column connections in fire

Engineering Structures 43 (2012) 194–209

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Efficient modelling of large deflection behaviour of restrained steel structures with realistic endplate beam/column connections in fire L. Chen, Y.C. Wang ⇑ School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M13 9PL, UK

a r t i c l e

i n f o

Article history: Received 25 July 2011 Revised 23 March 2012 Accepted 23 May 2012 Available online 27 June 2012 Keywords: Restrained beam Joints Component based method Large deflection Fire Elevated Temperatures Simulation methods

a b s t r a c t This paper compares the simulation results of three methods of using the commercial finite element package ABAQUS to model the very large deflection behaviour of steel structures with realistic endplate joints in fire. The results of a set of fire tests on restrained steel beam–column assemblies were used to check the accuracy of these different modelling methods. In the first modelling method, the fire exposed structural members, including the connections, were simulated using detailed solid elements to enable detailed behaviour of the structure to be faithfully represented. In the second method, the unexposed segments of the columns were represented by conventional line (beam) elements, the joints were represented using springs (Connector Elements) based on the component based method, and the beam was modelled using solid elements. In the third method, the joints were modelled using springs as in the second method and the beam and columns were simulated using line (beam) elements. As expected, the detailed simulation method was extremely time-consuming, but was able to produce accurate results. The simulation results from the second and third methods contained some inaccuracy, but depending on the simulation objective, their simulation results may be acceptable. In particular, the third simulation method was very efficient, suitable for simulating complete frame structures under very large deflections in fire. This paper will compare results from the three different simulation methods for different parts of the structure, including the fire exposed beam, the connection components and the columns, through different stages of fire exposure, from initial exposure to fire to the development of catenary action in the beam. From these comparisons of simulation results, this paper will recommend appropriate methods of modelling steel framed structures with realistic joints for different design objectives. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Fire induced structural collapse is an important topic of structural fire safety and the behaviour of joints plays the most critical role [26]. Until recently, steel joints are assumed to have higher fire resistance than the connected structural members due to lower temperatures in the joints. Consequently, the emphasis of structural fire resistance research and design has been on other structural components. The collapse of the World Trade Centre buildings in fire changed this perception and research on the fire behaviour of joints is attracting extensive attention from researchers worldwide. Under fire conditions, the connected beam will exert forces on the joints that would not have been allowed for in conventional design [25]. In particular, the presence of a tensile axial load in the connected beam could cause the joints to fracture, increasing the risk of progressive collapse. On the other hand, if the joints have sufficient strength and ductility, it is possible for the connected beams

⇑ Corresponding author. E-mail address: [email protected] (Y.C. Wang). 0141-0296/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2012.05.030

to develop catenary action in fire to achieve very high fire resistance [27–31]. Thorough understanding of the joint behaviour at elevated temperatures and joint interactions with other structural members is the key to designing a structure to withstand fire induced progressive collapse with or without fire protection. Although much research is still required to build a thorough understanding of steel joint behaviour in fire, much progress has been made in the last few years, starting from understanding the moment–rotation characteristics of joints at elevated temperatures [1–3,18] to the more recent efforts of incorporating shear and axial forces [6,7,20,22,23,32,33]. Methods for investigation of the influence of axial force on joint behaviour include empirical, analytical and mechanical (component based) methods, in addition to experiments. Among these, the component based method has found favour because it is simple to allow it to be incorporated in global structural analysis yet sufficiently flexible to allow the effects of different joint types under complex loading conditions to be treated using a limited set of connection component behaviour. The component based method for joints at ambient temperature is now incorporated in design codes of practice such as Eurocode EN 1993-1-8 [11].

L. Chen, Y.C. Wang / Engineering Structures 43 (2012) 194–209

195

Notations beff dw ly Fb,Rd Fu,h F Vt;Rd Ft,Rd F ut;wc;Rd

effective width of column web in tension clear depth of the column web (the distance between the root radii) yield length of column web in compression ultimate load carrying capacity of endplate in bearing ultimate resistance of column web in compression at h °C bolt tensile resistance in the presence of shear tensile resistance per bolt in the absence of shear ultimate resistance of column web in tension

F yt;wc;Rd Fv,Ed Fv,Rd Kc,wc,ini,h Ki,b Ki,v Kt,wc db,fract dwc,u

column web yield resistance in tension applied shear force per bolt ultimate load carrying capacity of bolt in shear initial column web stiffness in compression at h °C initial stiffness of endplate in bearing initial stiffness of bolt in shear initial stiffness of column web in tension bolt fracture deformation deformation capacity of column web in tension

This paper is focused on understanding interactions between joints and structural components through numerical modelling. The specific objective of this paper is to investigate the most effective and efficient method of simulating structural behaviour in fire with realistic joints and the whole range of structural behaviour. Depending on the objectives of simulation, models of different complexities may be constructed. This paper will investigate three numerical models built using the general finite element package ABAQUS. In the first method, the fire exposed structural members, including the joints, are simulated using detailed solid elements to enable detailed behaviour of the structure to be faithfully represented. This is extremely time-consuming, but has the capability of producing detailed and accurate simulation results. The most time-consuming aspect of this simulation method is tracing the joint behaviour in detail. Therefore, in the second method, the joints are represented using springs based on the component based method. In addition, if the main emphasis of the simulation is on the beam–joint interaction, the columns can be modelled using line (beam) elements. However, the beam section is still modelled by using solid elements. Going one step further, the third method uses line (beam) elements to represent the beams and columns. The second and third methods introduce approximations. Therefore they may not achieve the same degree of accuracy as the first method. However, they are more efficient in simulation time. Using the results of a series of fire tests of Wang et al. [26], this paper will compare the results from these three different simulation methods for different parts of the structure, including the fire exposed beam, the joint components and the columns, through different stages of fire exposure, from initial exposure to fire to the development of catenary action in the beam. The structural behaviour to be examined will include behaviour of the different joint components, detailed beam behaviour, global beam and joint behaviour in terms of the beam vertical deflection and axial force developments, and structural failure mode.

