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The Behaviour of Multi-storey Composite Steel Framed
Structures in Response to Compartment Fires

Susan Lamont

Doctor of Philosophy, University of Edinburgh, 2001.


Declaration

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).

Abstract

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.

Publications

The following papers and reports have heen produced as a result of this research:

Journal Papers

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).

Conference Papers

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.

Other publications

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.

Acknowledgements

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.

Contents

Declaration ii
Abstract iii
Publications v
Acknowledgements vii
Contents xiii
List of Figures xxv
List of Tables xxv

1 Introduction. 1

1.1 Background to the project. 2
1.2 Aims of this research. 3
1.3 Outline of thesis chapters. 4

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. 8
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
2.3 The Swedish Design Guide. 24
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. 28
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
2.6 Research into the behaviour of single elements of structure in fire. 41
2.6.1 Computer models for structures. 41
2.6.2 Columns. 42
2.6.3 Beams. 47
2.6.4 Slabs. 48
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
3.3.1 The Pre-flashover Fire. 59
3.3.2 The Post-flashover fire. 62
3.3.3 The decay period. 62
3.4 The burning regime: Ventilation vs. Fuel controlled fires. 63
3.4.1 Opening factor. 64
3.4.2 Differentiating between fuel and ventilation controlled fires. 64
3.4.3 Fuel controlled fire. 65
3.5 CIB compartment fire experiments. 66
3.6 Compartment fire modelling. 67
3.6.1 Model types. 67
3.6.2 Zone modelling. 68
3.6.3 Heat balance equation for an enclosure (Pettersson et al, 1976 [195]). 70
3.6.4 Empirical/Characteristic temperature curves. 74
3.7 Parametric T-t curves. 77
3.7.1 The Parametric T-t curve in EC1. [74] 77
3.7.2 Comparison with compartment fire test data. 80
3.8 The Natural Fire Safety Concept. [224] 81
3.9 Other factors influencing the rate of heat release in a compartment fire. 84
3.9.1 Vent location. 84
3.9.2 Fuel load. 85
3.9.3 Compartment dimensions. 86
3.9.4 Thermal inertia of the compartment boundaries, kpc. 87
3.10 Compartment fire models for computers. 88
3.10.1 Zone models for computers. 88
3.10.2 CED models. [85] [119] [196] [233] 90
3.11 Heat Transfer. 91
3.11.1 The Heat Transfer Equations. 91
3.11.2 Solving the Heat Transfer Equations. 93
3.12 Thermal properties of materials. 94
3.12.1 Steel. 95
3.12.2 Concrete. 96
3.13 Predicting steel temperatures. 98
3.13.1 Hp/A Concept. 99
3.13.2 Simple heat transfer models. 100
3.13.3 Uninsulated steel. [161] 100
3.13.4 Insulated steel. 101
3.13.5 Nomograms. 102
3.14 Modelling heat transfer in concrete. 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
4.2.1 Broadgate Phase 8. 108
4.2.2 Churchill Plaza building, Basingstoke. 109
4.3 Fire tests. 109
4.3.1 BHP William Street fire tests, Melbourne. [197] 109
4.3.2 Stuttgart-Vaihingen University fire tests, Germany. 110
4.3.3 Cardington frame fire tests. 111
4.4 The PIT Project. 118
4.4.1 The numerical models. 121
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
4.5 Numerical Modelling at Sheffield University. 133
4.6 Developments in Europe. 134
4.6.1 ECSC Project. [246] 134
4.7 Design guidance. 135
4.7.1 SCI design guide. 135
4.7.2 Design guidance developed in New Zealand. 136
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. 142
5.3 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. 145
5.6 Modelling and Analysis. 146
5.6.1 Model 1: No Metal Deck. 146
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 Model 2: Including the Metal Deck. 156
5.7.1 Prediction of Test 4 Temperatures. 160
5.8 Modelling Edge beams. 160
5.8.1 Edge beams in British Steel Test 3. 163
5.8.2 Edge beams in British Steel Test 4. 165
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. 175
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
6.3 Runaway in axially unrestrained and axially restrained beams. 193
6.3.1 The impact of loading on "runaway" in a pinned beam. 195
6.3.2 Implications. 199
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. 205
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 Effect of varying the slab mean temperature in British Steel test 1. 219
7.3.1 Slab mean temperature variation in longitudinal direction. 219
7.3.2 Mean temperature variation in transverse direction. 226
7.4 Conclusions. 231

