- Email: [email protected]
Numerical evaluation of the effects of fire on steel connections; Part 1: Simulation techniques
Case Studies in Thermal Engineering 12 (2018) 445–453
Contents lists available at ScienceDirect
Case Studies in Thermal Engineering journal homepage: www.elsevier.com/locate/csite
Numerical evaluation of the effects of fire on steel connections; Part 1: Simulation techniques
T
⁎
Rohola Rahnavarda, , Robert J. Thomasb a b
Graduate Student, Department of Civil and Environmental Engineering, Clarkson University, NY, USA Assistant Professor, Department of Civil and Environmental Engineering, Clarkson University, Potsdam, NY, USA
A R T IC LE I N F O
ABS TRA CT
Keywords: Temperature Steel connections Non-linear analysis Finite element methods
Steel connections are used to connect between beam and column in steel moment frame structures. As of present time, there is a huge lack of understanding of the performance of steel connections and their response to fire especially the uncontrolled fires. Therefore, in this paper, by using a finite element program ABAQUS and with the static analysis of coupled temperaturedisplacement and to fully understand the behavior of such connection under the fire scenario, developed a temperature-dependent models for different types of steel connections are implemented. Finite Element Analyses (FEA) of selected experimental models are performed to verify the implementation of these models. Fully detailed, field-variable-dependent conductivity element models of the connections are developed, and analyses are performed to determine the effects of heat on the behavior of the materials in the elastic and plastic areas are considered. Moreover, severe deformation in the nonlinear region was investigated.
1. Introduction Steel connections between beams, girders, and columns are an integral and critical part of the design of steel structures. Standard design practices for steel connections may not consider temperatures outside the normal ambient temperature range. It is critical to consider the effects of thermal loading on steel connections, otherwise the structure may suffer severe damage or destruction in a fire scenario. This was observed in the September 11, 2001 attack on the World Trade Center. The steel structure provided resistance for the service loads and withstood the aircraft impact. However, the resulting thermal loading from explosion and fire resulted in the complete collapse of both structures. Many researchers have studied the effects of fire and heat on steel structures, but relatively few have employed numerical methods for comparison with experimental results [1]. One possible explanation for such a gap in this area is the lack of laboratory equipment due to the huge cost associated with conducting these studies. Saedi Darian et al. (2009–2012) conducted a study on simple connections with seat angles, in welded and bolted states [2,3]. Lawson (1990) investigated the effect of fire on the rigid connection of steel. He found that the behavior of joints and concrete cover over the connection regions improves when they are exposed to fire [4]. Rahnavard et al. (2014) studied the rigid connection of steel on end plate connection proposed thermal modeling using the finite element program ABAQUS [5–7]. Selamet and Garlock (2010) numerically studied the behavior of simple steel connections. They found that the durability hole's diameter of bolts is crucial in predicting the simple behavior of connections [8]. Suleiman et al. (2017) used 3-D finite element modeling of extended single plate shear connections to examine whether at the unfactored loads, the lateral displacement of beams or extended plate connections are mainly associated with the torsional moment at the connection regions [9]. Kalogeropoulos et al. (2012)
⁎
Corresponding author. E-mail addresses: [email protected] (R. Rahnavard), [email protected] (R.J. Thomas).
https://doi.org/10.1016/j.csite.2018.06.003 Received 10 December 2017; Received in revised form 2 June 2018; Accepted 10 June 2018 Available online 19 June 2018 2214-157X/ © 2018 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
modeled bolted rigid connection plates with end plates via ABAQUS finite element software and evaluated the influence of parameters such as mechanical loads, the yield and ultimate stress of bolts and the holes of bolts [10]. Wald et al. (2006) proposed experimental models for rigid end plate connections and compared the failure mode and shift of the beam centers in these models [11]. Kruppa (1976), in his research investigated how some types of steel joints will behave at high temperatures. He found that failure of steel members occurred prior to the failure of high strength bolts [12]. Burgess (2008) studied an explicit dynamic solver [13]. Other studies focused on the cooling phase of fire and used an artificial neural network to describe the stress-strain relations of steel connections exposed to fire [14]. Qiang et al. (2014) studied the post-fire behavior of high strength steel end plate connections. The results of their experimental study showed that the use of a high-strength thin steel plate, compared with a thick steel plate with less yield stress, does not present an appropriate performance in the end plate connection and even higher rotation capacity after fire [15]. The 14th edition of the AISC Steel Construction Manual (2010) and Eurocode 3 provides equations to evaluate the need for stiffeners; these equations were developed based on the fundamental concepts of structural mechanics [16-19]. An analytical method to calculate temperatures of components of reverse channel connection to concrete filled steel section under fire conditions evaluated by Jana et al. (2016). Temperature analysis of partially heated steel members in fire conducted by Wong (2017) [20]. Other research projects involve the study of the cooling phase of a fire, as well as implementation of an artificial neural network for the description of the stress–strain relations of steel under fire [23,24]. Huang et al. using a component-based method evaluated the behavior and effects of beam-end buckling in fire [25–30]. The current study evaluates the effect of heat on common rigid connections of steel using computer program ABAQUS [18] and compares these connections in terms of deformation, rotation, and moment- capacity.