specimen consisted of two columns and one beam jointed together by two joints. The cross-section of the beams in all tests was the same (UKB 178  102  19). Two column sections (S355 steel grade UKC 254  254  73 (Tests 1–5) and S275 steel grade UC 152  152  23 (Tests 6–10)) were used to simulate two different levels of axial restraint to the beam. This paper will only consider the case of using the larger column size (S355 steel grade UKC 254  254  73). All the bolts and nuts used were M20 G8.8 except for the ones in Test 5 which used M20 G10.9 bolts and nuts to prevent premature failure of the bolts and nuts due to thread stripping. All connection members were steel grade S275. The furnace temperature was increased to follow the ISO 834 standard fire curve [14] while maintaining the two concentrated loads, each of 40 kN, until termination of the test, either due to connection fracture or to prevent the test beam from resting on the furnace floor. Measurements were made to obtain temperatures at different locations, the horizontal reaction forces in the columns, displacements in the beam and the columns. The concentrated loads were manually applied. However, it was difficult to maintain the load at precisely 40 kN when the test specimen was near failure. At this stage, the applied loads could not be maintained and severe asymmetrical behaviour of the beam was observed.

2. Fire tests

ABAQUS offers two solution strategies: static analysis and explicit analysis. Static analysis is based on static equilibrium and characterised by iterative solution of a set of simultaneous nonlinear equations. The Newton–Raphson method (general static analysis) can be used until the determinant of the stiffness matrix becomes zero or negative. The Arc-Length (or Riks) method may be used to deal with instability problems, but, it is not suitable when dealing with local instabilities such as surface wrinkling, material instability, or local buckling. The Riks method has been developed for numerical analysis in the load–displacement domain. Therefore, it cannot be used for the problems of this paper because the analysis is conducted in the temperature–displacement domain while maintaining the applied load. The other disadvantage of static analysis is that it is not easy to overcome the non-convergence problem when encountering complicated contacts. The explicit

The fire tests [26] that were recently carried out at the University of Manchester, UK, will be used to check the accuracy of the modelling results. Fig. 1 shows the test arrangement. In total, 10 tests were carried out using five different types of connections (fin plate, web cleat, flexible endplate, flush endplate and extended endplate) and two different levels of axial restraint to the beam (obtained by using two different column sizes). This paper will focus on the three tests using endplate connections (flexible endplate, flush endplate, extended endplate) with one level of axial restraint to the beam. The columns were free to move vertically but were horizontally restrained. Due to size limitation of the furnace, only the central segments of the columns were enclosed in the furnace. Each test

3. Modelling methods The general finite element package ABAQUS was used to simulate the fire tests. This section presents detailed simulation methods using the first method (detailed modelling using solid elements) and the second method (detailed modelling of the beam using solid elements, spring elements for the joint components and line elements for the columns). 3.1. Method 1 (referred to as Detailed Model): Using detailed finite element method (solid elements) to represent joint behaviour

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Fig. 1. Test arrangement [26].

analysis is a dynamic method. This analysis strongly depends on the displacements, velocities and accelerations at the beginning of each time increment. The advantage of the explicit analysis is that it is easy to solve the complicated contact problems. However, it is an extremely time consuming process due to the very small time step that can be used and it is also difficult to determine an appropriate step time. Despite the difficulty in dealing with nonconvergence problems in static analysis, it was decided to use the Newton–Raphson method (general static analysis) in this research owing to easy manipulation of the simulation process and less time consuming nature of this method. As will be explained later, pseudo-dynamic analysis, in the form of damping, may be introduced to deal with numerical non-convergence in static analysis. 3.1.1. Material properties Table 1 lists the ambient temperature mechanical properties of the different steel components. Except for the bolts, tensile coupon

tests were carried out to obtain the mechanical properties. It is noticed that the measured Young’s modulus values are quite different from the expected value of 210 kN/mm2. This is because the measured values were based on the tangent to the recorded stress– strain curve and the result would be sensitive to how the tangent was defined. Fortunately, since elastic deformation in only a small part of the total structural deformation in fire, no attempt was made to refine this value. The elevated temperature stress–strain curves for the different steel materials follow the recommendations in Eurocode EN-1993-1-2 [12]. 3.1.2. Temperature profiles In the fire tests, the temperature distribution was complex. Accurate specification of temperature profiles in every part of the structure is impossible, even if a lot of thermocouples were installed in the tests. Based on characteristics of the tests and for simplicity, the test assembly may be divided into six regions, each having the same temperature. These six regions are: beam bottom

Table 1 Steel material properties [26]. Steel component

Grade

Yield stress (MPa)

Ultimate yield stress (MPa)

Young’s modulus (kN/mm2)

Bolt Beam Column Endplate

G8.8/G10.9 S275 S355 S275

640/900 350 350 250

800/1000 500 510 450

210 233 194 167

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197

Column out of fire Top beam flange

Column in fire

Connection region

Beam Web Bottom beam flange

Fig. 2. Temperature profile regions for flush end plate connection (Test 03).

