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Modeling of bolted angle connections in fire
ARTICLE IN PRESS Fire Safety Journal 44 (2009) 976–988
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Modeling of bolted angle connections in fire Amir Saedi Daryan , Mahmood Yahyai Civil Engineering Department of K.N. Toosi University of Technology, Tehran, Iran
a r t i c l e in f o
a b s t r a c t
Article history: Received 29 March 2008 Received in revised form 3 March 2009 Accepted 15 June 2009 Available online 25 July 2009
Recent structural collapses caused by fire have focused attention on research concerning fire safety in building design. The high cost of experimental tests and limitations in the number of geometrical and mechanical parameters, in addition to advances in numerical methods that provide the ability to simulate complicated structures with numerous parameters, make the finite element method an attractive device for modeling the behavior of structural connections in fire. In this paper, the behavior of bolted angle connections was studied at ambient and elevated temperatures using the ANSYS finite element software. Steel members and connection components were considered to behave nonlinearly. Degradation of steel properties with increasing temperature was assumed to be in accordance with EC3 [Euro Code 3: Design of Steel Structures, Part 1.2: General Rules Structural Fire Design (drafts), Document CEN, European Committee for Standardization, 1995 [1]] recommendations. Finite element results and experimental tests conducted on bolted angle connections in fire conditions were compared, and modeled failure modes and moment–rotation–temperature characteristics were in good agreement with those associated with experimental tests. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Bolted angle connections Finite element modeling Fire modeling Elevated temperature
1. Introduction When exposed to high temperatures during fire conditions, steel experiences a significant and sudden decrease in strength and stiffness, resulting in decreased load carrying capacity. Therefore, steel structures should be constructed in a way that assures their safety during fires. Many experimental tests have been conducted in the last three decades to study the effect of fire on structures. These tests have been conducted either on full-scale steel structures or on isolated steel members like columns, beams and connections. In common steel structure design, beam-tocolumn connections were assumed to be rigid or pinned, and the connections were assumed to possess significant stiffness and strength at elevated temperatures. However, actual connection behavior exhibits a wide spectrum of characteristics between these two limits. Because these connections play an important role in the survival time of structures, experiments have been conducted to study the behavior of connections at elevated temperatures. Experimental tests provide reliable results that accurately describe the behavior of the beam-to-column connections. However, physical experiments are sometimes either not feasible or too expensive to conduct. In addition, the number of
Corresponding author. Tel.: +982122749398; fax: +982122749399.
E-mail addresses: [email protected] (A. Saedi Daryan), [email protected] (M. Yahyai). 0379-7112/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.firesaf.2009.06.005
geometrical and mechanical parameters is limited in experimental studies. As a result, significant advances in the finite element method have made it one of the most powerful numerical methods available for modeling the behavior of connections, especially at elevated temperatures. The use of finite element modeling to study connection behavior began in the early 1970s, as the potential for the application of computers to solving structural problems became evident. The modeling of the behavior of connections at elevated temperature was first performed in the 1990s. Early attempts at modeling connection behavior in fire were initiated by Liu and Morris [2] and Liu [3–6], who developed a finite element model, FEAST, to simulate the various types of connections under fire conditions. The beam, column, end plate and stiffeners were modeled using eight-node shell elements, and the nonlinear behavior of the material at elevated temperatures was considered. The stress–strain–temperature characteristics were adopted based on recommended values from experimental tests, and the models showed close agreement with experimental data. El-Houssieny et al. [7] developed a three-dimensional (3-D) finite element model to simulate the response of extended end plates at both ambient and elevated temperatures. Close agreement with experimental work was obtained, and subsequent parametric studies were conducted to investigate the influence of connection behavior at normal and elevated temperatures. Spyrou et al. [8] modeled T-stub specimens at elevated temperatures using the finite element program ANSYS. A close agreement was found
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between the experimental results and 3-D analyses. Rahman et al. [9] used ANSYS to study the behavior of fin plate connections in fire. For modeling the beams, columns, fin plates and bolts, the authors used 3D solid, prestressed and contact elements, respectively. Despite the prediction of realistic results by the model, no experimental data were used to quantify its accuracy. Sarraj et al. [10] also developed 3-D ABAQUS models of fin plate connections, which included the important contact interaction between the bolts and the fin plate and beam web. The models were validated against lap joint data at ambient temperature. In 2005, a fire test was conducted by Wald et al. [11] at the Czech Technical University. A finite element model was developed by Al-Jabri et al. [12] to study the behavior of flush end plate bare steel joints at elevated temperatures using the general purpose finite element software ABAQUS. The finite element model was used to establish the moment–rotation characteristics of the flush end plate bare steel joints with a concentrated force at elevated temperatures. The joint components were modeled using 3-D brick elements, while contact between the various components was modeled using Coulomb friction. Material nonlinearity was considered to model steel members and the joint components. Degradation of steel properties with increasing temperatures was taken in accordance with design code recommendations. The obtained FE-simulated failure modes and moment–rotation– temperature characteristics of the joints compared well with the experimental data in both the elastic and plastic regions. Lou and Li [13] used ANSYS to model the behavior of cruciform tests with extended end plates in fire. A sequential analysis was used; a transient thermal analysis was conducted first, followed by a static structural analysis. Non-uniform thermal expansion, geometric nonlinearity, temperature-dependent nonlinear material behavior, bolt pretension and surface-to-surface contact were all included in the analyses. Excellent correlation was achieved between the analyses and experimental results from two fire tests. Saedi et al. [14] carried out four experimental tests on Khorjini connections as semi-rigid connections at elevated temperature. The connections were modeled using ABAQUS finite element program.
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Comparison between the result of numerical models and experimental test results showed good agreement in elastic and plastic ranges. These results show that the finite element method is suitable for accurately predicting the behavior of connections at elevated temperatures, and can simultaneously consider several parameters, each of which would require a separate experimental test. In this article, a nonlinear finite element model of bolted angle connections with and without web angle at ambient and elevated temperatures using ANSYS [15] is presented, and the results of models and tests were compared. In addition, the accuracy of the analysis is compared to experimental tests at ambient and elevated temperatures. It should be noted that the design method details for angle bolted connections with and without web angle is presented in many construction codes [16,17]. In some countries such as Iran, these connections are widely used as semi-rigid connections in braced frames.