Fig. 1. (a) Laboratory test geometry [11]; (b) details of the rigid end plate connection. 446
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Table 1 Mechanical properties as a function of temperature. Temperature (°C)
20 100 200 300 400 500 600 700 800 900 1000
Beam, Column and End plate
Bolt
Weld
E (Gpa)
Fy (Mpa)
Fu (Mpa)
E (Gpa)
Fy (Mpa)
Fu (Mpa)
E (Gpa)
Fy (Mpa)
Fu (Mpa)
210 192 189 177 168 124 105 39 18 2 1
388 374 439 392 361 318 215 118 48 48 27
494 490 571 570 478 371 222 147 51 37 29
210 192 189 177 168 124 105 39 18 2 1
600 561 655 592 542 477 322 178 70 69 52
800 783 913 910 760 595 355 236 86 60 46
210 192 189 177 168 124 105 39 18 2 1
640 590 690 630 595 523 380 289 130 123 90
850 830 874 870 811 646 400 298 145 115 100
2. Finite element modeling In this study, finite element method is used to model three steel rigid connections, including two types of bolted end plate connections and a welded connection. All models were simulated in ABAQUS considering geometric nonlinearity. To validate the numerical model, numerical results are compared to experimental results reported by Wald et al. [11] for bolted and welded connections. For further validation, numerical results are compared to experimental results reported by Qiang et al. [15] for a second bolted connection. 2.1. Model Geometry Fig. 1-a shows the geometry of the laboratory specimens and connections tested by Wald et al. [11]. The assembly consists of a 5.7 m IPE300 beam carrying a concrete slab connected at mid-height to a 2.4 m HEA300 column. This geometry was replicated in the numerical model, except that only half the length of the beam was modeled. Fig. 1-b shows a detailed view of the bolted connection. The welded connection was identical except that the bolted end plate connection was replaced by a fully welded connection. Fig. 6-a shows the geometry of a second bolted connection experimentally evaluated by Qiang et al. [15]. 2.2. Material Properties The material properties were modeled using a bilinear stress-strain relationship with strain hardening [21-25]. The effect of temperature was considered by defining a series of stress-strain relationships for increasing temperature ranges. Table 1 lists the mechanical properties of the structural elements (beam, column, and end plate), bolts, and welds for the temperature ranges considered. Structural elements were steel with a yield stress of 388 MPa and ultimate stress of 494 MPa at 20 °C. Bolts were also steel with a yield stress of 600 MPa and ultimate stress of 800 MPa at 20 °C. Welds had a yield stress of 640 MPa and ultimate stress of 850 MPa at 20 °C. The material model was isotropic. 2.3. Loading and boundary conditions To simplify the numerical calculations, the concrete slab shown in Fig. 1 [11] was not modeled, but it was necessary to consider its dead load and effects on preventing the top beam flange from out of plane displacement. This was accomplished by applying a concentrated load of 20 kN on the to flange of the beam at a distance of 700 mm from the support [11]. The gravity loads (self-weight and applied load) are first applied to the model. The temperature is then ramped gradually to match the experimental conditions [11]. Fig. 2-a shows the model geometry split into two zones corresponding to the joint and the beam. Fig. 2-b shows the temperature in various regions of the joint and beam as a function of time. Similarly, Fig. 2-c shows the temperature in the bolts, end plate. Moreover, the weld temperature is the same as the joint temperature. The static coupled temperaturedisplacement model was then run in ABAQUS and numerical results were compared with laboratory results [11]. 2.4. Meshing Fig. 3 shows the meshed model for the bolted end plate connection. The model was meshed with C3D8T field-variable-dependent conductivity elements with eight nodes per element and three degrees of freedom per node. The mesh was refined near the connection as shown in Fig. 3. Reduced integration caused by the elements could reduce the math calculations. A sensitivity analysis was performed on the mesh size for each of the three model cases [11,15], and the model error relative to experimental results was reported in Table 2. The change between case numbers 5 and 6 was negligible, so the mesh size listed in case number 5 was selected for the study. The resulting mesh size was 5 mm for beam and column regions and 5 mm for bolts. 447
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Fig. 2. (a) Temperature regions; b) temperature in beam; (c) temperature in joint [11].
Fig. 3. Meshed model of bolted connection [11].