flange, beam web, beam top flange, the connection region, the heated segment of the column, and the rest of the column at ambient temperature. Fig. 2 shows these temperature regions for a flush end plate connection model (Test 03). 3.1.3. Numerical simulation stabilisation As mentioned in Section 3.1, the Riks method is not suitable for conducting structural analysis in fire. An alternative method has to be used to resolve the problem of numerical non-convergence. ABAQUS/Standard offers an option to stabilise the numerical modelling by applying damping throughout the model in such a way that the viscous forces introduced are sufficiently large to prevent instantaneous buckling or collapse but small enough not to affect the structural behaviour significantly while the simulation is stable. Two options may be used: stabilisation with dissipated energy fraction and stabilisation with damping factor. In this research, stabilisation with dissipated energy fraction was used. An appropriate dissipated energy fraction will help numerical convergence, but it may also compromise accuracy of the simulation results if this fraction is too high. In this research, the ratio of energy due to viscous damping dissipation (parameter ALLSD in ABAQUS) to the total strain energy (parameter ALLIE in ABAQUS) was controlled to be less than 5%. The effects of introducing pseudo damping may be checked by comparing the total applied load with the reaction force [8,10]. If the reaction force is the same as the total applied load, pseudo damping does not affect structural behaviour. Conversely, if the reaction force is much lower than the total applied load, the structure is experiencing instability (velocity) and some of the applied load is resisted by the artificial damping introduced in the model. This modelling methodology is introduced in all three simulation methods investigated in this paper. 3.1.4. Element type, mesh size and modelling geometry For detailed modelling, the ABAQUS element library offers a number of hexahedron, shell and beam elements with different features. Many detailed FE analyses [9,3,19] have shown that for detailed modelling of joint behaviour, three-dimensional finite elements are the best choice. For nonlinear problems, the first order elements are likely to be the best option because of their good accuracy and low demand on computation resources. In this study, the eight noded reduced integration brick element (C3D8R) was used. The advantage of this type of element is that it is accurate in modelling constitutive law integration and can avoid the shear lock problem. Fine mesh will be necessary in the connection region where high stress and strain gradients take place. Same to the numerical simulation research by Dai et al. [8], beam elements were used to simulate the cold parts of the column in order to reduce the computational time. Furthermore, due to symmetry of the test arrangement, only half of the testing geometry was built in ABAQUS to save computational time. Nevertheless, it should be

pointed out that in some of the tests, due to unsymmetrical heating condition in the furnace and difficulty in manually maintaining the applied loads in the two jacks, the tests experienced quite severe unsymmetrical behaviour. Although the aspect ratio of the plate thickness to width was very small, there was high stress variation through the plate thickness due to large deformations. Therefore, two layers of elements were used to represent the plate thickness for improved accuracy. The hexagon bolt heads were modelled as cylinders. 3.1.5. Contact There are many physical contacts in the tested structures. In the standard static analysis, ABAQUS provides surface to surface contact with the option of either finite-sliding formulation or small-sliding formulation. The finite-sliding formulation allows any arbitrary motion of the surfaces. The small-sliding formulation allows two bodies containing contacting surfaces to undergo large motions, but the contacting surfaces perform relatively small sliding movement to each other and arbitrary rotation of the bodies is permitted. Since the sliding movements involved in the structures are small and the small-sliding formulation is superior to the finite-sliding formulation in saving computational resource, the small sliding option was chosen in this study. When applying surface to surface contact in ABAQUS, assignment of the master surface and the slave surface should be carried out with great care. In principle, the master surface on the body should be the strong material. Furthermore, in this study, the simulation results were found not to be sensitive to the surface friction coefficient used and a nominal value of 0.3 was acceptable. For simulating bolts, the clearance between the bolt hole and bolt shank was 1 mm. 3.2. Method 2 (referred to as Hybrid Model): using the component based method (Connector Elements) to represent joints and solid elements to represent other structural parts In the component-based method, the overall joint is represented by assembling contributions from all the individual joint components. Each joint component is represented by a spring with a specified force–displacement–temperature relationship. This research uses the joint component behaviour from the works of Spyrou [22], Spyrou et al. [23], Beg et al. [5], Block [6], Block et al. [7], Sarraj [20] and Hu et al. [13]. Since this research attempts to understand the structural behaviour in fire under very large deformations, it is important that the joint component force–deformation relationship not only includes stiffness and maximum load, but also deformation capacity. Implementation of the component based method in an overall structural model includes identification of active connection components, specification of component load–deformation behaviour and assembling the components to other structural elements. For

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endplate connection, identification of active connection components is well established in Eurocode EN 1993-1-8 [11] and will not be repeated here. This section will summarise the joint component behaviour at elevated temperatures and the assembling procedure. 3.2.1. Load–displacement response for each individual joint component 3.2.1.1. Tension zone. The tension zone comprises the following components: column flange in bending, endplate in bending, bolt in tension, weld in tension and column web in tension. 3.2.1.1.1. T-stub (plate in bending and bolt in tension with weld in tension). The T-stub can develop a range of load–deformation behaviour, depending on the relative strength of the bolts and the plates. Spyrou [22] and Spyrou et al. [23] have presented experimentally validated models dealing with the three failure modes of T-stub. In all cases, the ultimate failure criterion was bolt fracture as shown in Fig. 3. The following outlines how to determine the load–deformation characteristics of a T-stub:

Fig. 4. Effective length of T-stub [22].

