- Email: [email protected]
Numerical modelling of structural fire behaviour of restrained steel beam–column assemblies using typical joint types
Engineering Structures 32 (2010) 2337–2351
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Numerical modelling of structural fire behaviour of restrained steel beam–column assemblies using typical joint types X.H. Dai, Y.C. Wang ∗ , C.G. Bailey School of Mechanical, Aerospace and Civil Engineering, University of Manchester, United Kingdom
article
info
Article history: Received 15 October 2009 Received in revised form 22 February 2010 Accepted 1 April 2010 Available online 15 May 2010 Keywords: Structural fire behaviour Numerical modelling Restrained steel frames Joints Robustness Catenary action
abstract This paper presents the results of a simulation study of 10 fire tests on restrained steel beam–column assemblies using five different types of joints: fin plate, flexible endplate, flush endplate, web cleat and extended endplate. This paper will provide details of the simulation methodology for achieving numerical stability and faithful representation of detailed structural behaviour, and compare the simulation and experimental results, including joint failure modes, measured beam axial forces and beam mid-span deflections. Good agreement between ABAQUS simulations and experimental observations confirms that the finite element models developed through the ABAQUS/Standard solver are suitable for predicting the structural fire behaviour of restrained structural assemblies with realistic steel joints undergoing different phases of behaviour in fire, including restrained thermal expansion and catenary action in the beams. The validated model may be used to conduct numerical parametric studies to generate theoretical data to help develop detailed understanding of steel joint behaviour and their effects on robustness of steel framed structures in fire. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The high profile Cardington structural fire research programme [1] and World Trade Center collapse [2,3] have firmly established steel joint behaviour in fire as the most important aspect of understanding the behaviour and robustness of steel structures in fire. Joints play a critical role in steel framed structure in controlling fire induced progressive structural collapse. When designing and analysing a steel framed structure at ambient temperature, the joints between beams and columns are commonly classified as either simple joints or moment resisting joints, based on their predominant bending moment capacity. Under the fire condition, the behaviour of the joint can be totally different owing to the presence of axial restraint offered to the connected beam by the surrounding structure. The qualitative behaviour of an axially restrained beam in fire is now well established [1]: (i) at low temperatures, the beam’s lateral deflection is small and its thermal expansion is high, therefore compressive axial forces are generated in the beam; (ii) as the beam’s temperature increases, the steel’s mechanical properties degrade and the beam’s lateral deflections increase, reducing the amount of axial extension of the beam. Combined with the reduced axial stiffness of the beam due to degrading mechanical properties, the beam’s axial compression
∗
Corresponding author. E-mail address: [email protected] (Y.C. Wang).
0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.04.009
decreases; (iii) when the beam’s bending moment capacity has reduced to the applied bending moment in the beam, the beam will undergo accelerated lateral deflections, which will induce sufficient shortening to cancel the beam’s thermal expansion. At this stage, the beam’s axial force returns to zero; the temperature at which the beam’s axial force is zero is very close to the limiting temperature of the beam without axial restraint, as confirmed by the results of a theoretical study by Yin and Wang [4–6]; (iv) after the beam’s axial compressive force has returned to zero, the beam will enter the catenary stage; if the joints have sufficient axial strength and ductility, the beam will be able to survive very high temperatures without failure. On the other hand, if the additional axial forces in the joint are not designed for or the joint does not have sufficient ductility to allow the beam to experience very large deflections, the joints may fracture due to either compression or tension, which may lead to progressive structural collapse. Failure of the seated bearing connections to columns 79–81 of the World Trade Center building 7 has been attributed to having initiated the progressive collapse of the building [3]. To improve understanding of the effects of joints on steel framed structural behaviour in fire and to help design better steel joints to mitigate against fire induced structural collapse, an experimental research project has recently been completed at the University of Manchester, in which fire tests were carried out to investigate interaction between joints and connected beams and columns in a H-shaped structural assembly. Details of this experimental programme and its principal findings are presented elsewhere [7,8]. In this research, fire tests and analyses were also
2338
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
performed to determine temperatures in different components of steel and composite joints with various fire protection schemes [9–12]. This research was carried out in collaboration with the University of Sheffield, which performed elevated temperature experiments and numerical analyses to investigate bolt behaviour [13], elevated temperature behaviour of isolated joint assemblies [14–17] and to develop component based method to characterise joint behaviour under different combinations of axial load, bending moment and shear [18–21]. The Manchester fire tests on structural assemblies provide experimental data to calibrate numerical simulation models, which will then be used to perform parametric studies to help develop detailed understanding of joint behaviour as well as to develop more effective joint details to reduce the risk of fire induced progressive collapse. These tests have been modelled by the authors using the general finite element package ABAQUS/standard solver. It has been a tremendous challenge to faithfully model detailed behaviour of restrained steel framed structural subassemblies with realistic joint details undergoing very large deflections and different modes of buckling and failure in fire. The main objective of this paper is to explain key aspects of the modelling technique to help future researchers to develop robust numerical simulation models for this type of structures. Validation of the numerical models is assessed through comparison of the simulation results with the ten fire tests on restrained steel structural assemblies carried out by the University of Manchester. 2. A brief summary of the structural assembly fire tests Details of the experimental set up and results have been presented elsewhere by the authors [8,7]. This section will only provide a brief description of the fire tests and the main experimental observations. 2.1. Structural fire tests As shown in Fig. 1, each specimen, in the form of ‘‘rugbygoalpost’’, consisted of one beam, two identical columns and two identical joints. The 4 ends of the two columns were restrained horizontally. In total, 10 fire tests were performed, covering 5 joint types (fin plate, flexible endplate, web cleat, flush endplate and extended endplate) and two column section sizes to simulate two different levels of axial restraint to the beam. Table 1 summarises the main member dimensions of the ten tests. The whole beam, the two joints and the central part of the two columns were exposed in fire inside the furnace. During the fire tests, the furnace temperatures were recorded by six thermocouples whose average temperature was intended to follow the standard fire condition in [22]. The beam was loaded by two point loads with a target value of 40 kN. The horizontal reaction forces at the column ends were measured by pin load cells installed at the column ends. 2.2. Main experimental conclusions The main experimental observations are as follows:
• Joint failure modes included weld tearing (fin plate, flexible endplate), beam web fracture (flexible endplate) and bolt thread stripping (flush endplate and some web cleat). However, there was no beam failure despite very large deflections (span/8–span/6). There was no structural failure during the beam-in-compression phase. Here failure is defined as complete collapse of the structure.
• Using different joint types had very little effect on the beam’s axial force development. In contrast, the beam axial force was heavily influenced by the different column sizes. This can be attributed to the very short length of the joint region and strongly suggests that the joints may be considered to have infinite axial rigidity so that the axial restraint is principally dependent on that of the connected columns. • The different types of joints possessed different levels of rotational capacity. The web cleat connections, through significant bending deformation of the heel, developed very high rotations. The extended end plate connections also developed a very ductile mode of behaviour through bending of the thin endplate. 3. Methodology of ABAQUS modelling The use of numerical modelling to analyse steel joint behaviour, either at ambient temperature or in fire, has had a long history of development. Bursi and Jaspart [23] built a simple model to simulate bolted connections at ambient temperature using the commercial program ABAQUS. In their ‘‘spin’’ model, an assembly of beam elements was adopted to represent a bolt. Swanson et al. [24] modelled bolted T-stub joints using ABAQUS, in which contact interactions between bolts and base materials and between connection plates were considered. Maggi et al. [25] investigated the structural behaviour of bolted endplate connections using ANSYS. AlJabri et al. [26,27] simulated the moment–rotationtemperature relationships of a series of fire tests on flexible and flush endplate connections using ABAQUS. In their models, surface to surface contact was used. Sarraj et al. [28] modelled fin plate connections in fire using ABAQUS, in which surface to surface contact with a small sliding option was used. Yu et al. [29] commented on the problem of simulating bolted joints due to numerous contact problems and developed a numerical simulation procedure using the ABAQUS/Explicit solver to model bolted joints at both ambient and elevated temperatures. By controlling the time step, it was shown to be possible to produce quasi-static responses. Shirh et al. [30] developed a 3D model using ANSYS to study the behaviour of flush end plate connection between beams and columns at elevated temperatures. A common feature of all the existing numerical simulations of joint behaviour is that the structural system was statically determinate. In particular, most of the investigations have focused on producing joint moment–rotation characteristics. In such a structural system, the appearance of large deformations in any part of the structure would signal failure of the system. Therefore, the existing researches only focused on simulating joint response before very large deformations and gross inaccuracy in predicting large joint displacements were overlooked. In contrast, in the fire tests conducted by the authors, the appearance of very large deformations merely means that the structure was going through a different phase of behaviour, the axial force in the beam changing from compression to tension. In order for the subsequent phase of structural behaviour (catenary action) to be accurately simulated, it is important to develop a robust numerical model to satisfactorily capture this stage of the structural behaviour. In this research, the authors used both ABAQUS/Static analysis and ABAQUS/Explicit analysis and finally decided to use the ABAQUS/Static solver due to the huge requirement on computational resources (both time and storage) and unstable structural behaviour when using the ABAQUS/Explicit solver. As shown in Fig. 1, the tested structure was symmetrical in geometry, loading arrangement and boundary conditions. However, during testing, some unsymmetrical heating was encountered due to unsymmetrical layout of the burners in the fire test furnace. Therefore, the observed structural behaviour was not exactly symmetrical. Nevertheless, it was considered
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2339
Fig. 1. Elevation view of the test set up. Table 1 Summary of specimen dimensions. Test ID
Joint type
Connection component dimension (mm)
Test-1 Test-2 Test-3 Test-4 Test-5 Test-6 Test-7 Test-8 Test-9 Test-10
Fin plate Flexible endplate Flush endplate Web cleat Extended endplate Fin plate Flexible endplate Flush endplate Web cleat Extended endplate
150 × 130 × 10 150 × 130 × 8 150 × 200 × 8 90 × 150 × 10 (depth: 130) 150 × 250 × 8 150 × 130 × 10 150 × 130 × 8 150 × 200 × 8 90 × 150 × 10 (depth: 130) 150 × 250 × 8
that the slight non-symmetrical heating had only minor effect on the behaviour of the restrained beam, which would be primarily dependent on the heating condition in the central region of the beam. As far as the joints were concerned, non-uniform heating would result in one joint being damaged more than the other. Since the main purpose of this simulation was to establish an appropriate simulation methodology, it was accepted that as long as the more severely damaged joint behaviour could be captured, the simulation results would be valid. Simulating detailed structural behaviour of the tested structural assembly was time consuming. Therefore, to save computational time, it was decided to include only half of the test assembly in the finite element model, of which Fig. 2 shows a typical one. Three-dimensional solid elements (C3D8) were used in modelling the main structural members as shown in Fig. 2. A series of ABAQUS models with different meshes were run to assess the sensitivity of simulation results to the FE mesh. The results of this sensitivity study suggested that the appropriate mesh size would be 10–20 mm for the main structural members such as the beam, the joint components and the column. Too small element size would consume too much computation time, while too coarse mesh (Fig. 3(b)) would cause numerical convergence problem and would not be able to reveal some important member buckling characteristics such as shown in Fig. 3(a). Also, in order to avoid premature beam web buckling, at least two layers of elements in the thickness direction of the beam web should be used. Furthermore, to reduce the number of elements and nodes in the FE model, the column was divided into three parts and only the central part
Column section
Beam section
UC 254 × 254 × 73 UB 178 × 102 × 19 UC152 × 152 × 23
Fig. 2. Typical FE model adopted in numerical modelling.