2. Connection geometry To study the behavior of steel connections at ambient and elevated temperatures, two series of experimental tests on bolted angle connections were selected. It should be noted that these two series of tests are selected from two different references and are completely independent.
2.1. Experimental tests at ambient temperatures Tests carried out by Azizinamini [18], which are valid references for numerical studies on angle connections, were selected. Dimensions, sizes and detailed properties of the test specimens are tabulated in Table 1. The test arrangement conducted by Azizinamini is shown in Fig. 1.
Table 1 Properties of connection components tested by Aziznamini. Specimen no.
8S1 8S2 8S3 8S4 8S5 8S6 8S7 8S8 8S9 8S10
Bolt diameter (mm)
19.1 19.1 19.1 19.1 19.1 19.1 19.1 22.3 22.3 22.3
Column section
W12 58 W12 58 W12 58 W12 58 W12 58 W12 58 W12 58 W12 58 W12 58 W12 58
Beam section
W8 21 W8 21 W8 21 W8 21 W8 21 W8 21 W8 21 W8 21 W8 21 W8 21
Top and seat angles
Web angle
Angle
Length (mm)
Gauge (mm)
Bolt spacing (mm)
Angle
Length (mm)
L6 3–1/2 5/16 L6 3–1/2 3/8 L6 3–1/2 5/16 L6 6 3/8 L6 4 3/8 L6 4 5/16 L6 4 3/8 L6 3–1/2 5/16 L6 3–1/2 3/16 L6 3–1/2 1/2
152.4 152.4 203.2 152.4 203.2 152.4 152.4 152.4 152.4 152.4
50.8 50.8 50.8 137.2 63.5 63.5 63.5 50.8 50.8 50.8
88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9
2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4
139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7
Fig. 1. Details of the test conducted by Azizinamini.
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2.2. Specimens tested at elevated temperatures The test carried out by Saedi [19] and Saedi and Yahyai [20] was chosen to study the behavior of bolted angle connections under temperature loading. The specimens were configured in a symmetrical cruciform arrangement that consists of a single 80-cm-high column of IPE300 section connected to two 250-cmlong cantilever beams of IPE 220 section. The load was applied on a point 2 m from the end of the beam. Details of the specimen arrangement and the test conducting method are shown in Fig. 2.
Load
40
All of the bolts in the specimens were tightened to 150 N m by a torque wrench to ensure consistency. The experimental tests were conducted on two different connection details: Connection group 1: Specimen without web angle (SOW) Connection group 2: Specimen with web angle (SWW) Connection group 1 (SOW) consisted of two angles, one connected to the top flange of the beam and the other connected to the bottom flange. The total system was bolted to the flange of
Bea, restrained horizontally
Load
200
Fig. 2. Arrangement of the test carried out by Saedi et al.
Fig. 3. Details of the test conducted by Saedi et al. (a) Connection group1 (SOW); (b) Connection group2 (SWW).
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the column. Each angle was bolted to the flange of the beam by six M16 bolts and to the flange of column by two M16 bolts. A detail of this group of connections is shown in Fig. 3(a). The connection group 2 (SWW) had two additional angles compared with connection group 1. These angles were bolted to the web of the beam on one side and to the flange of the column on the other side. Web angles were connected to the web of the beam by two M16 bolts and to the flange of the column by two M16 bolts. Details of this group of connections are shown in Fig. 3(b). Details of connections for each specimen are provided in Table 2.
2.2.1. Specimen loading The values of applied moment to each specimen in the tests are presented in Table 3. As it can be seen, first the rotation capacity of Table 2 Details of specimens tested by Saedi et al. Specimen no.
Group no.
Angle size (mm)
Grade of bolt
3 5 9 13
1 2 1 2
10010010 15010015 15010015 10010010
8.8 8.8 8.8 8.8
Table 3 The value of applied moment for each specimen in the tests carried out by Saedi et al. Specimen no.
Group no.
Moment (M) level
Applied M (kNm)
3 5 9 13
1 2 1 2
Mcc 0.4 Mcc 0.6 Mcc 0.8 Mcc
8.5 8.5 8.5 8.5
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connection is theoretically calculated and then the applied moment is selected as a coefficient of connection rotation capacity and is applied to the specimens during the test.
3. Finite element model The ANSYS multi-purpose finite element modeling code was used to perform numerical modeling of the connections. FE models were created using ANSYS Parametric Design Language (APDL). The geometrical and mechanical properties of the connection models were used as the parameters, thus the time required to create new models was considerably reduced. Numerical modeling of the connections was performed with the following considerations: All components of connections such as beam, column, angles and bolt heads and bolt shanks were modeled using eight-node first-order SOLID64 elements that can consider the thermal gradient used to apply the effect of fire. Pretensioned elements were used to model pretensioning forces in the bolts. Bolt holes were 1.6 mm larger than the bolt diameter. Only half of the connection was modeled because of the symmetry that exists about the web plane. The model contains only flanges and stiffeners of the column, because of the high rigidity of the column resulting from its stiffeners. The finite element model of the connection is shown in Fig. 4. ANSYS can model contact problems using contact pair elements that pair together in a way such that no penetration occurs during the loading process. The interaction between adjacent surfaces, including angle–beam flange, bolt head–nut, bolt hole–bolt shank and the effect of friction were modeled using these contact elements. Selected contact surfaces are shown in Fig. 5. The value of Coulomb friction coefficient is one of the significant parameters in studying the bolted connections that is used to consider the friction forces. AISC provision [16] proposes the value of 0.33 for A class surfaces. However, Refs. [21,22] have considered the value of 0.1 for this coefficient. In the present study, in contrast to the studies carried
Fig. 4. Finite element model of the connection
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Contact Surfaces
Bolt Clearance
Contact Surfaces
Fig. 5. Selected contact surfaces considered in the finite element model.
