on the structure, of systematically changing the temperature regime in the slab. The parametric study and the results are outlined in this chapter.
Chapter 8. Parametric studies on a small generic composite steel frame.
Two generic composite steel frames, different in plan and size from Cardington, were designed in accordance with Eurocode 4 Part 1.1 . This chapter describes the structural response of a small frame (2x2 bays in plan) to whole floor compartment fires with different ventilation characteristics. Changing the available ventilation and fuel in a compartment leads to fires of short or prolonged post-flashover duration and different thermal responses in the steel and concrete.
The Cardington frame survived several fire tests where all the steel beams were unprotected. The structural behaviour of the small generic frame to three fire protection configurations, 1) the edge and primary beams were protected, 2) only the edge beams were protected and 3) all beams were left unprotected, is also described. In each case the columns were always protected to their full height.
Chapter 9. Parametric studies on a large generic composite steel frame
This chapter describes results from a series of parametric studies on a 9x9 bay generic composite frame. Compartment fire scenarios in the corner and on the side of the building were analysed. The locations provided different boundary restraint conditions to the expanding compartment floor and different deflection and force patterns in the beams and slab. The effect of protecting the edge beams on the structural behaviour of the large frame is also described.
Chapter 10. Conclusions and Further work
An overview of structural fire safety design and research.
This overview of structural fire safety design and research includes three main topics.
- Traditional and Performance Based Design Methods.
- Factors affecting structures in fire.
- Literature review of single element behaviour in fire and steel frame analysis before the Cardington frame fire tests.
Factors affecting structural behaviour in fire are described, such as material degradation at elevated temperatures, restrained thermal expansion, thermal bowing and the degree of redundancy available when the structure acts as a whole. Each factor is addressed separately but in an integrated structure exposed to fire they will all interact to generate more complex structural behaviour.
This chapter also reviews research into the fire resistance of single elements of structure and early analysis of frames prior to the Broadgate Phase 8 fire and the Cardington frame fire tests. Chapter 4 looks at whole frame composite steel structures in fire and the new understanding developed over the last 10 years.
2.2 Traditional Design.
The term fire resistance is associated with the ability of an element of building construction to continue to perform its function as a barrier or structural component during the course of a fire. Traditionally the fire resistance of a building element (beam, column etc.) has been determined by testing a full scale sample (under load if necessary) to failure while subjected to a standard fire.
2.2.1 The fire resistance test.
Fire resistance testing of construction was formalised over 80 years ago although testing had been going on prior to that in an unplanned and informal manner.  The main reason for testing was that insurance companies needed to have some comparative evaluation between different types of construction. The earliest recorded tests were in the UK, Germany and the USA. The Associated Architects in the UK tested a floor in the 1790s. The Technical High School in Munich tested a column in 1884 and in the Denver Equitable Building in the USA a floor was tested in 1890.
Early tests were carried out in brick huts using wood as a fuel where the floor or wall under test was part of the hut itself. Early testing was very simple, construction was tested and observations made of its behaviour, primarily with reference to collapse and to the transfer of fire to the unexposed side of the wall or floor. The main test station in the UK at Borehamwood was opened in 1935.
It can be said that the fire resistance test assesses the behaviour of components and structures in the post-flashover stage of a fully developed fire. Techniques for conducting fire resistance tests have not changed significantly in the last 60 years.   Fire resistance testing consists of subjecting a prototype sample of the construction to prescribed heating conditions in a furnace and judging its performance based on specified criteria. The standard tests enable elements of construction such as walls, floors. columns and beams to be assessed according to their ability to: retain their stability: offer resistance to the passage of flame and hot gases and/or provide resistance to heat transmission. The failure criteria for load-bearing horizontal elements of construction is either when a deflection of L/20 is achieved or the rate of deflection (mm/min) calculated over 1 minute intervals exceeds L2/(9000d). However the latter limit should only be applied beyond a deflection of L/30. The time to failure in the fire resistance furnace determines the fire resistance rating of the element under test.
Standard fire tests are conducted worldwide and are defined by the International Standards Organisation in ISO 834. Standard fire tests in the United Kingdom are defined in BS 476: Parts 20-23: Fire tests on building materials and structures. 
- Part 20: Method for determination of the fire resistance of elements of construction (general principles)
- Part 21: Method for determination of the fire resistance of loadbearing elements of construction
- Part 22: Method for determination of the fire resistance of non-loadbearing elements of construction
- Part 23: Methods for determination of the contribution of components to the fire resistance of a structure
(2.1) T = T0 + 345 log(0.133t + 1)
where t = time (sec) and T = temperature of the furnace atmosphere next to the specimen (°C)
During the British Standards tests on load bearing elements the support conditions provided can be similar to that which would apply in service. However, when the service conditions are unknown the test beam or slab is installed as simply supported i.e axially unrestrained to thermal expansion.
The first ASTM standard for fire resistance testing, C19 (now E119), was published in 1918.  The standard fire curve is prescribed by a series of points rather than an equation but is almost identical to the British Standard curve. Both the BS temperature time curve and the ASTM curve are illustrated in Figure 2.1.
Figure 2.1: Standard Temperature-time curves
Several differences exist between the American and British tests. In terms of beams and floor slabs failure criteria for stability is based on deflections in the BS test but limiting temperatures in the ASTM test. The American standard also includes a restrained beam test, a restrained assembly test and a hose test.
E119 allows restrained floor assemblies with fire endurance classifications greater than 1 hour to have half the fire protection of an unrestrained assembly for specific temperature criteria. Therefore savings in fire protection can be made for longer fire resistance periods if the building element can be classified as restrained. ASTM E119 recognises the positive effects of restraint to thermal expansion of beams and floors but there is confusion in some parts of the USA about the application of restrained and unrestrained fire resistance ratings.  Gewain and Troup  have tried to address this confusion. Key conclusions of their paper are that a restrained assembly fire resistance rating is appropriate for steel beam floor and roof assemblies. The least stiff connection used in steel frame construction is adequate to develop restrained performance. Also unrestrained fire resistance tests of beam floor and roof systems have no relevance to the behaviour of these systems under fires in real buildings.
During the hose test, elements heated by the standard fire are subjected to the impact and cooling effects of a hose stream.
2.2.2 Critical steel temperature
Until recently 550°C has been classified as the upper limit for steel temperatures in fire. Steel loses 40% of its room temperature strength by 550°C. For this reason protection has traditionally been applied to reduce the heating rate of steel so that it retains sufficient strength and stiffness during its prescribed period of fire resistance. 
2.2.3 Fire protection
Fire protection of steel can be achieved by three methods 1) insulating the element with spray material or board type protection, 2) shielding or 3) hollow sections can filled with concrete or liquid to form a heat sink.
220.127.116.11 Traditional fire protection materials
Traditional fire protection materials have included concrete, blockwork and plasterboard. Until the late 1970�s concrete was the most common form of fire protection for steelwork.  The major disadvantages are cost, the increase in weight to the structure and the time it takes to apply on site. Nowadays modern lightweight sprays and boards have replaced these.
18.104.22.168 Modern fire protection materials
Passive fire protection materials insulate the structure from high temperatures. The insulation materials can be classified as non-reactive (e.g. boards and sprays) or reactive (e.g. intumescent coatings).
Boards are fixed dry usually to columns. Beams are more commonly protected with spray materials. The main advantages of spray coverings are, they are cheap and they easily cover complex details. However application is wet and may delay other work on site.
Site applied intumescent coatings are paint like substances or mastics. Paints are stable at low temperatures but swell at around 200°C to provide a charred layer of low conductivity material to insulate the steel. Mastics are applied using a trowel or as a heavy duty spray. They form a thick protective coating which is impervious at ambient and at high temperatures. They can be hard and ceramic in appearance or soft and tar like. The main advantage of intumescents paints over other protection products are their appearance. However they are more expensive than sprays and boards, application is wet and there is a limit to the fire resistance periods they can achieve typically 30 and 60 minutes.  A limited number provide longer fire resistance periods but the cost increases considerably. Paints are also applied off-site.
22.214.171.124 Partially exposed steelwork 
Standard fire tests on partially exposed steel have shown that structural members not fully exposed to the fire exhibit increased levels of fire resistance.    30 and 60 minutes fire resistance can be achieved using this approach and higher levels of fire resistance can be achieved with reduced fire protection thicknesses. The most common methods of achieving partially exposed steel are listed below.
- Web in-filled columns: Normal weight concrete is poured between the flanges of
the column. The load carrying capacity of the concrete is ignored in the design of
the column but during a fire as the steel weakens the load carried by the flanges
is transferred to the concrete providing up to 60 minutes fire resistance.
- Block in-filled columns: Concrete blocks are cemented between the flanges and
tied to the web achieving 30 minutes fire resistance. Longer periods can be reached
by protecting only the exposed flanges.
- Shelf angle floor beams: Shelf angle floor beams are beams with angles bolted to
the web to support the floor slab thus shielding the upper part of the beam from
the fire leaving only the bottom of the beam exposed. 60 minutes fire resistance
can be achieved using this method.
- Slim floor beams: There are two types of slim floor in the UK (SLIMFLOR and
SLIMDEK). Essentially the profiled concrete slab has a deep deck incorporating
the beams within the floor slab system thus the slab protects almost the whole
- Filled hollow sections: Hollow columns can gain enhanced fire resistance (up to
2 hours) by filling them with concrete. During a fire heat flows through the
steel to the low conductivity concrete. As the steel loses its yield strength with
increasing temperature the load is transferred to the concrete. Adding fibre or
bar reinforcement to the concrete can attain enhanced periods of fire resistance. 
- Water-filled sections: Hollow sections may be filled with water to reduce heating in fire. This method is expensive and infrequently used. 
The fire resistance test has been criticised by many researchers over many years. One major criticism is that the temperature of the furnace gases do not represent the fire exposure to the element under test because the fire exposure is dependent on the physical properties of the furnace. The construction shape influences the degree of turbulence and thus convective heat transfer. However most significantly the thermal inertia of the wall linings affect the radiative heat transfer to the element under test.  Indeed Drysdale  suggests that no two furnaces will give the same fire exposure. Furnaces also differ in the fuel adopted. They may be gas or oil fired.
Another criticism of the standard temperature-time curve is that it bears little resemblance to a real fire temperature-time history. It has no decay phase and as such does not represent any real fire although Malhotra  reports that it is designed to typify temperatures experienced during the post-flashover phase of most fires. Figure 2.2 illustrates the temperature-time histories of "real" fires, of varying fire load and ventilation, together with the standard curve. This highlights that the standard curve does not represent many real fires in the post-flashover phase or otherwise.
Several criticisms can be made with regard to the tests ability to represent real structural behaviour in fire. A major limitation of furnace tests is that the elements of construction are tested in isolation or as part of small assemblies none of which can expect to represent the behaviour of an integrated structural frame exposed to a real fire. The end restraint conditions applied during the tests are unrealistic. The code recommends that restraint conditions should represent those met in practise. This is difficult to achieve in test conditions as restraint is difficult to measure and is likely to change throughout the test. Very often elements are tested unrestrained. In a real building during a compartment fire the rest of the structure would restrain the heated elements from expanding and the behaviour of the element in terms of deflections and failure would be quite different from that in an unrestrained standard test. Large deflections or "runaway" in unrestrained steel beams at high temperatures are as a direct result of imposed loading on a weakened structure. Large deflections in restrained members are often present primarily because of thermal expansion and thermal bowing effects. Columns are only subjected to axial loads yet in real structures they carry axial load and bending moments.
Although the shortcomings of the fire resistance test are significant, standard fire resistance tests are the only universally recognised method of determining the fire resistance of elements of construction.
2.2.5 Equivalent fire exposure
Ingberg  proposed a solution to the problem of standard fire curves not representing real fires in the 1920s. Analysis of a small number of room fire tests revealed that fire load was an important factor in determining fire severity. He suggested that fire severity could be related to the fire load of a room and expressed as an area under the temperature-time curve. The severity of two fires were equal if the area under the temperature-time curves were equal (above a base line of 300°C). Thus any fire temperature-time history could be compared to the standard curve. Ingberg related fire load to an equivalent time in the standard furnace and produced Table 2.1. This approach was based on limited information of fire load densities thus has limited applicability. Drysdale  highlights that direct scaling between the heating effect of real fires and a standard fire is impossible because heat transfer when dominated by radiation depends upon radiative heat flux on T4, i.e., 10 minutes at 900°C will not have the same effect as 20 minutes at 600°C.
| Combustible content |
|(lb/ft2)||(kg/m2)||(kJ/m2 x 10-6)||(h)|
Table 2.1: Ingberg�s fuel load fire severity relationship 
Figure 2.2: Comparison of the standard fire curve and real temperature-time histories. The fire load is in kg/m2 and the ventilation is a fraction of one wall e.g. 15(1/2) corresponds to a fire load of 15kg/m2 and ventilation equal to half of one wall 
Most regulatory bodies accepted Ingberg�s fire severity approach and fire resistance testing to the standard temperature-time curve continued. Ingberg�s approach was used in the UK to define equivalent fire severities in the post-war building studies report No.20-Fire Grading of Buildings.  The requirements for fire resistance were related to the assumed levels of fire loads in different occupancies. This approach was inappropriate because it took no account of the factors which dictate the severity of a compartment fire namely, ventilation, compartment dimensions and the properties of the boundary wall linings. 
Since Ingberg�s early attempt at relating the severity of the standard fire to a real compartment fire many researchers have developed similar but more sophisticated time equivalent relationships.
The time equivalent concept makes use of the fire load and ventilation data in a real compartment fire to produce a value, which would be "equivalent" to the exposure time in the standard test. Law  defines t-equivalence as the exposure time in the standard fire resistance test which gives the same heating effect on a structure as a given compartment fire. Formulating equivalent fire exposures has traditionally been achieved by gathering data from room-burn experiments where protected steel temperatures were recorded and variables relating to the fire severity were systematically changed (e.g. ventilation, fire load, compartment shape). The concept is illustrated in Figure 2.3.
Figure 2.3: Equivalent fire severity on a temperature basis 
Law  developed a time equivalence relationship to include the effect of ventilation using data gathered from a CIB study of fully developed compartment fires.  This relationship is described by Equation 2.2. The floors (AF) were very well insulated so were not included in the total surface area of the compartment (At).
Law�s t-equivalence formula
(2.2) τe = 0.022 AFL/(At(Av - AF - Av))1/2
τe = Equivalent fire resistance (h)
AF = floor area (m2)
At = total area of the compartment boundaries including the compartment opening (m2)
Av= Area of the ventilation opening (m2)
L = Fire load (kg/m2)
Pettersson and co workers,  adopted Law�s method of t-equivalence but developed a new expression using the family of calculated temperature-time curves for particular compartments derived by Magnusson and Thelandersson.  Pettersson�s t-equivalence approach takes into consideration the effect of the thermal inertia of the compartment wall lining (see Equation 2.3).
Pettersson�s t-equivalence formula
(2.3) O.31C AFL/(AtAv√hv)1/2
C = factor depending on the thermal absorptivity of the compartment boundaries (hm3/4kg-1)
hv = height of ventilation opening (m)
The normalised heat load concept is one of the most recent developments in this area and was introduced by Harmathy  although it has not been readily adopted. The normalised heat load, HN(s1/2K), is defined as the heat absorbed by the element per unit surface area during fire exposure. Harmathy�s t-equivalence relationship is given by Equation 2.4.
Harmathy�s t-equivalence formula
(2.4) te = 6.6 + 9.6 x 104HN + 7.8 x 109HN2
for, 0 < HN < 9 x 104
(2.5) HN = 106(11δ+ 1.6)LAF/[At(kρc)1/2 + 1810(AFAvL√hv)1/2]
δ = 0.41(H3/[Av√hv])1/2 or 1 whichever is less
k = thermal conductivity of the compartment boundaries (W/mK)
ρ = density of the compartment boundaries (kg/m3)
c = heat capacity of the compartment boundaries (J/kgK)
H = compartment height (m)
Eurocode 1 Part 1.2  gives another approach to t-equivalence (Equation 2.6). The Equation is based on work by Schneider et al using the German multi-room fire code (MFRC) to calculate the fire behaviour, as cited by Law. 
EC1 Part 1.2 t-equivalence formula
(2.6) te,d = qf,d kb wf
te,d = equivalent time of fire exposure (minutes)
qf,d = design fire load density (MJ/m2)
kb = conversion factor for thermal properties of enclosure
wf =ventilation factor (m-1/2)
Characteristic fire load densities (qf,d) are listed in the Draft Eurocode or the actual fire load density can be calculated (method given in DD 240 ). The factor kb is related to the thermal inertia of the compartment boundaries (b = (ρcλ)1/2). The values range from 0.04 to 0.07 with the latter as default if no detailed information is known.
The ventilation factor (wf) considers the height of the fire compartment, the floor area and the areas of vertical openings. It also takes account of horizontal openings in the roof. For no horizontal openings and wf = 0.07,
(2.7) te,d = 1.26 Lwf/AF
(2.8) wf = (6/H)0.3 [0.62 + 90(0.4 - Av/AF)4]
Restrictions placed on the Eurocode t-equivalence relationship are given by relationships 2.9-2.12.
(2.9) bv = 12.5 (1 + 10αv - αv2)
(2.10) 6 [0.62 + 90(0.4 - αv)4]/[H(1 + bvαh)] > 0.5
(2.11) bv ≥ 10
(2.12) 0.025 ≤ αv ≤ 0.25
αv = Av/AF
αh = Ah/AF
Ah = the area of horizontal openings in the roof
The main difference between EC1 and Pettersson�s t-equivalent formula is that EC1 is independent of opening height but depends on ceiling height. Thus similar results are obtained in small compartments with tall windows but EC1 gives lower fire severities in large compartments where ceilings are tall and window heights low. However, neither formula has been tested for large or tall compartments. 
Law  compares the different t-equivalence formulae with experimental data for compartment fires. Pettersson�s formula and the approach by Law provide better results than EC1 for the data considered. Law  also highlights the problems with t-equivalence as a design tool. Although it gives an indication of the total heating effect of a compartment fire it does not differentiate between a short, hot post-flashover fire and a long, cooler post-flashover fire. Thus the impact on the heated structure of these fires is not considered. Long cooler fires allow protected steel and concrete to achieve much higher temperatures. Similarly, Thomas et al  in their review of the role of t-equivalence in structural fire design conclude that t-equivalent may be very inaccurate out with the range of data for which it was tested. In general t-equivalence is only applicable to protected steel members although EC1 allows it to be used with all construction materials. 
The concept of t-equivalence was innovative when the only fire exposure considered in structural fire design was the standard curve. In performance based design natural fire exposures should be used to give the design a rigorous, scientific basis.
2.2.6 Natural Fire method
With the t-equivalence approach the heating effect in a compartment is calculated based on real compartment fire behaviour and that heating is related back to the standard furnace test. In more recent times however, the energy and mass balance equations for the fire compartment are used to determine the actual thermal exposure and fire duration. This is known as the natural fire method. This method means the combustion characteristics of the fire load, the ventilation effects and the thermal properties of the compartment enclosure are considered. It is the most rigorous means of determining fire duration. This is not related in any way to the standard fire resistance test and therefore represents the real fire duration, once flashover has occurred. The standard fire curve, t-equivalence and natural fire curves can all be used to determine the behaviour of structures in fire. The standard fire resistance method being the most conservative and the natural fire method the most rigorous. Estimating natural fire exposures is discussed in Chapter 3.
2.2.7 Fire resistance by calculation
Fire resistance has traditionally been based upon the fire resistance test. However fire resistance of single elements or frames by calculation is becoming more common.