(400 mm for models with large columns and 800 mm for models with small columns) connected by the joint and exposed in fire in the furnace was actually modelled using the solid elements. The other two parts away from the joint zone was modelled using general beam elements with ‘‘I’’ cross section. The ABAQUS ‘‘Coupling’’ function was used to join the three column parts as shown in Fig. 4(a). Fig. 4(b) shows the actual configuration simulated using ABAQUS. In the test structures, many contact pairs exist in the joints, such as end plate to column, fin plate to beam web, bolt shanks and nuts to the connected members. The ABAQUS contact function was used to simulate the interaction between the contact pairs. A contact was defined as surface to surface contact with a small
2340
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
(a) Suitable beam mesh.
(b) Coarse beam mesh. Fig. 3. Effect of element sizes on structural deformation.
(a) User built model.
(b) ABAQUS abstracted model. Fig. 4. Column simulation method.
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2341
Fig. 5. Bolt model.
sliding option. ‘‘Hard contact’’ was assumed for the normal contact behaviour and a friction coefficient of 0.3 was used in the tangential direction of the contact pairs. The results of a sensitivity study confirmed that using a wide range of friction coefficient values had little effect on the simulation results. In the tests, ordinary Grade 8.8 M20 bolts were used and they were installed manually using spanners. Fig. 5 shows how the bolts were simulated. The bolt thread was not modelled because its modelling would be extremely time consuming. Except for the thread stripping failure mode, this simplification was considered acceptable because all other modes of failure were accurately simulated. All the contacts between the bolt shank and the edges of the holes in the connected members, between the bolt head (nut) and the connected plate (column flange, end plate) surfaces were simulated using the aforementioned contact pair method. To avoid numerical difficulty at the start of the simulation, the gap between the bolt shank and bolt hole was set at 0.1 mm and the gap between bolt head (nut) and connected plate was 0.001 mm. Due to the difficulty in measuring the real bolt initial stress, no pre-stress was applied to the bolts. The stress–strain constitutive relationships adopted in the FE models for the steel beams, columns and connection components were based on the steel tensile coupon tests at ambient temperature. Table 2 shows the average yield strength, ultimate tensile strength and elastic modulus of the joint assembly members. For ABAQUS simulation, the nominal engineering stress–strain model obtained from steel tensile coupon test was converted to the true stress–strain relationship according to: σtru = σnom (1 + εnom ) and εtru = ln(1 + εnom ), in which σtru and εtru represent the true stress and strain; and σnom and εnom are the nominal stress and strain respectively. Since no mechanical test was performed on the bolts and nuts, their mechanical properties were assumed to be elastic-perfectly-plastic. For Grade 8.8 bolts, the nominal yield strength and elastic modulus were assumed to be 640 MPa and 210 000 MPa respectively. The EC3 (EN 1993-1-2) [31] reduction factors, shown in Fig. 6, for carbon steel at elevated temperatures were used. Weld was not directly modelled. Instead, the welded elements were tied together using the ABAQUS ‘‘tie’’ function. The boundary conditions of the FE model were according to those in the test. The bottom of the columns was pinned in all three directions and the top of the columns was pinned in two directions but movement along the column axis was allowed. Since only half of the beam was included in the FE model as discussed earlier, the beam mid-section was fixed in the axial direction, which effectively prevented rotation about any axis in the beam cross section, but allowed the beam to twist about its longitudinal axis. The beam top flange was prevented from lateral movement to simulate the effect of the lateral restraining effect of the truss connected to the beam upper flange. However, for simplicity in modelling, the lateral restraining truss was replaced by 2 plates of 750 mm long and 50 × 8 mm in cross section as shown in Fig. 7. The truss replacement plate dimensions were determined
Fig. 6. Reduction factors for strength and elastic modulus of carbon steel at elevated temperatures (EN 1993-1-2).
by ensuring that the plates contributed the same as the lateral restraining truss to the bending capacity of the beam. Nevertheless, since this contribution was low, the beam’s behaviour would only be slightly influenced by the plate dimensions. As in the tests, the FE model applied the loads in two steps: (i) two point loads of 40 kN each to the beam at ambient temperature; (ii) increasing the structural temperatures while maintaining the structural loads. In the FE model, five different temperature–time curves based on the test measurements were adopted for different parts of the structure: temperature curves for the beam bottom flange, web and top flange; one temperature curve for the joint zone which included all the bolts, nuts and connection components (such as endplate, fin plate and web cleats) as well as 100 mm length of the beam in the joint zone; one temperature curve for the column segment (400 mm of the large column, 800 mm of the small column) in the joint region. The temperature of the column away from the joint zone was set at ambient temperature. Since the main objective of the fire tests was to investigate complete failure of the structures at elevated temperatures, the test specimens underwent a variety of temporary instabilities due to localised buckling and very large deformations. Any of these temporary instabilities could cause the numerical model to terminate and the numerical model would not be able to go through all the phases of structural behaviour as in the tests. To ensure that the numerical model was able to go through all the phases of structural behaviour experienced in the tests, an artificial viscous damping was applied to the numerical model. This artificial damping became active and dissipated the energy released during temporary instability of the structure so as to allow the numerical model to bypass the temporary numerical instability problem. After the numerical model bypassed temporary numerical instability and if the structure was still stable, the artificial damping became inactive. On the other hand, if the artificial damping was still active for a long period of time, then the numerical instability signified that the structure was approaching complete failure and was unable to sustain the applied load.
2342
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Table 2 Summary of key mechanical property values for different steel members. Component
Beam
Column
End plate
Fin plate
Web cleat
Elastic modulus (MPa) Yield strength (MPa) Maximum strength (MPa) Ultimate strain (%)
226 580 344 514 28.2
200 000 390 553 25
191 670 303 460 30.5
188 330 235 380 30.6
228 170 342 493 32.6
Fig. 7. Simulation of horizontal restraining truss.
(a) Dissipated energy fraction = 0.00001.
(b) Dissipated energy fraction = 0.0001.
Fig. 8. Effect of dissipated energy fraction on structural deformation.
In ABAQUS, the artificial viscous damping is specified using the ‘‘dissipated energy fraction’’. Determining an appropriate damping factor value was important to ensure that the numerical simulation model was robust when encountering temporary instability but that it did not give spurious results. Fig. 8 shows an example of the effects of using different damping factors on the simulated deformed shapes of the same structure. When a value of 0.00001 was used, the observed web buckling mode was correctly simulated. But when a value of 0.0001 was used, this mode of deformation was damped out. In general, the appropriate damping factor will be structure specific, which makes it difficult for the authors to provide detailed rules to help determine a suitable damping factor. According to the authors’ experiences, two quantities outputted from the simulation model may be checked to assess whether the damping factor used is appropriate. One quantity is the ratio of the dissipated energy by damping (parameter ALLSD in ABAQUS) to the total strain energy (parameter ALLIE in ABAQUS). Theoretically, this ratio should be less than the specified dissipated energy fraction. However, in the authors’ simulations, because the structure underwent very large deformations, the viscous damping dissipated energy was often higher than the specified dissipated energy fraction. However, as long as this ratio did not
exceed 0.1, the FE model results were in good agreement with the experimental results. For example, Fig. 9 compares the ALLSD and ALLIE quantities for the same structure using dissipated energy fractions of 0.00001 and 0.0001 respectively. It can be seen that before the structure collapsed, the ALLSD plot was stable and small and the ratio of ALLSD to ALLIE was less than 0.05 when a dissipated energy fraction of 0.00001 was adopted. In contrast, when using a dissipated energy fraction of 0.0001, the ratio of ALLSD to ALLIE was quite high for a significant period of time of the simulation time. In both cases, the ratio of ALLSD to ALLIE was large at the start of the fire simulation. This was a result of the total strain energy (ALLIE) being small when the structure deformation was very small. Another quantity that can be checked is the support reactions, i.e. they should be in static equilibrium with the applied loads. If the dissipated energy fraction is too high, too much of the applied loads may be resisted by viscous damping. For example, Fig. 10 compares the applied load (40 kN) with the vertical reaction force for using the aforementioned two different dissipated energy fractions. Clearly, using a fraction of 0.0001 was not appropriate because viscous damping contributed to supporting a large part of the applied load for a long period of time. The authors suggest that if the support reaction forces return to the level of the applied loads
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
(a) Dissipated energy fraction = 0.00001.
