Finite Element Modelling of Fin Plate Steel Connections in Fire

Finite Element Modelling of Fin Plate Steel Connections in Fire M. SARRAJ 1, I. W. BURGESS 2, J. B. DAVISON 3 AND R. J. PLANK 4 ABSTRACT Recent structural collapses caused by fire have focussed attention on research concerning fire safety in building design. Steel connections are an important component of any structural steel building as they provide links between the principal structural members. The evaluation of the performance of steel connections at elevated temperatures has been a topic of several research programs in the last few years. Determining the behaviour, available strength and stiffness of moment connections in fire conditions has been a dominant theme in these research works; however very little information on the behaviour of simple shear connections in fire conditions has been disseminated. Fin plate shear connections are easy to fabricate and install; as a result, they have gained popularity because of their economy. In this research, the robustness of simple fin plate beam-to-column connections is being investigated under catenary tension from highly deflected beams in fire. A highly detailed 3D finite element model has been created using the ABAQUS software. This is a complex model accounting for material nonlinearity, large deformation and contact behaviour. Contact is critical to model the shear behaviour of the joint, and contact elements have been used at the bolt-hole interface and also at the surface between the web of the beam and the fin plate, taking into consideration friction between the surfaces. The connection model has been analysed through the elastic and plastic ranges up to failure. Bolt shear and bending, and plate and web bearing have been observed as failure modes. A comparison with available experimental data at ambient and elevated temperatures and other analytical results shows that the model has a high level of accuracy. When the connection model was extended to include an attached beam, it was found that it eventually experiences large tensile force when exposed to fire. KEYWORDS Structural fire engineering; fin plate joints; shear connection; large deflection; catenary. 1 Ph.D., University of Sheffield, Dept of Civil & Structural Engineering, S1 3JD, UK, m.sarraj@shef.ac.uk 2 Professor, University of Sheffield, Dept of Civil & Structural Engineering, S1 3JD, UK, ian.burgess@shef.ac.uk 3 Senior lecturer, University of Sheffield, Dept of Civil & Structural Engineering,, S1 3JD, UK, j.davison@shef.ac.uk 4 Professor, University of Sheffield, School of Architectural Studies, S10 2TN, UK, r.j.plank@shef.ac.uk 1

1. INTRODUCTION In the last three decades, over 100 fire tests have been conducted in the UK on steel structural members that include beams 1, columns 2 and connections 3-19. This has led to an improved understanding of the behaviour and design of steel beam-to-column connections at elevated temperatures 3-19 mainly associated with their moment-rotation characteristics. Using the available test data for validation, further research was conducted, simulating the connection behaviour via FE modelling 10-14 ; this provides the opportunity for wider parametric investigations and eliminates some of the limitations associated with experimental studies. More recently, simplified analytical connection component models have been developed by a few researchers 15-19 with the intention of simplifying connection design for fire conditions. In fire large axial forces can often be generated in steel beams; due to the restraint to thermal expansion these forces are initially compressive. Nevertheless, at later stages the forces become tensile as catenary action starts to develop. Such action helps steel beams to survive by behaving like a suspension cable. They hang from the adjacent supporting members as a result of strength and bending stiffness losses, as shown by Liu et al. 20. Furthermore, during the cooling stage of the fire, the deformed beams contract considerably and experience additional tension forces as described by Bailey et al. 21. Beam-to-column connections are required to resist any resultant forces at the end of the beam and transfer them into the columns and surrounding cold structure. Consequently, for a structure to survive fire conditions, it is crucial for any connection to have sufficient strength to resist the induced actions. Recent research by Yin et al. 22 has shown that the level of axial force developed depends strongly on the stiffness of the joints and the surrounding structure. Evidently, overall analysis of steel structures and composite frame buildings in fire conditions needs reliable prediction methods that focus on joint stiffness as well as resistance in order to provide a realistic and safe connection design. An assessment of previous research conducted into steel connections in fire conditions 3-19 gives an obvious conclusion that the investigation of simple shear connections in such conditions is almost a missing topic. The low levels of available research on fin plate shear connections in fire, together with their economical popularity, has necessitated this research. The research presented here has focused on investigating the behaviour of fin plate shear connection in fire conditions. The creation of a reliable FE model to complement existing test results was a primary aim at the starting point of the research. Consequently, the FE model would form the main source of information and would be of great benefit when studying the influence of the connection parameters on the overall behaviour by allowing a wide ranging parametric study to be conducted which would be difficult to achieve in a laboratory environment. Additionally, the FE model results would enable a reliable simplified component model to be developed. Such a simplified model would be in demand for design/analysis software with great saving in terms of computing time. The FE model and the component model may be used to gain an insight into important issues such as the connection tying force capacity of a fin plate at ambient and elevated temperatures, bolt and plate bearing behaviour, and bolt shearing. 2. THE FINITE ELEMENT MODEL DESCRIPTION A three-dimensional FE model of a fin plate connection was developed in order to analyse and understand the behaviour of such a connection at ambient and elevated temperatures. The starting point for this model was a simple plate with a bolt bearing against a hole (Figure 1-a). This model was then developed to form a single lap joint (Figure 1-b). 2