The fire resistance of a structure or element must be greater than the fire severity. Fire resistance design can be in terms of time, temperature or strength:
- Time to failure in the fire resistance furnace (or equivalent time) must be greater than the fire duration as calculated or specified by code
- Temperature to cause failure must be greater than the maximum temperature reached in the fire duration
- Strength or load bearing capacity at elevated temperatures must be greater than the applied load during the fire
A design guide for structural fire safety was developed on behalf of the CIB (Conseil International du Batiment) in workshop CIB W14. Figure 2.4 forms the basis of this guide. It summarises the different methods for design of load bearing structures and structural elements under fire exposure conditions. Thermal exposure H1 is the standard fire, H2 is the t-equivalence concept and H3 are natural fire exposures. Similar degrees of sophistication exist for the structural model adopted. S1 considers a single element, S2 a sub-frame and S3 the complete structure. S1-H1 is the simplest design approach and is still very commonly used. S3-H3 is restricted to research although there are some examples of real structures designed this way.   
Figure 2.4: Fire and structural response models 
|Dry thickness in mm to provide fire resistance of:|
|Hp/A up to||1/2 hour||1 hour||3/2 hour||2 hour|
Table 2.2: Extracts from a typical table in the "Yellow Book" for Fendolite M11
126.96.36.199 Methods of calculating the fire protection requirements
In prescriptive guidance such as Approved Document B, the level of fire resistance for a particular building is related to the fire load available and the size or height of the building.  If the temperature of the steel structure exceeds the critical temperature in a period of time less than the fire resistance specified by Approved Document B then the fire protection thickness is prescribed using the "yellow book " or can be calculated using BS5950 Part 8 or EC3 part 1.2 or EC4 Part 1.2. All three methods only consider single elements of structure.
188.8.131.52.1 The Yellow Book 
The "yellow book" approach uses fire test data in accordance with BS 476 Part 21. All approved fire protection materials have been tested in accordance with BS 476 and the required thickness of each product has been evaluated with regard to fire resistance period and section factor (ratio of heated perimeter to cross-sectional area of a steel section). The performance requirements for fire protection are expressed in well defined steps of 30 minutes up to 240 minutes. These results are all based on a limiting steel temperature of 550°C. Table 2.2 shows a typical extract from a look-up table in the "yellow book". The section factor or Hp/A concept is the ratio of the heated perimeter, Hp (m) to the cross sectional area, A (m2) of the structural element. Figure 2.5 illustrates the Hp/A concept.
Figure 2.5: The Hp/A concept.
184.108.40.206.2 BS 5950: Part 8 
BS 5950 Part 8 is the British Standard code of practice for fire resistance design. It details fire resistance derived by tests. It also allows fire resistance by calculation using the Limiting Temperature Method or Moment capacity method. The engineer calculates the load ratio of the beam (Equation 2.13). If this value is low i.e. the load capacity at 20°C is high compared to the applied load at the fire limit state, then the upper limit of the steel temperature may be greater than 550°C. The limiting temperature method allows the designer to compare the temperature at which the member will fail with the member temperature at the required fire resistance time. The code details limiting temperatures for various load ratios.
(2.13) Load ratio = [The load at the fire limit state]/[The load capacity at 20°C]
The moment capacity method allows the designer to calculate the moment capacity using the temperature profile at the required fire resistance time. If the applied moment is less than the moment capacity, the section can be left unprotected. The moment capacity method can only be applied to beams with webs which are plastic or compact sections.
220.127.116.11.3 The Eurocodes
Methods described in EC3 Part 1.2 or EC4 Part 1.2 are very similar to BS 5950 Part 8.
The Eurocodes are a collection of the most recent methodologies for design. Eurocode 3: Design of Steel Structures, Part 1.2: Structural fire design and Eurocode 4: Design of steel and composite structures, Part 1.2: Structural fire design were formally approved in 1993. Each Eurocode is supplemented by a National Application Document (NAD) appropriate to the country. It details safety factors and other issues specific to that country. SCI have published a guide comparing EC3 and EC4 with BS 5950  to aid the transition for designers in the UK. All Eurocodes are presented in a limit state format where partial safety factors are used to modify loads and material strengths. EC3 and EC4 are very similar to BS 5950 Part 8 although some of the terminology differs. EC3 and EC4 Parts 1.2 and BS 5950 Part 8 are only concerned with calculating the fire resistance of steel or composite sections. Three levels of calculation are described in EC3 and 4. Tabular methods, simple calculation models and advanced calculation models (similar to figure 2.4). Tabular methods are look up tables for direct design based on parameters such as loading, geometry and reinforcement. They relate to most common designs. Simple calculations are based on principles such as plastic analysis taking into account reduction in material strength with temperature. These are more accurate than tabular methods. Advanced calculation methods relate to computer analyses and are not used in general design.
2.3 The Swedish Design Guide
Pettersson and co-workers published one of the most innovative design guides for fire safety design of structures over 25 years ago. The methodology and principles outlined in the guide are still applicable today and in many respects are an improvement on prescriptive design. The guide advocates the use of natural fire curves and heat transfer calculations to obtain protected and unprotected steel temperatures in fire. This aspect of the guide is described in more detail in Chapter 3.
Pettersson developed a series of calculation methods based on structural engineering principles for steel members in fire. Through experimental and theoretical studies an empirical equation for the critical deflection of beams was derived (Equation 2.14).
(2.14) ycr = L2/(800d)
ycr = Critical deflection at mid-span (m)
L = the beam (m)
d = depth of the beam (m)
From this, the critical load to cause a mid-span deflection ycr was derived and is described by Equation 2.15.
(2.15) Pcr = βCσsW/L
σs = yield stress at ambient
W = section modulus
C = constant dependent on the loading and end conditions of the beam
β is the ratio of load that causes ycr under fire conditions to load that produces σs at ambient. The ratio β is very similar to the load ratio in BS 5950 Part 8.
Pettersson plotted β for a number of loading and beam configurations against temperature for different heating rates, thus allowing for creep effects. The steel temperature and heating rate could be calculated from heat transfer.
Pettersson also includes an approach to the design of steel columns calculating the critical buckling stress ok taking into consideration the slenderness of the column, material degradation with temperature and the degree of restraint to thermal expansion. The results are plotted in design charts for various degrees of restraint, slenderness and temperature.
The Swedish design Guide like BS 5950 Part 8, EC3 and EC4 is relevant to single element behaviour but the approach is based on engineering logic taking into account all aspects of the elements behaviour in fire.
2.4 Performance based design
Building codes worldwide are moving from prescriptive to performance-based approaches. Performance based codes establish fire safety objectives and leave the means for achieving those objectives to the designer.  One of the main advantages of this is that the most recent models and fire research can be used by practising engineers inevitably leading to innovative and cost effective design. Prescriptive codes are easy to use and building officials can quickly determine if a design follows code requirements. However they are too onerous for many modern designs. This is especially true of modern steel framed buildings. The fire resistance ratings in building codes were not made for these types of structure. By assuming a worst case but realistic natural fire scenario and calculating the heat transfer to the steel, the load carrying capacity of the steel members can be checked at high temperatures and requirements for fire protection, if any, can be judged in a rational manner.
Performance based design has been documented in the literature extensively over the past 10 years.  [41-43]          Custer and Meacham  report that by 1996 there were 13 countries (Australia, Canada, Finland, France, England, Wales, Japan, The Netherlands, New Zealand, Norway, Poland Spain, Sweden and the USA) and 2 organisations (ISO and CIB) actively developing or using performance based design codes for fire safety.
Buchanan   in a description of the fire code development in New Zealand summarises the basic elements of performance based codes,
- State objectives clearly
- Specify performance requirements clearly
- Allow any solution which meets these requirements. Also aliow the use of new knowledge as it becomes available
Determine geometry, construction and use of the building Establish performance requirements Estimate maximum likely fuel loads Estimate maximum likely number of occupants and their locations Modify fire safety features Assume certain fire protection requirements Carry out fire engineering analysis Acceptable performance? NO YES Accept design
Figure 2.6: Outline of the New Zealand fire engineering design procedure
New Zealand had a performance based code and regulations by 1992 but they kept prescriptive codes as an alternative solution.  The code, in a similar manner to other performance based regulations encourages the use of engineering calculations based on a thorough understanding of fire behaviour. Computer based fire growth tools like FPETool and HAZARD1 are being widely used, for instance to model natural fires. smoke movement and sprinkler response. New Zealand is also in the process of reviewing a design guide prepared by The Heavy Engineering Research Association (HERA)  on the behaviour of composite multi-storey steel framed structures in fire. The aim of the guide is to reduce the number of beams with applied fire protection.
In England and Wales building regulations were published as a performance based document in 1985.  Britain produced a Draft British Standard Code of Practice for the Application of Fire Safety Engineering Principles to Fire Safety in Buildings, DD 240  in 1992. This is to be shortly replaced by a new standard BS 7974 and a series of published documents.  Also a new set of standards are being developed in the UK, BS9999 to replace BS 5588: Fire precautions in the design construction and use of buildings. The new standard is prescriptive but fire safety engineering methodologies are being used in their development.  
The Cardington frame fire tests and subsequent numerical modelling has shown that multi-storey steel-frame structures survive compartment fires when all the steel beams are unprotected, despite temperatures in the steel of > 1000°C. The SCI design guide "Fire safe design: A new approach to multi-storey steel framed buildings " was published in 2000. It is based on theoretical work by Bailey  and presents a performance based design approach to composite steel frames enabling fire protection to be omitted from secondary steel beams.
Australia produced a draft performance based code in 1995. Quantifiable performance based codes rely on risk assessment modelling. The Australian draft is an attempt to produce a probabilistic code. The Australians were among the first to move towards a performance based approach. The Warren centre conference and reports were a major influence.   
In Canada Harmathy published a Performance based guide "Design approach to fire safety in buildings" 25 years ago. More recently the NRCC (National Research Council of Canada) collaborated with Victoria University of Technology in Australia to establish fire risk assessment models.  As a result the NRCC fire lab have developed FIRECAM  (A FIRE risk Cost Assessment Model) a key element of their performance based code.
NFPA (National Fire Protection Association)  and SFPE (Society of Fire Protection Engineers) are key players in the establishment of performance based Codes in the USA. The SFPE Guide  and NFPA 10 now have performance based solutions. However legal responsibility for building and fire codes lies within 50 states.
Performance based fire safety engineering design is now implemented and accepted in many countries. The design methodology has key advantages over prescriptive based design.
2.5 Factors affecting the behaviour of structures in fire
Structural behaviour in fire depends upon a number of variables. These include material degradation at elevated temperature and restraint stiffness of the structure around the fire compartment. High temperatures and gradients in structural elements are the driving force behind large deflections and axial forces. This section analyses each factor on an individual basis. In buildings exposed to fire they all interact to define the structural behaviour.
2.5.1 Mechanical properties of steel at elevated temperatures
18.104.22.168 Thermal expansion
Thermal expansion is a measure of a materials ability to expand (or contract) in response to temperature changes. The coefficient of thermal expansion, α is defined as the expansion of a unit length of material when it is raised by 1°C,  see Equation 2.16
(2.16) α = εthermal/ΔT
εthermal = thermal strain
ΔT = Temperature change
Figure 2.7 shows the influence of temperature on the coefficient of thermal expansion for steel. Thermal expansion increases linearly up to 700°C when there is a temporary sudden shrinkage with any further increase in temperature. This is caused by the phase transformation from pearlite to austentite and a rearrangement of the crystal structure. The shrinkage is about 15% of the expansion from 20-700°C. The type and strength of steel seem to have little impact on the thermal expansion.    However, the temperature associated with phase transformation does depend upon the carbon content.  For design purposes an average thermal expansion is assumed. BS 5950 Part 8 assumes 14 x 10-6. 
Figure 2.7: Thermal expansion of steel with increasing temperature 
22.214.171.124 Poisson ratio
Poisson ratio is defined as the ratio of lateral strain to longitudinal strain. When a body is pulled it becomes longer and thinner when it is squashed it becomes shorter and thicker. There is very little data on the variation of Poisson ratio, ν, with increasing temperature. Values are also dependent on measured elastic and shear moduli (ν - E/(2G)). Errors in either value can cause large errors in ν.  Reported test data indicate values of 0.27 at ambient and 0.30 at 600°C.  There is very little variation with increasing temperature.
Creep is the deformation with time as a result of a constant load. At normal stress and ambient conditions creep is negligible. At higher stresses and temperatures creep can be significant.  The chemical composition and the degree of processing strongly influence creep behaviour, thus a common description for every type of steel is difficult to define. Creep strain can only be measured under steady-state conditions where the creep strain can be separated from thermal and stress induced strains. However, Anderberg  describes a method of coupling transient (load and temperature varying) creep with the steady state measurements. Eurocode 3 includes creep in its stress-strain curves implicitly.  
126.96.36.199 Stress-strain relationships
Figure 2.8 shows stress strain relationships for hot rolled steel with increasing temperature. At ambient there is a well defined yield between the elastic and plastic portions of the curve. With increasing temperature this form is lost. The σ-ε behaviour becomes highly non-linear with increasing temperature, with both strength and stiffness decreasing. At higher temperatures the concept of 1% proof stress is typically adopted. The stress is measured at a strain equal to 1% permanent deformation of its original length (see Figure 2.9). When calculating the structural performance of a steel member to BS 5950 Part 8 strains between 0.5 and 2% are considered. The level depends on whether the beam is acting compositely with a slab or whether it has any applied protection. For instance composite members protected with a material which has demonstrated its ability to remain intact at 2% strain in a fire resistance test can be designed to 2% proof stress. Non-composite members protected or unprotected are designed to 1.5% proof stress.
The strains induced in a structural element are described by Equation 2.17.
(2.17) Δε = εσ(σ,T) + εTh(T) + εcr(σ,T,t) + εtr(σ,T)
ε = Total strain
εσ = Mechanical strain
εTh = Thermal strain
εcr = Creep strain
εtr = Transient strain
Thermal strains depend on the temperature and thermal expansion of the material. Mechanical strains are a result of applied loading or restrained thermal strains. Creep strain is the long term deformation of material under constant load. Creep is more important at high temperatures but fires are of short duration so has less relevance. Transient strain is associated with the expansion of cement paste when concrete is heated for the first time under load. In fire the components of thermal and mechanical strains are of fundamental importance. Rotter et al   have used this relationship (Equation 2.17 less creep and transient strains) to understand structural behaviour in fire to fully explain the Cardington frame fire tests.
The strength properties of steel are generally determined by tensile testing. A test bar is stretched at constant rate and the loading and elongation are recorded. Tests at elevated temperatures are conducted in many ways. The two most common approaches are 1) Isothermal and 2) Anisothermal. Isothermal testing is steady state. The specimen is subject to constant temperature and strain is applied at a constant rate. In a transient anisothermal test the sample is loaded and then heated at a uniform rate 5-50°C/min until failure. Strain measurements are taken throughout. A zero load test is conducted to measure thermal strains which need to be subtracted from the loaded strain measurements. The test is repeated for several loads and σ-ε diagrams drawn.  
Neither test method is realistic of fire conditions. Isothermal tests are not transient and the loading on a structure is effected by restrained thermal expansion and bowing effects therefore the load is not constant as in an anisothermal test.
There is variability in test data primarily due to the quality and dimensions of the different test specimens and the accuracy of testing.
188.8.131.52.1 Stress-strain behaviour in design
A bilinear representation of the σ-ε behaviour is used for design at ambient. The steel behaves in a linear-elastic manner up to yield at which point it is allowed to strain infinitely with constant stress. A bilinear model of steel does not adequately represent the highly non-linear relationship at higher temperatures.  
EC3  behaviour of steel includes strain hardening below 400°C. EC3 curves are based on reduction factors for steel σ-ε behaviour at high temperatures (Figure 2.10). Twilt and Both  compared EC3 steel properties and those derived by Anderberg  showing the Anderberg model to be 1.3-1.5 times stronger at elevated temperatures.
The stress-strain temperature data in BS 5950 Part 8 was derived experimentally by Kirby. 
Modified Ramberg-Osgood stress-strain relationships are quoted in the literature as a means of calculating σ-ε-T relationships in numerical modelling techniques.   The original Ramberg-Osgood correlation was a simple power-law equation to approximate stress-strain behaviour up to yield. 
Figure 2.8: Stress-strain curves for typical-hot rolled steel at elevated temperatures 
Figure 2.9: Stress-strain curves for steel illustrating yield strength and proof strength 
Figure 2.10: Reduction in yield strength and modulus of elasticity of steel with temperature (EC3 1995) 
2.5.2 Mechanical properties of concrete at elevated temperature
184.108.40.206 Thermal Expansion
Thermal expansion like all other properties of concrete is complicated by the the complex nature of the composite material. α is dependent upon stress level, type of aggregate, % volume of cement paste and rate of heating.    Cement paste expands up to 150°C but contracts between 150-400°C (see Figure 2.11). This is associated with water evaporation and chemical changes. However the aggregates may still expand.  Figure 2.11 shows thermal expansion for different aggregate types. The figure shows that thermal expansion is non-linear with increasing temperature and that the main factor affecting the thermal strain is the type of aggregate. At very high temperatures (600-800° C) thermal expansion remains constant or decreases. 
Figure 2.11: Thermal expansion of concretes 
Eurocode 2 Design of concrete structures, Part 1.2: Structural fire design  assumes α(θ) = 8 x 10-6 for 20 ≤ θ ≤ 1000°C.
220.127.116.11 Poisson ratio
Just as data on Poisson ratio for steel was limited it is also very rare for concrete. Figure 2.12 shows the results of Ehm (1985) as cited by Schneider.  At 20°C ν is constant until 70% of the ultimate stress. At 450°C ν is only constant until 20%. In cases where ν > 0.5 these indicate material effects far beyond the elastic range. 
Figure 2.12: Poisson ratio 
Creep is more significant in concrete than steel. Concrete creep consists of the creep of the cement paste and the creep of the aggregate. The reason concrete does not disintegrate at high temperatures as a result of differential thermal expansion between the cement paste and the aggregate is the ability of the paste to creep. 
Conventional creep test data have little application to the behaviour of concrete structures under fire conditions.  Specimens are heated to constant temperature and a constant load is applied for days to get constant strain. Fires last a few hours and temperatures are transient. However short duration transient creep tests are useful.  Figure 2.13 show tests on gravel aggregate concrete on preloaded specimens. It shows that up to a temperature of 400°C creep is not significant for short duration heating but it is affected by preload and becomes significant at higher temperatures. Concrete elements exposed to fire on all four sides could reach very high temperatures despite its low conductivity especially if the fire has a long duration. However, concrete slabs exposed to fire on one side will only achieve high temperatures through a small depth of the concrete. In the latter case the mean temperature is not likely to exceed 200°C and creep effects will be less important.
18.104.22.168 Stress-strain relationships
Stress-strain behaviour of concrete is radically different in compression and tension. In tension concrete is often assumed to have zero tensile strength. Schneider  reports tensile strengths of about 10% of the compression strength. Strength is affected by type and size of aggregate, % cement paste and water/cement ratio at ambient and at elevated temperatures. Loading of a specimen is beneficial to its compressive strength. 
There can be large variation in test results  these are attributed to a large number of factors including the method of testing, rate of heating, duration of heating, size and shape of specimen and loaded or unloaded conditions.
22.214.171.124.1 Design stress-strain curves
The stress-strain behaviour of concrete can be described by a set of equations in EC2.  Figure 2.14 shows compressive stress-strain data for concrete at elevated temperatures according to EC2. High temperature creep is included implicitly. Concrete stiffness reduces much more than steel with increasing temperature resulting in greater strains. This can lead to large deflections in concrete members exposed to fire.