2343
(b) Dissipated energy fraction = 0.0001.
(c) Ratio of ALLSD to ALLIE. Fig. 9. Energy dissipation from different damping factors.
Fig. 10. Reaction forces at column ends.
after temporarily decreasing (due to damping), then the structural is stable and the damping factor is appropriate. However, if the support reaction forces decrease but do not return to the level of the applied loads after a long period of simulation time, then the damping factor is not appropriate (too high) and the simulation results are not correct. It must be pointed out that, according to the authors’ experiences, numerical instability may also be caused by low quality of the FE model such as coarse mesh and large gaps between contact pairs. Therefore, before using a high value of dissipated energy fraction to suppress the numerical instability, checks should be made to ensure that the FE simulation results are not sensitive to such factors. In the numerical model, the column ends were assumed to be able to rotate freely in the plane of the structure. However, as indicated in Fig. 1, the column flange at the ends was linked to the load cell at two locations using bolts. This arrangement may induce some rotational restraint at the column ends. In the first series of tests using the large column size, the column rigidity is
very high so this rotational restraint would not have any significant effect on the beam and joint behaviour, as evidenced by almost non discernible column deformation in tests 1–5. However, when the small column was used, the column rigidity may not be sufficiently high (evidenced by the large column local and global deformations in tests 6–10, see later) so that the effect of this additional restraint at the column ends should be assessed to ensure that the boundary conditions in the numerical simulation model was correct. An additional model of the structure for test 10 was created assuming complete rotational fixity at the column ends. Fig. 11 compares the simulation results for the models with pin and rigid column ends. With complete fixity at the column ends, the axial force in the beam, both in compression and in tension, is much greater than the measured results. In contrast, assuming pinned column ends produced results much closer to the test results. It can therefore be accepted that the actual column ends would be much closer to pin support than fixed end support, as assumed in all the numerical simulation models. 4. Comparison between FE model and test results All ten tests have been analysed using the ABAQUS modelling techniques described in the last section. This section presents comparisons between the simulation and test results to comprehensively validate the numerical modelling method. 4.1. Tests with large column size (UC 254 × 254 × 73) 4.1.1. Test 1: fin plate joint Fig. 12 shows that the observed deformations of the joint components and beam were followed by the numerical model. Fig. 13 confirms that the simulation results accurately captured
2344
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Fig. 11. Comparison of beam mid-span deflection and axial force in frames with different column end restraints.
Fig. 12. Comparison of simulation and observed deformation patterns of fin plate joints.
Fig. 13. Comparison of modelling and experimental results for mid-span deflection and axial force in the beam restrained by fin plate joints.
the transition process from compression to tension in the beam. In the test, the lower flange of the beam began to bear against the flange of the column towards the end of the test. However, the bearing force would not have been high, otherwise there would have been indication on the column flange from the beam’s lower flange. The numerical model produced lower beam deflections so this bearing action was not observed in the numerical model. However, Fig. 12 indicates that in the numerical model, the beam lower flange was very close to the column flange. Because of the large column size and column flange thickness, both the test and the numerical model show no sign of column deformation. The test specimen failed by fracture of the weld at the top. Since weld was not directly modelled, this failure mode could not be simulated. Instead, the numerical model failure was in the fin plate close to the weld under tension and shearing.
4.1.2. Test 2: flexible endplate joint Fig. 14 shows that Test 2 failed due to fracture of the beam web. This was predicted by the numerical model, as shown by the tensile and shear stress patterns in Fig. 14. The simulated flexible endplate deformation pattern is also very similar to the test observation. Fig. 15 compares the simulated and measured beam axial force and mid-span deflection. The agreement is satisfactory overall, with the simulation results slightly overestimating the transition temperature from compression to tension in the beam. However, the rapid deformation process was closely followed by the simulation model. 4.1.3. Test 3: flush endplate joint This test failed due to thread stripping of the bolts in tension, as shown in Fig. 16. This failure mode could not be reproduced by the
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
(a) Test observation.
(b) Model Mises stress.
(c) Model shear stress in web plane. Fig. 14. Comparison of simulation and observed deformation patterns of flexible endplate joint.
Fig. 15. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by flexible endplate joints.
Fig. 16. Comparison of simulation and observed deformation patterns of flush endplate joint.
2345
2346
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Fig. 17. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by flush endplate joints.
Fig. 18. Comparison of simulation and observed deformation patterns of web cleat joint.
Fig. 19. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by web cleat joints.
simulation model because the threads were not modelled. Instead, in the numerical model, the bolt tensile strength was exceeded. In both the numerical model and the test, failure was initiated from to top bolt. Hu et al. [13] tested Grade 8.8 bolts and their results indicate that when bolt thread stripping occurred, the bolt thread stripping strength was only slightly lower than the bolt tensile strength. Therefore, although the predicted bolt tensile failure mode was different from the observed thread stripping model, the tensile force in the bolt may be considered to be correctly predicted by the model. Fig. 16 also shows that the observed very severe distortion of the flush endplate was closely matched by the numerical model. Both the simulation and test results indicate some slight deflection of the column flange, due to larger tensile forces in the beam and the joint, compared to tests 1 and 2. Fig. 17 shows that the predicted beam axial force and beam midspan deflection match the measured results very well. 4.1.4. Test 4: web cleat joint Fig. 18 indicates that the observed deformation patterns of the various joint components were reproduced by the simulation
model. In particular, opening up of the web cleats at the heel, which gives this type of joint very high ductility, was closely followed in the simulation model. There was no failure in the test, which was terminated due to a lack of space for the beam to deflect in the test furnace. Fig. 19 indicates larger discrepancy between the predicted and recorded beam axial force and mid-span deflection characteristics when compared to other tests. This may be attributed to the more severe non-uniform heating encountered in this test. 4.1.5. Test 5: extended endplate joint To avoid thread stripping encountered in the flush endplate joint test (Test 3) and to recognise that the extended endplate connection would generate large forces in the bolts, Grade 10.9 bolts and nuts were used in this test. No failure (fracture) was encountered in either the test or the simulation model. Fig. 20 shows the simulated joint deformation and the observed ‘‘classical’’ ductile behaviour of the thin extended endplate, with very little sign of deformation in the bolts. Due to large compression force in the beam lower flange near the joint,
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2347
Fig. 20. Comparison of simulation and observed joint deformation patterns.
Fig. 21. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by extended endplate joints.
Fig. 22. Comparison of simulation and observed deformation patterns of fin plate joints.
the beam low flange experienced buckling in the test, which was clearly reproduced in the simulation model. Fig. 21 demonstrates very close agreement between simulation and test results for the beam axial force and beam mid-span deflection behaviour. 4.2. Tests with small column size (UC 152 × 152 × 23) 4.2.1. Test 6: fin plate joint Fig. 22 shows very similar simulated and observed deformed shapes of the structure, including local deformation at the column
flange in the joint zone and beam web distortion. Fig. 23 shows that the simulated mid-span deflection followed the test results very well before the large deformation phase but gave a slightly higher beam limiting temperature (defined as the temperature when the beam’s axial force returns to zero). Some weld fracture occurred at the top of the fin plate. Although this could not be simulated because the model did not incorporate a faithful weld model, the very high tensile stresses at the top of the fin plate (Fig. 22) gives clear suggestion of the most likely failure mode of this test.
2348
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Fig. 23. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by fin plate joints.
Fig. 24. Comparison of simulation and observed joint deformation pattern.