Bolt Fracture

FtV, Rd 0 .85 FtV, Rd

1. Calculate the T-stub capacity to form the inner plastic hinges. If this capacity is less than the bolt yield capacity, the final failure mode may be either failure mode 1 or 2. Otherwise, the failure mode is mode 3 bolt fracture and the T-stub load–deformation relationship follows that of mode 3. 2. To determine whether the failure mechanism is mode 1 or 2, compare the T-stub capacity to develop the outer plastic hinges with the bolt yield capacity. If the yield mechanism capacity is less than the bolt yield capacity, the load–deformation relationship of the T-stub follows mode 1. Otherwise, use that of mode 2.

Bolt Yield

δ b,fract Fig. 5. Force–displacement curve of bolt in tension [13].

For more general application of this method, two modifications were introduced by Block [6]. Firstly, for calculating the bolt deformations, the bolt lengths associated with the two T-stubs for the two connected plates should be split according to the stiffnesses of the T-stubs, as suggested by Kühnemund [16]. Secondly, Spyrou assumed that the yield lines of the T-stub were at 45° from the horizontal, starting from the washer edge, as shown in Fig. 4. A better alternative is to follow the UK’s Green Book [21] for moment connection design. In Spyrou’s T-stub model, there is no shear force in the bolt and the bolt behaviour is linear up to the failure load. Yu et al. [34] pointed out that this model may predict unreasonably high resistance and large ductility in some cases. To allow more realistic modelling of the bolts, Hu et al. [13] used Spyrou’s T-stub model only for the plate in bending and then added an extra spring for the bolt in tension. Due to a lack of bolt mechanical property

F

 SRF = 1 (T 6 300 °C).  SRF = 1.0  (T  300)  2.128  103 (300 < T 6 680°C).  SRF = 0.17  (T  680)  5.312  104 (680 < T 6 1000°C).

F

Bolt fracture Bolt yield

model, Hu et al. modified Swanson’s bolt model [24] and proposed the bilinear force–displacement curve for bolt under tensile force shown in Fig. 5. The maximum bolt deformation db,fract is obtained by multiplying the bolt length by the maximum bolt strain at the bolt ultimate tensile stress. The tensile resistance in Fig. 5 includes the effect of shear, determined using the interaction equation in FV F Eurocode EN 1993-1-8 [11] given by F m;Ed þ 1:4Ft;Rd 6 1:0. This interacm;Rd t;Rd tion equation is assumed to stand at elevated temperatures. The bolt strength reduction factor (SRF) is according to Kirby’s research [15] given below:

Mode (2)

Outer plastic hinges Mode (1)

Mode (3)

Inner plastic hinges

δ Fig. 3. Failure modes and corresponding force–displacement curves of a T-stub.

δ

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Furthermore, for flexible endplate connection, Hu et al. [13] added a further spring for weld in tension. The weld load–displacement relationship is linear until weld fracture. The strength of the weld can be determined according to Eurocode EN 1993-1-8 [11]. The maximum weld displacement at failure may be taken as 20% of the effective throat thickness and may be considered to be unaffected by temperature. 3.2.1.1.2. Column web in tension. A bi-linear force–displacement relationship (Fig. 6) was used to represent the column web in tension. In Fig. 6, F yt;wc;Rd is calculated according to EN 1993-1-8 [11] using the steel yield stress; F ut;wc;Rd is calculated in the same way but using the ultimate tensile stress of steel; Kt,wc is the web in tension stiffness calculated according to EN 1993-1-8 [11]. The deformation capacity of the column web in tension is established according to Beg et al. [5], who derived an analytical expression for ultimate deformation capacity of column web in tension, based on numerical simulation results.

3.2.1.2. Compression zone. For column web in compression, the model of Block [6] may be used. This model is based on the approach of Lagerqvist and Johansson [17], which although was originally developed for ambient temperature applications, was found by Block to be suitable for elevated temperature use. The maximum load carrying capacity of this approach is based on the yield line mechanism shown in Fig. 7, in which the yield length of the column web in compression (ly) is determined by considering equilibrium of the plastic hinge mechanism under loading by the applied force P and a reaction force provided by the plastic resistance of the web. For this calculation, a part of the column web (0.14dw) is included when calculating the plastic bending moment capacity of the column flange outside the load application zone. The initial stiffness may be calculated according to Aribert et al. [4], modified to take into consideration changes in the modulus of elasticity of steel elevated temperatures. Block further derived an empirical equation to calculate the deformation capacity of the column web, based on a parametric study.

3.2.1.3. Shear zone. The shear zone components include plates (endplate, column flange or web) in bearing and bolt in shear. This research adopts the method of Sarraj [20] who provided regression analysis equations for plates in bearing for bolts in shear based on extensive finite element simulations. Fig. 8 sketches the force–displacement curves for these two joint components.