The Eurocode provides guidelines on the tensile capacity of concrete but also allows designers to consider it to be negligible. Figure 2.16 shows design values from BS 8110 for the reduction of modulus of elasticity with temperature. Figure 2.15 gives design values for compressive strength with temperature. The dotted line in Figure 2.16 was introduced to correct for the fact that in Figures 2.15 and 2.16 the modulus of elasticity and compressive strength reach zero at different temperatures. 
Figure 2.13: Concrete creep 
126.96.36.199 Spalling 
Spalling is the loss of surface material from a concrete element and is dependent on aggregate, moisture content, stress level and temperature. Aggregate splitting is the splitting and hursting of silica containing aggregates due to physical changes in the crystalline structure at high temperatures. This is a surface effect and as such has little effect on the structural performance. Explosive spalling is characterised by large or small pieces of concrete being violently expelled from the surface often exposing reinforcement thus reducing the load hearing capacity of the structure. Normal weight concrete is much more susceptible to spalling than light weight concrete. Spalling is associated with differential expansion and thus can occur under heating or cooling.
2.5.3 Thermal Bowing and Thermal Expansion
Increasing temperature causes thermal expansion of structural elements and differential heating results in thermal bowing. In buildings experiencing real fires these two phenomena act together and are very often restrained leading to thermally induced stresses and large deflections.
Figure 2.14: Stress strain relationships for concrete at elevated temperatures (EC2 1993) 
Both effects can be illustrated by considering a single beam element. If the temperature of a beam of length l is increasing uniformly along its length and over its depth such that the whole beam is at the same temperature at any given time, the beam will expand with an increase in temperature ΔT according to Equation 2.18.
(2.18) Δl = αΔTl
Where α equals the thermal expansion coefficient of the constituent material. If the beam is axially unrestrained then the it will simply increase in length. If the beam is restrained from expanding at its ends then an equal but opposite compressive force will develop reacting against the expansion. This may result in the beam buckling at a critical compressive force accommodating expansions in downwards deflection or extensive elastic and plastic straining until the material yields.
Thermal gradients exist through the cross-section of elements of structure because of differences in the thermal diffusivity of materials and as a direct result of differential heating. If members are heated from one side such as edge beams or heated from underneath such as floor slabs gradients will develop across the section or through their depth.
Steel has a very high value of thermal conductivity so steel beams and columns subject to fire on all sides achieve uniform temperatures quickly and very low gradients exist.
Figure 2.15: Design values for reduction in compressive strength with temperature 
Beams supporting floor slabs will achieve higher temperatures in their lower flange than their top flange. This is due to less direct heat being applied to the top flange and the heat sink effect of the cooler slab. Differences between the top and bottom flange can be up to 100-200°C.  Concrete has a much lower thermal conductivity so slabs heated on one side for instance, achieve very high gradients. Composite slabs develop large gradients between the steel beam and the concrete slab. This is magnified if the fire is very hot but of short duration because the steel reaches high temperatures quickly and the concrete has little time to respond to heating.
Increasing temperatures cause materials to expand. Gradients through the depth of an element cause one side to expand more than the other, creating greater thermal strains on one side than the other. This results in the element trying to bow towards the source of heat. If the ends are axially and rotationally restrained from bowing this will result in the development of a moment along the element. If the ends are rotationally free the beam will deflect (Or bow) towards the heat. The thermal curvature φ associated with a linear gradient, T,y, through the depth of an element is given by Equation 2.19.
(2.19) φ = αT,y
α equals the thermal expansion coefficient of the constituent material.
Thermal gradients also exist along elements of structure. Columns invariably attain greater temperatures near the top of a compartment than near the floor. Beams and slabs may also experience gradients along their length as a result of localised heating. In beams, temperatures near the connections are very often cooler that at the centre. Pettersson  reports on early work by Thor which shows that there is an increase in the load carrying capacity compared with beams which have uniform temperatures along their length. In statically indeterminate beams Thor found the rise in load bearing capacity could be considerable.
Figure 2.16: Design values for reduction of modulus of elasticity 
Rotter et al  and Usmani et al  have considered the effects of thermal bowing and thermal expansion from first principles on the behaviour of restrained steel and composite beams. This work is summarised in Chapter 6 of this thesis alongside numerical calculations to verify the theory.
The effects of restrained thermal expansion and bowing have been observed in tests and analytical studies previously.      Cooke  reports a programme of tests carried out at the Warrington Fire Research Centre on simply supported reinforced concrete floor slabs of 4.5m span. Mid-span deflections and longitudinal deflections caused by thermal bowing were measured for slabs of 150mm and 250mm thickness made of normal weight and lightweight concrete. The slabs were exposed to one of two heating regimes the standard curve in BS476: Part 8: 1972 (now superseded by BS 476 Parts 20-23) or the more severe standard curve proposed for hydrocarbon fires by the Norwegian Petroleum Directorate. Results of the parametric study showed that the imposed load is responsible for only a small part of the deflection. This is in agreement with modelling of the Cardington tests.  The thermal bowing deflections of lightweight concrete slabs were significantly lower than the deflections experienced in similar normal weight concrete slabs. Cooke  attributed this to the different thermal expansion values of the respective aggregates. The more severe hydrocarbon fire produced higher deflections overall especially in the earlier stages of the test. Cooke does not explain this but the nominal curve for hydrocarbon fires reaches much higher temperatures (almost immediately in excess of 800°C) and would result in much higher gradients over the depth of the section.
The significance of restrained thermal expansion is acknowledged in design codes but little information is provided on how to include the effects in design thus is very often ignored.
Single determinate elements tested in the fire resistance furnace can only form one load path determined by equilibrium of the forces. Indeterminate or redundant structures are capable of transferring load through many alternate load paths and as a result the pattern of forces and stresses is determined by the relative stiffness of the elements of the structure as well as equilibrium and compatibility conditions. Redundant structures allow load transfer to stiffer parts of the structure when one or more elements fail allowing the structure to survive. The benefits of redundancy rely on ductility of the connected structure and the ability to form new load paths. The Broadgate building and the Cardington 8-storey composite steel test frame have shown considerable redundancy in fire.
In fire design the applied loads are assumed to be lower because the imposed loads are reduced by evacuation and contents burning. Design codes allow lower partial safety factors for loading in fire. Safety factors for loading in BS 5950 Part 8 and EC1/EC3 are given in Table 2.3. It has been proposed that in the next version of BS 5950 Part 8 the safety factor for imposed loading for fire design should be reduced from 0.8 to 0.5. This would mean a reduction in load ratio of the individual structural elements and a corresponding increase in limiting temperature according to BS 5950 Part 8, inevitably leading to a reduction in passive fire protection and savings for steel design. However, in large structures where phased evacuation is adopted i.e. parts of the building are evacuated whilst others remain occupied in areas protected by compartmentation measures, the imposed loading may still be high.
|Load||BS 5950 Part 8||EC1/EC3|
|Imposed Loads: permanent||1.0||1.0|
|Imposed Loads: non-permanent||0.8||0.5 to 0.9|
|Wind Loads||0.33||0 or 0.5|
Table 2.3: Load factors for fire limit state   
Also loading on the floors above the fire compartment (the load carried by the fire exposed weaker elements) will only be reduced by evacuation not by combustion of the contents. However, work at Edinburgh has shown that loading under fire conditions, where the elements of structure are axially restrained against thermal expansion, has little impact on the deflection response until near impending runaway failure.   Moreover, experience at Cardington has shown that it is very difficult to achieve imposed loads representative of those assumed in design. Covering the Cardington frame floors in sand bags  only achieved an imposed load of O.83kN/m2 during the tests. On this basis reducing the safety factor on imposed loads for fire seems reasonable, providing characteristic imposed loads assumed in ambient design are not excessively reduced in the future.
2.6 Research into the behaviour of single elements of structure in fire
Most analytical methods for determining the fire resistance of structures centred on single elements. The response of columns and beams under fire conditions has been investigated over many years but with increased intensity in the 80s.  At this time extensive testing was conducted in Europe in the UK, Germany, Netherlands, France and Belgium.   These test results have been extensively used for comparison with numerical models. The response of a whole building under fire has received less attention.
2.6.1 Computer models for structures
There are a number of numerical computer programs developed in research centres to calculate the behaviour of structures in fire. Some of the well known codes used for fire research include CEFICOSS  (ProfilARBED-Recherches, Luxembourg), DIANA (TNO Delft), VULCAN  (University of Sheffield), SAFIR (the next generation of CEFICOSS developed at the University of Liege, Belgium) and SISMEF (CTICM. France). CEFICOSS, DIANA and SAFIR include thermal analysis as well as structural analysis. All except CEFICOSS model 3D behaviour, CEFICOSS models 2D. VULCAN is based on the code JNSTAF. 
General finite element codes like ANSYS and ABAQUS  have also been used to analyse fire. ABAQUS is used at the University of Edinburgh, by CORUS and the University of Manchester. Imperial College have developed a research code ADAPTIC capable of modelling structural fire behaviour. 
The research described in this thesis is primarily concerned with the response of composite floor slabs in whole frame structures but the effect of restrained thermal expansion has been analysed more in columns than beams and slabs. Thus a review of column research aided understanding of restrained thermal expansion and thermal bowing.
Columns and beams both experience restrained thermal expansion in fire conditions but columns are further complicated by axial forces as a result of live loading, initial out of straightness, eccentric loading and bending moments as a result of expanding beams.
The European Convention for Constructional Steelwork (ECCS) proposed buckling curves for columns at ambient in the late 70s as cited by Lane.   There are 5 basic buckling curves (classified ao,a,b,c,d) which are applicable to cross-sections of different shapes. Beam-column connections are considered by including a factor to account for moment and eccentricity.
Janss and Minne  presented a method to calculate the buckling of steel columns under concentric and eccentric loading in fire conditions. They simply included temperature dependent material properties in the ECCS ambient buckling curves and calibrated the results against experiments from Belgium, Denmark and Germany. A correction factor was introduced to get better agreement with the experimental results. Only type "c" cross sections were considered because of limited test data on other sections.
In the 80s, Lie  described work carried Out at NRCC (National Research Centre of Canada) on developing mathematical models for calculating the fire resistance of compression members. Rubert  analysed the effects of load level (utilisation factor) and slenderness on the critical temperatures of steel columns. Also Anderberg et al  compared analytical predictions of the mechanical behaviour of fire exposed steel structures with experimental data on axially free and restrained columns tested in Norway and France. Results from the materially and geometrically non-linear finite element model Steelfire, developed by Forsen, are compared. Results from Steelfire agree well with the test data. The authors add that full axial restraint is very difficult to achieve in practise therefore test conditions are difficult to define especially at high restraint, thus some results may be fortuitous.
In 1990 Corradi  carried out a parametric study on the interaction diagrams of steel columns in fire conditions to study the influence of the slope of the hardening branch in steel stress-strain plots. Corradi found that a bi-linear approach was not adequate because it consistently overestimated the load carrying capacity even for small axial forces. Also in a tri-linear model the interaction curves were very sensitive to change in the slope of the hardening zone.
Wang and Moore  developed a simple analytical relationship for restrained thermal expansion in axially loaded columns assuming axial expansion could be explained by Figure 2.17. ΔP is the additional compressive load generated in the column as a result of restraining the expansion ΔεthLc. The equation is compared with parametric studies on a numerical model. The failure temperature of the column in the frame with stiffer beams (higher restraint to expansion) was generally lower. However, by increasing the applied load the reduction in failure temperature slowed. Wang and Moore concluded that the effect of restrained thermal expansion in columns generally increases the axial compression force and was particularly detrimental to slender columns. The magnitude of the additional axial forces depends on the column stiffness, restraining stiffness, column slenderness and applied axial load. The simple calculation was also tested against the squashing of columns at Broadgate. The failure temperature was found to coincide with the predicted failure temperature after the fire.
Baker et al  studied analytical and experimental results to determine the significance of local buckling, the post-buckled response and high temperature creep effects. Stocky (stub) columns were analysed and in all cases the columns exhibited local buckling and a stable post-buckling load-deflection response. ABAQUS non-linear shell elements were used to model the local buckling. Localised deflections were found in the hottest areas of the column (high temperature variations of up to (196°C)) initially and after local buckling. The material properties were determined by a series of tensile coupon tests at various temperatures and strain rates. There was good agreement with the analytical and experimental results. Conclusions state that rate dependent material properties are accurate enough to predict the behaviour of steel columns at elevated temperatures for a short time and at lower temperatures (below 400°C) for a long time.
Janss  highlights that discrepancies arise when the fire resistance is determined by test and by calculation. He attributes this to assuming characteristic material properties, uniform temperature distribution and design yield strength when carrying out a calculation. In tests there may be a considerable distribution in temperature leading to an increase in the failure temperature. By adopting a unified statistical evaluation procedure put in place to verify EC equations, adaptation factors are proposed to modify the design assumptions so that critical temperatures are found which are at the same level as standard tests.
Figure 2.17: Column expansion in fire
Ali et al  reports on an experimental program designed to investigate the effects of imposing axial restraint on steel columns in fire. The work was carried out at the University of Ulster. 45 fire test and 10 pilot studies were conducted on a rig capable of applying axial load and restraint. They defined the restraint stiffness (αk) as the ratio of the stiffness of the restraining element (Ks) to the axial stiffness of the expanding column (KcT). By studying two previously recorded load tests αk was found to be in the region 0.1-0.55 in practice. Tests were carried out to ensure uniform temperature over the height of the column. The tests were conducted under constant load and a heating rate of 10°C/min until failure. Preliminary reports of the pilot study concluded that imposing restraint reduces the fire resistance of the column. In unloaded columns increasing αk from 0.04 to 0.32 almost doubled the value of axial force induced in the column and reduced the failure temperature from 518°C to 223°C. This is in agreement with Wang and Moore.  When the columns were loaded to 64% of their capacity and for the same increase in αk the failure temperature reduced to 185°C.
Baker and Xie  studied elasto-plastic creep of steel columns exposed to fire. The research was carried out because it was thought at higher temperatures and loads in unexposed columns, creep and local buckling may become important. These were very often ignored by other researchers. They were not concerned with creep in protected columns over the length of a fire. Stub columns were heated locally mirroring the hottest layer of gases in a compartment near the top of the column. Gradients were ignored and only axial deflections were allowed. There was plastic shortening and local buckling within 0.3m of the top connection. This is very similar to the response of the columns in the Broadgate building and in British Steel Test 2  at Cardington. The columns in the Cardington test were only protected to 0.5m below the underside of the slab. Further analysis showed creep to dominate at high load levels beyond 600°C.
Researchers in Australia  have shown that the column effective length concept is valid at both ambient and elevated temperatures. They found that the time to collapse of unprotected steel columns was less for higher loads, medium slenderness ratios and lighter (less compact) column sections.
Franssen et al  reports on a comparison between five structural fire codes. CEFICOSS. DIANA, SAFIR, SISMEF and LENAS-MT developed jointly by CTICM and Takenaka in Tokyo. The five codes were to be used in an ECSC research project to determine the buckling curves of hot rolled H steel sections in fire for EC 3 Part 10 (now EC3 Part 1.2). The comparison was conducted to check the consistency of the results from all five codes. Eight tests including Lee�s frame, an eccentrically loaded column and an axially loaded column at ambient and elevated temperatures were analysed. The conclusions state that if bending is the predominant behaviour all five codes give very similar results. If axial loads dominate, slight differences occur although the greatest difference between any two codes was 6%.
In 1995 Franssen  et al proposed a simple model to determine the fire resistance of axially loaded members, similar to the ambient form in EC3 Part 1.1 (based on ECCS buckling curves). Thus the ultimate load of columns at elevated temperatures could be determined on a calculator. The initial relationship is for simply supported , axially loaded, symmetrically heated H columns. The extent of the analyses was considerable. 200,000 numerical tests were conducted analysing 2 yield strengths, 339 hot rolled H sections, 2 buckling axes, 10 slendernesses, 12 applied loads and two thermal regimes (constant temperature and the standard fire). These were matched with 80 experiments.
Recently Correia  has studied the critical temperatures of compressed steel elements with restrained thermal elongation. 168 tests on hinged bars with 4 slendernesses, 2 eccentricities and 6 levels of restraint were carried out. Test and computer simulation have shown that neglecting the effects of thermal axial restraint may result in overestimating the fire resistance of columns. The research found that restrained thermal elongation of centrally compressed elements with slenderness greater than 80 lead to reductions of Tcrit of 200°C. However if eccentricity was high there was no significant variation in critical temperature.
Bailey  analyses the assumption that columns designed to current design procedures are adequate when composite frames are designed to the new SCI guide i.e. passive fire protection is removed from secondary beams. The results do not concur that columns are stable. P-δ effects caused by expanding beams could cause column instability. The analyses showed that column instability was effected by beam-column heating rates, beam cross-section size, span of the beams, end rigidity of the heated column and column axial load. Nominal effects were column cross-section size, beam-column connection rigidity and horizontal restraint to the heated beams (provided realistic values were chosen).
It has been shown that axial restraint and its effect on thermally expanding columns has been researched for many years. Most of the research has been on single elements. Restrained thermal expansion of columns leads to increased axial forces and early failure of the elements.
In composite floor slabs buckling of the steel beams as a result of large compressions induced by restrained thermal expansions is a positive event. The buckle allows the increase in length as a result of thermal expansion to be accommodated in downward deflections relieving axial compressions. This is discussed in this thesis.
Burgess et al  developed a secant stiffness approach to fire analysis of steel beams with non-linear material behaviour. The moment-curvature-temperature relationships were derived using a Ramberg-Osgood Equation. Initially only uniform temperatures could be described, through the depth of the section and along its length. The secant stiffness approach was adopted because there were no limitations on the shape of the stress-strain curves and the model was stable at zero tangent stiffness (pure yield). Later modelling of non-uniform temperatures was incorporated in the model.  The effect of this was twofold. The neutral-axis depth changes and additional deformations due to non-uniform thermal expansion (bowing) had to be modelled. Thermal bowing was included by an equivalent moment at the ends of each beam element. The scope of the analysis did not include axial thrusts or semi-rigid connection behaviour. The secant approach was also used to study the connection stiffness and the behaviour of steel beams in fire.  There are significant increases in failure temperature when the rotational stiffness is increased from simply supported conditions. They conclude that the influence of the connection temperature is not critical.
In 1991 El-Rimawi et al  reported a series of numerical studies on the fire resistance of steel beams in fire. FIRES T2, originally developed at the University of California Berkeley, was used to calculate the thermal regime. They highlighted the increased fire resistance of beams exposed to fire on three sides (supporting a concrete slab) over 4-sided exposure. In this instance deflections were dominated by thermal bowing as a result of the gradient between the top and bottom flanges. By exploiting this phenomenon increased fire resistance was obtained in asymmetric sections. The effect of support conditions, span:depth ratio and design stress were also investigated. Some benefit was derived from partial heating over the length of a beam.
Liu  developed a 3D shell model using a tangential stiffness approach to analyse the behaviour of steel beams and connections in fire. The code was written in Fortran 77. The model is geometrically and materially non-linear. Non-uniform temperatures can also be modelled. Numerical results were compared with real fire test data on steel beams and beam-column connections. Good agreement with fire resistance ratings and deflection-time histories were obtained.
Bailey et al  considers the lateral torsional buckling of uniformly heated, unrestrained steel beams. Different sections, spans and load cases are considered. Failure is by lateral torsional buckling in all cases. When compared with limiting temperatures in BS 5950 Part 8 and EC3 Part 1.2 the model predicted lower temperatures than the code. In conclusion the authors recognise that beams in real structures are restrained therefore failure is unlikely to occur
More recently Becker  has considered the heat sink effects of slabs in Continuous construction on connection temperatures. A standard fire is assumed and a thermal analysis of insulated and non-insulated continuous construction conducted. The structural significance is tested with SAFIR. The temperature drop in bare steel is insignificant for practical purposes after 30-60 minutes standard fire exposure. However for insulated steel the effect of the heat sink on the non-uniformity of longitudinal temperature differences is much more significant. A one bay frame example is given in the paper and the structural model predicts a 16% increase in the fire resistance from 60-70 minutes when uniform and non-uniform temperatures are considered. Natural fires were not considered.