4.2.2. Test 7: flexible endplate joint Fig. 24 indicates that the simulation model accurately reproduced the deformation pattern in all parts of the flexible endplate joint specimen. Due to the smaller column size, the catenary force in the beam was low so there was no fracture in either the test specimen or the simulation model. The test was terminated when the beam deflection was too high for the fire test furnace to safely accommodate. Fig. 25 shows that the predicted results slightly overestimate the beam’s limiting temperature for bending. However, this is considered acceptable due to slight uncertainty with the measured temperatures as shown by the jagged curves. 4.2.3. Test 8: flush endplate joint The deformation patterns obtained by simulation and from the test are very close as shown in Fig. 26. Again, no failure was observed in both the test specimen and numerical model. Fig. 27 shows that both the numerical and measured beam axial force and beam mid-span deflection match very well. 4.2.4. Web cleat joint Fig. 28 shows that the simulated deformation patterns agree with the test observation in most cases, including opening up of
the web cleat at the heel, local deformation of the column flange in the joint zone and beam web distortion. However the simulation also indicated buckling in the column flange not attached to the web cleat, which was not observed in the test. This may have been caused by compressive stress on this side of the column when the column was pulled by an axial tensile force in the beam. The predicted beam axial force and mid-span deflection characteristics match the experimental observation very well as shown in Fig. 29. 4.2.5. Extended endplate joint No failure (fracture) was encountered in either the test specimen or the simulation model. However, it appears that due to a combination of catenary action in the beam and high hogging bending moment in the joint, a plastic hinge formed in the column at the joint zone, as shown in Fig. 30. The simulation deformation pattern agrees well with observation on the connection side, including the beam, the end plate and the column flange. On the un-connected side, the column flange experienced some deformation and the simulation result indicates severe distortion. The simulation model also indicates distortion in the column web at the level of the beam lower flange in compression and adjacent to the distorted column flange on the un-connected side. These simulated distortions may be qualitatively explained by the
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2349
Fig. 25. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by flexible endplate joints.
Fig. 26. Comparison of simulation and observed deformation patterns of flush endplate joint.
Fig. 27. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by flush endplate joints.
loading pattern in the column. With the beam in catenary action and the joint under substantial hogging bending moment, the unconnected column flange and the associated column web at the beam top flange level would be under compression, which could induce buckling and distortion. The column web at the beam lower flange level would be subjected to direct compression from the beam lower flange, which again would induce buckling in the column web. Although these were not observed in the test, the observed deformation in the column flange on the un-connected
side suggests that such distortions as indicated in the numerical model must have been imminent in the test specimen. Fig. 31 demonstrates very close agreement between simulation and test results for the beam mid-span deflection and beam axial force behaviour. In summary, the simulation models can be considered to provide faithful representations of the tests in all cases, in terms of deformation patterns of all the structural components, the failure modes, and beam axial force and mid-span deflection results.
2350
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Fig. 28. Comparison of simulation and observed deformation patterns of web cleat joint.
Fig. 29. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by web cleat joints.
Fig. 30. Comparison of simulation and observed joint deformation pattern.
5. Conclusions This paper has presented a simulation methodology, using ABAQUS/Static solver, to model restrained steel frame subassemblies using five different types of beam to column joint. Comparison was made between simulation and test results, for deformation patterns in different parts of the structures, failure modes (wherever available), beam axial forces and mid-span deflections at elevated temperatures. The following conclusions may be drawn:
(1) Because this study involved severe local deformations, detailed element types and fine finite element meshes should be used; (2) All test structures experienced very large global deflections and rapid transition in mode of behaviour (from compression to tension in the beam). Numerical simulation of this phenomenon was challenging and had to deal with the problem of numerical non-convergence. This problem may be solved by introducing pseudo damping in the model. Selection of an appropriate damping factor may be checked by limiting the ratio of the dissipated energy by damping to the total strain
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2351
Fig. 31. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by extended endplate joints.
energy to about 10% and by comparing the applied loads with the support reaction forces; (3) By using the recommended modelling methodology, the ABAQUS/Static solver has been demonstrated to be able to accurately reproduce the experimental results; (4) The failure modes of weld fracture and bolt thread stripping could not be simulated because they were not included in the ABAQUS models. However, in each case, there was an alternative failure mode (fin plate failure under shear and tension for weld fracture, bolt tensile failure for bolt thread stripping) with similar strength, the simulation and experimental results were still very close. Nevertheless, weld fracture and thread stripping may have to be included in numerical modelling to ensure complete faithful prediction of structural behaviour. Acknowledgements This research reported in this paper was funded by a research grant from the UK’s Engineering and Physical Science Research Council (EP/C003004/1). References [1] Wang YC. Steel and composite structures, behaviour and design for fire safety. London: Spon Press; 2002. [2] Federal Emergency Management Authority (FEMA 2002), World trade center building performance study. FEMA, USA. [3] National Institute of Standards and Technology (NIST 2008), Federal building and fire safety investigation of the world trade center disaster: structural response and probable collapse sequence of world trade center building 7, Volume 2, National Institute of Standards and Technology Report NIST NCSTAR 1-9. 2008. [4] Yin YZ, Wang YC. A numerical study of large deflection behaviour of restrained steel beams at elevated temperatures. J Construct Steel Res 2004;60:1029–47. [5] Yin YZ, Wang YC. Analysis of catenary action in steel beams using a simplified hand calculation method, Part 1: theory and validation for uniform temperature distribution. J Construct Steel Res 2005;61:183–211. [6] Yin YZ, Wang YC. Analysis of catenary action in steel beams using a simplified hand calculation method, Part 2: validation for non-uniform temperature distribution. J Construct Steel Res 2005;61:213–34. [7] Dai XH, Wang YC, Bailey CG. An experimental study of structural behaviour of joints in restrained steel frames in fires. In: International conference, Application of structural fire design. 2009. [8] Dai XH, Wang YC, Bailey CG. An experimental study of structural behaviour of joints in restrained steel frames in fires, Applications of Structural Fire Engineering. In: Wald F, Kallerova P, Chlouba J, editors. Proceedings of International Conference. Prague; 2009. p. 350–5. [9] Dai XH, Wang YC, Bailey CG. Temperature distribution in unprotected steel connections in fire. In: Wang, Choi, editors. Proceedings of the 3rd international conference on steel and composite structures. Taylor & Francis Group; 2007.
[10] Dai XH, Wang YC, Bailey CG. Temperature developments in partially protected steel–concrete composite joints using intumescent coating. In: Proceedings of the fifth international conference. 2008. [11] Dai XH, Wang YC, Bailey CG. Effects of partial fire protection on temperature developments in steel joints protected by intumescent coating. Fire Saf J 2009; 44:376–86. [12] Dai XH, Wang YC, Bailey CG. A simple method to predict temperatures in steel joints with partial intumescent coating fire protection. Fire Technol 2010;46: 19–35. [13] Hu Y, Davison JB, Burgess IW, Plank RJ. Comparative study of the behaviour of BS 4190 and BS EN ISO 4014 bolts in fire. In: Wang, Choi, editors. Proceedings of the 3rd international conference on steel and composite structures. Taylor & Francis Group; 2007. [14] Yu HX, Burgess IW, Davison JB, Plank RJ. Experimental investigation of the behaviour of fin plate connections in fire. In: Wang, Choi, editors. Proceedings of the 3rd international conference on steel and composite structures. Taylor & Francis Group; 2007. [15] Yu HX, Burgess IW, Davison JB, Plank RJ. Experimental investigation of the behaviour of flush endplate connections in fire. In: Proceedings of the fifth international conference (SiF’08). 2008. [16] Yu HX, Burgess IW, Davison JB, Plank RJ. Experimental investigation of the tying capacity of web cleat connections in fire. In: The 5th European conference on steel structures. 2008. [17] Hu Y, Davison JB, Burgess IW, Plank RJ. Experimental study on flexible end plate connections in fire. In: The 5th European conference on steel structures. 2008. [18] Yu HX, Burgess IW, Davison JB, Plank RJ. Tying capacity of web cleat connections in fire, Part 1: test and finite element simulation. Eng Struct 2009; 31:651–63. [19] Yu HX, Burgess IW, Davison JB, Plank RJ. Tying capacity of web cleat connections in fire, Part 2: Development of component-based model. Eng Struct 2009;31:697–708. [20] Yu HX, Burgess IW, Davison JB, Plank RJ. Experimental investigation of the behaviour of fin plate connections in fire. J Construct Steel Res 2009;65: 723–36. [21] Hu Y, Burgess IW, Davison JB, Plank RJ. Modelling of flexible end plate connections in fire using cohesive elements. In: Proceedings of the fifth international conference. 2008. [22] International Organization for Standardization (ISO 834 1975). Fire resistance tests, elements of building construction. Geneva: International Organization for Standardization. [23] Bursi OS, Jaspart JP. Benchmarks for finite element modelling of bolted steel connections. J Construct Steel Res 1997;43:17–42. [24] Swanson JA, Kokan DS, Leon RT. Advanced finite element modelling of bolted T-stub connection components. J Construct Steel Res 2002;58:1015–31. [25] Maggi YI, Goncalves RM, Leon RT, Ribeiro LF. Parametric analysis of steel bolted endplate connections using finite modeling. J Construct Steel Res 2005;61: 689–708. [26] Al-Jabri KS, Burgess IW, Plank RJ. Spring-stiffness model for flexible end-plate bare beam joints in fire. J Construct Steel Res 2005;61:1672–91. [27] Al-Jabri KS, Seibi A, Karrech A. Modelling of sustiffened flush endplate bolted connections in fire. J Construct Steel Res 2006;62:151–9. [28] Sarraj M, Burgess IW, Davison JB, Plank RJ. Finite element modelling of fin plate steel connections in fire. J Fire Safety 2007;42:408–15. [29] Yu HX, Burgess IW, Davison JB, Plank RJ. Numerical simulation of bolted steel connections in fire using explicit dynamic analysis. J Construct Steel Res 2008; 64:515–25. [30] Shirh A, Adeeb R, Al-Jabri KS. Finite element analysis of flush end-plate bare steel connection at elevated temperature. Adv Struct Eng 2009;12(3):311–24. [31] ENV 1993-1-2, Eurocode 3: Design of steel structures, part 1.2: general rules— structural fire design. London: British Standards Institution; 2005.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Numerical modelling of structural fire behaviour of restrained steel beam–column assemblies using typical joint types X.H. Dai, Y.C. Wang ∗ , C.G. Bailey School of Mechanical, Aerospace and Civil Engineering, University of Manchester, United Kingdom
article
info
Article history: Received 15 October 2009 Received in revised form 22 February 2010 Accepted 1 April 2010 Available online 15 May 2010 Keywords: Structural fire behaviour Numerical modelling Restrained steel frames Joints Robustness Catenary action
abstract This paper presents the results of a simulation study of 10 fire tests on restrained steel beam–column assemblies using five different types of joints: fin plate, flexible endplate, flush endplate, web cleat and extended endplate. This paper will provide details of the simulation methodology for achieving numerical stability and faithful representation of detailed structural behaviour, and compare the simulation and experimental results, including joint failure modes, measured beam axial forces and beam mid-span deflections. Good agreement between ABAQUS simulations and experimental observations confirms that the finite element models developed through the ABAQUS/Standard solver are suitable for predicting the structural fire behaviour of restrained structural assemblies with realistic steel joints undergoing different phases of behaviour in fire, including restrained thermal expansion and catenary action in the beams. The validated model may be used to conduct numerical parametric studies to generate theoretical data to help develop detailed understanding of steel joint behaviour and their effects on robustness of steel framed structures in fire. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The high profile Cardington structural fire research programme [1] and World Trade Center collapse [2,3] have firmly established steel joint behaviour in fire as the most important aspect of understanding the behaviour and robustness of steel structures in fire. Joints play a critical role in steel framed structure in controlling fire induced progressive structural collapse. When designing and analysing a steel framed structure at ambient temperature, the joints between beams and columns are commonly classified as either simple joints or moment resisting joints, based on their predominant bending moment capacity. Under the fire condition, the behaviour of the joint can be totally different owing to the presence of axial restraint offered to the connected beam by the surrounding structure. The qualitative behaviour of an axially restrained beam in fire is now well established [1]: (i) at low temperatures, the beam’s lateral deflection is small and its thermal expansion is high, therefore compressive axial forces are generated in the beam; (ii) as the beam’s temperature increases, the steel’s mechanical properties degrade and the beam’s lateral deflections increase, reducing the amount of axial extension of the beam. Combined with the reduced axial stiffness of the beam due to degrading mechanical properties, the beam’s axial compression
∗
Corresponding author. E-mail address: [email protected] (Y.C. Wang).