900 800 S-1
Temperature (c)
700
S-2 S-3
600
S-4
500
S-5
400
S-7
300
S-9
S-6
S-8 S-10
200
S-11 S-12
100 0 0
20
40
60
80
100
120
140
Time (min) Fig. 6. Average temperatures of each specimen.
600
Table 4 Material properties of specimens tested by Saedi et al.
500 stress (MPa)
strain=0.0485
400
Material
Yield stress (N/mm2)
Ultimate stress (N/mm2)
Modulus of elasticity (N/mm2)
Beam–column–angle Bolts 8.8
235 740
420 866
2.06 105 2.06 105
stress= 510
300 strain=0.0013
200
stress=276.9
is found to be the best value for this type of connections. Consequently, the value of Coulomb coefficient is assumed to be 0.25 in the present study. [23–25].
100 A36 steel
0 0
0.02
0.04
0.06
0.08
strain
4. Boundary conditions and applied loads Fig. 7. Stress–strain curve for A36 steel [30].
out in Refs. [21,22], nuts and bolt heads are modeled as hexahedral which are similar to the real shape. According to the sensitivity studies carried out by the first author, the value of 0.25
Since the geometry of the connection is symmetric, just onefourth of the connection was modeled and the displacements perpendicular to the symmetric plane were closed. It is noted that since the beams of the connections were compact sections,
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55
8S1
36
moment (kNm)
moment (kNm)
45
27 18 TEST FE Citipitioglu et al
9
8S2
44 33 22 TEST FE Citipitioglu et al
11 0
0 0
5
10
15
20
25
30
0
5
50
8S3
30 moment (kNm)
moment (kNm)
40 30 20 TEST FE Citipitioglu et al
10
20
25
30
8S4
24 18 12 TEST FE Citipitioglu et al
0 0
5
10
15
20
25
30
0
8
rotation (mrad) 40 moment (kNm)
40 30 20 TEST FE Citipitioglu et al
10
16
24
32
40
rotation (mrad)
8S5
50 moment (kNm)
15
6
0
8S6
32 24 16 TEST FE Citipitioglu et al
8
0
0 0
8
16
24
32
40
0
8
45
8S7
24
32
40
8S8
50 moment (kNm)
36 27 18 TEST FE Citipitioglu et al
9
16
rotation (mrad)
rotation (mrad)
moment (kNm)
10
rotation (mrad)
rotation (mrad)
40 30 20 TEST FE
10
0
0 0
8
16
24
32
40
0
5
65
85
8S9 moment (kNm)
52 39 26 TEST FE Citipitioglu et al
13
10
15
20
25
30
rotation (mrad)
rotation (mrad)
moment (kNm)
981
8S10
68 51 34 TEST FE Citipitioglu et al
17
0
0 0
8
16
24
rotation (mrad)
32
40
0
5
10
15
20
rotation (mrad)
Fig. 8. Comparison between the results of finite element and experimental test.
25
30
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the local buckling instabilities occur in the inelastic range or high stress levels. The Von Mises stress distribution in FE models clarifies that the beam remains nearly elastic and so the local buckling failure mode can be ignored in the FE models. For the specimens tested at ambient temperature, 50 mm vertical displacement was applied monotonically on the nodes located at the end of beam to apply the moment on the connections. This displacement at the end of the beam causes an approximately 0.03 rad rotation. The amount of bending moment and relative rotation of connection can be computed by Eqs. (1) and (2): M ¼ PL R¼
e1 e2 h
ð1Þ ð2Þ
where M is the applied connection moment, P is the summation of the reaction forces of the applied displacement on beam end nodes, L corresponds to beam length, R is relative rotation of connection, h is beam depth, e1 and e2 are the top and bottom flange horizontal displacements, respectively. In the tests carried out at elevated temperatures, the specified concentrated force was first applied at a distance 200 cm from the column flange, in order to create the necessary moment in the connection. A uniform temperature in the neighborhood of the connections was then gradually increased to the desired level to study the effect of temperature on the structural behavior of the beam–column configuration. The column is assumed to be fixed at the bottom, since no displacements were expected to take place at nodes far away from the connections, and was free to move at the top, in order to reflect the experimental test set-up. The beam was allowed to deflect downward only, while horizontal movement was restrained to prevent any possibility of premature failure of the beam by lateral torsional buckling. The beam was also allowed to expand freely along the longitudinal axis, thus ensuring no thermal stresses were generated. Only the area around the connection was subjected to the full temperature regime whereas sections away from the connection were subjected to ambient temperature in order to simulate the
Fig. 9. Deformation of the connection S5 from the experimental tests.
experimental tests. In the tests conducted on these series of connections at elevated temperatures, the temperature of furnace is increased according to the curves provided by ASTME119 and ISO834 [26,27]. As a result of increase in the temperature of furnace, the temperature of specimens is also increased and is recorded by thermocouples connected to each specimen. The average values of recorded thermocouple temperatures for each specimen are presented in Refs. [19,20]. In the present study, these values are used as input temperatures for the software. Fig. 6 shows the average temperature of each specimen. The rotational degrees of freedom were not active for solid elements in ANSYS; therefore, the vertical deflection was determined at a certain point along the beam from which the connection rotation, j, can be estimated using the following equation [28]:
j ¼ tan1 ðu=LÞ
Fig. 10. Predicted deformation of the connection S5.
ð3Þ
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where u is the vertical deflection of the point along the beam, and L is the distance from the connection centerline to the point where the deflection was taken.
5. Material properties Different material properties were used for the two series of tests performed at ambient and elevated temperatures. 5.1. Material properties of specimens conducted by Azizinamini (ambient temperature) The stress–strain relation for all connection components, except for bolts, was represented using a three linear constitutive model. An isotropic hardening rule with a Von Mises yielding criterion was used to simulate plastic deformations of connection components, and fracture of material was not considered.