448
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Table 2 Mesh sensitivity results. Case Number
1 2 3 4 5 6
Mesh Size (mm)
Error (%)
Beam and Column
Bolt
Bolted FE Model based on [12]
Bolted FE Model based on [15]
Welded FE Model based on [12]
80 70 60 50 10 5
30 20 10 5 5
9 8.5 8 6 1.5 1.5
10 10 8 6 3 2.5
9 8 8 6 1 1
40
2.5. Interaction Interaction between the beam and column in the bolted connection was modeled using surface-to-surface contact. This type of contact will not allow any penetration during the loading process. Friction between the surfaces was modeled using the classical Coulomb model with a friction coefficient of 0.2 [9]. Hard contacts were used to simulate the properties of a normal contact. In the welded connections, a tie constraint was selected to define the weld [9]. 3. Validation This section presents the results of validation of the proposed numerical model for the effects of fire on bolted end plate and welded steel connections. 3.1. Bolted end plate connections The bolted end plate connection from [11] was modeled using the procedure defined above. The resulting mid-span deflection
Fig. 4. Comparison of results for bolted connection [11]: (a) mid-span deflection; (b) bolt force. 449
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Fig. 5. Deformation of bolted connection: (a) experimental [11]; (b) numerical.
and axial force on the bolts are compared to experimental results in Fig. 4. Fig. 5 shows a comparison of the failure modes predicted by the numerical model and those observed in the experiments. The mid-span deflection and axial blot forces predicted by the numerical model were in very close agreement with the experimental results. Similarly, the predicted failure mode closely resembled that observed in the experiments. This suggests that the proposed modeling procedure is well conditioned to predict the effects of fire on bolted steel connections. To further validate the numerical model, the bolted connection from [15] was examined. The resulting moment-rotation relationship is compared to experimental results in Fig. 6. The maximum moment observed during the experiment was 255 kN m. The maximum moment predicted by the numerical model was 261 kN m, a difference of only 2%. Furthermore, the moment at the connection in both experimental and numerical results reduced suddenly near 240 mrad rotation. Fig. 7 compares the resulting deformations between numerical and experimental models; the failure mode predicted by the numerical model is remarkably similar to that observed in the experiment. This provides further evidence of the power of the proposed numerical model to predict the effects of fire on bolted steel connections.
Fig. 6. (a) Model of bolted connection [15]; (b) comparison of experimental and numerical moment-rotation relationship. 450
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Fig. 7. Deformations of bolted connection [15].
3.2. Welded connection The previous subsection provided good evidence in favor of the ability of the numerical model to predict the effects of fire on bolted steel connections. This subsection will investigate the use of the proposed model for predicting the effects of fire on welded connections. The welded connection from [11] was modeled and resulting the mid-span displacement and failure modes were compared to experimental results. Fig. 8-a shows the mid-span deflection, which closely followed experimental observations, with a maximum deflection near 0.35 m at a time of about one hour. The experimental connection deformation is shown in Fig. 8-b. The deformation predicted by the numerical model, shown in Fig. 8-c, closely matches the experimental result. These results show that the numerical model is also able to accurately predict the effects of fire on welded steel connections. 4. Summary of results This paper presents the results of a static non-linear coupled temperature-displacement finite element analysis of the effects of fire 451
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Fig. 8. Results for welded connection [11]: (a) mid-span deflection; (b) experimental deformation; (c) numerical deformation.
on bolted and welded steel connections. The authors selected three steel connections—two bolted and one welded—that had been experimentally evaluated under fire loading by other authors. These connections were modeled using the proposed method, and the predicted behavior was compared to the experimental results. The results were remarkably similar with very little error in the predicted mechanical response or ultimate displacements and failure modes. This provides conclusive evidence that the proposed model is well conditioned to predict the effects of fire on bolted and welded steel connections. References [1] Federal Building and Fire Safety Investigation of the World Trade Center Disaster: Final Report of the National Construction Safety Team on the Collapses of the World Trade Center Tower, September, 2005. [2] A. Pirmoz, A.S. Khoei, E. Mohammad Rezapour, A.S. Daryan, Moment-rotation behavior of bolted top-seat angle connections, J. Constr. Steel Res. 65 (4) (2009) 973–984. [3] M. Yahyai, A.S. Daryan, The study of welded semi-rigid connections in fire (801), Struct. Des. Tall Spec. Build. 