Ultimately, the entire fin plate connection was then assembled and modeled using a series of lap joints in which the plate on one side was the fin plate, and the second plate was the beam web. The three main parts of the fin plate connections - beam, fin plate and the bolts (Figure 1-c) - were modelled using eight-node continuum hexahedral brick elements. This element has the capability of representing large deformation and geometric and material nonlinearity 23, 24. However, to capture accurately the stress behaviour in the region around the bolt holes where likely failures would initiate, an intensive mapped mesh was made within the vicinity of the bolt holes. The bolt holes were modeled 2mm larger than the bolt shank diameter and the hexagon bolt heads were modeled as cylinders. The flange of the column was modeled as a rigid surface, assuming that it was sufficiently rigid and connected to the fin plate. (c) (a) (b) Figure 1: FE model development (a) Single bolt in bearing (b) Lap splice (c) Fin plate and beam model Surface-to-surface contact, with a small sliding option, was used for all the contacting surfaces to fully transfer the load from the beam web to the fin plate and, eventually, to the supporting member. The contact areas in the fin plate connection comprise the bolt shank-tobolt holes, bolt head-to-fin plate, nut-to-beam web and fin plate-to-beam web surface (Figure 2). The contact surfaces of the bolt shank, bolt head, and bolt nut were always chosen to be master surfaces (as the bolt is of stiffer material) with all the other contact surfaces considered as slaves. Pre-tension was not applied to the bolts during the analysis study and a friction coefficient of µ = 0.25 was adopted for all the contact surfaces. 3

Fixed edge Fin plate Contact element y z x Nut Centre node A Beam web Figure 2: Contact elements distribution (Plan section on a fin plate connection) Simulating the contact interaction between the parts of a shear joint using ABAQUS/Standard is a very (sensitive and difficult issue to achieve and at the same time it is of satisfactory accuracy when is established. The difficulties arise because of special arrangements needed to bring the connection parts into initial contact. Firstly, the mesh should be fine enough for each element s norm of the master surface to face a corresponding norm of the slave surface elements. Secondly, the load should be applied extremely slowly until contact is established. Lastly, the boundary conditions need to be assigned in a proper way to achieve a sensible behaviour at the connection and move away from any singularity problem that may arise. Therefore, each bolt was restrained at only one node (Node A) by preventing movement in the z-direction for the first analysis step, then for the later steps bolts are freed of any restraint as the contact is already established. The fin plate was fixed along the edge welded to the column flange (Figure 2). The beam was restrained at selected nodes along its flange in the z-direction to prevent lateral movement, simulating the restraint provided by the floor slab 3. VALIDATION AGAINST EXPERIMENAL DATA AT AMBIENT TEMPERATURE Where possible, numerical simulations should be validated against experiment results. The evaluation process for the current FE model included two stages; the first being one at ambient temperature and the second at elevated temperature. Well-documented experimental data from other researchers 28, 29 was used for the comparison with the FE model. 3.1. Comparison of the FE model with lap joint tests at ambient temperature Richard 25 reported data from several tests conducted on steel lap joints at ambient temperature. One of these tests was chosen for comparison with the finite element model analyses. The plates in the lap joint specimen were of two different thicknesses, 9.525 mm and 12.7 mm (3/8 inch, 1/2 inch). Both plates were ASTM A36 steel of yield stress 250 N/mm 2 and ultimate stress 400 N/mm 2. The bolt was ASTM A325 of 19mm (3/8 inch) diameter, installed in over-sized holes of 20.6mm (13/16 inch). A 3-D finite element model was created for the lap joint using the material properties specified above. Comparison of the FE results with the experimental load-deflection curve (Figure 3) shows good agreement, with the same general behaviour and a maximum difference of 6%. An observation of the FE deformation shape and mode of failure shows a similarity to what would be expected in a lap joint tensile test (Figure 4), that is bolt twisting due to the load eccentricity, and bolt shearing failure. 4