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Since the steel properties of connection components is not clearly mentioned in Ref. [18], the properties that were assumed for Azizinamini tests by the Citipitioglu et al. [29] is used here that provide good results. The yield stress and ultimate strength of bolts were assumed based on nominal properties of A325 bolts. Bolt materials were modeled as bilinear with 634.3 MPa yield stress and an ultimate stress of 930 MPa at 8% strain. Modulus of elasticity and Poisson’s ratio were considered as 210 GPa and 0.3, respectively. Fig. 7 shows the stress–strain relation of A36 steel used for beam and angle materials in Citipitioglu et al.’s study. 5.2. Material properties of specimens tested by Saedi et al. (elevated temperatures) At elevated temperatures, the connection undergoes large plastic deformation; therefore, an elastic–plastic material model was adopted. Analytical models are considered as simplified models; however, it is sufficient to incorporate the main parameters (i.e.,
Fig. 11. Detail of deformation of the connection S5 components.
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stiffness and strength) representing the degradation of material properties with temperature. For this purpose, the stress–strain characteristics of structural steel at elevated temperatures are defined in the design codes BS5950, Part 8 [31] and EC3: Part 1.2. The equations for degradation of bolts steel were defined from these codes. The steel properties and bolt properties of the specimens are obtained from Ref. [20]. It should be noted that the results of Coupon test for each specimen is presented in Ref. [19] and just the results of Mill test is presented in Table 4.
6. Model verification In this section, the results of finite element models were compared to those of the experimental test conducted by Azizinamini at ambient temperatures. The models were then loaded according to the test carried out by Saedi et al., and the ability of the models to simulate the experimental behavior of connections at elevated temperatures was verified.
6.1. Verification of the models using the tests conducted by Azizinamini (ambient temperature) To evaluate the accuracy of the numerical models, 10 finite element models were developed according to the specimens tested by Azizinamini and the results were compared. In Fig. 8, moment–rotation curves obtained by analysis of finite element models were compared to those from the experimental tests conducted by Azizinamini and those obtained by Citipitiuglu using numerical methods. Fig. 8 shows that the results of the finite element models were in close agreement with the experimental test results. Differences between the numerical simulations and the experimental results may be due to several causes, such as numerical modeling simplification, test specimen defects, residual stress and contact surface interactions, frictional forces, and bolt pretensioning forces. Bolt pretension and the friction coefficient were two major factors that affect the behavior of the connections, especially in the nonlinear regime. These factors are difficult to
700 800 600 700 500 Temperature (c)
Temperature (c)
600 500 400 300
400
300
200 200 S5-EXP S5-FE
100
S13-EXP S13-FE
100
0
0 0
50
100 150 Rotation (Millirads)
200
0
250
20
40 60 80 Rotation (Millirads)
100
120
800
700
700
600
600 Temperature (c)
Temperature (c)
500 400 300 200
500 400 300 200
S3-EXP S3-FE
100
S9-EXP S9-FE
100 0
0 0
20
40
60
80
Rotation (Millirads)
100
120
0
50
100 150 Rotation (Millirads)
Fig. 12. Comparison of FE and experimental results for four different tests.
200
250
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S5
S9
60
45 40
50 40
Moment (kNm)
Moment (kNm)
35 20 c 400 c 500 c
30
600 c 650 c
20
30
20 c
25
400 c 500 c
20
600 c 650 c
15 10
10 5 0
0 0
50
100
150
200
250
0
50
100
150
Rotation (Millirads)
Rotation (Millirads)
S3
S13
200
250
25 35 20
25
15
Moment (kNm)
Moment (kNm)
30
20 c 400 c 10
500 c 550 c 600 c
20 c
20
400 c 15
500 c
10
550 c 600 c
5 5 0
0 0
50 100 Rotation (Millirads)
150
0
50 100 Rotation (Millirads)
150
Fig. 13. Moment–rotation–temperature curves.
estimate. Another major influence on connection behavior arises from the nonlinear constitutive laws for materials, especially for situations where only uniaxial values of the stress–strain curves are available. This is the cause for the increased difference between the curves in the nonlinear portion of the curve. As can be seen from Fig. 8, in specimens 8S3 and 8S4, the difference between the finite element modeling results and the test data was higher than for other specimens, while the two finite element results (the present study and that by Citipitioglu) were in close agreement. This difference is most likely due to test specimen defects such as geometrical measuring or bolt pretensions.
6.2. Verifying the models using the tests conducted by Saedi et al. (elevated temperatures) The FE results were compared with the experimental data generated by Saedi et al. in terms of temperature–rotation characteristics and failure modes of the connections. Figs. 9 and 10 show comparison between predicted deformations and real deformations for connection S5. Fig. 11 shows the deformation modes of the same
connection components in comparison with the real connection components deformations after the test. Fig. 9 shows a local deformation at the top and bottom angles, particularly around the top bolt, where it is subjected to the highest tensile stresses. Because of the high strength of columns used in the test, the columns were not deformed compared to the angles. The bolts used at the vertical leg of the top angle were subjected to the highest tensile stresses and failed. Distortion did not occur in the other bolts. This behavior was closely predicted by the FE model, as shown in Fig. 10. Fig. 11 shows the deformed shapes of each component of the connection assembly in comparison with the same component after the test, where damage in terms of permanent deformation takes place in the top and bottom angles. The critical stress at the end of bolt is clearly visible and the same thing can be seen in the real components of the connection. The column and beam have no significant deformation. In order to validate the results from the FE analysis, four elevated temperature tests were modeled. A comparison of the temperature–rotation response of the connections at different moments is shown in Fig. 12. The temperature–rotation response curves of the connections agree well with tests at the elastic and plastic stages. Differences between the numerical simulations and
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the test results may be due to several causes, such as numerical modeling simplification, test specimen defects, residual stress, contact surface interactions, frictional forces and bolt pretensions or nonlinear constitutive models of materials at elevated temperatures. As it can be clearly seen in Fig. 12, specimens 3 and 13 whose angle thickness is 10 mm failed significantly before the failure of specimens 9 and 5 whose angle thickness is 15 mm. As it can be seen in Table 3, the applied moment for all specimens is 8.5 kN m. This amount of moment is equal to 0.4 Mcc for specimen 5 whereas, it is 0.8 Mcc for specimen 13 that is similar to specimen 5 and the only difference is the thickness of angle that is 10 mm in specimen 13. As it can be concluded, although the moment applied to the specimens is the same, but the specimens are under different moment from the rotation capacity point of view. Now, it can be said that during the tests, the specimens are affected by two subjects, i.e. the moment applied by the jacks and the deterioration of steel stiffness and strength due to the increase of temperature and a combination of these two parameters leads to the failure of specimens. It can be seen that first, the specimens whose angle thickness is 10 mm are under greater moment from the rotation capacity point of view and this is an important reason for the premature failure of these specimens in comparison with the specimens whose angle thickness is 15 mm. Secondly, the stiffness and strength of specimens with smaller angle thickness deteriorate more quickly. Considering these two subjects, it is observed that the specimens with smaller angle thickness are in worse condition and the combination of these two subjects leads to the quicker failure of them in comparison to the time of failure of connections with thicker angle. One of the most important and applicable curves in connection design is the moment–rotation curve; this curve is shown in Fig. 13 for four types of connections at different temperatures using the finite element models. For all the tests, deterioration of connection characteristics due to temperature increase was predicted well by the models. Fig. 13 shows that the moment resistance of the connection was severely decreased. In general, these types of angle connections who have been made by usual constructional steel and bolts have no moment resistance at temperatures more than 800 1C.