22 (10) (2011) 783 (801). [4] R.M. Lawson, Behavior of steel beam-to-column connections in fire, Struct. Eng. Lond. 68 (14) (1990) 263–271. [5] Akbar Hassanipour, Rohola Rahnavard, Ali Mokhtari, Najaf Rahnavard, Numerical investigation on reduces web beam section moment connections under the effects on cyclic loading, J. Multidiscip. Eng. Sci. Technol.(JMEST) 2 (8), 3159–0040. [6] Rohola Rahnavard, Navid Siahpolo, Mohammad Naghavi, Akbar Hassanipour, Analytical Study of common rigid steel connections under the effect of Heat, Adv. Civil. Eng. 2014 (2014), http://dx.doi.org/10.1155/2014/692323 (Article ID 692323, 10 pages). [7] R. Rahnavard, A. Hassanipour, N. Siahpolo, Analytical study on new types of reduced beam section moment connections affecting cyclic behavior, Case Stud. Struct. Eng. 3 (2015) 33–51. [8] S. Selamet, M.E. Garlock, Robust fire design of single plate shear connections, Eng. Struct. 32 (8) (2010) 2367–2378. [9] Mohamed F. Suleiman, Bahram M. Shahrooz, Herbert L. Bill, Patrick J. Fortney, William A. Thornton, “3-D Finite element modeling of extended single plate shear connections: predicting the mode of failure, Int. J. Steel Struct. 17 (2) (2017) 525–534. [10] A. Kalogeropoulos, G.A. Drosopoulos, G.E. Stavroulakis, Thermal-stress analysis of a three-dimensional end-plate steel joint, Constr. Build. Mater. 29 (2012) 619–626. [11] F. Wald, L. Sim˜oes da Silva, D.B. Moore, et al., Experimental behavior of a steel structure under natural fire, Fire Saf. J. 41 (7) (2006) 509–522. [12] J. Kruppa, R´esistance en feu des assemblages par boulous, CTICM Report 1013-1, Centre Technique Industrial de la Construction Metallique, St. Re’my les Chevreuse, France, 1976. [13] H. Yu, I.W. Burgess, J.B. Davison, R.J. Plank, Numerical simulation of bolted steel connections in fire using explicit dynamic analysis, J. Constr. Steel Res. 64 (5) (2008) 515–525. [14] T. Hozjan, G. Turk, S. Srpˇciˇc, Fire analysis of steel frames with the use of artificial neural networks, J. Constr. Steel Res. 63 (10) (2007) 1396–1403. [15] Xuhong Qiang, Xu Jiang, Frans S.K. Bijlaard, Henk Kolstein, Yongfeng Luo, Post-fire behaviour of high strength steel endplate connections — Part 1: experimental study, J. Constr. Steel Res (2014), http://dx.doi.org/10.1016/j.jcsr.2014.10.028. [16] Eurocode 3, Design of steel structures part 1.2: general rules structural fire design, ENV 1993-1-2, in: Proceedings of the European Committee for Standardization, Brussels, Belgium, 2001. [17] Eurocode 3, prEN-1993-1-8: 20, Part 1.8: Design of joints. Eurocode 3: Design of steel structures, draft2 rev, in: Proceedings of the European Committee forStandardization, Brussels, Belgium, 2000. [18] Abaqus user’s manual, 2011. [19] American Institute of Steel Construction. Manual of Steel Construction, 14th edition. [20] M.B. Wong, Temperature analysis of partially heated steel members in fire, J. Constr. Steel Res. 128 (2017) 1–6. [21] Rohola Rahnavard, Akbar Hassanipour, Ali Mounesi, Numerical study on important parameters of composite steel-concrete shear walls, J. Constr. Steel Res. 121 (2016) 441–456.
452
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
[22] Rohola Rahnavard, Akbar Hassanipour, Mohamed Suleiman, Ali Mokhtari, Evaluation on eccentrically braced frame with single and double shear panels, J. Build. Eng. 10 (2017) 13–25. [23] H. Yu, I.W. Burgess, J.B. Davison, R.J. Plank, Numerical simulation of bolted steel connections in fire using explicit dynamic analysis, J. Constraction Steel Res. 64 (2008) 515–525. [24] Rohola Rahnavard, Faramarz Fathi Zadeh Fard, Ali Hosseini, Mohamed Suleiman, Nonlinear analysis on progressive collapse of tall steel composite buildings, Case Stud. Constr. Mater. 8 (2018) 359–379. [25] Guan Quan, Shan-Shan Huang, Ian Burgess, The behaviour and effects of beam-end buckling in fire using a component-based method, Eng. Struct. 139 (2017) 15–30. [26] Zhen Guo, Shan-Shan Huang, Behaviour of restrained steel beam with reduced beam section exposed to fire, J. Constr. Steel Res. 122 (2016) 434–444. [27] Guan Quan, Shan-Shan Huang, Ian Burgess, Component-based model of buckling panels of steel beams at elevated temperatures, J. Constr. Steel Res. 118 (2016) 91–104. [28] Hongbo Liu, Xiangwei Liao, Zhihua Chen, Shan-Shan Huang, Post-fire residual mechanical properties of steel butt weld — experimental study, J. Constr. Steel Res. 129 (2017) 156–162. [29] Guan Quan, Shan-Shan Huang, Ian Burgess, An analytical approach to modelling shear panels in steel beams at elevated temperatures, Eng. Struct. 85 (2015) 73–82. [30] Rohola Rahnavard, Mohammad Naghavi, Maryam Abudi, Mohamed Suleiman, Investigating modeling approaches of Buckling-restrained braces under cyclic loads, Case Stud. Constr. Mater. 8 (2018) 476–488.