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. 234
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
8.3 Parametric Studies. 244
8.4 Results. 244
8.4.1 Short versus long post-flashover fires in the 2x2 bay frame with edge beams protected. 244
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
8.5 Conclusions. 317

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. 324
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
9.7 Large versus small frames. 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
10.3.1 Further development of FEAST. 366
10.3.2 Further parametric studies. 366
10.3.3 Spreading fires. 367
10.3.4 Cardington Frame Fire Test Data. 367
10.3.5 Future fire tests. 369
10.3.6 Development of design codes 369

References. 387

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. [66] 15
2.3 Equivalent fire severity on a temperature basis. [42] 16
2.4 Fire and structural response models. [238] 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. [143] 29
2.8 Stress-strain curves for typical-hot rolled steel at elevated temperatures. [99] 32
2.9 Stress-strain curves for steel illustrating yield strength and proof strength. [42] 32
2.10 Reduction in yield strength and modulus of elasticity of steel with temperature (EC3 1995). [42] 33
2.11 Thermal expansion of concretes. [228] 34
2.12 Poisson ratio. [228] 35
2.13 Concrete creep. [157] 36
2.14 Stress strain relationships for concrete at elevated temperatures (EC2 1993). [42] 37
2.15 Design values for reduction in compressive strength with temperature. [42] 38
2.16 Design values for reduction of modulus of elasticity. [42] 39
2.17 Column expansion in fire. 44
2.18 Complete load-deflection curve for a reinforced concrete slab. [252] 49
2.19 Tensile membrane load carrying mechanism in a slab with clamped edges. [252] 50
2.20 Tensile membrane load carrying mechanism in a simply supported slab. [252] 51

3.1 The course of a well-ventilated compartment fire. [66] 57
3.2 The effect of enclosure on the rate of burning of a slab of polymethylmethacrylate (Friedman 1975 as cited by Drysdale [66]). 58
3.3 t2 fire growth according to Equation 3.4. [66] 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. [195] 65
3.6 Schematic diagram showing the variation of mass burning rate with ventilation parameter AwH1/2 and fuel bed area Af. [44] 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. [241] 67
3.8 2 zones in a compartment fire model. 68
3.9 Illustration of the heat balance in a fire compartment (Pettersson, 1976 [195]). 71
3.10 Theoretical temperature-time curves for compartment fires with different fire load densities and opening factors (Pettersson, 1976 [195]). 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 [195]). 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 [195]). 76
3.13 A comparison of Temperature-time curves (Lie, 1974 [144]). 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 [145]). 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 [145]). 78
3.16 Scope of the Natural Fire Safety Concept Research. [224] 82
3.17 Scope of the Natural Fire Safety Concept Research. [224] 84
3.18 Plot of the recorded atmosphere temperatures in British Steel long compartment test 6. 87
3.19 Thermal properties of steel. [42] 96
3.20 Density of structural concrete at high temperatures. [228] 97
3.21 Thermal properties of different structural concretes. [228] 98
3.22 Thermal properties of concrete. [42] 99
3.23 Typical nomogram for estimating maximum steel temperatures using the "Element factor". [129] 103
3.24 Temperature contours in concrete beams exposed to the standard fire from EC2. [42] 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. [197] 119
4.12 Average atmosphere temperatures recorded in the BRE large compartment test (1/2 floor). [197] 120
4.13 Steel material behaviour in Eurocode 3 Part 1.2. [76] 121
4.14 Compressive concrete material behaviour in Eurocode 2 Part 1.2. [75] 122
4.15 Flowchart describing the program SRAS. [87] 125
4.16 Flowchart describing the details of stress calculation within SRAS. [87] 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. [23] 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 [249]). 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. [195] 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. [66] 15
2.2 Extracts from a typical table in the "Yellow Book" for Fendolite Mu. 22
2.3 Load factors for fire limit state. [40] [74] [76] 41
3.1 Parameters used for t2 fires (Evans 1995 as cited by Drysdale 1998) [66] 60
3.2 Fire growth parameters and time to reach the rate of heat release Qg =1000kW for t2 fires in DD 240 [114]. 60
3.3 List of major deterministic post-flashover models. [10] 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. [63] 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. [6] 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