3.2.2. Assembly of joint components in FE modelling Using the component based joint model, Sarraj [20] and Hu et al. [13] carried out simplified analysis of global joint behaviour using ABAQUS. In their simulations, they used ABAQUS element SPRINGA to represent a joint component. However, in this present study, the ABAQUS element type AXIAL CONNECTOR will be used. Both SPRINGA and AXIAL CONNECTOR elements simulate translational behaviour along the line joining two nodes. However, the AXIAL CONNECTOR element has advantages over the SPRINGA element. First, the AXIAL CONNECTOR element can be directly operated in ABAQUS CAE whilst the SPRINGA element can only be edited in the INPUT FILE. Secondly, the AXIAL CONNECTOR element can model elastic–plastic behaviour but the SPRINGA element can only model elastic behaviour, even though the elastic behaviour may be nonlinear. Thirdly, the failure criterion for each joint component can be defined in the AXIAL CONNECTOR element by limiting the maximum deflection in CAE. At elevated temperatures, a flexible endplate connection always experiences two rotation stages. Initially, the rotation is about the bottom edge of the endplate. Afterwards, the centre of rotation shifts to the centre line of the bottom flange of the beam with increasing lever arm. In the detailed simulation model (Method 1), only half of the test structure was simulated to save computation time, even though the fire test using flexible endplate connection experienced highly asymmetrical behaviour due to non-uniform heating in the furnace and due to difficulty in manual control to reach the same applied concentrated loads through the two jacks (Fig. 1). Using Method 2 allows the entire test assembly to be simulated. Fig. 9 shows the simulation model for the flexible endplate connection test (Test 2 of Wang et al. [26]) and the blow up figure in Fig. 9 shows the various joint components simulated using ABAQUS AXIAL CONNECTOR elements. In this model, components CWC01 and CWC02 represent the aforementioned two stages of beam rotation (before and after contact with column). The other components are column web in tension (CWT), column flange in bending (CFB), weld in tension (WT), bolt in tension (BT), endplate in bending (EPB), bolt in shear (BS) and endplate in bearing (EPS). Similar models were built up for flush endplate and extended endplate connection tests. 3.3. Comparison between numerical modelling (Methods 1 and 2) and test results 3.3.1. Flexible end plate connection (Test 2 of Wang et al. [26]) Fig. 10 compares the Detailed Model (Method 1), Hybrid Model (Method 2) and test results in respect of the beam mid-span

N Failure Point

u

Ft , wc, Rd Ft ,ywc, Rd F

F beff

Kt , wc

δ wc,u

N Fig. 6. Column web in tension with force–displacement curve [5].

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Outer plastic hinge on flange

Outer plastic hinge on flange

Fu,θ =2Fel,θ

Inner plastic hinge on flange

0.14dw

Force (P) on column flange Fel,θ

kc , wc, ini ,θ

δ el ,θ

Yield length of web (ly)

δ u ,θ

Fig. 7. Assumed plastic hinge mechanism of column web under concentrated load and typical force–displacement curve [6].

Plate in Bearing

Fb , Rd

Bolt in Shearing

Fv , Rd

Ki , b

Ki ,v Hole elongation

Bolt deflection

Fig. 8. Typical force–displacement curves at elevated temperatures for plates in bearing and bolts in shear.

Fig. 9. Proposed component based representation of flexible endplate connection with large size column (Test 2 of Wang et al. [26]).

deflection–temperature curve and the beam axial force–temperature curve for the flexible endplate connection test. Since the Detailed Model only simulated the left hand side of fire test, the maximum middle-span deflection was slightly lower than the test and Hybrid Model results. The other small difference is the temperature at which the beam started to accelerate in deflection. The small change of the axial force from compression to tensile may have been caused by the yield stress used in the model being slightly lower than the actual yield stress of the beam. In the test, the beam web adjacent to the weld on the right hand side fractured and the endplate developed large deformation on the left hand side in the fire test. The Detailed Model successfully reproduced the large endplate deformation pattern on the left

hand side (Fig. 11b). Fig. 11c also shows that the Hybrid Model was able to accurately reproduce the unsymmetrical beam behaviour as observed in the test. Fig. 12 shows the Hybrid Model results for the endplate T-stub deformation against temperature and Fig. 13 presents the Hybrid Model results for the weld deformation against temperature and the associated failure envelope. Very large endplate T-stub deformations are found at the top bolt row (Fig. 12). At about 660 °C, Fig. 13 shows that the weld at the top toe on the right hand side started to break (weld deformation greater than its deformation capacity). These Hybrid Model phenomena reproduce the experimental observations, confirming that the Hybrid Model is capably of accurately predicting detailed component behaviour, including failure.

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Middle-Span Deflection Vs Temperature

Axial Force Vs Temperature

0

40 0

100

200

300

400

500

600

700

800

20

-100 Test -150 -200

Hybrid Model Detailed Model

-250 -300

Axial Force (kN)

Deflection (mm)

-50

0 -20 0

100

200

300

400

500

600

700

800

-40 -60 -80

Test

-100

Hybrid Model

-120

Detailed Model

-140

Temperature (oC)

Temperature (oC)

Fig. 10. Comparison between simulation and experimental results for beam mid-span deflection and axial force for flexible endplate connection test (Test 2 of Wang et al. [26]).

Fig. 11. Comparison of deformation shapes between Detailed Model and Hybrid Model with experimental results for flexible endplate connection (Test 2 of Wang et al. [26]).