The most important phenomena in slabs with regards to their behaviour in fire is membrane action. Compressive and tensile membrane action provide reserves of strength allowing whole frame structures to survive fire.     Traditionally slab designs are based on yield line theory with no consideration of membrane effects.
Compressive membrane forces only occur if the edges of the slab are fixed. They are induced when deflections cause the slab edges to move outward and react against the lateral restraint, producing arching action of the slab between the boundaries. Compressive membrane forces in the slab result in an increase of the flexural strength. 
At large deflections the slab edges tend to move inwards and if the edges are suitably laterally restrained tensile membrane forces are induced which may enable the slab to carry significant load by catenary action of the reinforcing steel. Compressive membrane action relies on in-plane restraint from the boundaries therefore can only occur in fixed boundary conditions. Tensile membrane action can occur in fixed or simply supported conditions. 
Figure 2.18 shows the classic load-deflection response for a clamped and simply supported slab. Initially a restrained slab will arch from boundary to boundary inducing compressive membrane action. As deflection increases, load increases. Point B is the maximum compressive force, several times greater than the strength according to yield-line theory. As deflections increase further the depth of the cracked slab increases therefore composite strength diminishes. At point C the slab has cracked over its whole depth and tensile membrane action has developed (Figure 2.19). The load is supported by the mesh anchored at the supports. As the deflection increases further, load carrying capacity increases until rupture at point D. In a simply supported slab compressive membrane action is limited. However at large deflections slabs can develop an in-plane ring beam in compression  to support the tensile membrane action (Figure 2.20). ln a simply supported slab there is a smooth transition from flexural behaviour to tensile membrane action.
Compressive membrane action is not stable and realistic support conditions are seldom completely restrained which explains why designers will not rely on its benefits. Tensile membrane action is stable but occurs at large deflections which would exceed serviceability conditions. This is less of problem in fire conditions. When considering membrane action the yield-line pattern, yield condition, geometric compatibility, force equilibrium and the work method of plastic analysis must all be considered. 
Figure 2.18: Complete load-deflection curve for a reinforced concrete slab 
188.8.131.52 Membrane action at ambient
In 1952 a series of tests were carried out on a reinforced concrete building in Johannesberg. From two tests to destruction on interior slab panels in both tests the collapse load was more than twice that predicted by the yield line method.  Ockleston who was responsible for the tests later showed that the result can be explained by the arching action due to the development of compressive membrane stresses in the concrete slab. 
Park was actively researching membrane actions in slabs in the 60s   experimentally and analytically. He derived expressions for the ultimate strength of uniformly loaded, axially restrained, two-way concrete slabs with and without reinforcement including compressive membrane action.
Figure 2.19: Tensile membrane load carrying mechanism in a slab with clamped edges 
Park also developed an analytical solution for slabs in tensile membrane action with clamped edges.  Wood developed a solution for tensile membrane action in simply supported circular plates and Kemp for simply supported square slabs as cited by Christiansen.  Later Wang  adopted Kemp�s approach modifying it for rectangular slabs.
In recent years Eyre and Kemp  have analysed the various methods of predicting the ultimate load capacity of reinforced concrete slabs including compressive membrane action and discuss the implications associated with the assumed stiffness of the slab itself. They found when very rigid supports are used the theory predicts an overly stiff load-deflection response.
Guice  report tests on one-way reinforced concrete strips with partial lateral and rotational restraint. The tests were carried out because in reality idealised boundaries do not exist and there is little data on partial restraint. They found lateral restraint is essential in developing both compressive and tensile actions. Small rotational freedoms significantly enhance tensile membrane capacity. Increasing the area of steel and slab thickness also enhances the compressive membrane capacity and sufficient ductility in the steel reinforcement must be provided to ensure tensile membrane resistance.
184.108.40.206 Membrane action at elevated temperatures
Tensile membrane action played an important role in the survival of the Cardington frame fire tests. This was highlighted in the numerical modelling.     Test data to support the theory was not conclusive. A major concern was that there were no measurements to prove a compressive membrane ring had developed at the edge
Figure 2.20: Tensile membrane load carrying mechanism in a simply supported slab 
of the compartments to support tensile membrane action at the centre. Consequently Bailey  et al conducted a large scale ambient test (additional deflections as a result of thermal gradients were not considered) to understand and record tensile membrane action. They conducted the large scale test on a profiled composite slab similar to that used at Cardington. The test slab measured 9.5m x 6.5m in plan. It was supported on composite edge beams with shear stud connectors around the slabs perimeter. During the Cardington tests the metal deck de-bonded from the slab so this was removed for the test. Tensile membrane action was observed and the failure load was double that predicted by classic yield-line theory.
Wang   has conducted the most recent analytical work on tensile membrane action in fire. He developed a procedure for rectangular slabs based on Kemp�s methodology for square slabs and predicted the final deflection after cooling in the BRE corner test. Huang  has reported a series of analyses using linear and non-linear slab elements in VULCAN. A comparison is made between the different levels of restraint in all the Cardington frame fire tests and the effect on the slab. Conclusions include that tensile membrane action is minimised if the floor slab is only in single curvature, observed in the half floor test.
2.7 Frame Analysis
The increased benefit in fire resistance of studying frames has been realised for some time. Frame analysis has concentrated on developing numerical models. Unfortunately whole frame experiments are expensive and the models are very often tested on experimental data from single elements or sub-frames.
Saab and Nethercot  developed a non-linear analysis of 2D steel frames under fire conditions by extending the finite element model INSTAF. Non-linear stress-strain temperature relationships are based on the Ramberg-Osgood equation and creep is included implicitly. The solver is an incremental Newton-Raphson method. The model allows variation of temperature distribution both along and across each member. It was verified against test results on frames and columns. In 1996 Najjar  reports on further development of INSTAF, to model 3D steel frames in fire. Bailey  extended INSTAF considerably to include continuous concrete floor slabs, semi-rigid connections, lateral torsional buckling and strain reversal in steel.
Modelling strain reversal is important for cooling. El-Rimawi  included unloading of the steel stress-strain curve in the model NARR2 with a hi-linear unloading curve. The approach adopted by Bailey was curvi-linear based on the Ramberg-Osgood stress-strain relationship.  Bailey assumed the loading and unloading paths separate in the inelastic range and the upper bound of the elastic limit is 0.1% proof stress at elevated temperatures. A comparison between a spreading fire and simultaneous heating of a whole compartment was conducted. The authors acknowledge the limited study but preliminary conclusions included that there were higher deflections in the source bays of the spreading fire studies than with simultaneous heating of the same member. Extra compressions and deflections were induced in cooling beams adjacent to beams heating up.
In two papers Wang   describes the development and verification of a finite element program at BRE to study the structural response of steel frames at elevated temperatures. Two and three dimensional frames can be modelled. The model can also include concrete.
Franssen  analysed a 2D unprotected steel frame tested at Cardington. The application of 1D, 2D and 3D heat flow models was discussed. The effects of restraint, frame continuity and thermal expansion were highlighted. The calculation of frame stability was compared with the draft EC3.  A possible outcome of the research was the ability to test scenarios where it was safe to use the simplified EC3 approach. Conclusions included that the yield stress at ambient has an influence on the fire resistance and the variation of lateral in-plane restraint has a major effect on the fire resistance. Also the calculated fire resistance of a single beam has a much lower value than the frame. Finally the influence of thermal expansion cannot be ignored.
El-Rimawi et al  developed the secant stiffness method for beams to include thermal degradation characteristics of the connection between members and the effects of axial force. It highlights that survival can be significantly enhanced by connection characteristics. In a further paper  the same method was adopted to analyse a "rugby-frame" model of an external bay in the bottom storey of a building.
There was significant research in Japan in the late 80s and early 90s into the behaviour of whole steel frames in fire. In two papers Hirota et al  and Nakamura et al  describe the results of 50 experiments on 2D, 2 storey and 3D, 3 storey steel frames. In each study a column or girder or column and girder were heated by an electric furnace. The results were compared with analytical theory derived in the 60s by Saito. The theory is based on the stiffness method and takes into account the effects of restrained thermal expansion. They found that the structural behaviour was influenced more by a heated girder than a heated column. Nakamura et al  also conducted tests on a 6 storey full-scale steel frame. Again single columns were heated. Local buckling of a column influenced the whole structure.
A method of calculating the stress and deformation behaviour of a high rise steel structure exposed to a compartment fire is studied by Saito et al  The structure is split into 3 sections. The first is the structure exposed to fire (local substructure), second is the adjacent substructure and the third comprises the remainder of the cool structure. The structure exposed directly to fire is analysed in the elasto-plastic range. The adjacent substructure is analysed in the elastic range. The calculation is for the restrained forces acting on the local substructure (fire compartment) as a result of restrained thermal expansion and the deflections of the adjacent substructure. The calculation method was carried out on 48 buildings.
Lane  studied column collapse in a series of pairs of laboratory-scale five storey, two bay, plane steel frames. The pairs of frames were designed to show restrained column collapse in one frame and column collapse due to hinges forming in the restraining beams in the other. The tests were conducted at ambient and at elevated temperature. At ambient the pairs of frames collapsed under the same load but by the two different collapse mechanisms showing the design was reliable at ambient. Elevated temperature tests involved heating various combinations of columns and/or beams. The various tests showed the importance of restrained thermal expansion. Although full restraint could not be achieved in any of the tests. The experiments were compared with an elastic frame analysis based on the slope-deflection method and the simple column design method in EC3. The thesis overall highlights the need for a more intelligent approach to fire resistance design moving away from single element behaviour in the fire resistance test. This work was conducted after the Broadgate fire and at the same time as the Cardington tests.
After the Broadgate Phase 8 fire and the Cardington frame tests there were benchmarks to test composite frame models. Research intensified because almost all the tests had unprotected steel beams but collapse was not seen. This research is discussed in Chapter 4.
A detailed definition of fire resistance has been given and methods of calculating fire resistance of structural elements has been outlined. The fire resistance test is inadequate in a number of respects not least because the fire exposure is not representative of real fires or that single elements are tested to failure and the results used in the design of whole frames.
The history and development of performance based design in fire safety has been described.
Factors influencing the behaviour of steel and composite structures in fire have been analysed. Each factor was discussed separately although in a real structure they would interact to define the behaviour. Early research into the behaviour of structures in fire centred around single elements of structure. Columns and beams have been analysed for many years. More recently research into membrane behaviour of slabs in fire has been investigated although membrane action at ambient has been researched since the 60s. Large deflections in slabs during a fire allow tensile membrane action to develop. This enhances the strength thus the fire resistance of the slab. Many computer codes have been developed to model steel frames in fire. Later the inclusion of slab models enabled composite frame response to be modelled. This was the state of the art before the Cardington frame fire tests.
Thermal response of structures to real fire.
Reliable structural analysis for fire requires the atmosphere temperatures during the compartment fire and the subsequent heat transfer to the structural elements to be known with reasonable accuracy. The validity of the standard fire curve as a fire exposure has already been described in Chapter 2. The curve bears little resemblance to any natural fire curves and is not representative of many. Researchers tried to resolve this problem with the concept of t-equivalence. However the most accurate method for fire design is to model the actual expected fire curve given a compartment of specific dimensions, fire load and ventilation characteristics. In structural fire engineering reliable natural fire models can provide a sound basis for realistic heat transfer analysis and thus temperature histories of the connected structure. This chapter reviews methods of determining natural fires. The advantages and disadvantages of complex mathematical models, computer models and simple empirical and parametric relationships are considered.
Just as there are many approaches to calculating natural fire curves there are also many models (with varying degrees of sophistication) for calculating heat transfer. Methods developed and available to the designer will be reviewed. The basis of any heat transfer analysis are the input data. The heating regime is essential but the thermal characteristics of the material are also important. Published information on the thermal properties of steel and concrete will also be reviewed.
3.2 Natural Fire Curves
The standard fire curve describes the variation of the temperature of the fire gases within a standard furnace but bears little resemblance to any natural fire curve. It takes no account of the different thermal exposures which result from different compartment geometries, ventilation conditions, fire loads and compartment boundary materials.  With the t-equivalence approach the heating effect in a compartment is calculated based on real compartment fire behaviour and that heating is related back to the standard furnace test. However, the energy and mass balance equations for the fire compartment can be used to determine the actual thermal exposure and fire duration. This is known as the natural fire method. This method allows the combustion characteristics of the fire load, the ventilation effects and the thermal properties of the compartment enclosure to be considered. It is the most rigorous means of determining fire duration. This is not related in any way to the standard fire resistance test and represents the real fire duration, once flashover has occurred. Local fires can only be determined by natural fire curves.
Figure 3.1: The course of a well-ventilated compartment fire 
3.3 Compartment Fires
The compartment fire process can be described by three distinct phases, the pre-flashover fire, the fully-developed fire (or post-flashover fire) and the cooling phase. There is a rapid transition stage called flashover between the pre-flashover and fully developed fire. This is shown in Figure 3.1  which illustrates the whole process in terms of heat released against time. While still small (during the growth phase) the compartment fire will behave as it would in the open. As it grows the confinement of the compartment begins to influence its behaviour (Figure 3.2). If there is sufficient fuel and ventilation the fire will develop to flashover and its maximum intensity, when all combustible surfaces are burning. If the fire is extinguished before flashover or if the fuel or ventilation is insufficient there will only be localised damage. Post-flashover the whole enclosure and its contents will be devastated. Structural damage and fire spread beyond the compartment of origin is also likely unless the fire is in a fire rated enclosure. Structural fire engineers are concerned with elements of structure subjected to high temperatures for a prolonged period of time. Post-flashover fires provide the worst case scenario. However localised heating of key elements of structure must also be considered.
Flashover is defined as the "relatively rapid transition between the primary fire which is essentially localised around the item first ignited, and the general conflagration when all surfaces within the compartment are burning. " It is a transition period as a result of several mechanisms each one contributing to the growth of the fire to a size at which flashover becomes inevitable. If there is insufficient fuel, ventilation or propensity for fire spread then a compartment fire may not achieve a rate of heat release sufficient for flashover to occur. The fire will remain small around the items first ignited (represented by the broken line in Figure 3.1).
Figure 3.2: The effect of enclosure on the rate of burning of a slab of polymethylmethacrylate (Friedman 1975 as cited by Drysdale )
Many researchers have investigated the flashover process. Several attempts have been made at predicting the onset of flashover associated with the compartment fire reaching a critical size in terms of its rate of heat release. The onset of flashover has been linked with radiant heat fluxes at floor level in excess of 20kW/m2 and temperatures of 600°C under the ceiling (for typical ceiling heights of 2.5-3m).    The onset of continuous flaming out through the openings is an indication that flashover has occurred. The rate of heat release and so the onset of flashover depends on the size of the compartment, the thermal characteristics of the boundaries, the amount and type of fuel and the available ventilation. Thomas  developed a criterion for flashover based on the size of the ventilation openings. Analysis of a large number of compartment fires showed that flashover would only occur if the heat release from the fire reached a certain level. Thomas�s flashover criterion is described by Equation 3.1.
(3.1) Qfo = 0.0078At + 0.378Av√Hv
Qfo = Critical value of heat release for flashover (MW)
At = the total internal surface area of the compartment (m2)
Av√Hv = opening factor (m5/2)
3.3.1 The Pre-flashover Fire
During the growth phase of any fire the flames form a buoyant plume above the items first ignited. In a compartment, if the fire grows to a size where the plume impinges upon the ceiling a ceiling jet will develop radiating outwards from the central axis of the plume. When the flow of hot gases meet the walls of the enclosure a hot smokey layer builds up under the ceiling, radiating heat back down towards the lower compartment and the fuel below. The development of the smoke layer is important for flashover. The radiative heat feedback from the dense, hot smoke results in the ignition of many more items in the room which in turn increases the level of hot gases near the ceiling. An understanding of pre-flashover fires is very important for life safety. The prime objective of the fire safety engineer is to prevent or delay flashover providing adequate time for the occupants of the building to escape. In multi-storey structures this is achieved by designing early detection and sprinkler systems. Activation times of sprinklers and detectors need to be calculated. Thus a design rate of fire growth has to be predicted based on the type, orientation and amount of fuel and available ventilation. Other calculations may include the depth and temperature of the smoke layer. These calculations are often performed by 2 zone computer models (discussed in Section 3.10.1). Hand calculations are described by Walton and Thomas. 
Several empirical correlations exist for the fire plume and ceiling jet (Equations 3.2 and 3.3). They estimate the temperature (T) or velocity (U) of the flames at a particulai height (H) in the plume or radius (r) along a ceiling jet. They are used in design to predict the activation times of sprinklers and detectors. Alpert  developed the original correlations from large scale quasi-steady fire experiments although others exist.   In general the relationships are only applicable to large spaces with flat unobstructed ceilings. 
(3.2) ΔT = kTQ2/3/H5/3
(3.3) U = ku(Q/H)1/3
|Growth rate||Typical scenario||α (kW/s2)|
|Slow||Densely packed paper products||0.00293|
|Medium||Traditional mattress or armchair||0.01172|
|Fast||PU mattress (horizontal) or PE pallets stacked 1m high||0.0469|
|Ultra fast||High rack storage, PE rigid foam stacked 5m high||0.1876|
Table 3.1: Parameters used for t2 fires (Evans 1995 as cited by Drysdale 1998) 
| Fire Growth |
| Fire growth parameter α |
| Time for Qg = 1000kW |
Table 3.2: Fire growth parameters and time to reach the rate of heat release Qg = 1000kW for t2 fires in DD 240 
220.127.116.11 t2 Fires
Power law fires are commonly used to define fire growth rates. t2 fires are the most common (Equation 3.4, Figure 3.3 and Table 3.1). They describe the growth rate of a design fire such that the rate of heat release is directly proportional to the time squared. DD240 gives the growth parameters listed in table 3.2 and guidance on the building occupancy associated with each growth rate. For instance an office is associated with a medium growth rate and industrial storage an ultrafast growth rate.  The t2 relationship fits well with measured test data but only after ignition is well established. A time t0 is specified as the period between ignition and initial flaming. 
Temperature and velocity relationships have also been devised for power law fires. Heskestad et al (as cited by Mowrer ) developed non-dimensional correlations for temperature rise and velocity using t2 fire data.
(3.4) Q' = α(t - t0)2
Q' = heat release rate (kW)
α = fire growth constant see Table 3.1
t0 = delay between ignition and initial flaming (s)
t = time (s)
Figure 3.3: t2 fire growth according to Equation 34 
18.104.22.168 Heat Release data
Burning rates are often given as mass loss rates (m') in kg/s or Rates of Heat Release (RHR), q' in kW. Mass loss data is less useful. The advent of oxygen consumption calorimetry provided an accurate method of measuring RIHR in the open. RHR data from tests on pool fires, wood cribs and in furniture calorimeters provide some information on growth rates. Items tested include upholstered chairs, mattresses, pillows and televisions. 
22.214.171.124 Calculating Rate of Heat Release (RHR) to Eurocode 1
Eurocode 1  presents a method for calculating the maximum, constant rate of burning in a fully developed fire. The rate of burning is equated to a RHR by multiplying the rate of burning by the effective heat of combustion of wood.