0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.04.009
decreases; (iii) when the beam’s bending moment capacity has reduced to the applied bending moment in the beam, the beam will undergo accelerated lateral deflections, which will induce sufficient shortening to cancel the beam’s thermal expansion. At this stage, the beam’s axial force returns to zero; the temperature at which the beam’s axial force is zero is very close to the limiting temperature of the beam without axial restraint, as confirmed by the results of a theoretical study by Yin and Wang [4–6]; (iv) after the beam’s axial compressive force has returned to zero, the beam will enter the catenary stage; if the joints have sufficient axial strength and ductility, the beam will be able to survive very high temperatures without failure. On the other hand, if the additional axial forces in the joint are not designed for or the joint does not have sufficient ductility to allow the beam to experience very large deflections, the joints may fracture due to either compression or tension, which may lead to progressive structural collapse. Failure of the seated bearing connections to columns 79–81 of the World Trade Center building 7 has been attributed to having initiated the progressive collapse of the building [3]. To improve understanding of the effects of joints on steel framed structural behaviour in fire and to help design better steel joints to mitigate against fire induced structural collapse, an experimental research project has recently been completed at the University of Manchester, in which fire tests were carried out to investigate interaction between joints and connected beams and columns in a H-shaped structural assembly. Details of this experimental programme and its principal findings are presented elsewhere [7,8]. In this research, fire tests and analyses were also
2338
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
performed to determine temperatures in different components of steel and composite joints with various fire protection schemes [9–12]. This research was carried out in collaboration with the University of Sheffield, which performed elevated temperature experiments and numerical analyses to investigate bolt behaviour [13], elevated temperature behaviour of isolated joint assemblies [14–17] and to develop component based method to characterise joint behaviour under different combinations of axial load, bending moment and shear [18–21]. The Manchester fire tests on structural assemblies provide experimental data to calibrate numerical simulation models, which will then be used to perform parametric studies to help develop detailed understanding of joint behaviour as well as to develop more effective joint details to reduce the risk of fire induced progressive collapse. These tests have been modelled by the authors using the general finite element package ABAQUS/standard solver. It has been a tremendous challenge to faithfully model detailed behaviour of restrained steel framed structural subassemblies with realistic joint details undergoing very large deflections and different modes of buckling and failure in fire. The main objective of this paper is to explain key aspects of the modelling technique to help future researchers to develop robust numerical simulation models for this type of structures. Validation of the numerical models is assessed through comparison of the simulation results with the ten fire tests on restrained steel structural assemblies carried out by the University of Manchester. 2. A brief summary of the structural assembly fire tests Details of the experimental set up and results have been presented elsewhere by the authors [8,7]. This section will only provide a brief description of the fire tests and the main experimental observations. 2.1. Structural fire tests As shown in Fig. 1, each specimen, in the form of ‘‘rugbygoalpost’’, consisted of one beam, two identical columns and two identical joints. The 4 ends of the two columns were restrained horizontally. In total, 10 fire tests were performed, covering 5 joint types (fin plate, flexible endplate, web cleat, flush endplate and extended endplate) and two column section sizes to simulate two different levels of axial restraint to the beam. Table 1 summarises the main member dimensions of the ten tests. The whole beam, the two joints and the central part of the two columns were exposed in fire inside the furnace. During the fire tests, the furnace temperatures were recorded by six thermocouples whose average temperature was intended to follow the standard fire condition in [22]. The beam was loaded by two point loads with a target value of 40 kN. The horizontal reaction forces at the column ends were measured by pin load cells installed at the column ends. 2.2. Main experimental conclusions The main experimental observations are as follows:
• Joint failure modes included weld tearing (fin plate, flexible endplate), beam web fracture (flexible endplate) and bolt thread stripping (flush endplate and some web cleat). However, there was no beam failure despite very large deflections (span/8–span/6). There was no structural failure during the beam-in-compression phase. Here failure is defined as complete collapse of the structure.
• Using different joint types had very little effect on the beam’s axial force development. In contrast, the beam axial force was heavily influenced by the different column sizes. This can be attributed to the very short length of the joint region and strongly suggests that the joints may be considered to have infinite axial rigidity so that the axial restraint is principally dependent on that of the connected columns. • The different types of joints possessed different levels of rotational capacity. The web cleat connections, through significant bending deformation of the heel, developed very high rotations. The extended end plate connections also developed a very ductile mode of behaviour through bending of the thin endplate. 3. Methodology of ABAQUS modelling The use of numerical modelling to analyse steel joint behaviour, either at ambient temperature or in fire, has had a long history of development. Bursi and Jaspart [23] built a simple model to simulate bolted connections at ambient temperature using the commercial program ABAQUS. In their ‘‘spin’’ model, an assembly of beam elements was adopted to represent a bolt. Swanson et al. [24] modelled bolted T-stub joints using ABAQUS, in which contact interactions between bolts and base materials and between connection plates were considered. Maggi et al. [25] investigated the structural behaviour of bolted endplate connections using ANSYS. AlJabri et al. [26,27] simulated the moment–rotationtemperature relationships of a series of fire tests on flexible and flush endplate connections using ABAQUS. In their models, surface to surface contact was used. Sarraj et al. [28] modelled fin plate connections in fire using ABAQUS, in which surface to surface contact with a small sliding option was used. Yu et al. [29] commented on the problem of simulating bolted joints due to numerous contact problems and developed a numerical simulation procedure using the ABAQUS/Explicit solver to model bolted joints at both ambient and elevated temperatures. By controlling the time step, it was shown to be possible to produce quasi-static responses. Shirh et al. [30] developed a 3D model using ANSYS to study the behaviour of flush end plate connection between beams and columns at elevated temperatures. A common feature of all the existing numerical simulations of joint behaviour is that the structural system was statically determinate. In particular, most of the investigations have focused on producing joint moment–rotation characteristics. In such a structural system, the appearance of large deformations in any part of the structure would signal failure of the system. Therefore, the existing researches only focused on simulating joint response before very large deformations and gross inaccuracy in predicting large joint displacements were overlooked. In contrast, in the fire tests conducted by the authors, the appearance of very large deformations merely means that the structure was going through a different phase of behaviour, the axial force in the beam changing from compression to tension. In order for the subsequent phase of structural behaviour (catenary action) to be accurately simulated, it is important to develop a robust numerical model to satisfactorily capture this stage of the structural behaviour. In this research, the authors used both ABAQUS/Static analysis and ABAQUS/Explicit analysis and finally decided to use the ABAQUS/Static solver due to the huge requirement on computational resources (both time and storage) and unstable structural behaviour when using the ABAQUS/Explicit solver. As shown in Fig. 1, the tested structure was symmetrical in geometry, loading arrangement and boundary conditions. However, during testing, some unsymmetrical heating was encountered due to unsymmetrical layout of the burners in the fire test furnace. Therefore, the observed structural behaviour was not exactly symmetrical. Nevertheless, it was considered
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2339
Fig. 1. Elevation view of the test set up. Table 1 Summary of specimen dimensions. Test ID
Joint type
Connection component dimension (mm)
Test-1 Test-2 Test-3 Test-4 Test-5 Test-6 Test-7 Test-8 Test-9 Test-10
Fin plate Flexible endplate Flush endplate Web cleat Extended endplate Fin plate Flexible endplate Flush endplate Web cleat Extended endplate
150 × 130 × 10 150 × 130 × 8 150 × 200 × 8 90 × 150 × 10 (depth: 130) 150 × 250 × 8 150 × 130 × 10 150 × 130 × 8 150 × 200 × 8 90 × 150 × 10 (depth: 130) 150 × 250 × 8
that the slight non-symmetrical heating had only minor effect on the behaviour of the restrained beam, which would be primarily dependent on the heating condition in the central region of the beam. As far as the joints were concerned, non-uniform heating would result in one joint being damaged more than the other. Since the main purpose of this simulation was to establish an appropriate simulation methodology, it was accepted that as long as the more severely damaged joint behaviour could be captured, the simulation results would be valid. Simulating detailed structural behaviour of the tested structural assembly was time consuming. Therefore, to save computational time, it was decided to include only half of the test assembly in the finite element model, of which Fig. 2 shows a typical one. Three-dimensional solid elements (C3D8) were used in modelling the main structural members as shown in Fig. 2. A series of ABAQUS models with different meshes were run to assess the sensitivity of simulation results to the FE mesh. The results of this sensitivity study suggested that the appropriate mesh size would be 10–20 mm for the main structural members such as the beam, the joint components and the column. Too small element size would consume too much computation time, while too coarse mesh (Fig. 3(b)) would cause numerical convergence problem and would not be able to reveal some important member buckling characteristics such as shown in Fig. 3(a). Also, in order to avoid premature beam web buckling, at least two layers of elements in the thickness direction of the beam web should be used. Furthermore, to reduce the number of elements and nodes in the FE model, the column was divided into three parts and only the central part
Column section
Beam section
UC 254 × 254 × 73 UB 178 × 102 × 19 UC152 × 152 × 23
Fig. 2. Typical FE model adopted in numerical modelling.