Fig. 14 indicates that the endplate T-stub deformation curves from Detailed Model and Hybrid Model are slightly different in the temperature range between 350 °C and 450 °C, but they start to converge later. In the Hybrid Model, the first endplate T-stub on the right hand side developed large deformations which were not observed in the fire test (Fig. 11a). This may be due to the assumed endplate temperature on the right hand side being higher than experienced in the test (but not measured). Nevertheless, the Hybrid Model correctly predicted weld failure on the right hand side (Fig. 13). 3.3.2. Flush end plate connection (Test 3 of Wang et al. [26]) As shown in Fig. 15, the global results of the two numerical simulation methods are in very good agreement with the test results. In the fire test, the two bolt pairs on the left hand side of the test failed in thread stripping (Fig. 16a). This bolt failure mode could not be modelled in the Detailed Model, but the top pair of bolts stretched and necked at high tensile stresses (Fig. 16b), indicating imminent tensile failure. Fig. 17 presents deformations of the top

bolt pair from these two simulations, clearly showing good agreement and also indicating that the top bolts on the left hand side fractured under severe heating. This confirms that the Detailed Model and Hybrid Model predicted the same structural failure mode and the corresponding steel temperature. Owing to good agreement between the predicted failure temperatures, Fig. 18 shows that the endplate T-stub behaviour is in good agreement between the two simulation methods. Furthermore, the Hybrid Model has reproduced the same asymmetrical beam deformation pattern as in the fire test (Fig. 16c). In summary, both Detailed Model and Hybrid Model are capable of predicting the very large structural behaviour at high elevated temperatures. 3.3.3. Extended end plate connection test (Test 5 of Wang et al. [26]) Fig. 19 shows good agreement between the test and the two simulation results for the beam deflection–temperature and beam axial force–temperature relationships. Owing to high strength and good ductility of the endplate used, there was only top bolt failure under combined shear and tension

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Endplate Deformation Vs Temperature

20

Deformation (mm)

18

1st T-stub (LHS)

16

LHS

2nd T-stub (LHS)

14

st

12

1 T-stub (RHS)

10

2nd T-stub (RHS)

8 6 4

RHS

2 0 0

100

200

300

400

500

600

700

800

Temperature (oC) Fig. 12. Deformation curves of endplate T-stubs from the Hybrid Model for flexible endplate connection (Test 2 of Wang et al. [26]).

Weld Deformation Vs Temperature 2.5

Deformation (mm)

2 LHS

RHS

RHS

1.5

Failure Envelope

1

0.5

0 0

100

200

300

400

500

600

700

800

900

1000

Temperature (oC) Fig. 13. Deformation curves of weld from the Hybrid Model for flexible endplate connection (Test 2 of Wang et al. [26]).

Endplate Deformation Vs Temperature (LHS) 14

Deformation (mm)

12

1st T-stub (Hybrid Model)

10

1st T-stub (Detailed Model)

8

2nd T-stub (Hybrid Model)

6

2nd T-stub (Detailed Model)

4 2 0 -2

0

100

200

300

400

500

600

Temperature (oC)

Fig. 14. Comparison of the left hand endplate T-stub deformations between the Detailed Model and Hybrid Model for flexible endplate connection (Test 2).

on the right hand side in this fire test (Fig. 20), and substantial development of catenary action was developed.

Fig. 20 shows that that both simulation models accurately reproduced the deformed shapes of the beam, including web buck-

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Middle-Span Deflection Vs Temperature

Axial Force Vs Temperature

0

100

0

100

200

300

400

500

600

700

-150 -200

Axial Force (kN)

Deflection (mm)

-50 -100

Test

800

Test Hybrid Model Detailed Model

-250 -300

Hybrid Model

50

Detailed Model 0

0

100

200

300

400

500

600

700

800

-50 -100 -150

o

Temperature ( C)

Temperature (oC)

Fig. 15. Comparison between simulation and experimental results for beam mid-span deflection and axial force for flush endplate connection (Test 3 of Wang et al. [26]).

Fig. 16. Comparison of deformation shapes between Detailed Model and Hybrid Model with experimental results for flush endplate connection (Test 3 of Wang et al. [26]).

ling. The Detailed Model gave very similar endplate deformation shape as in the test. Although the Hybrid Model cannot visually show the deformation shape of the extended endplates, a comparison of the endplate T-stub behaviour in Fig. 21 between the two simulation models indicates very close match. Moreover, the Hybrid Model predicted top bolt failure in tension on the right side which is identical to the fire test (Fig. 22). In fact, due to the beam having predominately symmetrical behaviour as assumed in the Detailed Model, the agreement between the two simulation results as shown in Fig. 20 is much better than for the other two tests (see Figs. 11 and 16) which exhibited stronger asymmetrical behaviour. In summary, both the Detailed Model (Method 1) and Hybrid Model (Method 2) were capable of simulating detailed beam and joint behaviour, including the global beam behaviour (deformation and axial force) and detailed beam and joint behaviour (including beam web distortion and detailed joint component behaviour) and failure mode.

3.4. Method 3 (referred to as Beam Model): Further simplification of Hybrid Model The Hybrid Model (Method 2), in combination with detailed beam section, is able to simulate the detailed connection behaviour, and the simulations are considerably less expensive in computation effort than the Detailed Model (Method 1). Nevertheless, the simulations still would take a lot of time to run as shown in Table 2. In Method 3 (referred to as Beam Model), the joints were modelled as in the Method 2, but the beam and columns were simulated using line (beam) elements. Table 2 shows using Method 3 can drastically reduce computation time from hours to seconds. This section assesses accuracy of this method. Fig. 23 shows the numerical simulation Method 3 (Beam Model) generated smaller deflection and lower axial tension force. This was mainly due to the line elements not being able to model the beam web distortion which was observed in the more detailed

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Bolt Deformation Vs Temperature (LHS) 8

Deformation (mm)

7 6

Failure Envelope

5 4

Top Bolt (Hybrid Model)

3

Top Bolt (Detailed Model) 2 1 0 0

100

200

300

400

500

600

700

800

900

1000

Temperature (oC) Fig. 17. Left hand top bolt deformation curves from the Detailed Model and Hybrid Model for the fire test using flush endplate connection (Test 3 of Wang et al. [26]).