(3.5) R = min [L/τF , 0.18(1 - e0.036η)Aw(haW/D)1/2]
R = rate of burning (kg of wood/s)
L = total fire load (kg of wood)
τF = free burning fire duration (assumed to be 1200s)
Aw = sum of window area on all walls (m2)
ha = weighted average of window heights on all walls (m)
W = width of wall containing window/s (m)
D = depth of fire compartment (m)
η = AT/(Aw√h) (m-1/2)
AT = area of all surfaces minus the area of windows (m2)
The two terms in Equation 3.5 indicate whether the fire is ventilation controlled (burning is controlled by the rate of air in-flow) or fuel controlled (dependent on the surface area and burning characteristics of the fuel). The first term determines the RHR under fuel bed controlled conditions and the second term under ventilation controlled conditions. Neither growth or decay RHR are calculated. The free burning fire duration τF is always assumed to equal 1200 seconds.
3.3.2 The Post-flashover fire
After flashover high temperatures are sustained until the fuel is almost completely consumed. The compartment is engulfed with hot gases and products of combustion. RHR is at its highest. External flaming through the windows will also occur as the unburnt pyrolysis products in the fuel rich atmosphere flow out of the window and burn in the presence of air. Intensive research into compartment fires has centred around the post-flashover fire because the fire is most severe in this period but also because the compartment can be treated as one volume of uniform temperature and composition, simplifying modelling. Many compartment fire models only consider this stage.   Growth and decay are not easily treated theoretically. 
3.3.3 The decay period
The rate of decay of a compartment fire depends on the shape and material of the fuel, the size of the openings and the thermal properties of the wall linings. It is not easy to predict. Large openings allow heat to escape very quickly. Walls of low thermal inertia store less heat so decay rates are more rapid. However walls of low thermal inertia also have low thermal conductivity which insulates the compartment, retaining heat if there is any further burning. 
The decay period is assumed to start after the average temperature has dropped by 80% of the maximum value.  In design if considerable knowledge of the contents is known and a limited amount of fuel can burn then measured RHR data may provide information to the designer on decay rates. 
3.4 The burning regime: Ventilation vs. Fuel controlled fires
The influence of ventilation on compartment fires was first realised by Kawagoe in the late 50s.  Kawagoe was one of the first researchers to try and understand compartment fires using scaled experimental models. By studying the burning of wood cribs in enclosures he found that the rate of burning was independent of the amount of fuel but highly dependent on the ventilation particularly the height of the opening. He correlated the rate of mass loss R (kg/s) with the area (Aw) and height (H) of the opening semi-empirically (Equation 3.6).
(3.6) R = 0.092AwH1/2
The relationship fits very well with the data analysed. However, Thomas et al  have shown that the relationship breaks down at high ventilation rates. Kawagoe�s experiments were all ventilation controlled i.e. the rate of burning equals the rate of ingress of air.
The empirical relationship can also be derived theoretically by analysing the flow of gases in and out of the compartment. Drysdale  describes this. Several assumptions are made,
- The gases are uniform throughout the compartment
- There is no net flow by buoyancy in the compartment
- Hot gases leave the compartment through the opening above a neutral plane and cold air enters below the neutral plane (See Figure 3.4)
- The flow in and out of the opening is driven by buoyancy
- There is no interaction between the in flowing and out flowing gases
The empirical and theoretical equations are exactly the same. Drysdale regards the emergence of exactly the same constant of proportionality as fortuitous when all the assumptions are considered but the emergence of the combined term, Aw√H, as significant.  The combination of Aw√H is called the ventilation factor.
Figure 3.4: Pressure profile over the opening in a compartment resulting in cold air flowing in and hot gases flowing out
3.4.1 Opening factor
The opening factor is defined as the ventilation factor divided by the total surface area At of the enclosure (Equation 3.7). Magnusson and Thelandersson  were the first to use the opening factor. It was derived to reduce the number of independent variables when describing different compartment fire curves. Magnusson and Thelandersson divided the fire load and the ventilation factor by the total enclosure surface area (At) thus three variables affecting the development of compartment fires were reduced to two.  Both the ventilation factor and the opening factor are a method of expressing the available ventilation to a compartment and are highly dependent on the height of the opening, H.
(3.7) OF = Aw√H/At
In rooms where there are more than one opening a weighted value of Aw√H is calculated based on Figure 3.5.
3.4.2 Differentiating between fuel and ventilation controlled fires
Differentiating between a fuel controlled and a ventilation controlled fire is an important part of predicting the behaviour of a compartment fire. In the ventilation controlled regime there is insufficient air in the room thus the burning rate is dependent on the air supply. Duration of the fire is dependent on the total fire load.  A fuel-controlled fire exists if the supply of air is large and the burning rate depends on the surface area and the burning characteristics of the fuel.
Aw=A1 + A2 + .. A4 = b1h1 + b2h2 +...+ b4h4
H = (A1h1 + A2h2 +...+ A4h4)/A
At = 2(l1l2 + l1l3 + l2l3)
Figure 3.5: Determination of a weighted value of Aw√H for enclosures with more than one opening 
Harmathy   developed a semi-empirical equation based on experimental data to define whether a fire is fuel or ventilation controlled.
Bullen and Thomas  showed that beyond a certain value of Aw√H the rate of burning became independent of the ventilation. Shown by a rapid drop in burning rate in Figure 3.6. Figure 3.6 also shows that as the area of the fuel surface increases the transition between the two regimes occurs at larger values of Aw√H.
Most fires in buildings are ventilation controlled, although in modern buildings with large windows and small fuel surface areas, fuel controlled burning may result. The duration of the fire in both regimes depends on the absolute fire load available. 
3.4.3 Fuel controlled fire
Calculating the rate of burning in a fuel controlled fire is not simple. However it is known that fuel controlled fires are normally less severe  (See Figure 3.7). This can be attributed to the excess air cooling the fire. Harmathy  suggested designing buildings to ensure fuel-controlled fires because they are less severe thus reducing the need for fire protection. This is not practical because it is almost impossible to restrict the fuel load over the lifetime of a building. Moreover, designing for a ventilation controlled fire is conservative.
Figure 3.6: Schematic diagram showing the variation of mass burning rate with ventilation parameter Aw√H1/2 and fuel bed area Af 
3.5 CIB compartment fire experiments
In the 1960s eight countries collaborated under the CIB (Conseil Internationale du Batiment) in a major experimental programme to improve understanding of the behaviour of fully developed compartment fires. Over 400 experiments were conducted in small-scale compartments 0.5m, 1.0m and 1.5m high of various shapes, areas of ventilation and fuel load (in the form of wood cribs). The effect of wind was also treated. Thomas and Heselden  report on this work. Several conclusions were reached. They found that m'/AwH1/2 is not a constant as Kawagoe suggests in Equation 3.6 but depends on compartment shape and At (in this case the surface area of the enclosure minus the area of the openings and the floor area). The intensity of radiation correlated with the rate of burning except for small ventilation openings and the maximum temperature in a given compartment fire occurred just inside the ventilation controlled regime. Law used these data in determining a t-equivalence model for fire resistance  as discussed in Chapter 2. Law related the CIB fires to the fire resistance time in a standard furnace in terms of failure of a protected steel column at 400°C and 550°C. Law  wanted to understand the effect on structural temperatures of the rate of burning. By reducing the rate of burning, the fire duration increased but the atmosphere temperatures decreased thus the effect on structural temperature may have been small. The main factor affecting t-equivalence was L/(AwAT)1/2. She found that scale and stick thickness of the wood cribs had negligible effects on t-equivalence. Closer stick spacing gave longer values of t-equivalence because of increased fire duration.
Figure 3.7: Average compartment temperatures during the steady burning period for wood crib fires in model enclosures as a function of the "opening factor". Symbols refer to different compartment shapes. 
Thomas and Law  also used the CIB data to study the behaviour of flames outside ventilation openings. This work formed the basis for the SCI design guide Fire Safety of Bare External Structural Steel.
3.6 Compartment fire modelling
The development of a temperature-time curve to be able to describe the temperature history of a compartment fire has been researched for decades. The earliest significant work was carried Out by Kawagoe and Sekine  in the 60s.
3.6.1 Model types
Compartment fire models can be split into three categories,
- Mathematical models
- Empirical or parametric models
- Computer models
3.6.2 Zone modelling
Zone modelling is a simple representation of the compartment fire process and the basis for almost all compartment fire modelling so is discussed first. The approach emerged in the 1970s.  During the pre-flashover fire the compartment can be described by 2 zones and the fire plume. There is a hot upper volume representing the smoke layer under the ceiling and a cooler lower volume as a result of thermal stratification due to buoyancy (See Figure 3.8) near the floor. Each layer is of relatively uniform temperature and composition. Post-flashover, turbulent gases completely fill the compartment and the enclosure can be represented by one well-mixed volume of uniform temperature and gas concentration. 
126.96.36.199 Mathematical models
Mathematical fire models are separated into two types, deterministic and probabilistic. Probabilistic models rely on probability data. They describe a building fire as a series of events.  The transition from one event to the next defines the development of the fire. Each transition has a probability of occurrence associated with it. However due to the lack of reliable probability data these models are very restricted.
|Kawagoe and Sekine ||1958-1963||Transient|
|Magnusson and Thelandersson  ||1970-1974||Transient|
|Tsuchiya and Sumi ||1971||Transient|
|Harmathy  ||1972||Steady|
|Thomas and Nilsson ||1973||Steady|
|Bullen and Thomas ||1977-1980||Transient|
|Babrauskas and Williamson  ||1978-1981||Transient|
|Babrauskas and Wickstrom ||1979||Transient|
|Schneider and Haksever as cited by ||1980||Transient|
|Nakaya and Akita ||1983||Transient|
Table 3.3: List of major deterministic post-flashover models 
Deterministic models are based on scientific algorithms of the important physical phenomena in a compartment fire. Deterministic models encompass simple one zone models where the whole compartment is one volume to field models where the compartment may be split into hundreds of thousands of 3D elements. A numerical solution for the Equations of conservation of mass, species, momentum and energy is required for each volume.
Many deterministic models of post-flashover fires have been developed starting in the early 60s.  All post-flashover models are based on the assumption that the gas temperature in the compartment is uniform. The major models are listed in table 3.3 adapted from Janssens.  Most of the models described as transient i.e. varying with time, are quasi-steady because transients are normally ignored in the gas phase. 
Computer zone models are based on deterministic modelling and are developing all the time. These will be reviewed in Section 3.10.1. OZone,  a one zone compartment fire model is the most recent model of its type in Europe and is currently being developed in Belgium at the University of Liege.
In terms of the basic concepts all the models listed in Table 3.3 are very similar. To be able to determine the temperature course of a fire it is necessary to know at each moment in time the rate at which heat is produced and the rate at which heat is lost to exposed materials and surroundings i.e. The Heat Balance for the enclosure.
Kawagoe and Sekine  developed the earliest Heat Balance model. The compartment was rectangular with one opening and walls of single thickness and material. The model only allowed temperatures in the post-flashover regime to be estimated. Independently Odeen  derived the same relationship for opening factor as Kawagoe. He also derived a method to estimate the cooling phase. Magnusson and Thelandersson  modelled the post-flashover fire and the cooling phase. They considered ventilation controlled fires as a conservative approach using Kawagoe�s relationship (Equation 3.6) for the postflashover phase and developed a new relationship for the cooling phase because Equation 3.6 is not valid during cooling. Tsuchiya and Sumi  considered the composition and geometrical shape of fuel in their heat balance calculation.
3.6.3 Heat balance equation for an enclosure (Pettersson et al, 1976 )
Pettersson and co workers published a detailed description of their work in defining T-t curves for compartment fires in the Swedish design guide.  The curves are often referred to as Pettersson curves but the model was developed by Magnusson and Thelandersson.  Pettersson used their curves to check steel temperatures for design. The solution of the heat balance allows the T-t history in the post-flashover and the decay phase of the fire to be defined. The full heat balance relationship is described by Equation (3.8) and illustrated in Figure 3.9.
(3.8) qC' = qL' + qW' + qR' + qB'
qC' = the heat released during combustion (W),
qL' = the heat removed due to the replacement of the hot gases by cold air (W),
qW' = the heat dissipated to and through the wall, ceiling and floor structures (W),
qR' = the heat dissipated by radiation through openings in the fire compartment (W)
qB' = the quantity of heat stored in the gas volume in the fire compartment per unit time (W).
A series of assumptions were made in order to solve the heat balance, 
- combustion is complete and takes place exclusively inside the fire compartment
- at every instant the temperature is uniformly distributed within the entire fire compartment
- at every instant the surface coefficient of heat transfer for the internal enclosing surface of the fire compartment is uniformly distributed
- The heat flow to and through the enclosing structures is unidimensional and with the exception of any door and window openings, is uniformly distributed for each type of enclosing structure
Figure 3.9: Illustration of the heat balance in a fire compartment (Pettersson, 1976 )
The term qC' representing the heat released during combustion can be written as
(3.9) qC' = O.O9AWH1/2ΔHc
ΔHc = Heat of combustion of wood (J/kg)
The fire is assumed to be ventilation controlled throughout the post-flashover phase with the mean rate of combustion described by Equation 3.9 (Kawagoe�s relationship. Equation 3.6). If the fire is in the fuel-controlled regime Equation 3.6 will overestimate the rate of burning.  qC' is assumed to remain constant immediately after flashover until all the fuel has been consumed.
Heat losses by convective flow through the openings (qL') are governed by the fact that there is a linear pressure distribution in the vertical direction over the opening (Figure 3.4 illustrated this) and a neutral layer where there is no difference between the static pressure outside and inside. Assuming a neutral layer and the whole fire compartment is at the same temperature (the compartment gases are well mixed) the quantity of gas flowing out and the quantity of cool air flowing inwards can be calculated using Bernouilli�s theorem.
To calculate the dissipation of heat through the walls (qW') the equations of conduction have to be solved numerically considering the changing thermal properties of the wall material with increasing temperature. The enclosing boundary is divided into n layers each of thickness Δx. A series of first order difference equations describing conduction can then be solved for each layer, over time intervals Δt.
The quantity of heat which is lost by radiation through the openings in the fire compartment can be calculated using the Stefan-Boltzman Law.
(3.10) qR' = AWεFσ(Tg4 - T04)
AW = the total area of the openings (m2)
εF = effective emissivity of the gases within the compartment
σ = Stefan-Boltzmann constant (W/m2K4)
g = is the gas temperature inside the fire compartment (K)>
T0 = is the outside ambient temperature (K)
The final component of Equation (3.8) is the term qB' which can safely be ignored because the quantity of heat stored in the gas volume is insignificant in comparison with the other heat quantities. 
188.8.131.52 Solution to the heat balance
Equation 3.11 is the solution to the heat balance for any post-flashover, ventilation controlled fire. The Equation is solved by numerical integration. Graphical (Figure 3.10) and tabulated values of the solution are available. 
(3.11) ADD GIF
(3.12) γi = εrσ(Tg4 - Ti4)/(Tg - Ti) + 0.023
Figure 3.11 shows the T-t histories of many compartment fire tests with one of the theoretical curves. Good agreement is found.
The effects of different boundary materials on the fire temperature can also be included. Compartments are split into 8 categories (A-H). Compartment type A is the base case and has thermal properties corresponding to average values for brick, concrete and lightweight concrete. A conversion factor is applied to the base case for compartments with different boundary materials. Figure 3.12 illustrates this. Compartment type C is made from highly insulating lightweight concrete thus resulting in the highest temperatures. The lowest temperatures are in compartment type F of 80% uninsulated steel sheeting and 20% concrete.
Magnusson and Thelandersson�s heat balance approach is based on ventilation controlled conditions. If the fire load is low and there are large openings in the compartment fuel controlled conditions may persist. Determining the rate of combustion is difficult in these fires because the combustion process is determined by the method of storage and the degree of distribution of the fuel (fuel surface area). In fire compartments with large openings the assumption that gas flow out and airflow in only has a horizontal velocity component (as in Figure 3.4) weakens. The horizontal pressure difference is reduced and the flow of hot gases out and air in reduces. Pettersson  reports on work by Magnusson and Thelandersson on increasing the openings in fire compartments. They calculated natural fire curves based on 60% of the rate of combustion in the ventilation controlled regime. They also assumed a decrease in the gas interchange through the opening. When qL was equal to 80% of the value under ventilation controlled conditions the agreement with experimental data was good. If only 60% of the fuel is burning in fuel controlled conditions this implies the compartment is supplied with excess cool air, cooling the fire and making it less severe.
Slightly later Babrauskas and Williamson  developed a theoretical model which enables the calculation to assume fuel or ventilation controlled conditions at every stage in the analysis. This is more sophisticated than Pettersson�s model which assumes ventilation
Figure 3.10: Theoretical temperature-time curves for compartment fires with different fire load densities and opening factors (Pettersson, 1976 )
controlled conditions throughout the fully developed fire. Their model requires details of the fuel nature and distribution. Babrauskas  also developed a hand calculation "a closed form approximation" to calculate approximate post-flashover temperatures. The approach can be used for any fire providing the fuel release rate is known or can be estimated.
3.6.4 Empirical/Characteristic temperature curves
In parallel to the mathematical modelling many research groups have analysed experimental data and arrived at simple empirical relationships. In Figure 3.13  curve (a) illustrates a fire temperature time curve derived theoretically for a certain building while curve (b) is for the same scenario but it is assumed that the rate of burning remains constant until all combustible materials are consumed then the fire temperature drops linearly to room temperature. Curve (b) is slightly different to (a) but it is much easier to define. Lie  suggests that the lengthy computation involved in calculating the temperature-time curve from the heat balance equation is excessive especially when you consider the assumptions and possible causes of error in the compartment fire model. A characteristic T-t curve "whose effect, with reasonable probability will not be exceeded during the use of the building" is simpler.
Figure 3.11: Gas temperature-time curves in full-scale fire. Solid lines represent experimental data for a fire load density of 96MJ/m2 and an opening factor, Aw√H/AT = O.068m1/2. The dashed line is the calculated temperature-time curve using the measured rate of burning (Pettersson, 1976 )
Lie  analysed two compartments with very different boundary materials (Table 3.4). Using Kawagoe�s heat balance approach he calculated curves in the post-flashover phase for several opening factors. The curves could be reasonably described by an exponential function in terms of opening factor, time and a constant taking into account the properties of the boundaries (see Equation 3.13). Similar exponential relationships are used for the ECI  parametric T-t curve and in the Swedish Design Codes referenced by Pettersson et al.  Lie also derived an expression for the decay period based on observations made by other researchers.     In general the longer the post-flashover phase the lower the rate of decrease in temperature in the decay phase.
Figure 3.12: Theoretical temperature-time curves for fully developed fires in compartments of different boundaries: A, materials with thermal properties corresponding to the average values for concrete, brick and lightweight concrete; B, concrete (500kg/in3); F, 80% uninsulated steel sheeting, 20% concrete. In all cases the fire load and ventilation factor were consistent(Pettersson, 1976195)
(3.13) T = 250(10 O)0.1/O0.3e-O2t[3(1 - e-0.6t) - (1 - e-3t) + 4(1 e-12t)] + C(600/O)0.5
T = the fire temperature (°C)
t = time (h)
O = opening factor (m1/2)
C = a constant taking into account the properties of the boundary material (C=O for heavy materials and C=1 for light materials)
The Equation is valid for
(3.14) t < 0.08/O + 1
Figure 3.13: A comparison of Temperature-time curves (Lie, 1974 )
|Thermal properties||Heavy material||Light material|
|(ρ ≥ 1600kg/m2)||(ρ < 1600kg/m2)|
|ρc (J/m3K)||2150 x 10||1075 x 10|
|Thickness of the bounding material (m)||0.15||0.15|
Table 3.4: The thermal properties of compartment boundary materials
A comparison of the curves calculated using Equation 3.13 and the heat balance method can be seen in Figures 3.14 and 3.15. These show that temperature-time curves can be developed for fires with mainly cellulosic fuels that reasonably describe the curves derived from solving the heat balance. The study also highlights the importance of including the properties of the boundary materials even if it is only in a simple manner.