7. Study of the connection failure mechanism using finite element model In this part, the verified finite element model presented above is used to study the failure mechanism of the 4 specimens and interpret the obtained results. The analysis results are presented as Von Mises stresses. The results showed that in specimens S3 and S13 whose angle thickness is 10 mm, critical stress is formed at the connection place of vertical and horizontal legs of top angle. This shows that the failure mechanism of these connections is the failure of top angle that is confirmed by the results of experimental test (Fig. 14a). Whereas, in the case of specimens S5 and S9 whose angle thickness is 15 mm, critical stress is formed at the bolts who connect the top angle to column and the failure mode is in the form of failure in these bolts (Fig. 14b). This result determines the weak points of connection that can be fortified to improve the connection behavior. For example, the angle thickness of connection S3 whose failure mode was the failure of top angle is increased from 10 to 15 mm and the connection is called S3 (1). The specimen is again analyzed and as it can be seen in Fig. 15, the specimen S3 (1) tolerated higher temperature and the failure mode is changed to failure of bolts. Besides, the main difference between specimens S3 and S3 (1) is the rotation capacity value, i.e., increasing the thickness of bolts and preventing the premature angle failure lead to higher rotations of
Fig. 14. Failure mechanism of connections.
the connection. In the next step, 10.9 bolts are used instead of 8.8 bolts to improve the behavior of connection (specimen S3 (2)). As it can be seen in Fig. 15, the temperature strength and rotation capacity are significantly increased, but the failure mode is still the failure of bolts. It should be noted that the results of numerical models about the effects of increasing the angle thickness and using 10.9 bolts instead of 8.8 bolts are confirmed by the results of experimental test of Ref. [20] and this shows the ability of numerical models to predict behavior of connection at elevated temperatures and improving the connection behavior. It should be noted that according to the results of Ref. [32], a problem which is observed in the behavior of angle bolted connections at elevated temperature is thread stripping in bolts and exiting of nut from bolt without failure of bolt. [32]. Since the finite element model
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987
800 700
Temperature (c)
600 500 400 300 200 S-3 S3(1)
100
S3(2)
0 0
50
100 150 Rotation (Millirads)
200
250
Fig. 15. Comparison between rotation–temperature curves of specimens S3, S3 (1) and S3 (2).
present in the paper is not able to consider such mechanism, and the analysis of such mechanism is very time consuming, and besides, this new model should be verified again, the effects of thread stripping can be considered using safety factors in analysis to consider the decrease in temperature strength.
8. Conclusions Considering the high cost of experimental tests at elevated temperatures and the limitation in the number of parameters in tests for study the behavior of a specific connection at elevated temperatures, availability of an accurate numerical model that is able to accurately simulate the behavior of the connection at elevated temperature is of great importance. Without such a model, comprehensive investigation about the behavior of connections at elevated temperature is practically impossible. Besides, angle bolted connections are used widely in some countries as semi-rigid connections and numerical simulation is necessary to study the behavior of such connections at elevated temperatures. Since no previous research has been carried out before, the need for such study is felt twice. To do this, a 3-D finite element analysis was conducted to study the behavior of bolted top and bottom angle connections with and without web angles at elevated temperatures using the general purpose finite element software, ANSYS. The connection components were modeled using three-dimensional brick elements, while contacts between the components were modeled using contact elements based on the Coulomb friction law. Material nonlinearity was considered for both steel members and connection components. The whole stress–strain–temperature curves were incorporated in the model to simulate the degradation of the connection characteristics at elevated temperatures. Simulation results were compared with experimental data. The results obtained showed a good agreement between the predicted and measured responses in both the elastic and plastic ranges. This demonstrates that the FE technique is capable of predicting connection response at elevated temperatures to an acceptable degree of accuracy. The purpose of the present study is not just to investigate the feasibility of simulation of angle bolted connections. In more advanced step, the numerical model, whose accuracy has been verified by comparing to experimental test results at ambient and elevated temperatures, is used to study the connection failure mechanisms. According to
the type of failure, proper method is used to increase the temperature strength of the connections.