453
Contents lists available at ScienceDirect
Case Studies in Thermal Engineering journal homepage: www.elsevier.com/locate/csite
Numerical evaluation of the effects of fire on steel connections; Part 1: Simulation techniques
T
⁎
Rohola Rahnavarda, , Robert J. Thomasb a b
Graduate Student, Department of Civil and Environmental Engineering, Clarkson University, NY, USA Assistant Professor, Department of Civil and Environmental Engineering, Clarkson University, Potsdam, NY, USA
A R T IC LE I N F O
ABS TRA CT
Keywords: Temperature Steel connections Non-linear analysis Finite element methods
Steel connections are used to connect between beam and column in steel moment frame structures. As of present time, there is a huge lack of understanding of the performance of steel connections and their response to fire especially the uncontrolled fires. Therefore, in this paper, by using a finite element program ABAQUS and with the static analysis of coupled temperaturedisplacement and to fully understand the behavior of such connection under the fire scenario, developed a temperature-dependent models for different types of steel connections are implemented. Finite Element Analyses (FEA) of selected experimental models are performed to verify the implementation of these models. Fully detailed, field-variable-dependent conductivity element models of the connections are developed, and analyses are performed to determine the effects of heat on the behavior of the materials in the elastic and plastic areas are considered. Moreover, severe deformation in the nonlinear region was investigated.
1. Introduction Steel connections between beams, girders, and columns are an integral and critical part of the design of steel structures. Standard design practices for steel connections may not consider temperatures outside the normal ambient temperature range. It is critical to consider the effects of thermal loading on steel connections, otherwise the structure may suffer severe damage or destruction in a fire scenario. This was observed in the September 11, 2001 attack on the World Trade Center. The steel structure provided resistance for the service loads and withstood the aircraft impact. However, the resulting thermal loading from explosion and fire resulted in the complete collapse of both structures. Many researchers have studied the effects of fire and heat on steel structures, but relatively few have employed numerical methods for comparison with experimental results [1]. One possible explanation for such a gap in this area is the lack of laboratory equipment due to the huge cost associated with conducting these studies. Saedi Darian et al. (2009–2012) conducted a study on simple connections with seat angles, in welded and bolted states [2,3]. Lawson (1990) investigated the effect of fire on the rigid connection of steel. He found that the behavior of joints and concrete cover over the connection regions improves when they are exposed to fire [4]. Rahnavard et al. (2014) studied the rigid connection of steel on end plate connection proposed thermal modeling using the finite element program ABAQUS [5–7]. Selamet and Garlock (2010) numerically studied the behavior of simple steel connections. They found that the durability hole's diameter of bolts is crucial in predicting the simple behavior of connections [8]. Suleiman et al. (2017) used 3-D finite element modeling of extended single plate shear connections to examine whether at the unfactored loads, the lateral displacement of beams or extended plate connections are mainly associated with the torsional moment at the connection regions [9]. Kalogeropoulos et al. (2012)
⁎
Corresponding author. E-mail addresses: [email protected] (R. Rahnavard), [email protected] (R.J. Thomas).
https://doi.org/10.1016/j.csite.2018.06.003 Received 10 December 2017; Received in revised form 2 June 2018; Accepted 10 June 2018 Available online 19 June 2018 2214-157X/ © 2018 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
modeled bolted rigid connection plates with end plates via ABAQUS finite element software and evaluated the influence of parameters such as mechanical loads, the yield and ultimate stress of bolts and the holes of bolts [10]. Wald et al. (2006) proposed experimental models for rigid end plate connections and compared the failure mode and shift of the beam centers in these models [11]. Kruppa (1976), in his research investigated how some types of steel joints will behave at high temperatures. He found that failure of steel members occurred prior to the failure of high strength bolts [12]. Burgess (2008) studied an explicit dynamic solver [13]. Other studies focused on the cooling phase of fire and used an artificial neural network to describe the stress-strain relations of steel connections exposed to fire [14]. Qiang et al. (2014) studied the post-fire behavior of high strength steel end plate connections. The results of their experimental study showed that the use of a high-strength thin steel plate, compared with a thick steel plate with less yield stress, does not present an appropriate performance in the end plate connection and even higher rotation capacity after fire [15]. The 14th edition of the AISC Steel Construction Manual (2010) and Eurocode 3 provides equations to evaluate the need for stiffeners; these equations were developed based on the fundamental concepts of structural mechanics [16-19]. An analytical method to calculate temperatures of components of reverse channel connection to concrete filled steel section under fire conditions evaluated by Jana et al. (2016). Temperature analysis of partially heated steel members in fire conducted by Wong (2017) [20]. Other research projects involve the study of the cooling phase of a fire, as well as implementation of an artificial neural network for the description of the stress–strain relations of steel under fire [23,24]. Huang et al. using a component-based method evaluated the behavior and effects of beam-end buckling in fire [25–30]. The current study evaluates the effect of heat on common rigid connections of steel using computer program ABAQUS [18] and compares these connections in terms of deformation, rotation, and moment- capacity.