3.7 Parametric T-t curves
Parametric temperature-time curves    are relatively simple relationships relating fire load, ventilation and properties of the wall lining materials. They assume the temperature within the compartment is uniform thus only predict post-flashover fires. They are easy to use and can be solved using a spreadsheet.
3.7.1 The Parametric T-t curve in EC1 
The parametric T-t curve in EC1  is designed to predict the T-t history of post-flashover compartment fires for any combination of fuel load, ventilation and wall lining materials.
Figure 3.14: Comparison between T-t curves obtained by solving a heat balance and those described by an analytical expression for ventilation-controlled fires in enclosures bounded by dominantly heavy materials (ρ < 1600kg/m3). (Lie, 1995 )
Figure 3.15: Comparison between T-t curves obtained by solving a heat balance and those described by an analytical expression for ventilation-controlled fires in enclosures bounded by dominantly light materials (ρ ≥ 1600kg/m3) (Lie,1995 )
The origins of the curve are unknown but it seems to be based on the standardised curve in the Swedish building regulations. Equation 3.15 describes the parametric T-t curve as described in the proposed Eurocode. The parametric curve valid for compartments up to a floor area of 100m2 and compartment height of 4.5m.
(3.15) θg = 1325(1 - 0.324e-0.2t* - 0.204e-1.7t* - 0.472e-19t*)
θg = temperature in the fire compartment (°C)
t*= tΓ (h)
t =time (h)
(3.16) Γ = (O/b)2/(0.04/1160)2
b = (ρck)1/2 and 1000 < b < 2000
O = opening factor: Av√H/At and 0.02 < O < 0.20 (m1/2)
Av = Area of vertical openings (m2)
At = Area of enclosure (walls, ceiling, floor and openings) (m2)
ρ = density of the boundary of the enclosure (kg/m3)
c = specific heat of the boundary of the enclosure (J/kgK)
k = thermal conductivity of the boundary of the enclosure (W/mK)
Franssen  has shown that when O = 0.04 and b = 1160 i.e. Γ = 1 and t* = t the parametric curve is almost identical to the ISO standard fire curve for the duration of the post-flashover phase.
The duration of the fire is determined by the fire load in Equation 3.17.
(3.17) t* = 0.13 x 10-3qt,d Γ/O
Af (3.18) qt,d = qf,d Af/At
and 50 ≤ qt,d ≤ 1000
qt,d = design value of the fire load density (MJ/m2) related to the surface area At (m2) of the enclosure
qf,d = design value of the fire load density related to the surface area of the floor (MJ/m2).
The temperature-time curves in the cooling phase are given by:
(3.19) θg = θmax - 625(t* - td*)
(3.20) θg = θmax - 250(3 - t*)(t* - td*)
(3.21) θg = θmax - 25O(t* - td*)
θg = maximum temperature in the heating phase (°C) for t* = td*
The standard fire curve of the Swedish design codes is described by Equation 3.22. The obvious difference between the two curves is the introduction of the thermal properties (thermal inertia) of the compartment boundaries in Equation 3.15. The cooling phase in the Swedish building regulations is a linear reduction in temperature (10°C/min) whereas the cooling phase in the new parametric T-t curve is given by Equations 3.19, 3.20 and 3.21. Equations 3.19, 3.20 and 3.21 are dependent on the design fire load related to the surface area of the floor and the compartment.
(3.22) θt - θ0 = 1325 - 430e0.2t - 270e1.7t - 625e19t
θt = gas temperature at time, t (°C)
θ0 = gas temperature at time, t=0 (°C)
t = time (h).
3.7.2 Comparison with compartment fire test data
As part of the research conducted for this thesis, Edinburgh University in collaboration with British Steel through the DETR PiT project "Development of the UK and European design codes-Natural fires and the response of structural steel " investigated the validity of the parametric equations given in Eurocode 1. The parametric curve was compared directly with measured compartment fire test temperatures. The data were gathered from experiments carried out in America, France and UK. However the experiments carried out by Kirby and Wainman180 in Britain were the most comprehensive. The tests were originally conducted to record unloaded, unprotected steel temperatures but atmosphere temperatures were also taken. The report can be found in Appendix A.
Conclusions of the report included:
- Parametric temperature-time curves overestimate the temperatures achieved in wood fires although they are "better" for higher fire load densities and low opening factors.
- There is good correlation for wood/plastic fires although there is a possibility that the parametric T-t curve will underestimate the real fire.
Franssen  analysed the validity of the curve against data from 48 fire tests. A comparison of the air temperature was made for each test. Also a comparison of the maximum temperatures calculated in 2 hypothetical steel sections (one protected and one unprotected). The agreement is poor for the air and unprotected steel. Better agreement is found with the protected steel. Improvements are suggested based on modifying the consideration of multiple wall layers. In EC1 the wall model is not realistic. For example it assumes a 2 layer wall with a thick layer of concrete on the outside and light insulation on the inside is the same as a 2 layer wall with thick concrete on the inside and insulation on the outside. The material on the inside nearest the fire has the greatest influence on the fire development. Fraussen also makes suggestions to improve the predicted temperatures in fuel-controlled fires. The parametric model is based on post-flashover ventilation controlled fires so this is not valid.
Pettersson compared the Eurocode parametric curves with Magnusson and Thelandersson�s model for an opening factor of 0.04m1/2 and found very poor agreement with the cooling phase (as cited by Karlsson ).
3.8 The Natural Fire Safety Concept 
The research project "Competitive steel buildings through natural fire safety concept" was undertaken by 11 European partners co-ordinated by PROFIL-ARBED-Research, starting in June 1994 and running until December 1998. The scope of the research is illustrated in Figure 3.16.
Figure 3.16: Scope of the Natural Fire Safety Concept Research 
There were 5 working groups (WG) each contributing to a different aspect of the project.
- WG1 - Natural fire models
- WG2 - Equivalent ISO time methods
- WG3 - Fire characteristics for use in a natural fire design of building structures
- WG4 - Statistics
- WG5 - Methodology to deduce from the probability data the "Design Natural Fire Curve"
Working group 2 reviewed t-equivalence relationships from the literature and design codes. These methods were analysed at an early stage in the project but are not relevant to the Natural Fire Safety Concept because they relate to the standard T-t curve. This was acknowledged by the authors.
Working group 3 was responsible for supplying ready to use data and guidance on the input data for natural fire design for those with no expert knowledge of compartment fire dynamics. General information is given on various types of compartment fire model. Methods of calculating fire load and RHR are reviewed. RHR from t2 fires and experimental data are discussed. The calculation method in EC1 for determining the maximum RHR is also reviewed. A proposed RHR curve for the NFSC is given. The curve includes a t2 growth phase, a steady state phase equal to that given in EC1 and a linear decay phase after 70% of the fire load has been consumed. This is illustrated in Figure 3.17. This approach forms the basis of the OZone model. The OZone model is based on post-flashover fire theory where it is assumed that the whole compartment is always at uniform temperature. These assumptions are not true pre-flashover and invalidates the growth phase used in the OZone model. The flashover criteria in Figure 3.17 is also not present in the OZone model. The shortcomings of OZone are discussed later in this chapter and in Appendix.
Working groups 4 and 5 consisted of the same team members. Statistics from real fires in Switzerland, France, Finland and the UK over the period 1986-1995 were gathered into a single database covering 40,000 losses. Probabilities deduced from the database formed the basis for a risk analysis of fire start considering the influence of active fire fighting measures (fire fighters and sprinkler systems) and occupancy type. This information was quantified in terms of factors on the fire load. The factors consider compartment size, building type and active fire protection measures. The characteristic fire load is multiplied by all factors to obtain the design fire load. The design fire load is then input to OZone to calculate the natural fire curve.
The NFSC project has gathered together a considerable amount of information available to designers to calculate natural fire curves. The statistical analysis was significant. However OZone needs to be fully validated as a reliable design tool. This is discussed in greater detail in later sections.
Figure 3.17: Scope of the Natural Fire Safety Concept Research 
3.9 Other factors influencing the rate of heat release in a compartment fire
3.9.1 Vent location
The opening factor is applicable to vertical openings but horizontal openings may also exist. Openings in the ceiling result in hot gases escaping through the roof while cool air enters from the windows on the wall.  Smoke extraction techniques use this principle to remove hot products of combustion from the smoke layer thus reducing the likelihood of flashover. Pettersson et al  address openings in the roof with a modified ventilation parameter. Ah1/2/AT is multiplied by a correction coefficient fk determined from a nomogram in the Swedish design guide. The nomogram assumes flow through the horizontal openings is not dominant. An upper bound is imposed on the model above which the flow conditions are no longer relevant. This upper bound is achieved when the neutral axis depth coincides with the top of the vertical opening. i.e. all combustion gases are vented through the horizontal opening.
Cross ventilation resulting from windows present in opposite walls causes a high intake of air and cooling effects. Law  reports that in compartments without cross ventilation air is entrained into a compartment through the same window as the flames emerge. The flames occupy the upper two thirds and the air enters through the lower third. However, in through draft conditions with windows on the opposite sides of the compartment the flames will emerge from the whole area of the window.
If the window area is large in relation to the cross-sectional area of the compartment the pressure differences between the room and ambient air may be quite small. Air may be entrained into the compartment by the turbulence of the flames.   Compartment fire models calculate air intake on the basis of a pressure difference between inside and outside the compartment and cannot predict air being entrained by turbulent flames.
3.9.2 Fuel load
The fire load for an enclosure is a measure of the total energy released by combustion of all combustible materials in the enclosure.  Traditionally the fuel load has been expressed in equivalent kilograms of wood. The characteristics of fire loads in buildings evolve as the nature of building contents change. A modern office may contain lots of plastics, yet many compartment fire models are based on data from experiments with wood crib fires bringing their validity into question.
The results of several extensive fuel load surveys are detailed in the CIB guide.  Eurocode 1 gives five classes of fire load ranging from 250-2000MJ/m2 floor area. Buchanan  states that for safe fire design the fire load should have less than a 10% probability of being exceeded in the 50 year life of the building.
184.108.40.206 Fuel shape
Smaller fuel packages with increased surface area produce higher maximum temperatures but large fuel packages result in longer decay periods.  Decay periods vary with the size of the fuel rather than opening factor or wall material properties.
Tall fuel loads and combustible wall linings tend to decrease the time to flashover. Flame spread over vertical surfaces is much faster than over horizontal fuel beds. Flames hugging the vertical surface raise the temperature of the fuel in front of the flame front thus fire spread is more rapid. Flames and hot products of combustion collect under the ceiling much more rapidly leading to early flashover. 
3.9.3 Compartment dimensions
Most models for compartment fires are tested on regular shaped compartments with small openings. Buchanan  states that compartments with floor areas up to 6m x 6m can be modelled with confidence. This seems conservative although researchers have always recognised that the validity of compartment models to large, long or tall compartments is questionable. Law recognised the need for an understanding of deep compartments in the 70s. 
220.127.116.11 Long compartments
The most comprehensive analysis of compartment fires in long enclosures has been conducted by Thomas and Bennetts.  They conducted an experimental program designed to investigate the enclosure shape and opening width and their effect on the burning rate. Fire tests were conducted on enclosures 1500mm by 600mm by 300mm high with vents of several widths. The main conclusions were that the fuel mass loss rates of fires in long and wide enclosures differ markedly if the width of the ventilation opening is less than the full width of the enclosure.
Kirby et al  conducted a series of 6 experiments on long compartments. The ventilation was provided by a window at one end of the compartment (short elevation). Tests were conducted with each of the four ventilation levels, 1, 1/2, 1/4 and 1/8 of the end wall. The wood cribs were situated in lines over the depth of the compartment. The cribs furthest from the ventilation were lit first. The fire moved towards the ventilation igniting each line of cribs. At the same time the cribs at the back of the compartment ceased burning. The cribs near the vents burned until there was no fuel left then the fire moved back over the cribs again towards the rear of the compartment. Figure 3.18 shows the recorded atmosphere temperatures in test 6 of the British Steel long compartment tests. This pattern of behaviour was observed in all six tests. It was also observed by Thomas and Bennetts.  The behaviour of compartment fires in long compartments is still not well understood however it is clear the behaviour is quite different from our understanding of "regular" compartment fire dynamics.
The importance of the compartment fire temperatures are their impact on structural elements. Deep compartments may exhibit different temperatures over the depth of the compartment but is this more detrimental to the structure than a uniform temperature? Kirby et al  included protected steel sections in their long compartments. Six 254x146x43UBs and six 203x203x52UCs were fixed to the insulated roof slabs at each measuring station over the depth of the compartment. Maximum temperature differences of 100°C were recorded. However in Test 6 (atmosphere temperatures shown in Figure 3.18) the maximum difference between any two recorded steel temperatures was only 50°C. Test 6 had the smallest ventilation at only 1/8 of the end wall. Overall the greatest steel temperatures were recorded midway back through the compartment when the ventilation equalled the area of one end wall. For ventilation of 1/2 and 1/4 of one end wall the greatest steel were recorded at gridline 10 near the vent. Unprotected steel is very fast to react to temperature changes in the atmosphere therefore greater differences may have existed if the steel was unprotected. Research into temperature gradients along steel beams has shown that there is increased load carrying capacity when the steel beams are cooler near the connections.  However Bailey  has shown that extra deflections and forces are induced in cooling beams during a spreading fire than when the whole structure is heated to the one temperature. This is probably a much more severe situation than the cooling and heating in the deep compartment tests. Further research is needed into the effect of deep compartment fires on steel temperatures.
Figure 3.18: Plot of the recorded atmosphere temperatures in British Steel long compartment test 6
3.9.4 Thermal inertia of the compartment boundaries, kρc
The inclusion of kρc in the parametric T-t curve is one of the major differences between EC1 and the Swedish building regulations. It has long been recognised that the combination of the thermal properties k, ρ and c where, k is the thermal conductivity, ρ is the density and c the thermal capacity, of a material has an important role to play in the time constant of heating materials and the growth of fires.   Thomas and Bullen  compared the time to flashover for a compartment with two different lining materials. For high values of kρc where the compartment boundaries (walls, ceiling. floor) have been treated as a semi-infinite slab kρc affects the time to flashover as (kρc)1/2 or a lesser power. At low values of kρc the flashover times become dependent on other physical processes notably the convective flow. 
3.10 Compartment fire models for computers
Fire models enable us to make an assessment of the fire risk, to assess the likely severity and extent of the fire, to estimate the influence of suppression systems, model evacuation of people (egress models), improve research and understanding of fire development and in some situations resolve litigation issues. In general fire models can compute temperatures (atmosphere and surface), flow rates of gas through openings, heat fluxes, smoke movement, toxic gas production, activation times for sprinklers and detectors.
3.10.1 Zone models for computers
Computer based compartment fire models can be classified as zone models or field models. A zone model is normally made up of a small number of (2-5) zones. However, in post-flashover models a one zone model is acceptable. These assume the whole compartment is at a uniform temperature and gas concentration.
Some of the more complex zone models allow radiation calculations between the upper layer and room objects. They may also allow multiple fire plumes and multiple compartment analysis with mass exchange between each compartment. Zone models use numerical methods to evaluate the temperature of the gases during the development of a compartment fire.
A number of authors have reviewed computer based fire models for design.    Friedman has carried out an extensive survey of fire and smoke models 31 of which were zone models. Most of the models are very similar. Some go further by calculating the consequences of the fire for instance HAZARD1, one of the many models developed at the Building and Fire Research Laboratory (bfrl) at the National Institute for Standards and Technology (NIST).
The bfrl at NIST formally the Centre for Fire Research at the National Bureau of Standards have produced a series of compartment fire zone models.  FPETool is an early model, it is made up of a set of routines including FIREFORM which is a collection of individual calculations such as Thomas�s correlation for flashover. FIREFORM also estimates smoke temperatures, detector or sprinkler response and a very simplistic model for egress time. MAKEFIRE is another routine of FPETool used to generate RHR data. FIRE SIMULATOR is the 2 zone model within EPETool and can generate the effects of a pre-flashover and a post-flashover fire including the amount of CO, CO2 and O2 in the smoke, the temperature-time history of the environment and a prediction of the heat transfer through the walls and ceiling.
CFAST, also developed at NIST is a zone model capable of predicting fire spread to many compartments (the most recent version allows up to 15 compartments). Output includes RHR data, temperatures of the upper and lower layers and smoke toxicity. The radiant heat feedback from the upper layer to objects in the room below is also estimated allowing ignition calculations.
FASTLite  is the most recent hybrid of FPETool introduced in 1996. It builds upon the routine FIREFORM in FPETool and a simplified version of CFAST (modelling 3 rooms only).
The programs ASET and FIRST reviewed by Walton  were also developed at the National Bureau of Standards. ASET (available safe egress time) calculates the temperature and position of the hot smoke layer in a single room with closed windows. ASET-B is a compact version of ASET for personal computers. FIRST is a descendant of the HARVARD  programs and is able to predict the development of a fire (ignition of up to three targets) and the resulting conditions.
One of the most recent computer zone models, OZone is being developed at the University of Liege, Belgium. OZone  was originally developed as part of a European Coal and Steel Community project entitled the Natural Fire Safety Concept.  It created considerable interest in Europe and it was suggested that it could replace the parametric temperature-time relationship in Eurocode 1. As part of the DETR PIT project "Development of the UK and European design codes-Natural fires and the response of structural steel " the first version of OZone was evaluated in detail by Lamont et al.  The full report can be found in Appendix B. OZone was tested against experimental data from fire tests conducted by CORUS Research, Development and Technology, Swinden Technology Centre.   In general the correlation between the measured and predicted results was found to be poor. Moreover using the software proved to be confusing and it was possible to set the model running using input files that were clearly nonsensical. While some of these aspects could be addressed by improving the software there were concerns about the theoretical background to the model. One major concern was the use of a "design" rate of Heat Release (RHR) curve based on a t2 growth phase, a constant release phase and a linear descending branch after 70% of the fire load has been consumed. A one zone model can only be used to predict post-flashover temperatures and should not contain a growth phase. Further developments in the software are being made which could solve the problems associated with using the code. However dissimilarities between measured and predicted temperatures may still exist.
18.104.22.168 Limitations of zone models
The zones within the models assume uniform temperatures therefore localised heating/cooling effects near the fire plume or near openings are not accounted for. Flow regimes within the space are not predicted and plume interactions are not modelled because the zone model assumes only one plume in the space.
3.10.2 CFD models    
Field models are fire adaptations of Computational fluid dynamics (CFD) computer programs. CFD computer codes solve the Navier Stokes Equations for fluid flow. The domain is divided into 3-dimensional cells or control volumes and the equations describing the conservation of heat, mass, momentum and species are solved for each cell. This type of model is computationally demanding, time consuming and difficult to use. Zone models can model the fire compartment with very few zones whereas a typical field model will need thousands of cells to model the same space. Codes include CFX, a general purpose CFD code developed by AEA Technology Engineering Software, JASMINE a fire specific CFD program developed at Fire Research Station, SOFIE and SMARTFIRE also both fire specific, developed at the University of Cranfield and the University of Greenwich respectively.