Acknowledgment The authors would like to thank the Y.M.A Engineering Company for their great support which is much appreciated. References [1] Euro Code 3: Design of Steel Structures, Part 1.2: General Rules Structural Fire Design (drafts), Document CEN, European Committee for Standardization, 1995. [2] T.C.H. Liu, L.J. Morris, Theoretical modeling of steel bolted condition under fire exposure, in: Proceedings of the International Conference on Computational Mechanics, 1994. [3] T.C.H. Liu, Finite element modeling of behavior of steel beams and connections in fire, Journal of Constructional Steel Research 35 (3) (1996) 181–199. [4] T.C.H. Liu, Effect of connection flexibility on fire resistance of steel beams, Journal of Constructional Steel Research 45 (1998) 99–118. [5] T.C.H. Liu, Three-dimensional modeling of steel/concrete composite connection behavior in fire, Journal of Constructional Steel Research 45 (1–3) (1998) (paper no. 361). [6] T.C.H. Liu, Moment–rotation–temperature characteristics of steel/composite connections, Journal of Structional Engineering 125 (10) (1999) 1188–1197. [7] O.M. El-Houssieny, S. Abdel Salam, G.A.M. Attia, A.M. Saad, Behavior of extended end plate connections at high temperature, Journal of Constructional Steel Research 45 (1–3) (1998) (paper no. 172). [8] S. Spyrou, B. Davison, I. Burgess, R. Plank, Component-based studies on the ~ behavior of steel joints at elevated temperatures, in: A. Lamas, L. Simoes da Silva (Eds.), Proceedings of the Third European Conference on Steel Structures, University de Coimbra, Coimbra, 2002, pp. 1469–1478. [9] R. Rahman, R. Hawileh, M. Mahamid, The effect of fire loading on a steel frame and connection, in: C.A. Brebbia, W.P. Wilde (Eds.), High Performance Structures and Materials II, WIT Press, 2004, pp. 307–316. [10] M. Sarraj, I.W. Burgess, J.B. Davison, R.J. Plank, Finite element modeling of finplate steel connections in fire, in: Proceedings of the Fourth International Workshop on Structures in Fire, Aveiro, Portugal, 2006, pp. 315–326. [11] F. Wald, L. Simones da Silva, D.B. Moore, T. Lennon, M. Chaldna, M. Santiago, et al., Experimental behavior of a steel structure under natural fire, Fire Safety Journal 41 (2006) 509–522. [12] K.S. Al-Jabri, A. Seibi, A. Karrech, Modeling of un-stiffened flush endplate bolted connections in fire, Journal of Constructional Steel Research 62 (2006) 151–159. [13] G.-B. Lou, G.-Q.Li, Non-linear finite element modeling of behavior of extended end-plate bolted moment connections in fire, in: Proceedings of the Fourth International Workshop on Structures in Fire, Aveiro, Portugal, 2006, pp. 327–343. [14] A. Saedi Daryan, H. Bahrampoor, The study of behavior of Khorjini Connections in Fire, Fire Safety Journal 44(2009) 659–664.
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[15] ANSYS User’s Manual, Version 9. [16] AISC, Manual of Steel Construction—Load and Resistance Factor Design, American Institute of Steel Construction, Chicago, IL, 1995. [17] Standard Code for Connections in Steel Structures no 264, Published by Iranian Management and Programming Organizations, ISBN:964-425-424-4. /http://www.mporg.irS. [18] Azizinamini, Monotonic response of semi-rigid steel beam to column connections, MS thesis, University of South Carolina, Columbia, 1982. [19] A. Saedi Daryan, A Study on Behavior of Connections in Fire, MS thesis, K.N. Toosi University, Tehran, Iran, 2006. [20] A. Saedi Daryan, M. Yahyai, Behavior of bolted top-seat angle connections in fire, Journal of Constructional Steel Research 65 (2009) 531–541. [21] N. Kishi, A. Ahmed, N. Yabuki, Nonlinear finite element analyses of top and seat-angle with double web-angle connections, Journal of Structural Engineering and Mechanics 12 (2001) 201–214. [22] Ahmed, N. Kishi, K. Matsuoka, M. Komuro, Nonlinear analysis on prying of top- and seat-angle connections, Journal of Applied Mechanics (2001) 227–236. [23] F. Danesh, A. Pirmoz, A. Saedi Daryan, Effect of shear force on the initial stiffness of top and seat angle connections with double web angles, Journal of Constructional Steel Research 63 (2007) 1208–1218.
[24] A. Pirmoz, A. Saedi Daryan, A. Mazaheri, H. Ebrahim Darbandi, Behavior of bolted angle connections subjected to combined shear force and moment, Journal of Constructional Steel Research 64 (2008) 436–446. [25] A. Pirmoz, A. Seyed Khoei, E. Mohammadrezapour, A. Saedi Daryan, Moment–rotation behavior of bolted top–seat angle connections, Journal of Constructional Steel Research 65 (2009) 973–984. [26] ISO 834. Fire resistance tests—elements of building construction, 2002. [27] ASTM- E 119–05a. Standard Test Methods for Fire Tests of Building Construction and Materials, 2003. [28] K.S. Al-Jabria, A. Seibib, A. Karrechc, Modeling of unstiffened flush end-plate bolted connections in fire, Journal of Constructional Steel Research 62 (2006) 151–159. [29] A.M. Citipitioglu, R.M. Haj-Ali, D.W. White, Refined 3D finite element modeling of partially restrained connections including slip, Journal of Constructional Steel Research 8 (2002) 995–1013. [30] Bulent Akbas, Jay Shen, Seismic behavior of steel buildings with combined rigid and semi-rigid frames, Turkish Journal of Engineering and Environmental Sciences 27 (2003) 253–264. [31] BS 5950. Structural use of steelwork in buildings, Part 8: Code of Practice for Fire Resistance Design, British Standard Institution BSI, London, 1990. [32] B.R. Kirby, The behavior of high-strength grade 8.8 bolts in fire,, Journal of Constructional Steel Research 33 (1995) 3–38.