Fig. 1. (a) Laboratory test geometry [11]; (b) details of the rigid end plate connection. 446
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Table 1 Mechanical properties as a function of temperature. Temperature (°C)
20 100 200 300 400 500 600 700 800 900 1000
Beam, Column and End plate
Bolt
Weld
E (Gpa)
Fy (Mpa)
Fu (Mpa)
E (Gpa)
Fy (Mpa)
Fu (Mpa)
E (Gpa)
Fy (Mpa)
Fu (Mpa)
210 192 189 177 168 124 105 39 18 2 1
388 374 439 392 361 318 215 118 48 48 27
494 490 571 570 478 371 222 147 51 37 29
210 192 189 177 168 124 105 39 18 2 1
600 561 655 592 542 477 322 178 70 69 52
800 783 913 910 760 595 355 236 86 60 46
210 192 189 177 168 124 105 39 18 2 1
640 590 690 630 595 523 380 289 130 123 90
850 830 874 870 811 646 400 298 145 115 100
2. Finite element modeling In this study, finite element method is used to model three steel rigid connections, including two types of bolted end plate connections and a welded connection. All models were simulated in ABAQUS considering geometric nonlinearity. To validate the numerical model, numerical results are compared to experimental results reported by Wald et al. [11] for bolted and welded connections. For further validation, numerical results are compared to experimental results reported by Qiang et al. [15] for a second bolted connection. 2.1. Model Geometry Fig. 1-a shows the geometry of the laboratory specimens and connections tested by Wald et al. [11]. The assembly consists of a 5.7 m IPE300 beam carrying a concrete slab connected at mid-height to a 2.4 m HEA300 column. This geometry was replicated in the numerical model, except that only half the length of the beam was modeled. Fig. 1-b shows a detailed view of the bolted connection. The welded connection was identical except that the bolted end plate connection was replaced by a fully welded connection. Fig. 6-a shows the geometry of a second bolted connection experimentally evaluated by Qiang et al. [15]. 2.2. Material Properties The material properties were modeled using a bilinear stress-strain relationship with strain hardening [21-25]. The effect of temperature was considered by defining a series of stress-strain relationships for increasing temperature ranges. Table 1 lists the mechanical properties of the structural elements (beam, column, and end plate), bolts, and welds for the temperature ranges considered. Structural elements were steel with a yield stress of 388 MPa and ultimate stress of 494 MPa at 20 °C. Bolts were also steel with a yield stress of 600 MPa and ultimate stress of 800 MPa at 20 °C. Welds had a yield stress of 640 MPa and ultimate stress of 850 MPa at 20 °C. The material model was isotropic. 2.3. Loading and boundary conditions To simplify the numerical calculations, the concrete slab shown in Fig. 1 [11] was not modeled, but it was necessary to consider its dead load and effects on preventing the top beam flange from out of plane displacement. This was accomplished by applying a concentrated load of 20 kN on the to flange of the beam at a distance of 700 mm from the support [11]. The gravity loads (self-weight and applied load) are first applied to the model. The temperature is then ramped gradually to match the experimental conditions [11]. Fig. 2-a shows the model geometry split into two zones corresponding to the joint and the beam. Fig. 2-b shows the temperature in various regions of the joint and beam as a function of time. Similarly, Fig. 2-c shows the temperature in the bolts, end plate. Moreover, the weld temperature is the same as the joint temperature. The static coupled temperaturedisplacement model was then run in ABAQUS and numerical results were compared with laboratory results [11]. 2.4. Meshing Fig. 3 shows the meshed model for the bolted end plate connection. The model was meshed with C3D8T field-variable-dependent conductivity elements with eight nodes per element and three degrees of freedom per node. The mesh was refined near the connection as shown in Fig. 3. Reduced integration caused by the elements could reduce the math calculations. A sensitivity analysis was performed on the mesh size for each of the three model cases [11,15], and the model error relative to experimental results was reported in Table 2. The change between case numbers 5 and 6 was negligible, so the mesh size listed in case number 5 was selected for the study. The resulting mesh size was 5 mm for beam and column regions and 5 mm for bolts. 447
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Fig. 2. (a) Temperature regions; b) temperature in beam; (c) temperature in joint [11].
Fig. 3. Meshed model of bolted connection [11].