NIST have recently developed a new CFD type model called Fire Dynamics Simulator (FDS).  EDS simulates smoke and or air flow movement caused by fire. The results are viewed in Smokeview. The equations solved in FDS differ from those in CFD codes. Most CFD models to date adopt the k-ε turbulence model which is a time-averaged approximation to the conservation equations of fluid dynamics. This smoothes the results of the model and hinders modelling of the evolution of large eddy structures in fire plumes and local transient events. FDS uses an approximate form of the Navier Stokes equations to be used with low Mach number applications suitable for the low speed motion of gas driven by chemical heat release and buoyancy forces. FDS can conduct Large Eddy Simulations (LES) to model building fires for instance or Direct Numerical Simulations (DNS) which could model small-scale combustion experiments.
3.11 Heat Transfer
Once the rate of heat release or temperature history of a compartment fire is known the temperature of the structure can be calculated by heat transfer analysis.
Heat energy travels from areas of high temperature to areas of lower temperature by three means, conduction, convection and radiation.
Conduction occurs in solids and involves hot energetic molecules within the solid passing energy to adjacent less energetic molecules. These molecules in turn become hot and and pass energy to further adjacent molecules. This process continues along the solid. The greater the thermal conductivity of a material the faster heat will dissipate through it.
Convection occurs in fluids. As a region of hot fluid increases in temperature it expands and decreases in density. The less dense hot fluid rises and colder fluid take its place resulting in a convection current. Convective flow is important in the early stages of a fire.
Thermal radiation is a type of electro-magnetic radiation and requires no substance to transfer heat. Radiation in all parts of the electro-magnetic spectrum can be absorbed transmitted or reflected at a surface. It becomes the dominant mode of heat transfer in the later stages of a fire and determines the growth and spread of fires in a compartment. 
3.11.1 The Heat Transfer Equations
Fourier�s Law states that heat is transferred in proportion to the temperature gradient and can be expressed by Equation 3.23.
(3.23) qx'' = - k ΔT/Δx
where ΔT is the temperature difference over a distance Δx, k is thermal conductivity (W/mK) and qx'' is the heat flux or amount of heat penetrating a unit area of the surface per unit time (here, "q dot" has been rendered "q bar" = q due to the limitations of HTML code). The negative sign indicates the heat flow is from higher temperatures to lower temperatures. Equation 3.24 describes Fourier�s Law in differential form.
(3.24) qx'' = - k dT/dx
Equations 3.23 and 3.24 describe steady state conduction and do not consider the heat required to change the temperature of material being heated or cooled.  Equations for non-steady state conduction also exist.
Newton recognised that convective heat transfer is a function of the temperature difference between the solid (Ts) and the temperature of the surrounding fluid or gas (Tf). The empirical relationship by Newton is described by Equation 3.25,
(3.25) qx'' = h(Ts - Tf)
h (W/m2K) is the convective heat transfer coefficient. Convection heat transfer also depends on the characteristics of the system, the geometry of the solid and the properties of the fluid including the flow parameters. Typical values of h for a fire exposed structural element are in the range 20-25 W/m2K.      In the compartment fire hot gases are transferring heat to a solid structural element therefore convection can be treated as a boundary condition. However in porous materials convection will also occur inside the pores of the material.
Thermal radiation is heat transferred by electro-magnetic waves. An ideal thermal radiator (a black body) will emit energy at a rate proportional to the 4th power at the absolute temperature of the body (Equation 3.26),
(3.26) qx'' = εσT4
where σ = Stefan Boltzman Constant (5.669 x 10-8W/m2K4) and ε = emissivity. ε = 1 for a blackbody and ε < 1 for all other surfaces. Thermal radiation is the main mode of heat transfer in compartments from flames and smoke to the fuel and the surrounding structure. It also a major factor in fire spread from building to building.
The intensity of the radiation falling on a surface remote from the emitter can be found by using the appropriate "configuration factor" (φ) which takes into account the geometrical relationship between the emitter and the receiver,
(3.27) qx'' = φεσT4
where, ε = resultant emissivity of the emitting and receiving surfaces.
3.11.2 Solving the heat transfer Equations
Only the simplest heat transfer calculations can be solved analytically, e.g. steady state analyses where the geometry and boundary conditions are well known. Lumped heat capacity methods are used where the material can be assumed to be at constant temperature. A semi-infinite slab approximation is assumed where the heat transfer is essentially 1D and the heat is absorbed before reaching the unexposed side.
Simple lumped mass, heat transfer expressions are used in design to calculate the temperatures of protected and unprotected steel under quasi-steady conditions. These can be solved using an iterative spreadsheet calculation.   
The most powerful tools for calculating heat transfer are numerical methods using finite difference or finite element formulations. These provide solutions for transient heat transfer problems where the materials� thermal properties are complex. A typical example is heat transfer to concrete where the effects of moisture make modelling difficult. Finite element models specific to fire design include CEFICOSS,  FIRES-T3,  TASEF  and THELMA (developed at BRE). General finite element codes will also calculate heat transfer. For instance the commercial code ABAQUS.  A criticism of computer codes is that they are often non-user friendly.
A reliable heat transfer model relies on accurate input data including material properties and boundary conditions. The finite element model must have adequate mesh and time discretisation. It must also be validated by testing against benchmarks of known solution or by comparison with experimental data. Wickstrom  highlights three issues to be considered when using a computer code,
- validity of the calculation method
- accuracy of the material properties
- accuracy and reliability of the computer code.
3.12 Thermal properties of materials
Mechanical, physical, chemical and thermal properties of materials can all be affected by fire.              The mechanical properties of steel and concrete and how they alter under heating were discussed in Chapter 2 in the context of the structural behaviour. In this context we are concerned with the thermal properties (conductivity, k and specffic heat, c) and how they change with increasing temperature. Material density and moisture content (free and chemically bound) with changing temperature are also important.
Heat transmission solely by conduction can only occur in poreless non-transparent solids. In most building materials the mechanism of heat transfer is by conduction, convection and radiation. However if the pore size is less than 5mm the contribution of the pores to convective heat transmission is negligible.  Radiation becomes the dominant mode of heat transfer at high temperatures in fire because of the T4 dependence.
Thermal properties influence the rate of heat transfer into the construction. The thermal inertia kρc, of the material affects the surface temperature in the early stages of fire exposure. Thermal inertia is normally associated with low density insulating materials and has been primarily considered in the design of the exposed surface linings of furnaces but may have some relevance for aerated lightweight concretes.  Under transient heating the thermal conductivity of the material and the specific heat capacity are related in terms of the thermal diffusivity in m2/h (Equation 3.28),
(3.28) α = k/(ρc)
k = thermal conductivity (J/sm°C)
ρ = density (kg/m3)
c = specific heat (J/kg°C)
The thermal diffusivity is a measure of the rate of heat transport from the exposed surface to the inside and of the temperature rise at a depth in the material. The larger the diffusivity the larger the temperature rise. 
The properties of materials at high temperatures are difficult to measure experimentally and are not readily available. During the mid forties the Building Research Station provided some data on the high temperature properties of concrete and steel as part of the notes on repair to damaged buildings.  However most of the work on material properties at high temperatures has been carried out since the mid-fifties. 
Due to the increasing application of numerical methods in fire engineering the International Organisation on Testing and Research on Materials and Structures (RILEM) set up a committee in 1979, under the chairmanship of Malhotra,  to consolidate data on material properties at high temperatures. One of the major outcomes of this committee was to identify the differences in data caused by different testing techniques. A definite distinction has to be made between the studies conducted under steady state conditions and those under transient conditions. Data on the properties of building materials are found throughout the literature. One of the most extensive references is by Harmathy  where the properties of steel, concrete and other building materials are reviewed.
Steel is an exceptionally good conductor thus reaches uniform temperatures when exposed to fire. At ambient steel has a thermal conductivity, k of 54W/mK which decreases to half this value by 800°C. Beyond 800°C it remains constant (Figure 3.19(a)). The specific heat of steel at 20°C is about 450J/kgK increasing to 700J/kgK at around 600°C. At 730°C steel undergoes a chemical transformation from ferrite-pearlite to austentite. This is associated with a huge increase in specific heat, shown in Figure 3.19(b). The specific heat of steel seems to be independent of the grade of the steel.  The density of steel is approximately 7850kg/m3 decreasing slightly with increasing temperature.
Figure 3.19: Thermal properties of steel 
Concrete covers a vast array of different materials all of which are formed by the hydration of Portland cement. The hydrated cement paste accounts for only about 24-43 volume percent of the materials present so that the aggregate used has a significant effect on the properties.  Three common aggregates are siliceous aggregates (gravel, granite and flint), calcareous aggregates (limestones) and lightweight aggregates made from sintered fuel ash.  Concrete has excellent fire resisting properties. Compared with steel it has a very low conductivity, thus low thermal diffusivity. A major disadvantage of concrete is spalling, the loss of surface material as a result of high temperatures (Chapter 2).
Lightweight concretes (LWC) have the best thermal properties with half the thermal conductivity of normal weight concrete (NWC). Typical densities of LWC range 1200-1900kg/m3 but they can be as low as 1000kg/m3. NWC is in the range 2000-2900kg/m3. Densities show only a slight temperature dependence, mostly due to moisture losses. Limestone concretes are an exception. They show a significant drop in density at about 800°C due to the decomposition of the aggregate  (Figure 3.20).
Thermal conductivity of concrete depends upon the nature of the aggregate, the porosity of the concrete and, until dry, the moisture content. The conductivity of most concretes vary linearly with moisture content. Up to 100°C conductivity of NWC increases with temperature after which there is a reduction. LWCs tend to be more constant  (See Figure 3.21)(a).
Figure 3.20: Density of structural concrete at high temperatures 
In fire, water is driven out therefore the conductivity of dry concrete is also an issue. A general picture of concrete conductivity with increasing temperature is given by Figure 3.22(a). At 800°C the value is about 50% of the value at 20°C.
Specific heat of NWC increases with temperature and LWC is almost constant. All concretes with free water experience a sudden rise in specific heat as water evaporates around 100°C (See Figures3.21(b) and 3.22(b)).
22.214.171.124 Moisture in Concrete
Concrete like most building materials contains two phases a solid phase and a gaseous phase in the solid matrix. The pores of a solid may be interconnected or non-interconnected Fluids can only move through the pores if they are interconnected. Vapour migrates through the capillaries to the outer surfaces turning to steam on the hot side and condensing on the cool side, termed "weeping". The loss of moisture will reduce the density by a small amount but for practical purposes this can be ignored.  However wet concretes show specific heat values nearly twice as high as oven-dried concretes. 
Free water evaporates from concrete at 100 - 150°C whilst chemically bound water remains until temperatures of 450°C.  Moisture absorbed by the concrete significantly increases its thermal conductivity because the conductivity of air is lower than water. In lightweight concrete an increase in moisture content of 10% increases the conductivity by 50%. However the conductivity of the water is less than half that of the hydrated cement paste so the lower the water content of the mix the higher the conductivity of the hardened concrete. 
(a) Conductivity (b) Specific heat
Figure 3.21: Thermal properties of different structural concretes 
In materials with large effective pore space or high permeabilities the moisture can retreat to the cooler surface (unexposed face of the element) ahead of the heat flow.
3.13 Predicting steel temperatures
Predicting steel temperatures for design is achieved by heat transfer analysis using simple quasi-steady lumped mass models     or sophisticated numerical tools. Nomograrns are also available in the literature and design guides.
(a) Conductivity (b) Specific heat
Figure 3.22: Thermal properties of concrete 
The heating rate of a steel section is dependent on the size, shape and the location of the member in the compartment and the thickness and nature of any protection applied. The steel location in relation to the flames is very important. Typical locations which can give widely varying heating rates include,
- A column placed inside a compartment and exposed to flames on four sides
- A column placed outside a building
- A beam which is either protected by a suspended ceiling or is high enough above the fire so that the upper limit of the flames is below the bottom flange. The latter is only possible during localised pre-flashover fires.
- A beam supporting a floor slab in which the flames reach the underside of the slab
- Embedded columns and beams
- Cross-sectional shapes e.g. circular or H-section
The heating rate of a steel section in a fire depends upon, the perimeter of steel exposed to flames and, the cross-sectional area of the section. The Hp/A ratio sometimes called the section factor is the ratio used to quantify the heating rate of steel in a fire. Hp is the heated perimeter of the section and A the cross-sectional area of the steel section. The Hp value varies according to the size of the element and where it is located in the building e.g if the same section was in the wall or in the middle of the room. Tables are available presenting Hp/A values for the standard steel section sizes. 
The position of the steel member is taken into account by calculating a resultant emissivity value which has values in the range 0.3-0.7, 0.7 being associated with a member totally engulfed in flames and 0.3 relating to a member which is remote from direct flame impingement 
3.13.2 Simple heat transfer models
3.13.3 Uninsulated steel 
Equation 3.29 is a typical example of a quasi-steady lumped mass model for estimating unprotected steel heating rates. It calculates the net heat transferred per unit length of steel in time Δt. The assumptions are that at all times the temperature of the steel is uniform and the heat flow is unidimensional (corners and edges ignored) 
(3.29) ΔTs - αAs(Tt - Ts)Δt/ρscsVs
(3.30) α = αc + αr
α = surface heat transfer coefficient (kW/m2K)
αc = Convective portion of heat transfer (kW/m2K)
αr = Radiative portion of heat transfer (kW/m2K)
(3.31) &alpha = 0.023 + 56.7 x 10-12εr(Tt4 - Ts4)/(Tt - Ts)
ρ = density of the steel (kg/m3)
cs = heat capacity of the steel (kJ/kg)
As = Area of the steel per unit length (m2/m)
Vs = Volume of the steel per unit length (m3/m)
Tt = Temperature of the compartment gases (atmosphere) (K)
Ts = Temperature of the steel (K)
Δt = Time increment (s)
Q = Heat transferred to the steel (kJ/m)
εr = Resultant emissivity
Equation 3.29 was tested against measured steel temperatures (see Appendix A). The correlation was very good.
3.13.4 Insulated steel
Similar but more complex relationships exist for protected steel.  
Net heat transferred to the steel in time Δt:
(3.32) Q = Ai(Tt - Ts)Δt/(1/α + di/ki)
(3.33) Q = ρscsVsΔTs
(3.34) ΔTs = Ai(Tt - Ts)Δt/(ρscsVs(1/α + di/ki))
Equation 3.34 assumes the temperature gradient in the insulation is linear at all times i.e. the thermal capacity of the insulation is negligible. This approximation cannot be assumed for thick, dense insulating materials.
In fire 1/α << di/ki, so
(3.35) ΔTs = kiAi(Tt - Ts)Δt/(ρscsVsdi)
Ai = Cross-sectional area of insulation per unit length of column (m2/m)
ki = thermal conductivity of the insulation (W/mK)
di = thickness of insulation (m)
As a simple rule the thermal capacity of a material can be considered low if,
(3.36) csρsAs > cidiρiHpi
If the thermal capacity must be accounted for then,
(3.37) ΔTs = λiHpi(Tt - Ts)Δt/(dicsρsA(1 + ξ)) - ΔTt/(1 + 1/ξ)
(3.38) ξ = cidiρiHpi/(2csρsA)
Hpi = Internal surface area of insulation per unit length of column (m2/m)
ci= specific heat of the insulation (J/kgK)
The heat transfer to unprotected and protected steel can be calculated using the Equations in Eurocode 3 Design of steel structures, Part 1.2: General rules (Structural Fire Design).  They are very similar to Equations 3.29 and 3.37.
Nomograrns for critical steel temperatures exposed to the standard fire curve are given in the literature.  Pettersson  gives nomograms for natural fires assuming the set of natural fire curves given by Magnusson and Thelandersson. 
More recently nomograms for unprotected steel temperatures were developed by Kirby and Tomlinson  as part of a DETR PIT project.  They plot design fire load density against maximum steel temperature for various steel "Element factors" and properties of the compartment boundaries b. Element factors were introduced by Kirby.  They are similar in concept to the section factor Hp/A but the element factor considers only the critical part of the steel member exposed to fire. It is defined as the ratio of the surface area of a flange or web of a section exposed to fire to the cross section area of that part of the section. Hp/A considers the whole cross-section. Nomograms exist for a number of opening factors. The data were obtained by using the parametric curve in EC1: Part 2.2 to describe the various fire exposures and the heat transfer equation for unprotected steel in EC3. Maximum steel temperatures were calculated for the critical "element" of the steel member. An example of one of the nomograms is given in Figure 3.23.
3.14 Modelling heat transfer in concrete
Heat transfer to steel is reasonably easy and accurate to calculate. Concrete is considerably more complex. Moisture evaporation, water migration, reinforcing steel and radiation and convection heat transfer in the pores are a few of the problems associated with modelling concrete.
Nomograins based on the standard fire test have been produced for concrete sections (Figure 3.24). To calculate the heating effect of natural fires numerical heat transfer analysis using computer software is necessary. There was considerable progress in this field in terms of concrete temperatures throughout the 70s and early 80s       particularly by the nuclear industry. The development of performance based design codes in fire engineering has rekindled interest in this subject.
Figure 3.23: Typical nomogram for estimating maximum steel temperatures using the "Element factor" 
Modelling heat transfer into concrete is complicated by the presence of moisture within the free pores of the material. An increase in temperature causes an increase in pore pressure which in turn causes migration of water vapour, and eventually drying of the concrete. This is gradual and develops as the interface between the "dry" and "wet" concrete moves into the material (see Figure 3.25). This Figure also shows that the water vapour can either escape towards the heated surface or recondense on the cool side of the interface. This has been recognised by researchers    and is illustrated in Figure 3.25.
Many researchers have looked at the problem of moisture migration caused by temperature differences in porous media.     Others have investigated the specific problem with respect to concrete nuclear reactors    and the thermal response and integrity of a concrete building during and after a fire.     Some examples of specific research are highlighted now.
Siang et al  developed differential Equations and numerical solutions for simultaneous heat and mass transfer of naturally drying cement paste in concrete slabs. They also reviewed contemporaneous theories about moisture migration. More recently Ahmed et al  developed and numerically solved a mathematical model to predict heat and mass transfer in concrete structures subjected to fire. The model simulates changes in pore pressure, temperature and moisture with corresponding changes in concrete properties and has also been able to predict "moisture clog" and the spalling of concrete. Ahmed et al  modelled pore pressure, moisture and temperature in high-strength concrete columns. Model predictions agreed well with test data.
Figure 3.24: Temperature Contours in concrete beams exposed to the standard fire from EC2 
Figure 3.25: A slab heated on one face showing the dry-wet interface
Although there are now models which are capable of predicting moisture concentrations and pore pressures these are complex and expensive to process. Very often the use of simpler, faster models capable of predicting temperatures with reasonable accuracy is valid. This is especially true if spalling of the concrete is unlikely and the moisture can migrate to an unheated surface and escape. In terms of obtaining temperature data as input for a structural analysis a simple approach including moisture evaporation but ignoring moisture migration may be all that is required. A slightly conservative estimate of the real temperatures will be achieved because the high localised moisture concentrations, experienced near the dry-wet interface are not modelled.
There are various heat transfer programs available for determining the temperature of structural elements exposed to fire. One of the earliest computer codes developed was FIRES-T   at the University of California. This has since been superseded by FIRES-T3.  Milke  gives a review of FIRES-T3 and another similar code TASEF.  When modelling concrete both programs include moisture evaporation but ignore moisture migration. Selih et al  compares a model which includes moisture migration and calculates pore pressures with two simpler models where all liquid water evaporates at 100°C and moisture migration is ignored. CEFICOSS  is a code capable of dealing with the thermal and structural response during a fire. THERMIN, developed by Luyckx et al  is designed to deal with composite sections and internal voids within structural elements. The aim of this code is to overcome the problem of modelling sections where one material has a very high conductivity and is thermally thin and one material has a low conductivity and is considerably thicker as is common in modern steel and concrete composite sections.