(400 mm for models with large columns and 800 mm for models with small columns) connected by the joint and exposed in fire in the furnace was actually modelled using the solid elements. The other two parts away from the joint zone was modelled using general beam elements with ‘‘I’’ cross section. The ABAQUS ‘‘Coupling’’ function was used to join the three column parts as shown in Fig. 4(a). Fig. 4(b) shows the actual configuration simulated using ABAQUS. In the test structures, many contact pairs exist in the joints, such as end plate to column, fin plate to beam web, bolt shanks and nuts to the connected members. The ABAQUS contact function was used to simulate the interaction between the contact pairs. A contact was defined as surface to surface contact with a small
2340
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
(a) Suitable beam mesh.
(b) Coarse beam mesh. Fig. 3. Effect of element sizes on structural deformation.
(a) User built model.
(b) ABAQUS abstracted model. Fig. 4. Column simulation method.
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2341
Fig. 5. Bolt model.
sliding option. ‘‘Hard contact’’ was assumed for the normal contact behaviour and a friction coefficient of 0.3 was used in the tangential direction of the contact pairs. The results of a sensitivity study confirmed that using a wide range of friction coefficient values had little effect on the simulation results. In the tests, ordinary Grade 8.8 M20 bolts were used and they were installed manually using spanners. Fig. 5 shows how the bolts were simulated. The bolt thread was not modelled because its modelling would be extremely time consuming. Except for the thread stripping failure mode, this simplification was considered acceptable because all other modes of failure were accurately simulated. All the contacts between the bolt shank and the edges of the holes in the connected members, between the bolt head (nut) and the connected plate (column flange, end plate) surfaces were simulated using the aforementioned contact pair method. To avoid numerical difficulty at the start of the simulation, the gap between the bolt shank and bolt hole was set at 0.1 mm and the gap between bolt head (nut) and connected plate was 0.001 mm. Due to the difficulty in measuring the real bolt initial stress, no pre-stress was applied to the bolts. The stress–strain constitutive relationships adopted in the FE models for the steel beams, columns and connection components were based on the steel tensile coupon tests at ambient temperature. Table 2 shows the average yield strength, ultimate tensile strength and elastic modulus of the joint assembly members. For ABAQUS simulation, the nominal engineering stress–strain model obtained from steel tensile coupon test was converted to the true stress–strain relationship according to: σtru = σnom (1 + εnom ) and εtru = ln(1 + εnom ), in which σtru and εtru represent the true stress and strain; and σnom and εnom are the nominal stress and strain respectively. Since no mechanical test was performed on the bolts and nuts, their mechanical properties were assumed to be elastic-perfectly-plastic. For Grade 8.8 bolts, the nominal yield strength and elastic modulus were assumed to be 640 MPa and 210 000 MPa respectively. The EC3 (EN 1993-1-2) [31] reduction factors, shown in Fig. 6, for carbon steel at elevated temperatures were used. Weld was not directly modelled. Instead, the welded elements were tied together using the ABAQUS ‘‘tie’’ function. The boundary conditions of the FE model were according to those in the test. The bottom of the columns was pinned in all three directions and the top of the columns was pinned in two directions but movement along the column axis was allowed. Since only half of the beam was included in the FE model as discussed earlier, the beam mid-section was fixed in the axial direction, which effectively prevented rotation about any axis in the beam cross section, but allowed the beam to twist about its longitudinal axis. The beam top flange was prevented from lateral movement to simulate the effect of the lateral restraining effect of the truss connected to the beam upper flange. However, for simplicity in modelling, the lateral restraining truss was replaced by 2 plates of 750 mm long and 50 × 8 mm in cross section as shown in Fig. 7. The truss replacement plate dimensions were determined
Fig. 6. Reduction factors for strength and elastic modulus of carbon steel at elevated temperatures (EN 1993-1-2).
by ensuring that the plates contributed the same as the lateral restraining truss to the bending capacity of the beam. Nevertheless, since this contribution was low, the beam’s behaviour would only be slightly influenced by the plate dimensions. As in the tests, the FE model applied the loads in two steps: (i) two point loads of 40 kN each to the beam at ambient temperature; (ii) increasing the structural temperatures while maintaining the structural loads. In the FE model, five different temperature–time curves based on the test measurements were adopted for different parts of the structure: temperature curves for the beam bottom flange, web and top flange; one temperature curve for the joint zone which included all the bolts, nuts and connection components (such as endplate, fin plate and web cleats) as well as 100 mm length of the beam in the joint zone; one temperature curve for the column segment (400 mm of the large column, 800 mm of the small column) in the joint region. The temperature of the column away from the joint zone was set at ambient temperature. Since the main objective of the fire tests was to investigate complete failure of the structures at elevated temperatures, the test specimens underwent a variety of temporary instabilities due to localised buckling and very large deformations. Any of these temporary instabilities could cause the numerical model to terminate and the numerical model would not be able to go through all the phases of structural behaviour as in the tests. To ensure that the numerical model was able to go through all the phases of structural behaviour experienced in the tests, an artificial viscous damping was applied to the numerical model. This artificial damping became active and dissipated the energy released during temporary instability of the structure so as to allow the numerical model to bypass the temporary numerical instability problem. After the numerical model bypassed temporary numerical instability and if the structure was still stable, the artificial damping became inactive. On the other hand, if the artificial damping was still active for a long period of time, then the numerical instability signified that the structure was approaching complete failure and was unable to sustain the applied load.
2342
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Table 2 Summary of key mechanical property values for different steel members. Component
Beam
Column
End plate
Fin plate
Web cleat
Elastic modulus (MPa) Yield strength (MPa) Maximum strength (MPa) Ultimate strain (%)
226 580 344 514 28.2
200 000 390 553 25
191 670 303 460 30.5
188 330 235 380 30.6
228 170 342 493 32.6
Fig. 7. Simulation of horizontal restraining truss.
(a) Dissipated energy fraction = 0.00001.
(b) Dissipated energy fraction = 0.0001.
Fig. 8. Effect of dissipated energy fraction on structural deformation.
In ABAQUS, the artificial viscous damping is specified using the ‘‘dissipated energy fraction’’. Determining an appropriate damping factor value was important to ensure that the numerical simulation model was robust when encountering temporary instability but that it did not give spurious results. Fig. 8 shows an example of the effects of using different damping factors on the simulated deformed shapes of the same structure. When a value of 0.00001 was used, the observed web buckling mode was correctly simulated. But when a value of 0.0001 was used, this mode of deformation was damped out. In general, the appropriate damping factor will be structure specific, which makes it difficult for the authors to provide detailed rules to help determine a suitable damping factor. According to the authors’ experiences, two quantities outputted from the simulation model may be checked to assess whether the damping factor used is appropriate. One quantity is the ratio of the dissipated energy by damping (parameter ALLSD in ABAQUS) to the total strain energy (parameter ALLIE in ABAQUS). Theoretically, this ratio should be less than the specified dissipated energy fraction. However, in the authors’ simulations, because the structure underwent very large deformations, the viscous damping dissipated energy was often higher than the specified dissipated energy fraction. However, as long as this ratio did not
exceed 0.1, the FE model results were in good agreement with the experimental results. For example, Fig. 9 compares the ALLSD and ALLIE quantities for the same structure using dissipated energy fractions of 0.00001 and 0.0001 respectively. It can be seen that before the structure collapsed, the ALLSD plot was stable and small and the ratio of ALLSD to ALLIE was less than 0.05 when a dissipated energy fraction of 0.00001 was adopted. In contrast, when using a dissipated energy fraction of 0.0001, the ratio of ALLSD to ALLIE was quite high for a significant period of time of the simulation time. In both cases, the ratio of ALLSD to ALLIE was large at the start of the fire simulation. This was a result of the total strain energy (ALLIE) being small when the structure deformation was very small. Another quantity that can be checked is the support reactions, i.e. they should be in static equilibrium with the applied loads. If the dissipated energy fraction is too high, too much of the applied loads may be resisted by viscous damping. For example, Fig. 10 compares the applied load (40 kN) with the vertical reaction force for using the aforementioned two different dissipated energy fractions. Clearly, using a fraction of 0.0001 was not appropriate because viscous damping contributed to supporting a large part of the applied load for a long period of time. The authors suggest that if the support reaction forces return to the level of the applied loads
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
(a) Dissipated energy fraction = 0.00001.