Chapter 1

Introduction

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. [115] 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. [115] 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 [101] 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 [23] 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, The key parameters investigated were the temperature distributions in the structural elements for various compartment fires and the restraint provided by the edge beams (protected or unprotected) or the surrounding cooler structure to the fire compartment. A clear understanding of compartment fire dynamics and heat transfer was necessary to create design fires and compute the heat transfer to the structural elements. Thus a detailed review of the tools available to fire engineers to calculate compartment fire exposures and heat transfer was conducted.

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 [77]. 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

Chapter 2.

An overview of structural fire safety design and research.

2.1 Introduction

This overview of structural fire safety design and research includes three main topics.
  1. Traditional and Performance Based Design Methods.
  2. Factors affecting structures in fire.
  3. Literature review of single element behaviour in fire and steel frame analysis before the Cardington frame fire tests.
Traditionally steel fire design has been based upon fire resistance testing although fire resistance by calculation has also been implemented for many years. The fire resistance test and its shortcomings are discussed and fire resistance by calculation is introduced. Methods given in BS 5950 Part 8, EC3 and EC4 are described. The history of performance based design for steel is then outlined.

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. [156] 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. [15] [16] 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. [39] The heating conditions in the furnace are described by a standard temperature-time curve. The British Standard temperature-time curve is given by Equation 2.1, first published in 1932. [15] [16] [156] The temperature of the furnace is programmed by controlling the rate of supply of fuel. Traditionally fire resistance design in the UK has assumed fire exposure to equal the British Standard standard fire curve.

(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. [156] 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. [86] Gewain and Troup [86] 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. [160]

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.

2.2.3.1 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. [64] 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.

2.2.3.2 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. [189] A limited number provide longer fire resistance periods but the cost increases considerably. Paints are also applied off-site.

2.2.3.3 Partially exposed steelwork [64]

Standard fire tests on partially exposed steel have shown that structural members not fully exposed to the fire exhibit increased levels of fire resistance. [64] [189] [204] 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.
  1. 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.

  2. 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.

  3. 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.

  4. 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 beam section.

  5. 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. [64]

  6. Water-filled sections: Hollow sections may be filled with water to reduce heating in fire. This method is expensive and infrequently used. [42]
2.2.4 Shortcomings of the fire resistance test

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. [157] Indeed Drysdale [66] 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 [156] 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 [113] 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 [66] 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 
(wood equivalent)		   Equivalent   Standard fire
duration
(lb/ft2)(kg/m2)(kJ/m2 x 10-6)(h)
10490.901
15731.341.5
20981.802
301462.693
401953.594.5
502444.496
602935.397.5


Table 2.1: Ingberg’s fuel load fire severity relationship [66]



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 [66]

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. [103] 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. [66]

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 [138] 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 [42]

Law [138] developed a time equivalence relationship to include the effect of ventilation using data gathered from a CIB study of fully developed compartment fires. [241] 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

where,

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, [195] 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. [154] 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

where,

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 [98] 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]

where,

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 [74] 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. [139]

EC1 Part 1.2 t-equivalence formula

(2.6)        te,d = qf,d kb wf

where,

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 [114]). 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

where,

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. [42]

Law [139] 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 [139] 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 [234] 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. [74]

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: A typical fire resistance calculation involves estimating an expected natural fire exposure, conducting a heat transfer analysis to calculate the temperature of the structural elements and then calculating the load capacity taking into account material degradation at high temperatures.