448
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Table 2 Mesh sensitivity results. Case Number
1 2 3 4 5 6
Mesh Size (mm)
Error (%)
Beam and Column
Bolt
Bolted FE Model based on [12]
Bolted FE Model based on [15]
Welded FE Model based on [12]
80 70 60 50 10 5
30 20 10 5 5
9 8.5 8 6 1.5 1.5
10 10 8 6 3 2.5
9 8 8 6 1 1
40
2.5. Interaction Interaction between the beam and column in the bolted connection was modeled using surface-to-surface contact. This type of contact will not allow any penetration during the loading process. Friction between the surfaces was modeled using the classical Coulomb model with a friction coefficient of 0.2 [9]. Hard contacts were used to simulate the properties of a normal contact. In the welded connections, a tie constraint was selected to define the weld [9]. 3. Validation This section presents the results of validation of the proposed numerical model for the effects of fire on bolted end plate and welded steel connections. 3.1. Bolted end plate connections The bolted end plate connection from [11] was modeled using the procedure defined above. The resulting mid-span deflection
Fig. 4. Comparison of results for bolted connection [11]: (a) mid-span deflection; (b) bolt force. 449
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Fig. 5. Deformation of bolted connection: (a) experimental [11]; (b) numerical.
and axial force on the bolts are compared to experimental results in Fig. 4. Fig. 5 shows a comparison of the failure modes predicted by the numerical model and those observed in the experiments. The mid-span deflection and axial blot forces predicted by the numerical model were in very close agreement with the experimental results. Similarly, the predicted failure mode closely resembled that observed in the experiments. This suggests that the proposed modeling procedure is well conditioned to predict the effects of fire on bolted steel connections. To further validate the numerical model, the bolted connection from [15] was examined. The resulting moment-rotation relationship is compared to experimental results in Fig. 6. The maximum moment observed during the experiment was 255 kN m. The maximum moment predicted by the numerical model was 261 kN m, a difference of only 2%. Furthermore, the moment at the connection in both experimental and numerical results reduced suddenly near 240 mrad rotation. Fig. 7 compares the resulting deformations between numerical and experimental models; the failure mode predicted by the numerical model is remarkably similar to that observed in the experiment. This provides further evidence of the power of the proposed numerical model to predict the effects of fire on bolted steel connections.
Fig. 6. (a) Model of bolted connection [15]; (b) comparison of experimental and numerical moment-rotation relationship. 450
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Fig. 7. Deformations of bolted connection [15].
3.2. Welded connection The previous subsection provided good evidence in favor of the ability of the numerical model to predict the effects of fire on bolted steel connections. This subsection will investigate the use of the proposed model for predicting the effects of fire on welded connections. The welded connection from [11] was modeled and resulting the mid-span displacement and failure modes were compared to experimental results. Fig. 8-a shows the mid-span deflection, which closely followed experimental observations, with a maximum deflection near 0.35 m at a time of about one hour. The experimental connection deformation is shown in Fig. 8-b. The deformation predicted by the numerical model, shown in Fig. 8-c, closely matches the experimental result. These results show that the numerical model is also able to accurately predict the effects of fire on welded steel connections. 4. Summary of results This paper presents the results of a static non-linear coupled temperature-displacement finite element analysis of the effects of fire 451
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
Fig. 8. Results for welded connection [11]: (a) mid-span deflection; (b) experimental deformation; (c) numerical deformation.
on bolted and welded steel connections. The authors selected three steel connections—two bolted and one welded—that had been experimentally evaluated under fire loading by other authors. These connections were modeled using the proposed method, and the predicted behavior was compared to the experimental results. The results were remarkably similar with very little error in the predicted mechanical response or ultimate displacements and failure modes. This provides conclusive evidence that the proposed model is well conditioned to predict the effects of fire on bolted and welded steel connections. References [1] Federal Building and Fire Safety Investigation of the World Trade Center Disaster: Final Report of the National Construction Safety Team on the Collapses of the World Trade Center Tower, September, 2005. [2] A. Pirmoz, A.S. Khoei, E. Mohammad Rezapour, A.S. Daryan, Moment-rotation behavior of bolted top-seat angle connections, J. Constr. Steel Res. 65 (4) (2009) 973–984. [3] M. Yahyai, A.S. Daryan, The study of welded semi-rigid connections in fire (801), Struct. Des. Tall Spec. Build. 