Endplate Deformation Vs Temperature (LHS) 14

Deformation (mm)

12 10 1st T-stub (Hybrid Model)

8

2nd T-stub (Hybrid Model) 6 1st T-stub (Detailed Model) 4

2nd T-stub (Detailed Model)

2 0 0

100

200

300

400

500

600

700

800

Temperature (oC) Fig. 18. Comparison of the left hand endplate T-stub deformations between Detailed Model and Hybrid Model for flush endplate connection (Test 3).

Middle-Span Deflection Vs Temperature

Axial Force Vs Temperature

0 0

100

200

300

400

500

600

700

800

-100 -150 -200

Test Hybrid Model

-250

Detailed Model

-300 -350

Axial Force (kN)

Deflection (mm)

-50

60

Test Hyrbid Model Detailed Model

40 20 0 -20 0

100

200

300

400

500

600

700

800

-40 -60 -80 -100 -120 -140

Temperature (oC)

Temperature (oC)

Fig. 19. Comparison between simulation and experimental results for beam mid-span deflection and axial force–temperature relationships for extended endplate connection (Test 5 of Wang et al. [26]).

models using solid elements for the beam and in the fire tests. However, since the beam webs were sufficiently compact, the effect of beam web distortion was small and the component based simulations using line elements for the beams were still able to predict similar joint component behaviour and structural failure modes. For example, Figs. 24 and 25 compare results for different

connection components using flexible endplate connection. The agreement between Hybrid Model and Beam Model results is excellent. Similar results are obtained for flush endplate and extended endplate connections. The above examples appear to indicate that using the line elements in ABAQUS to represent a physical beam was not able to

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Fig. 20. Comparison of deformation shapes between simulation and experimental results for extended end plate connection with large column (Test 5 of Wang et al. [26]).

Endplate Deformation Vs Temperature (LHS) 20 1st T-stub (Hybrid Model)

18

2nd T-stub (Hybrid Model)

Deformation (mm)

16 14

3rd T-stub (Hybrid Model)

12

1st T-stub (Detailed Model)

10

2nd T-stub (Detailed Model)

8

3rd T-stub (Detailed Model)

6 4 2 0 0

100

200

300

400

500

600

700

800

Temperature (oC) Fig. 21. Comparison of the left hand endplate T-stub deformations between Detailed Model and Hybrid Model for the fire test of extended endplate connection (Test 5 of Wang et al. [26]).

accurately simulate the beam behaviour if the beam underwent significant distortion. However, because of the relatively minor effect of this phenomenon for the type of beams used in practice, the line element representation gave similar joint component behaviour and failure temperatures. Therefore, the line element model is considered acceptable. 4. Comparison between different methods for catenary action beam behaviour In the comparisons in Section 3, the development of catenary was limited due to physical limits of the test specimens. This section assesses whether the most simplified model (Method 3: Beam

Model) is capable of reproducing the detailed connection behaviour when the beam develops substantial catenary action at very large deflections. For this purpose, a new structure was created, based on the aforementioned fire test using flush endplate connection. Details of the modifications are (see Fig. 26): 1. Beam length = 4 m. 2. Joint zone temperatures = 0.7 times the beam temperatures. 3. Applied load = 20 kN (to maintain the same load ratio as in the test). From the following Figs. 26–28, it is clear that the three simulation methods gave results in close agreement with each other. In

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Bolt Deformation Vs Temperature (RHS) 12

Deformation (mm)

10 8 6

Failure Envelope 4 Top Bolt (Hybrid Model) 2 0 0

200

400

600

800

1000

o

Temperature ( C) Fig. 22. Top bolt deformation on right side from Hybrid Model for the fire test of extended endplate connection (Test 5 of Wang et al. [26]).

Fig. 28, the predicted deformations of the endplate T-stubs using the Method 1 (Detailed Model) are slightly higher than from the other two models which used component-based models for the joints. But the difference is small. The explanation is that the effect of thermal expansion in the joint components was included in the Detailed Model, but not in the component based modelling of the joints (Hybrid Model and Beam Model). Fig. 29 shows that the top pair of bolts followed very similar pattern of behaviour.

Table 2 Comparison of the computational time for three methods. Simulation

Time

Flexible endplate connection (Method 1, half model) Flexible endplate connection (Method 2) Flexible endplate connection (Method 3) Flush endplate connection (Method 1, half model) Flush endplate connection (Method 2) Flush endplate connection (Method 3) Extended endplate connection (Method 1, half model) Extended endplate connection (Method 2) Extended endplate connection (Method 3)

1 h 15 min 18 s 57 min 6 s 1 min 7 s 2 h 26 min 15 s 1 h 33 min 3 s 2 min 22 s 1 h 53 min 54 s 1 h 2 min 13 s 2 min 3 s

5. Conclusions This paper has presented the results of using three methods of numerical simulation, all using ABAQUS, to model a series of fire

Middle-Span Deflection Vs Temperature

Axial Force Vs Temperature

0 0

100

200

300

400

500

600

700

800

Axial Force (kN)

Deflection (mm)

-50 -100 Test -150 Hybrid Model -200

Beam Model

-250

60

Test

40

Hybrid Model

20

Beam Model

0 -20 0

100

200

300

400

500

600

700

800

-40 -60 -80 -100 -120

-300

-140

Temperature (oC)

Temperature (oC)

Fig. 23. Comparison of mid-span deflection and axial force against temperature for the test using flexible endplate connection.