2343
(b) Dissipated energy fraction = 0.0001.
(c) Ratio of ALLSD to ALLIE. Fig. 9. Energy dissipation from different damping factors.
Fig. 10. Reaction forces at column ends.
after temporarily decreasing (due to damping), then the structural is stable and the damping factor is appropriate. However, if the support reaction forces decrease but do not return to the level of the applied loads after a long period of simulation time, then the damping factor is not appropriate (too high) and the simulation results are not correct. It must be pointed out that, according to the authors’ experiences, numerical instability may also be caused by low quality of the FE model such as coarse mesh and large gaps between contact pairs. Therefore, before using a high value of dissipated energy fraction to suppress the numerical instability, checks should be made to ensure that the FE simulation results are not sensitive to such factors. In the numerical model, the column ends were assumed to be able to rotate freely in the plane of the structure. However, as indicated in Fig. 1, the column flange at the ends was linked to the load cell at two locations using bolts. This arrangement may induce some rotational restraint at the column ends. In the first series of tests using the large column size, the column rigidity is
very high so this rotational restraint would not have any significant effect on the beam and joint behaviour, as evidenced by almost non discernible column deformation in tests 1–5. However, when the small column was used, the column rigidity may not be sufficiently high (evidenced by the large column local and global deformations in tests 6–10, see later) so that the effect of this additional restraint at the column ends should be assessed to ensure that the boundary conditions in the numerical simulation model was correct. An additional model of the structure for test 10 was created assuming complete rotational fixity at the column ends. Fig. 11 compares the simulation results for the models with pin and rigid column ends. With complete fixity at the column ends, the axial force in the beam, both in compression and in tension, is much greater than the measured results. In contrast, assuming pinned column ends produced results much closer to the test results. It can therefore be accepted that the actual column ends would be much closer to pin support than fixed end support, as assumed in all the numerical simulation models. 4. Comparison between FE model and test results All ten tests have been analysed using the ABAQUS modelling techniques described in the last section. This section presents comparisons between the simulation and test results to comprehensively validate the numerical modelling method. 4.1. Tests with large column size (UC 254 × 254 × 73) 4.1.1. Test 1: fin plate joint Fig. 12 shows that the observed deformations of the joint components and beam were followed by the numerical model. Fig. 13 confirms that the simulation results accurately captured
2344
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Fig. 11. Comparison of beam mid-span deflection and axial force in frames with different column end restraints.
Fig. 12. Comparison of simulation and observed deformation patterns of fin plate joints.
Fig. 13. Comparison of modelling and experimental results for mid-span deflection and axial force in the beam restrained by fin plate joints.
the transition process from compression to tension in the beam. In the test, the lower flange of the beam began to bear against the flange of the column towards the end of the test. However, the bearing force would not have been high, otherwise there would have been indication on the column flange from the beam’s lower flange. The numerical model produced lower beam deflections so this bearing action was not observed in the numerical model. However, Fig. 12 indicates that in the numerical model, the beam lower flange was very close to the column flange. Because of the large column size and column flange thickness, both the test and the numerical model show no sign of column deformation. The test specimen failed by fracture of the weld at the top. Since weld was not directly modelled, this failure mode could not be simulated. Instead, the numerical model failure was in the fin plate close to the weld under tension and shearing.
4.1.2. Test 2: flexible endplate joint Fig. 14 shows that Test 2 failed due to fracture of the beam web. This was predicted by the numerical model, as shown by the tensile and shear stress patterns in Fig. 14. The simulated flexible endplate deformation pattern is also very similar to the test observation. Fig. 15 compares the simulated and measured beam axial force and mid-span deflection. The agreement is satisfactory overall, with the simulation results slightly overestimating the transition temperature from compression to tension in the beam. However, the rapid deformation process was closely followed by the simulation model. 4.1.3. Test 3: flush endplate joint This test failed due to thread stripping of the bolts in tension, as shown in Fig. 16. This failure mode could not be reproduced by the
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
(a) Test observation.
(b) Model Mises stress.
(c) Model shear stress in web plane. Fig. 14. Comparison of simulation and observed deformation patterns of flexible endplate joint.
Fig. 15. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by flexible endplate joints.
Fig. 16. Comparison of simulation and observed deformation patterns of flush endplate joint.
2345
2346
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Fig. 17. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by flush endplate joints.
Fig. 18. Comparison of simulation and observed deformation patterns of web cleat joint.
Fig. 19. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by web cleat joints.
simulation model because the threads were not modelled. Instead, in the numerical model, the bolt tensile strength was exceeded. In both the numerical model and the test, failure was initiated from to top bolt. Hu et al. [13] tested Grade 8.8 bolts and their results indicate that when bolt thread stripping occurred, the bolt thread stripping strength was only slightly lower than the bolt tensile strength. Therefore, although the predicted bolt tensile failure mode was different from the observed thread stripping model, the tensile force in the bolt may be considered to be correctly predicted by the model. Fig. 16 also shows that the observed very severe distortion of the flush endplate was closely matched by the numerical model. Both the simulation and test results indicate some slight deflection of the column flange, due to larger tensile forces in the beam and the joint, compared to tests 1 and 2. Fig. 17 shows that the predicted beam axial force and beam midspan deflection match the measured results very well. 4.1.4. Test 4: web cleat joint Fig. 18 indicates that the observed deformation patterns of the various joint components were reproduced by the simulation
model. In particular, opening up of the web cleats at the heel, which gives this type of joint very high ductility, was closely followed in the simulation model. There was no failure in the test, which was terminated due to a lack of space for the beam to deflect in the test furnace. Fig. 19 indicates larger discrepancy between the predicted and recorded beam axial force and mid-span deflection characteristics when compared to other tests. This may be attributed to the more severe non-uniform heating encountered in this test. 4.1.5. Test 5: extended endplate joint To avoid thread stripping encountered in the flush endplate joint test (Test 3) and to recognise that the extended endplate connection would generate large forces in the bolts, Grade 10.9 bolts and nuts were used in this test. No failure (fracture) was encountered in either the test or the simulation model. Fig. 20 shows the simulated joint deformation and the observed ‘‘classical’’ ductile behaviour of the thin extended endplate, with very little sign of deformation in the bolts. Due to large compression force in the beam lower flange near the joint,
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2347
Fig. 20. Comparison of simulation and observed joint deformation patterns.
Fig. 21. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by extended endplate joints.
Fig. 22. Comparison of simulation and observed deformation patterns of fin plate joints.
the beam low flange experienced buckling in the test, which was clearly reproduced in the simulation model. Fig. 21 demonstrates very close agreement between simulation and test results for the beam axial force and beam mid-span deflection behaviour. 4.2. Tests with small column size (UC 152 × 152 × 23) 4.2.1. Test 6: fin plate joint Fig. 22 shows very similar simulated and observed deformed shapes of the structure, including local deformation at the column
flange in the joint zone and beam web distortion. Fig. 23 shows that the simulated mid-span deflection followed the test results very well before the large deformation phase but gave a slightly higher beam limiting temperature (defined as the temperature when the beam’s axial force returns to zero). Some weld fracture occurred at the top of the fin plate. Although this could not be simulated because the model did not incorporate a faithful weld model, the very high tensile stresses at the top of the fin plate (Fig. 22) gives clear suggestion of the most likely failure mode of this test.
2348
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Fig. 23. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by fin plate joints.
Fig. 24. Comparison of simulation and observed joint deformation pattern.
4.2.2. Test 7: flexible endplate joint Fig. 24 indicates that the simulation model accurately reproduced the deformation pattern in all parts of the flexible endplate joint specimen. Due to the smaller column size, the catenary force in the beam was low so there was no fracture in either the test specimen or the simulation model. The test was terminated when the beam deflection was too high for the fire test furnace to safely accommodate. Fig. 25 shows that the predicted results slightly overestimate the beam’s limiting temperature for bending. However, this is considered acceptable due to slight uncertainty with the measured temperatures as shown by the jagged curves. 4.2.3. Test 8: flush endplate joint The deformation patterns obtained by simulation and from the test are very close as shown in Fig. 26. Again, no failure was observed in both the test specimen and numerical model. Fig. 27 shows that both the numerical and measured beam axial force and beam mid-span deflection match very well. 4.2.4. Web cleat joint Fig. 28 shows that the simulated deformation patterns agree with the test observation in most cases, including opening up of
the web cleat at the heel, local deformation of the column flange in the joint zone and beam web distortion. However the simulation also indicated buckling in the column flange not attached to the web cleat, which was not observed in the test. This may have been caused by compressive stress on this side of the column when the column was pulled by an axial tensile force in the beam. The predicted beam axial force and mid-span deflection characteristics match the experimental observation very well as shown in Fig. 29. 4.2.5. Extended endplate joint No failure (fracture) was encountered in either the test specimen or the simulation model. However, it appears that due to a combination of catenary action in the beam and high hogging bending moment in the joint, a plastic hinge formed in the column at the joint zone, as shown in Fig. 30. The simulation deformation pattern agrees well with observation on the connection side, including the beam, the end plate and the column flange. On the un-connected side, the column flange experienced some deformation and the simulation result indicates severe distortion. The simulation model also indicates distortion in the column web at the level of the beam lower flange in compression and adjacent to the distorted column flange on the un-connected side. These simulated distortions may be qualitatively explained by the
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2349
Fig. 25. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by flexible endplate joints.