Contents lists available at ScienceDirect
Fire Safety Journal journal homepage: www.elsevier.com/locate/firesaf
Modeling of bolted angle connections in fire Amir Saedi Daryan , Mahmood Yahyai Civil Engineering Department of K.N. Toosi University of Technology, Tehran, Iran
a r t i c l e in f o
a b s t r a c t
Article history: Received 29 March 2008 Received in revised form 3 March 2009 Accepted 15 June 2009 Available online 25 July 2009
Recent structural collapses caused by fire have focused attention on research concerning fire safety in building design. The high cost of experimental tests and limitations in the number of geometrical and mechanical parameters, in addition to advances in numerical methods that provide the ability to simulate complicated structures with numerous parameters, make the finite element method an attractive device for modeling the behavior of structural connections in fire. In this paper, the behavior of bolted angle connections was studied at ambient and elevated temperatures using the ANSYS finite element software. Steel members and connection components were considered to behave nonlinearly. Degradation of steel properties with increasing temperature was assumed to be in accordance with EC3 [Euro Code 3: Design of Steel Structures, Part 1.2: General Rules Structural Fire Design (drafts), Document CEN, European Committee for Standardization, 1995 [1]] recommendations. Finite element results and experimental tests conducted on bolted angle connections in fire conditions were compared, and modeled failure modes and moment–rotation–temperature characteristics were in good agreement with those associated with experimental tests. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Bolted angle connections Finite element modeling Fire modeling Elevated temperature
1. Introduction When exposed to high temperatures during fire conditions, steel experiences a significant and sudden decrease in strength and stiffness, resulting in decreased load carrying capacity. Therefore, steel structures should be constructed in a way that assures their safety during fires. Many experimental tests have been conducted in the last three decades to study the effect of fire on structures. These tests have been conducted either on full-scale steel structures or on isolated steel members like columns, beams and connections. In common steel structure design, beam-tocolumn connections were assumed to be rigid or pinned, and the connections were assumed to possess significant stiffness and strength at elevated temperatures. However, actual connection behavior exhibits a wide spectrum of characteristics between these two limits. Because these connections play an important role in the survival time of structures, experiments have been conducted to study the behavior of connections at elevated temperatures. Experimental tests provide reliable results that accurately describe the behavior of the beam-to-column connections. However, physical experiments are sometimes either not feasible or too expensive to conduct. In addition, the number of
Corresponding author. Tel.: +982122749398; fax: +982122749399.
E-mail addresses: [email protected] (A. Saedi Daryan), [email protected] (M. Yahyai). 0379-7112/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.firesaf.2009.06.005
geometrical and mechanical parameters is limited in experimental studies. As a result, significant advances in the finite element method have made it one of the most powerful numerical methods available for modeling the behavior of connections, especially at elevated temperatures. The use of finite element modeling to study connection behavior began in the early 1970s, as the potential for the application of computers to solving structural problems became evident. The modeling of the behavior of connections at elevated temperature was first performed in the 1990s. Early attempts at modeling connection behavior in fire were initiated by Liu and Morris [2] and Liu [3–6], who developed a finite element model, FEAST, to simulate the various types of connections under fire conditions. The beam, column, end plate and stiffeners were modeled using eight-node shell elements, and the nonlinear behavior of the material at elevated temperatures was considered. The stress–strain–temperature characteristics were adopted based on recommended values from experimental tests, and the models showed close agreement with experimental data. El-Houssieny et al. [7] developed a three-dimensional (3-D) finite element model to simulate the response of extended end plates at both ambient and elevated temperatures. Close agreement with experimental work was obtained, and subsequent parametric studies were conducted to investigate the influence of connection behavior at normal and elevated temperatures. Spyrou et al. [8] modeled T-stub specimens at elevated temperatures using the finite element program ANSYS. A close agreement was found
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between the experimental results and 3-D analyses. Rahman et al. [9] used ANSYS to study the behavior of fin plate connections in fire. For modeling the beams, columns, fin plates and bolts, the authors used 3D solid, prestressed and contact elements, respectively. Despite the prediction of realistic results by the model, no experimental data were used to quantify its accuracy. Sarraj et al. [10] also developed 3-D ABAQUS models of fin plate connections, which included the important contact interaction between the bolts and the fin plate and beam web. The models were validated against lap joint data at ambient temperature. In 2005, a fire test was conducted by Wald et al. [11] at the Czech Technical University. A finite element model was developed by Al-Jabri et al. [12] to study the behavior of flush end plate bare steel joints at elevated temperatures using the general purpose finite element software ABAQUS. The finite element model was used to establish the moment–rotation characteristics of the flush end plate bare steel joints with a concentrated force at elevated temperatures. The joint components were modeled using 3-D brick elements, while contact between the various components was modeled using Coulomb friction. Material nonlinearity was considered to model steel members and the joint components. Degradation of steel properties with increasing temperatures was taken in accordance with design code recommendations. The obtained FE-simulated failure modes and moment–rotation– temperature characteristics of the joints compared well with the experimental data in both the elastic and plastic regions. Lou and Li [13] used ANSYS to model the behavior of cruciform tests with extended end plates in fire. A sequential analysis was used; a transient thermal analysis was conducted first, followed by a static structural analysis. Non-uniform thermal expansion, geometric nonlinearity, temperature-dependent nonlinear material behavior, bolt pretension and surface-to-surface contact were all included in the analyses. Excellent correlation was achieved between the analyses and experimental results from two fire tests. Saedi et al. [14] carried out four experimental tests on Khorjini connections as semi-rigid connections at elevated temperature. The connections were modeled using ABAQUS finite element program.
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Comparison between the result of numerical models and experimental test results showed good agreement in elastic and plastic ranges. These results show that the finite element method is suitable for accurately predicting the behavior of connections at elevated temperatures, and can simultaneously consider several parameters, each of which would require a separate experimental test. In this article, a nonlinear finite element model of bolted angle connections with and without web angle at ambient and elevated temperatures using ANSYS [15] is presented, and the results of models and tests were compared. In addition, the accuracy of the analysis is compared to experimental tests at ambient and elevated temperatures. It should be noted that the design method details for angle bolted connections with and without web angle is presented in many construction codes [16,17]. In some countries such as Iran, these connections are widely used as semi-rigid connections in braced frames.
2. Connection geometry To study the behavior of steel connections at ambient and elevated temperatures, two series of experimental tests on bolted angle connections were selected. It should be noted that these two series of tests are selected from two different references and are completely independent.
2.1. Experimental tests at ambient temperatures Tests carried out by Azizinamini [18], which are valid references for numerical studies on angle connections, were selected. Dimensions, sizes and detailed properties of the test specimens are tabulated in Table 1. The test arrangement conducted by Azizinamini is shown in Fig. 1.
Table 1 Properties of connection components tested by Aziznamini. Specimen no.