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. [90] [92] [203]




Figure 2.4: Fire and structural response models [238]


  Dry thickness in mm to provide fire resistance of: 
Hp/A up to1/2 hour1 hour3/2 hour2 hour
3010101011
11010101825
25010132434


Table 2.2: Extracts from a typical table in the "Yellow Book" for Fendolite M11

2.2.7.1 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. [61] 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 [7]" 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.

2.2.7.1.1 The Yellow Book [7]

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.

2.2.7.1.2 BS 5950: Part 8 [40]

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.

2.2.7.1.3 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 [141] 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)

where,

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

where,

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. [258] 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. [30] [41-43] [80] [90] [94] [118] [159] [193] [202] [244] [258] Custer and Meacham [202] 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 [41] [42] in a description of the fire code development in New Zealand summarises the basic elements of performance based codes,
  1. State objectives clearly
  2. Specify performance requirements clearly
  3. Allow any solution which meets these requirements. Also aliow the use of new knowledge as it becomes available
Buchanan also states that performance goals should specify a level of safety that is independent of prescriptive building codes. Very often requirements are descriptive rather than quantitative which causes problems in determining whether performance criteria have been met. This is one of the major reasons why prescriptive codes are still in use. Figure 2.6 is an outline of the New Zealand Performance Based Fire engineering design procedure. [42] It essentially requires a number of possible worst case scenarios to be analysed. For instance the worst fire load and ventilation condition to produce the most severe fire.

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. [43] 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) [54] 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. [202] Britain produced a Draft British Standard Code of Practice for the Application of Fire Safety Engineering Principles to Fire Safety in Buildings, DD 240 [114] in 1992. This is to be shortly replaced by a new standard BS 7974 and a series of published documents. [52] 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. [91] [230]

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 [170]" was published in 2000. It is based on theoretical work by Bailey [23] 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. [29] [43] [118]

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. [202] As a result the NRCC fire lab have developed FIRECAM [31] (A FIRE risk Cost Assessment Model) a key element of their performance based code.

NFPA (National Fire Protection Association) [171] and SFPE (Society of Fire Protection Engineers) are key players in the establishment of performance based Codes in the USA. The SFPE Guide [62] 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

2.5.1.1 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, [142] see Equation 2.16

(2.16)        α = εthermal/ΔT

where,

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. [4] [55] [142] However, the temperature associated with phase transformation does depend upon the carbon content. [55] For design purposes an average thermal expansion is assumed. BS 5950 Part 8 assumes 14 x 10-6. [40]



Figure 2.7: Thermal expansion of steel with increasing temperature [143]

2.5.1.2 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. [55] Reported test data indicate values of 0.27 at ambient and 0.30 at 600°C. [228] There is very little variation with increasing temperature.

2.5.1.3 Creep

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. [142] 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 [4] 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. [137] [245]

2.5.1.4 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)

where,

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 [207] [249] 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. [4] [141]

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.

2.5.1.4.1 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. [55] [125]

EC3 [76] 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 [246] compared EC3 steel properties and those derived by Anderberg [4] 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. [126]

Modified Ramberg-Osgood stress-strain relationships are quoted in the literature as a means of calculating σ-ε-T relationships in numerical modelling techniques. [19] [210] The original Ramberg-Osgood correlation was a simple power-law equation to approximate stress-strain behaviour up to yield. [137]




Figure 2.8: Stress-strain curves for typical-hot rolled steel at elevated temperatures [99]




Figure 2.9: Stress-strain curves for steel illustrating yield strength and proof strength [42]




Figure 2.10: Reduction in yield strength and modulus of elasticity of steel with temperature (EC3 1995) [42]

2.5.2 Mechanical properties of concrete at elevated temperature

2.5.2.1 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. [123] [157] [227] 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 exp