Fig. 26. Comparison of simulation and observed deformation patterns of flush endplate joint.
Fig. 27. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by flush endplate joints.
loading pattern in the column. With the beam in catenary action and the joint under substantial hogging bending moment, the unconnected column flange and the associated column web at the beam top flange level would be under compression, which could induce buckling and distortion. The column web at the beam lower flange level would be subjected to direct compression from the beam lower flange, which again would induce buckling in the column web. Although these were not observed in the test, the observed deformation in the column flange on the un-connected
side suggests that such distortions as indicated in the numerical model must have been imminent in the test specimen. Fig. 31 demonstrates very close agreement between simulation and test results for the beam mid-span deflection and beam axial force behaviour. In summary, the simulation models can be considered to provide faithful representations of the tests in all cases, in terms of deformation patterns of all the structural components, the failure modes, and beam axial force and mid-span deflection results.
2350
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
Fig. 28. Comparison of simulation and observed deformation patterns of web cleat joint.
Fig. 29. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by web cleat joints.
Fig. 30. Comparison of simulation and observed joint deformation pattern.
5. Conclusions This paper has presented a simulation methodology, using ABAQUS/Static solver, to model restrained steel frame subassemblies using five different types of beam to column joint. Comparison was made between simulation and test results, for deformation patterns in different parts of the structures, failure modes (wherever available), beam axial forces and mid-span deflections at elevated temperatures. The following conclusions may be drawn:
(1) Because this study involved severe local deformations, detailed element types and fine finite element meshes should be used; (2) All test structures experienced very large global deflections and rapid transition in mode of behaviour (from compression to tension in the beam). Numerical simulation of this phenomenon was challenging and had to deal with the problem of numerical non-convergence. This problem may be solved by introducing pseudo damping in the model. Selection of an appropriate damping factor may be checked by limiting the ratio of the dissipated energy by damping to the total strain
X.H. Dai et al. / Engineering Structures 32 (2010) 2337–2351
2351
Fig. 31. Comparison of simulation and experimental results for mid-span deflection and axial force in the beam restrained by extended endplate joints.
energy to about 10% and by comparing the applied loads with the support reaction forces; (3) By using the recommended modelling methodology, the ABAQUS/Static solver has been demonstrated to be able to accurately reproduce the experimental results; (4) The failure modes of weld fracture and bolt thread stripping could not be simulated because they were not included in the ABAQUS models. However, in each case, there was an alternative failure mode (fin plate failure under shear and tension for weld fracture, bolt tensile failure for bolt thread stripping) with similar strength, the simulation and experimental results were still very close. Nevertheless, weld fracture and thread stripping may have to be included in numerical modelling to ensure complete faithful prediction of structural behaviour. Acknowledgements This research reported in this paper was funded by a research grant from the UK’s Engineering and Physical Science Research Council (EP/C003004/1). References [1] Wang YC. Steel and composite structures, behaviour and design for fire safety. London: Spon Press; 2002. [2] Federal Emergency Management Authority (FEMA 2002), World trade center building performance study. FEMA, USA. [3] National Institute of Standards and Technology (NIST 2008), Federal building and fire safety investigation of the world trade center disaster: structural response and probable collapse sequence of world trade center building 7, Volume 2, National Institute of Standards and Technology Report NIST NCSTAR 1-9. 2008. [4] Yin YZ, Wang YC. A numerical study of large deflection behaviour of restrained steel beams at elevated temperatures. J Construct Steel Res 2004;60:1029–47. [5] Yin YZ, Wang YC. Analysis of catenary action in steel beams using a simplified hand calculation method, Part 1: theory and validation for uniform temperature distribution. J Construct Steel Res 2005;61:183–211. [6] Yin YZ, Wang YC. Analysis of catenary action in steel beams using a simplified hand calculation method, Part 2: validation for non-uniform temperature distribution. J Construct Steel Res 2005;61:213–34. [7] Dai XH, Wang YC, Bailey CG. An experimental study of structural behaviour of joints in restrained steel frames in fires. In: International conference, Application of structural fire design. 2009. [8] Dai XH, Wang YC, Bailey CG. An experimental study of structural behaviour of joints in restrained steel frames in fires, Applications of Structural Fire Engineering. In: Wald F, Kallerova P, Chlouba J, editors. Proceedings of International Conference. Prague; 2009. p. 350–5. [9] Dai XH, Wang YC, Bailey CG. Temperature distribution in unprotected steel connections in fire. In: Wang, Choi, editors. Proceedings of the 3rd international conference on steel and composite structures. Taylor & Francis Group; 2007.
[10] Dai XH, Wang YC, Bailey CG. Temperature developments in partially protected steel–concrete composite joints using intumescent coating. In: Proceedings of the fifth international conference. 2008. [11] Dai XH, Wang YC, Bailey CG. Effects of partial fire protection on temperature developments in steel joints protected by intumescent coating. Fire Saf J 2009; 44:376–86. [12] Dai XH, Wang YC, Bailey CG. A simple method to predict temperatures in steel joints with partial intumescent coating fire protection. Fire Technol 2010;46: 19–35. [13] Hu Y, Davison JB, Burgess IW, Plank RJ. Comparative study of the behaviour of BS 4190 and BS EN ISO 4014 bolts in fire. In: Wang, Choi, editors. Proceedings of the 3rd international conference on steel and composite structures. Taylor & Francis Group; 2007. [14] Yu HX, Burgess IW, Davison JB, Plank RJ. Experimental investigation of the behaviour of fin plate connections in fire. In: Wang, Choi, editors. Proceedings of the 3rd international conference on steel and composite structures. Taylor & Francis Group; 2007. [15] Yu HX, Burgess IW, Davison JB, Plank RJ. Experimental investigation of the behaviour of flush endplate connections in fire. In: Proceedings of the fifth international conference (SiF’08). 2008. [16] Yu HX, Burgess IW, Davison JB, Plank RJ. Experimental investigation of the tying capacity of web cleat connections in fire. In: The 5th European conference on steel structures. 2008. [17] Hu Y, Davison JB, Burgess IW, Plank RJ. Experimental study on flexible end plate connections in fire. In: The 5th European conference on steel structures. 2008. [18] Yu HX, Burgess IW, Davison JB, Plank RJ. Tying capacity of web cleat connections in fire, Part 1: test and finite element simulation. Eng Struct 2009; 31:651–63. [19] Yu HX, Burgess IW, Davison JB, Plank RJ. Tying capacity of web cleat connections in fire, Part 2: Development of component-based model. Eng Struct 2009;31:697–708. [20] Yu HX, Burgess IW, Davison JB, Plank RJ. Experimental investigation of the behaviour of fin plate connections in fire. J Construct Steel Res 2009;65: 723–36. [21] Hu Y, Burgess IW, Davison JB, Plank RJ. Modelling of flexible end plate connections in fire using cohesive elements. In: Proceedings of the fifth international conference. 2008. [22] International Organization for Standardization (ISO 834 1975). Fire resistance tests, elements of building construction. Geneva: International Organization for Standardization. [23] Bursi OS, Jaspart JP. Benchmarks for finite element modelling of bolted steel connections. J Construct Steel Res 1997;43:17–42. [24] Swanson JA, Kokan DS, Leon RT. Advanced finite element modelling of bolted T-stub connection components. J Construct Steel Res 2002;58:1015–31. [25] Maggi YI, Goncalves RM, Leon RT, Ribeiro LF. Parametric analysis of steel bolted endplate connections using finite modeling. J Construct Steel Res 2005;61: 689–708. [26] Al-Jabri KS, Burgess IW, Plank RJ. Spring-stiffness model for flexible end-plate bare beam joints in fire. J Construct Steel Res 2005;61:1672–91. [27] Al-Jabri KS, Seibi A, Karrech A. Modelling of sustiffened flush endplate bolted connections in fire. J Construct Steel Res 2006;62:151–9. [28] Sarraj M, Burgess IW, Davison JB, Plank RJ. Finite element modelling of fin plate steel connections in fire. J Fire Safety 2007;42:408–15. [29] Yu HX, Burgess IW, Davison JB, Plank RJ. Numerical simulation of bolted steel connections in fire using explicit dynamic analysis. J Construct Steel Res 2008; 64:515–25. [30] Shirh A, Adeeb R, Al-Jabri KS. Finite element analysis of flush end-plate bare steel connection at elevated temperature. Adv Struct Eng 2009;12(3):311–24. [31] ENV 1993-1-2, Eurocode 3: Design of steel structures, part 1.2: general rules— structural fire design. London: British Standards Institution; 2005.