There are a whole range of design tools available to the engineer to calculate first the compartment fire history and secondly the heat transfer to the elements of construction.
The advent of reliable and powerful computers has enabled very sophisticated modelling of fires and heat transfer. The level of sophistication necessary depends on the fire engineering design. In most cases a simple parametric calculation of the post-flashover fire is all that is required. Detailed examination of two compartment fire models has highlighted the shortcomings of these tools however in general, they over predict compartment fire temperatures leading to safe designs. These were reported in Appendix A and B.
Heat transfer to steel can be calculated by hand or spreadsheet because its high conductivity and homogeneity make simple calculations accurate. Concrete temperatures are more difficult to predict and require finite element models to get accurate data. However simple nomograms for concrete sections exposed to standard fires also exist.
Composite steel frame structures in fire: Research and design developments
Since the Broadgate phase 8 fire in the late 8Os and the realisation that composite steel deck floor systems are under utilised when designing for the fire limit state, research into the behaviour of whole frame, composite steel structures in fire has increased considerably. The most notable work in the UK are the Cardington frame fire tests on an 8-storey composite steel frame. Researchers in the UK and Europe have studied and simulated these tests numerically.    Subsequently, new design guidance for composite steel structures in fire has been developed. SCI have produced a design guide  based on a theoretical analysis by Bailey.  New Zealand have also produced a draft design guide  based on the Cardington Frame fire tests and work by Wang.  The most recent developments in this field will be reviewed in this chapter.
4.2 Case studies
4.2.1 Broadgate Phase 8
The Broadgate fire was introduced in Chapter 1 of this thesis. Structural damage caused by the fire included distortion of a number of trusses and universal beams and axial shortening of five columns by 100mm. The deflection of the trusses produced dishing of the floor of up to 600mm relative to the columns. The concrete floor slab separated from its metal decking in some areas but generally followed the level of its deflected supporting members. Despite large deflections, the structure behaved well and there was no collapse of any of the columns, beams or floors. 
The behaviour of the structure and the floor members showed that a steel frame designed to BS 5950 Part 8 is structurally safe when exposed to a severe fire. The study  carried out after the Broadgate fire showed that when fire affects only part of a structure (compartmentation) and when the framework acts as a total entity structural stability is improved.
Detailed studies of the material properties at high temperatures were carried out and it was concluded that apart from the concrete to the first floor no material showed significant loss of strength due to the fire. Detailed metallurgical investigations were carried out to asses the temperatures reached by the quenched and tempered bolts recovered from several of the beam to column connections in the areas of the fire which showed most damage. These indicated that the most severe temperatures achieved by the bolts during the fire or during manufacture were limited to 540°C. Similar evidence from a truss indicated that the member had been heated to around 600°C. The principles of BS5950 Part 8 would suggest that these members would transfer load to cooler parts of the structure until temperatures of about 700~800°C but the investigations suggest that the temperatures achieved did not exceed 600°C so an alternative explanation for the deformations observed was needed.
4.2.2 Churchill Plaza building, Basingstoke
In 1991 a fire took hold in the Mercantile Credit Insurance building in Basingstoke.  The twelve storey high building was constructed in 1988 and was of composite steel and concrete construction. The columns and the composite floor beams had applied fire protection but the soffit of the floor slab was unprotected. The fire rating of the building was 90 minutes.
The fire started on the 8th floor and spread to the tenth floor as external glazing failed. The protection materials performed well and there was no permanent deformation of the steel frame or damage to the protected connections. Similar to Broadgate the metal deck showed signs of debonding from the concrete floor slab probably due to the steam from the concrete. Load tests on the most damaged parts of the slab showed it had adequate strength to be used unrepaired. No structural repair was required on the protected steel. The cost of repair to the building was �5 million but most of this was repairing smoke damage.
4.3 Fire tests
4.3.1 BHP William Street fire tests, Melbourne 
Built in 1971 in the centre of Melbourne, 140 William street at 41 storeys high was the tallest building in Australia. This building is also of composite construction similar to Broadgate and Mercantile centre, with a square plan and central square inner core. The steelwork around the inner core and the external columns were protected with concrete whereas the beams and the soffit of the composite steel deck floors were protected with asbestos based material. In 1990 during a refurbishment programme the decision was made to remove the hazardous asbestos material. Prior to the refurbishment the fire resistance rating of the building was 120 minutes. To maintain this level after refurbishment the regulations at the time required fire protection to the steel beams and the soffit of the lightly reinforced concrete slab. The light hazard sprinkler system would also have had to be upgraded. In the 1990s the fire resistance of buildings was a matter for debate in Australia and the refurbishment of the William street building provided an opportunity to determine whether these measures were really necessary.
Two risk assessments were conducted. The second was the most interesting. It assumed no protection to the beams or the soffit of the slab and use of the existing sprinkler system.
A series of four fire tests were carried out on a purpose built test building at BHP Research Melbourne Laboratories. The test simulated a 12m x 12m corner bay of the real building and was furnished to resemble a typical office with a 4m x 4m small office constructed near the perimeter of the building. Water tanks provided the imposed loading. The first two tests were concerned with testing the performance of the existing light hazard sprinkler system. Test 3 was designed to test the composite slab. The soffit of the slab was left unprotected although a non-fire-rated suspended ceiling was in place. The supporting beams were partially protected. The fire was started in the open plan area and allowed to develop fully. A maximum atmosphere temperature of 1254°C was achieved. The ceiling remained intact during the tests and was beneficial in protecting the slab. In test 4 the ability of the steel beams to withstand a fire without protection was assessed. The fire was started in the small office but unfortunately did not spread to the rest of the compartment and another fire was set in the open plan area. The atmosphere temperature reached 1228°C whilst the steel beams reached temperatures of 632°C. Deflections of 120mm were recorded in one of the beams during the test. The steel beams and slab were shielded by the ceiling resulting in relatively low steel temperatures and small deflections in comparison with Broadgate. The results of the various fire tests concluded that the William street building did not need fire protection on the beams or the underside of the slab and the existing sprinkler system was adequate.
4.3.2 Stuttgart-Vaihingen University fire tests, Germany
In 1985 a fire test was undertaken on a four storey steel-framed demonstration building at the Stuttgart-Vaihingen University in Germany.  The building was a test building and as such was constructed from many different types of composite elements including various types of composite floors. The main fire test was conducted on the third floor in a compartment covering approximately one third of the building. The fire load was provided by wooden cribs. The atmosphere temperature exceeded 1000°C whilst the steel temperatures reached 650°C. Investigation of the beams after the test showed spalling of the infilled webs but the behaviour of the beams was very good with no significant permanent deformations after the fire. The composite floor reached deflections of 60mm and retained its integrity.
Figure 4.1: Plan view of the Cardington 8-storey frame showing the 4 British Steel Tests
4.3.3 Cardington frame fire tests
The Broadgate fire provided the greatest insight into the ability of composite structures to resist fire. In all the other case studies and tests there was some form of protection to the steel. In the Chuchill Plaza building the steel frame was completely protected. The tests in Australia provided protection to the slab and beams with an unrated suspended ceiling and in Germany all the steel sections were protected by heat sinks of concrete. The tests at Cardington were much closer to the Broadgate scenario thus fully testing the capacity of the frame.
Over a period of September 1995-June 1996 British Steel (now CORUS) conducted 4 fire tests on the 8-storey composite steel frame structure at BRE�s (Building Research Establishment) large scale test facility at Cardington. BRE carried out two further complementary tests around the same period. Figures 4.1 and 4.2 show the 4 tests conducted by CORUS and the two further tests carried out by BRE respectively.  
126.96.36.199 Physical aspects of the tests
188.8.131.52.1 British Steel Test 1: Restrained Beam.
Test 1 illustrated in Figure 4.1 was carried out on the 7th floor of the 8-storey frame and involved a single 305 x 165mm beam and the surrounding concrete floor spanning 9m between a pair of 254 x 254mm columns. The beam was surrounded by a gas fired furnace but the columns and connections were left outside. The furnace was 8m long x 3m wide x 2m high; insulated with mineral wool and ceramic fibre. During the test the beam was heated at between 3-10°C/min until temperatures of 800-900°C were achieved.   The test beam and surrounding structure were extensively instrumented to measure temperatures, strains, deflections and rotations. The temperatures in the steel beam were recorded at many points along its length and through the depth. The temperatures through the slabs depth were only recorded at four points on plan (at two points between the beam and furnace wall and two locations over the tested joist). Maximum deflections of 232mm were recorded at 887°C.  
Figure 4.2: Plan view of the Cardington 8-storey frame showing the 2 BRE Tests
The aftermath of the test is shown in Figure 4.3. Local buckles in the flange near the connections and folds in the web can be observed. The local buckles are caused by a combination of the high compressions in the highly restrained expanding hot beam and the additional compressions as a result of the high gradient in the composite. The gradient causes a hogging moment, thus increased compressions in the lower part of the beam. The folds in the web may have occurred during cooling. On cooling the beam tries to retract into its original shape. However not all of the deflected shape can be recovered because of plastic straining thus the beam is effectively shorter. Tension folds probably develop in the web as the beam is pulled back into position. This phenomena can be seen in all the British Steel tests. In most cases some bolts or part of the plates forming the connections have failed releasing the tension forces developed during cooling (Figure 4.5).
Figure 4.3: British Steel Test 1: Restrained beam test
184.108.40.206.2 British Steel Test 2: Plane frame.
The second test involved heating a series of beams and columns across the full 21m width of the building on the fourth floor using a gas furnace. A furnace 21m long x 3m wide x 4m high was constructed using 190mm lightweight concrete blockwork. It was lined with 50mm thick ceramic fibre blanket to reduce heat losses.37� 128,197 Natural gas was supplied to eight industrial burners installed along one side of the furnace. Maximum atmosphere temperatures of 7500 C were achieved. The primary and secondary beams were unprotected. The top 800mm of the columns including the connections were also unprotected. The supporting columns were squashed by 180mm (pictured in Figure 4.4) at unprotected column temperatures of 670°C.197 As a direct result of this squashing all further tests had protected columns to the underside of the slab.    
Figure 4.4: Column squashing in British Steel Test 2: Plane frame test
Figure 4.5: Connection failure in British Steel Test 2: Plane frame test
Figure 4.6: Local buckling of beams in British Steel Test 3: Corner test
220.127.116.11.3 British Steel Test 3: Corner fire.
Test 3 was carried out in the South East corner of the 8-storey frame on the first floor in a compartment 10m x 7.5m x 4.0m high. The fire load comprised wood cribs giving a total fire load density of 45kg/m2. The fire was designed using the parametric Equations in EC1 Part 2.2 to achieve atmosphere temperatures greater than 1000°C. The edge beams and columns were protected in this test.     The greatest steel temperature (935°C) and deflection (428mm) were recorded in beam EF between gridlines 1 and 2 (See Figure 4.1). The deflection recovered to 296mm after cooling.  Protected steel members were placed in the compartment in order to compare protected steel temperatures measured in the test with the time to achieve these temperatures in a standard ISO 834 test. The equivalent time in the fire resistance test was 86 minutes. 
Figure 4.7: Compartment fire in progress in British Steel Test 4: Office demonstration test
18.104.22.168.4 British Steel Test 4: Office Demonstration.
The office fire demonstration was the largest British Steel compartment fire test incorporating a floor space 18m wide and up to 10m deep (135m2). It was conducted on the first floor in the North East corner and simulated a typical open plan office with real office equipment (and some wood cribs) providing a total fire load density of 46kg/m2. The area of ventilation was equal to 20% of the floor area.  The height of the compartment was 4.0m. In this test only the columns were protected. The unprotected beams achieved temperatures of up to 1150°C. Maximum deflections reached 640mm. Figure 4.7 is a picture of the test in progress. Figures 4.8 and 4.9 show the structure after the fire. As in other tests the flanges of the beams experienced extensive buckling and there were signs tensions developed during cooling (Figure 4.9). The equivalent time of fire exposure in the standard test was shorter than test 3, 74 minutes. No concrete temperatures were measured during this test, hindering accurate numerical modelling of the structural behaviour.
Figure 4.8: Aftermath of the British Steel Test 4: Office demonstration test.
Figure 4.9: Local buckling of the lower flange and folding of the webs in British Steel Test 4: Office demonstration test.
22.214.171.124.5 BRE Test 1: Corner test.
The BRE corner test was conducted on the 2nd floor over an area 54m2. The internal compartment boundaries were steel stud fire resistant board partitions (120 minutes fire resistance with a displacement head of 15mm). All structural steelwork excluding the columns were left unprotected. Twelve timber cribs provided 40kg/m2 fire load. At the start of the test all windows and doors were closed, the fires development was strongly influenced by the lack of oxygen. Atmosphere temperatures of 1051°C were recorded after 102 minutes but in the initial stages the fire died down very quickly and smoldered until after 55 minutes. The fire brigade intervened twice breaking windows to feed the fire with oxygen. The temperature-time history of the fire atmosphere is shown in Figure 4.11 The bottom flange of the central secondary beam achieved a maximum temperature of 903°C after 114 minutes. The max recorded slab deflection (269mm) occurred after 130mins recovering to 160mm after cooling. Unlike the British Steel corner test the compartment walls were directly below the axis of the beams on column lines thus the edge beams experienced high gradients across the width of the cross-section. One of the edge beams distortionally buckled over its length as a result of these gradients and restraint to thermal expansion. Unlike all the other Cardington frame fire tests there was no local buckling of the beams and no evidence of cooling in the form of failed connections or folds in the web. 
126.96.36.199.6 BRE Test 2: Large Compartment.
The large compartment test was constructed on the second floor extending over the full width of the building, between gridline A and 0.5m from gridline C see Figure 4.2. The total floor area of the compartment was 340m2. 40kg/m 2fire load was placed in the form of 42 wooden cribs. The compartment was formed by constructing a fire resistant stud partition wall across the width of the building and around the vertical access shafts. Double-glazing was installed on two sides of the building along gridlines 1 and 4. The middle third of the glazing was left open on both sides to allow sufficient ventilation for the fire to develop. All steel beams including the edge beams were left unprotected but the columns were protected.
Rapid ignition resulted in the windows breaking during the early part of the test but the maximum temperature achieved was fairly low at 763°C. The steel reached a maximum temperature of 691°C and a maximum displacement of 557mm was recorded halfway between gridlines 2 to 3 and B to C. The residual displacement after the structure had cooled was 481mm. Overall the structure behaved very well and there were no signs of collapse. Most internal beams showed evidence of local buckling in the lower flange and the web near the connections. In some of the partial depth end plates the plate had fractured down one side and in one instance the web had fractured. The deflection of the slab caused integrity failure of the compartment wall because it was greater than the 15mm allowance.
188.8.131.52.7 Atmosphere temperatures.
The atmosphere temperatures recorded in all six tests are illustrated in Figures 4.10-4.12 for comparison. British Steel test 1 and 2 have very similar heating rates. British Steel test 4 was the shortest duration fire. The BRE corner test achieved the highest temperatures but for a very short time while the BRE large compartment barely reached an average of 700°C during the most intense phase of the fire.
Figure 4.10: Average atmosphere temperatures recorded in the British Steel tests.
Figure 4.11: Average atmosphere temperatures recorded in the BRE corner test. 
Figure 4.12: Average atmosphere temperatures recorded in the BRE large compartment test (1/2 floor). 
4.4 The PIT Project
In 1995 Edinburgh University in collaboration with CORUS and Imperial College proposed a project to model the 4 British Steel fire tests on the Cardington frame. It was funded by the DETR "Partners in Technology" scheme. The title of the project was
"The behaviour of steel framed structures under fire conditions" and the main objective was described as, "To understand and exploit the results of the large scale fire tests at Cardington so that rational design can be developed for composite steel frameworks at the fire limit state "
The PIT project started in March 1996 running for four years ending in March 2000. Although the main research team consisted of Edinburgh University, CORUS and Imperial College, BRE and SCI also provided valuable input. SCI was primarily responsible for the design output from the project. Sheffield University were part of the steering committee.
Figure 4.13: Steel material behaviour in Eurocode 3 Part 1.276
The numerical models of the tests ranged in complexity from very simple grillage models to detailed shell representations of the beams and slab. The University of Edinburgh and CORUS used the commercial code ABAQUS whilst Imperial College made use of their in-house finite element code ADAPTIC. The output from all the models were comparable and agreed with the measured test data. Conclusions of the project were,
- The Cardington composite steel framed building exhibited very stable behaviour under the various fire scenarios tested because of the nature of its highly redundant structural form.
- The thermo-mechanical phenomena observed (a combination of restrained thermal expansion and thermal bowing) defines the structural behaviour and depends upon the frame layout and the thermal regime of the fire compartment
Rigorous finite element models were developed by all of the three main contributors. The ability to reliably model material and geometrical non-linearities was a key factor in choosing the finite element codes. ABAQUS is a commercially available well accepted package tested rigorously by multiple users modelling a variety of problems. ADAPTIC has been developed over many years and is also a very reliable research code. All models were thoroughly checked against real test data. The results from corresponding models showed the same structural behaviour reinforcing the individual models results.
184.108.40.206 Material models
The stress-strain material definitions in EC2 Part 1.2 and EC3 Part 1.2 were assumed for concrete and steel respectively. The steel material model is elasto-platic and includes enhancement from strain hardening above 400°C. The steel model may be conservative as was discussed in Chapter 2. Both sets of properties include degradation with increasing temperature and are illustrated in Figures 4.13 and 4.14.
Figure 4.14: Compressive concrete material behaviour in Eurocode 2 Part 1.2 
220.127.116.11 The University of Edinburgh Numerical Models
The University of Edinburgh modelled British Steel test 1 and test 3 using ABAQUS. Both grillage  and shell models were developed.  Depth integration techniques are normally used to model materially non-linear plate structures using plate or shell finite elements. Stresses are calculated at integration points through the depth of the elements and section forces are obtained by integration of these stresses.
Several attempts were made to model the Cardington tests using the ABAQUS concrete model and this approach. Convergence of the problem was never achieved. Thus a Stress-resultant approach was tried. Stress-resultants enable the geometry of the plate and the material behaviour to be described by one set of equations. Forces and moments per unit width of the plate are calculated based on the strain, curvature and temperature of the plates reference surface. Gradients can also be incorporated. However results are in terms of stress resultants only so the variation of stress over the depth of the plate is not given. Both the grillage and shell representations developed by Edinburgh adopt a stress-resultant approach.
For ABAQUS to model plates using a stress resultant approach an additional user defined sub-routine is required. Hence Gillie  developed a suite of programs called FEAST. FEAST is used in the research presented in this thesis to model generic composite steel frames. Therefore an understanding of the code and its assumptions are stated here.
18.104.22.168.1 Development of FEAST 
FEAST (Finite Element Analysis of Shells at High Temperatures) enables analysis of generic composite plates like the Cardington floor slab at high temperatures.
The FEAST suite consists of 3 programs,
- SRAS - Stress Resultant Analysis of Shells. The program defines the force-strain and moment-curvature relationship for user defined plates over a given range of stress-strain-temperature states
- FEAI - Finite Element Analysis Interface. This program allows stress resultant based calculations for user defined plates to be undertaken by ABAQUS
- MFDU - Moment-Force Diagram Utility. This program produces moment-force interaction diagrams for plates analysed by SRAS
(4.1) εl = εr + zl φ
εl = average strain in the layer
εr = reference surface strain
zl = distance of the centre of a layer from the reference surface
φ = curvature of the reference surface
The temperature in the layer depends upon the reference surface T and the thermal gradient through the depth of the plate.
SRAS allows polynomials to describe the gradient through the depth, over a number of reference surface temperature ranges. The layers of the plate may also be separated