22 (10) (2011) 783 (801). [4] R.M. Lawson, Behavior of steel beam-to-column connections in fire, Struct. Eng. Lond. 68 (14) (1990) 263–271. [5] Akbar Hassanipour, Rohola Rahnavard, Ali Mokhtari, Najaf Rahnavard, Numerical investigation on reduces web beam section moment connections under the effects on cyclic loading, J. Multidiscip. Eng. Sci. Technol.(JMEST) 2 (8), 3159–0040. [6] Rohola Rahnavard, Navid Siahpolo, Mohammad Naghavi, Akbar Hassanipour, Analytical Study of common rigid steel connections under the effect of Heat, Adv. Civil. Eng. 2014 (2014), http://dx.doi.org/10.1155/2014/692323 (Article ID 692323, 10 pages). [7] R. Rahnavard, A. Hassanipour, N. Siahpolo, Analytical study on new types of reduced beam section moment connections affecting cyclic behavior, Case Stud. Struct. Eng. 3 (2015) 33–51. [8] S. Selamet, M.E. Garlock, Robust fire design of single plate shear connections, Eng. Struct. 32 (8) (2010) 2367–2378. [9] Mohamed F. Suleiman, Bahram M. Shahrooz, Herbert L. Bill, Patrick J. Fortney, William A. Thornton, “3-D Finite element modeling of extended single plate shear connections: predicting the mode of failure, Int. J. Steel Struct. 17 (2) (2017) 525–534. [10] A. Kalogeropoulos, G.A. Drosopoulos, G.E. Stavroulakis, Thermal-stress analysis of a three-dimensional end-plate steel joint, Constr. Build. Mater. 29 (2012) 619–626. [11] F. Wald, L. Sim˜oes da Silva, D.B. Moore, et al., Experimental behavior of a steel structure under natural fire, Fire Saf. J. 41 (7) (2006) 509–522. [12] J. Kruppa, R´esistance en feu des assemblages par boulous, CTICM Report 1013-1, Centre Technique Industrial de la Construction Metallique, St. Re’my les Chevreuse, France, 1976. [13] H. Yu, I.W. Burgess, J.B. Davison, R.J. Plank, Numerical simulation of bolted steel connections in fire using explicit dynamic analysis, J. Constr. Steel Res. 64 (5) (2008) 515–525. [14] T. Hozjan, G. Turk, S. Srpˇciˇc, Fire analysis of steel frames with the use of artificial neural networks, J. Constr. Steel Res. 63 (10) (2007) 1396–1403. [15] Xuhong Qiang, Xu Jiang, Frans S.K. Bijlaard, Henk Kolstein, Yongfeng Luo, Post-fire behaviour of high strength steel endplate connections — Part 1: experimental study, J. Constr. Steel Res (2014), http://dx.doi.org/10.1016/j.jcsr.2014.10.028. [16] Eurocode 3, Design of steel structures part 1.2: general rules structural fire design, ENV 1993-1-2, in: Proceedings of the European Committee for Standardization, Brussels, Belgium, 2001. [17] Eurocode 3, prEN-1993-1-8: 20, Part 1.8: Design of joints. Eurocode 3: Design of steel structures, draft2 rev, in: Proceedings of the European Committee forStandardization, Brussels, Belgium, 2000. [18] Abaqus user’s manual, 2011. [19] American Institute of Steel Construction. Manual of Steel Construction, 14th edition. [20] M.B. Wong, Temperature analysis of partially heated steel members in fire, J. Constr. Steel Res. 128 (2017) 1–6. [21] Rohola Rahnavard, Akbar Hassanipour, Ali Mounesi, Numerical study on important parameters of composite steel-concrete shear walls, J. Constr. Steel Res. 121 (2016) 441–456.
452
Case Studies in Thermal Engineering 12 (2018) 445–453
R. Rahnavard, R.J. Thomas
[22] Rohola Rahnavard, Akbar Hassanipour, Mohamed Suleiman, Ali Mokhtari, Evaluation on eccentrically braced frame with single and double shear panels, J. Build. Eng. 10 (2017) 13–25. [23] H. Yu, I.W. Burgess, J.B. Davison, R.J. Plank, Numerical simulation of bolted steel connections in fire using explicit dynamic analysis, J. Constraction Steel Res. 64 (2008) 515–525. [24] Rohola Rahnavard, Faramarz Fathi Zadeh Fard, Ali Hosseini, Mohamed Suleiman, Nonlinear analysis on progressive collapse of tall steel composite buildings, Case Stud. Constr. Mater. 8 (2018) 359–379. [25] Guan Quan, Shan-Shan Huang, Ian Burgess, The behaviour and effects of beam-end buckling in fire using a component-based method, Eng. Struct. 139 (2017) 15–30. [26] Zhen Guo, Shan-Shan Huang, Behaviour of restrained steel beam with reduced beam section exposed to fire, J. Constr. Steel Res. 122 (2016) 434–444. [27] Guan Quan, Shan-Shan Huang, Ian Burgess, Component-based model of buckling panels of steel beams at elevated temperatures, J. Constr. Steel Res. 118 (2016) 91–104. [28] Hongbo Liu, Xiangwei Liao, Zhihua Chen, Shan-Shan Huang, Post-fire residual mechanical properties of steel butt weld — experimental study, J. Constr. Steel Res. 129 (2017) 156–162. [29] Guan Quan, Shan-Shan Huang, Ian Burgess, An analytical approach to modelling shear panels in steel beams at elevated temperatures, Eng. Struct. 85 (2015) 73–82. [30] Rohola Rahnavard, Mohammad Naghavi, Maryam Abudi, Mohamed Suleiman, Investigating modeling approaches of Buckling-restrained braces under cyclic loads, Case Stud. Constr. Mater. 8 (2018) 476–488.
453