Failure Envelope

Hybrid Model Beam Model

0

100

200

300

400

500

600 o

700

Temperature ( C)

800

900 1000

Deformation (mm)

Deformation (mm)

Weld Deformation Vs Temperature (LHS) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Weld Deformation Vs Temperature (RHS)

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Hybrid Model Beam Model

Failure Envelope

0

100

200

300

400

500

600

700

800

900 1000

o

Temperature ( C)

Fig. 24. Comparison of the weld deformation for the test using flexible endplate connection between Hybrid Model and Beam Model.

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Endplate Deformation Vs Temperature (LHS)

Endplate Deformation Vs Temperature (RHS)

1st T-stub (Hybrid Model)

10

Deformation (mm)

Deformation (mm)

12

2nd T-stub (Hybrid Model)

8

st

1 T-stub (Beam Model) 6

2nd T-stub (Beam Model)

4 2 0 0

100

200

300

400

500

20 18 16 14 12 10 8 6 4 2 0

600

1st T-stub (Hybrid Model) 2nd T-stub (Hybrid Model) 1st T-stub (Beam Model) 2nd T-stub (Beam Model)

0

100

200

Temperature (oC)

300

400

500

600

700

800

Temperature (oC)

Fig. 25. Comparison of the endplate T-stub deformation for the test using flexible endplate connection between Hybrid Model and Beam Model.

Fig. 26. Modified structural model.

Middle-Span Deflection Vs Temperature

Axial Force Vs Temperature 100

0 0

100 200 300 400 500 600 700 800 900 1000

50

-200 -300 -400

Hybrid Model Beam Model Detailed Model

-500 -600

Axial Force (kN)

Deflection (mm)

-100

0 -50

0

100 200

300 400

500

600 700

800 900 1000

-100 -150

Hybrid Model Beam Model

-200

Detailed Model

-250

Temperature (oC)

Temperature (oC)

Fig. 27. Comparison of mid-span deflection and axial force against temperature for the structure in Fig. 26 between the three simulation methods.

tests on restrained beam–column subassemblies using end-plate connections, recently conducted at the Manchester University. Method 1 (detailed finite element model) is based on using three-dimensional brick elements (C3D8R) for all the structural

components. Method 2 uses the component based connection model for the connection components and 3-D brick elements for the other structural elements. Method 3 is the most simple, using the component based method for connection components and line

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Endplate Deformation Vs Temperature

Deformation (mm)

7 6

1st T-stub (Hybrid Model)

5

2nd T-stub (Hybrid Model) 1st T-stub (Beam Model)

4

2nd T-stub (Beam Model)

3

1st T-stub (Detailed Model) 2nd T-stub (Detailed Model)

2 1 0 0

100

200

300

400

500

600

700

Temperature (oC) Fig. 28. Endplate T-stub deformation comparison between the three simulation methods for the structure in Fig. 26.

Top Bolt Tensile Force Vs Connection Temperature 120 Hybrid Model

Force (kN)

100

Beam Model Detailed Model

80 60 40 20 0 0

150

300

450

600

750

Temperature (oC) Fig. 29. Top bolt axial force comparison between the three simulation methods for the structure in Fig. 26.

elements for the beams and columns. From comparisons of the simulation results with test results and between the three simulation methods, the following conclusions may be drawn: (1) Both Methods 1 and 2 (Detailed and Hybrid Models) can simulate the test results accurately, for the detailed deformed shapes of the test structures (including severe distortions of the beam web), the global beam behaviour (axial load and deflection–temperature relationships) and behaviour and failure of the different connection components. (2) As expected, Method 2 is much less time consuming than Method 1. However, using Method 2 is predicated on having available accurate connection component behaviour models. Through accurate prediction of a number of failure modes experienced by the fire tests, it appears that the various existing endplate connection component models that have been developed by other researchers have good accuracy in their predictions of load–deformation behaviour until failure. (3) Using Method 3 (Beam Model) cannot predict beam web distortion, leading to a slight overestimation of the beam limiting temperature (defined as the beam temperature when its axial force returns to zero). However, for realistic beam

cross-section dimensions, such a small discrepancy is unlikely to be of any importance. Since Method 3 uses the same component based connection behaviour models, Method 3 can predict the connection behaviour and failure with the same degree of accuracy as the other two methods. (4) Once the beam is in the catenary action stage, any difference in the predicted results using the three different methods becomes diminishingly small. (5) As recommendation, Method 2 should be used if detailed beam behaviour is desired. However, when studying complete frame behaviour using realistic connections and under very large deflections, such as investigating the effects of connections on robustness of steel framed structures incorporating catenary action in beams, Method 3 can be used. References [1] Al-Jabri KS. The behaviour of steel and composite beam-to-column connections in fire, PhD thesis, University of Sheffield; 1999. [2] Al-Jabri KS, Burgess IW, Plank RJ. Spring-stiffness model for flexible end-plate bare–steel joints in fire. J Constr Steel Res 2005;61:1672–91. [3] Al-Jabri KS, Seibi A, Karrech A. Modelling of unstiffened flush endplate bolted connections in fire. J Constr Steel Res 2006;62:151–9. [4] Aribert JM, Younes I, Lachal A. Low-cycle fatigue of steel sections subjected to a transverse concentrated load: experimental investigation and practical

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