Load [kn] 160 140 120 100 80 60 40 20 Richard Ralph Experiment ABAQUS Model 0 0 1 2 3 4 5 6 7 8 9 Deflection [mm] Figure 3: Load-Deflection comparisons between FE model and test data for a steel lap joint Y X Z Fixed edge Figure 4: Steel lap joint FE model, deformation and Von Mises stress contours 3.2. Evaluation of the FEM to fin plate connection test at ambient temperature Richard 25 also investigated the moment rotation characteristics of fin plate steel connections. Full scale experiments were conducted on two, three, five and seven-bolted connections. The three bolted fin plate connection test has been chosen to evaluate the capability of the finite element model to predict the moment rotation. This test was carried out on a W18 35 beam connected to a fin plate of 9.5mm (3/8 inch) thickness. Both the beam and fin plate are ASTM A36 steel. The bolts were ASTM A325 of 19mm (3/4 inch) diameter inserted into 20.6 mm (13/16 inch) over-sized hole. The final deformation and von Mises stress contours are shown in Figure 5. It is clear from the analysis that the middle bolt acts as the centre of rotation, whereas the top hole undergoes a high deflection as the top bolt bears toward the small edge distance of the web. In contrast, the bottom bolt has to bear in 5

the opposite direction, where the web material is not limited by the close proximity of an edge. Consequently, the bottom bolt deforms more than the top bolt and suffers high shearing stresses. Figure 5: FE model of steel fin plate connection, deformation and Von Mises stress contours Figure 6 shows the moment-rotation response for the FE model in comparison with the experimental results. In general, the FE model analyses agree well with the experimental data of Richard s test. 16 14 12 Moment [kn.m] 10 8 6 4 2 0 Richard Experiment ABAQUS Model 0 0.5 1 1.5 2 2.5 3 3.5 4 Rotation [Degree] Figure 6: Moment Rotation comparison of FE model and test data for fin plate connection 6

3.3. Evaluation of the FE model at elevated temperature Although the shear behaviour of the FE model has proved satisfactory compared with test results at ambient temperature, the lack of suitable fire test data at this time for a steel fin plate connection including its supported steel beam makes it difficult to evaluate the model at elevated temperature. Because of this lack of data, a model was created for an isolated beam and this was evaluated by comparison with existing test data. If the beam model worked well, the only remaining uncertainty about the behaviour of the complete assembly at elevated temperature would be the fin plate itself. El-Rimawi et al 26 performed a numerical analysis using a stiffness approach to investigate different factors affecting steel beam behaviour under fire conditions. Their analyses compared well with tests conducted in the UK 1, but it has to be noted that this study did not consider the effect of axial restraint at the beam ends. For the evaluation of the current model, one of El-Rimawi s analytical results and corresponding test data for a beam under large deflections in fire conditions was used. The beam was a UB254 146 43 section spanning 4.5m, supported on roller bearings at both ends and with a uniformly distributed load of 16.34kN/m. The values of the modulus of elasticity and yield stress of steel at ambient temperature were assumed to be 205kN/mm 2 and 275 N/mm 2 respectively, and the mechanical properties of steel at elevated temperatures were assumed to follow Eurocode 3 Part 1.2 27. The beams supported a concrete slab on the top flange exposing it to three-side heating under fire conditions. The time-temperature relationships for the beam web and flanges are shown in Figure 7. 800 700 600 Temperature [ C] 500 400 300 200 100 0 Web & Bottom Flange. Upper Flange. 0 4 8 12 16 20 24 28 32 Time [min.] Figure 7: Time-temperature relationships used in the El-Rimawi et al analysis A comparison of the beam mid span deflection against the bottom flange temperature is shown in Figure 8 for the test data, the current FE model and El-Rimawi s analysis. Additionally, the results of an independent analysis using the VULCAN software 28 are included. It is clear that the 3-D ABAQUS beam model is in very good agreement with the other analytical results and the experimental data. 7

250 200 W=16.34 kn/m 4.50 m Deflection [mm] 150 100 50 ABAQUS El-Rimawi Test Data VULCAN 0 0 150 300 450 600 750 900 Temperature [ C] Figure 8: Comparison between Temperature-Deflection relationships of the ABAQUS simulation, El-Rimawi et al, test data and VULCAN software 3.4. Beam and connection behaviour in fire In 2005 Wald and Ticha conducted a fire test on a steel fin plate connection at the Czech Technical University (Figure 9). A three-bolt fin plate connection, 6 60 125mm, was assembled using fully threaded 8.8 high strength bolts of 12mm diameter. The beam was an IPE160 cross section 3m long and the loads were applied by two hydraulic jacks (60 kn each) 250mm from the beam ends. The fin plates and beam were both of Grade S235. The furnace gas temperature was controlled to follow the Cardington 29 fire test No. 7 for the heating and cooling stages. The deflection of the beam was recorded at the load points. A comprehensive FE model for the tested connection and supported beam was created to match the test condition. By using symmetry it was only necessary to model half of the tested beam. The deformed shape and failure mode determined by the FE analysis are shown in Figure 10 and are clearly consistent with the test observations. Bolt shearing was the predominant failure mode in the test and similarly in the FE model. Figure 9: Wald and Ticha fin plate connection test 8

60 kn 60 kn 250 mm 2500 mm 250 mm Figure 10: FE model of the tested fin plate connection and the connected beam Comparison of the time-deflection curves for the tested beam and the FE model (Figure 11) shows a reasonable agreement. Although there are slight differences in the runaway stage it can be seen that the point at which runaway starts is approximately 32 minutes for both the test and the FE model. The complexity of the test arrangement, in particular the special lateral restraint arrangement and composite action, may account for the small differences. 0 0 4 8 12 16 20 24 28 32 36 40 Deflection [mm] -10-20 -30-40 -50-60 -70-80 Time [min] ABAQUS-Model Test Figure 11: Time-Deflection comparisons of the FE simulation and test data 9

4. CONCLUSION 3D finite element models incorporating contact interaction, geometric non-linearity and non-linear material properties have been used to accurately model fin plate steel connections behaviour. The contact elements were particularly important in this context. A connection-beam model has successfully been created and validated against the limited test data available. This can now be used in parametric studies, for example to account for different time-temperature histories. Parametric studies of factors that influence the strength and stiffness of steel joints are difficult to control in any laboratory testing due to of the dimensional and physical variability in joints and test arrangements. Empirical parametric studies are also expensive and time consuming. The reasonable accuracy of the FE model for reproducing the experimental behaviour of steel joints makes it a useful model for both analytical and parametric studies. Although validation with experimental test data is needed, a numerical simulation carefully created and validated against test data enables cost-efficient parametric investigation that may lead to improvements in joint configuration and joint performance. In reality this research programme has gone farther than the development of the FE model and its validation. Examination and evaluation of a component spring model assembly, at ambient an elevated temperature, for the fin plate connection is now in process. In addition, the plate bearing and bolt single shear component were introduced and described in detail. ACKNOWLEDGMENT The authors gratefully acknowledge the kind assistance of Prof. Frantisek Wald and Alena Ticha of the Czech Technical University in Prague for providing the test data for their experimental work on fin plate steel connections, and to the Engineering and Physical Sciences Research Council of the UK for their sponsorship of the principal author. REFERENCES [ 1] British Steel Corporation, Compendium of UK standard fire test data on unprotected structural steel. Contract report for Department of Environment, (1987). [2] Shepherd, P.G., The Performance in Fire of Restrained Columns in Steel-Framed Construction, PhD Thesis, University of Sheffield, (1999). [3] Kruppa, J. Résistance en feu des assemblages par boulous, Centre Technique Industriel de la Construction Métallique, St. Remy Chevreuse, France, CTTICM Report, Document No. 1103-1, English translation available entitled Fire Resistance of Joints with High Strength Bolts, (1976). [4] British Steel, The Performance of Beam/Column/Beam Connections in the BS5950: part 8 Fire Test, British Steel (Swinden labs), Report T/RS/1380/33/82D and T/RS/1380/34/82D. Rotherham, (1982). [5] Leston-Jones, L.C., The Influence of Semi-Rigid Connections on the Performance of Steel Framed Structures in Fire, PhD. Thesis, Department of Civil and Structural Engineering, University of Sheffield. (1997). 10

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