8S1 8S2 8S3 8S4 8S5 8S6 8S7 8S8 8S9 8S10
Bolt diameter (mm)
19.1 19.1 19.1 19.1 19.1 19.1 19.1 22.3 22.3 22.3
Column section
W12 58 W12 58 W12 58 W12 58 W12 58 W12 58 W12 58 W12 58 W12 58 W12 58
Beam section
W8 21 W8 21 W8 21 W8 21 W8 21 W8 21 W8 21 W8 21 W8 21 W8 21
Top and seat angles
Web angle
Angle
Length (mm)
Gauge (mm)
Bolt spacing (mm)
Angle
Length (mm)
L6 3–1/2 5/16 L6 3–1/2 3/8 L6 3–1/2 5/16 L6 6 3/8 L6 4 3/8 L6 4 5/16 L6 4 3/8 L6 3–1/2 5/16 L6 3–1/2 3/16 L6 3–1/2 1/2
152.4 152.4 203.2 152.4 203.2 152.4 152.4 152.4 152.4 152.4
50.8 50.8 50.8 137.2 63.5 63.5 63.5 50.8 50.8 50.8
88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9
2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4 2L4 3–1/2 1/4
139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7
Fig. 1. Details of the test conducted by Azizinamini.
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2.2. Specimens tested at elevated temperatures The test carried out by Saedi [19] and Saedi and Yahyai [20] was chosen to study the behavior of bolted angle connections under temperature loading. The specimens were configured in a symmetrical cruciform arrangement that consists of a single 80-cm-high column of IPE300 section connected to two 250-cmlong cantilever beams of IPE 220 section. The load was applied on a point 2 m from the end of the beam. Details of the specimen arrangement and the test conducting method are shown in Fig. 2.
Load
40
All of the bolts in the specimens were tightened to 150 N m by a torque wrench to ensure consistency. The experimental tests were conducted on two different connection details: Connection group 1: Specimen without web angle (SOW) Connection group 2: Specimen with web angle (SWW) Connection group 1 (SOW) consisted of two angles, one connected to the top flange of the beam and the other connected to the bottom flange. The total system was bolted to the flange of
Bea, restrained horizontally
Load
200
Fig. 2. Arrangement of the test carried out by Saedi et al.
Fig. 3. Details of the test conducted by Saedi et al. (a) Connection group1 (SOW); (b) Connection group2 (SWW).
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the column. Each angle was bolted to the flange of the beam by six M16 bolts and to the flange of column by two M16 bolts. A detail of this group of connections is shown in Fig. 3(a). The connection group 2 (SWW) had two additional angles compared with connection group 1. These angles were bolted to the web of the beam on one side and to the flange of the column on the other side. Web angles were connected to the web of the beam by two M16 bolts and to the flange of the column by two M16 bolts. Details of this group of connections are shown in Fig. 3(b). Details of connections for each specimen are provided in Table 2.
2.2.1. Specimen loading The values of applied moment to each specimen in the tests are presented in Table 3. As it can be seen, first the rotation capacity of Table 2 Details of specimens tested by Saedi et al. Specimen no.
Group no.
Angle size (mm)
Grade of bolt
3 5 9 13
1 2 1 2
10010010 15010015 15010015 10010010
8.8 8.8 8.8 8.8
Table 3 The value of applied moment for each specimen in the tests carried out by Saedi et al. Specimen no.
Group no.
Moment (M) level
Applied M (kNm)
3 5 9 13
1 2 1 2
Mcc 0.4 Mcc 0.6 Mcc 0.8 Mcc
8.5 8.5 8.5 8.5
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connection is theoretically calculated and then the applied moment is selected as a coefficient of connection rotation capacity and is applied to the specimens during the test.
3. Finite element model The ANSYS multi-purpose finite element modeling code was used to perform numerical modeling of the connections. FE models were created using ANSYS Parametric Design Language (APDL). The geometrical and mechanical properties of the connection models were used as the parameters, thus the time required to create new models was considerably reduced. Numerical modeling of the connections was performed with the following considerations: All components of connections such as beam, column, angles and bolt heads and bolt shanks were modeled using eight-node first-order SOLID64 elements that can consider the thermal gradient used to apply the effect of fire. Pretensioned elements were used to model pretensioning forces in the bolts. Bolt holes were 1.6 mm larger than the bolt diameter. Only half of the connection was modeled because of the symmetry that exists about the web plane. The model contains only flanges and stiffeners of the column, because of the high rigidity of the column resulting from its stiffeners. The finite element model of the connection is shown in Fig. 4. ANSYS can model contact problems using contact pair elements that pair together in a way such that no penetration occurs during the loading process. The interaction between adjacent surfaces, including angle–beam flange, bolt head–nut, bolt hole–bolt shank and the effect of friction were modeled using these contact elements. Selected contact surfaces are shown in Fig. 5. The value of Coulomb friction coefficient is one of the significant parameters in studying the bolted connections that is used to consider the friction forces. AISC provision [16] proposes the value of 0.33 for A class surfaces. However, Refs. [21,22] have considered the value of 0.1 for this coefficient. In the present study, in contrast to the studies carried
Fig. 4. Finite element model of the connection
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Contact Surfaces
Bolt Clearance
Contact Surfaces
Fig. 5. Selected contact surfaces considered in the finite element model.
900 800 S-1
Temperature (c)
700
S-2 S-3
600
S-4
500
S-5
400
S-7
300
S-9
S-6
S-8 S-10
200
S-11 S-12
100 0 0
20
40
60
80
100
120
140
Time (min) Fig. 6. Average temperatures of each specimen.
600
Table 4 Material properties of specimens tested by Saedi et al.
500 stress (MPa)
strain=0.0485
400
Material
Yield stress (N/mm2)
Ultimate stress (N/mm2)
Modulus of elasticity (N/mm2)
Beam–column–angle Bolts 8.8
235 740
420 866
2.06 105 2.06 105
stress= 510
300 strain=0.0013
200
stress=276.9
is found to be the best value for this type of connections. Consequently, the value of Coulomb coefficient is assumed to be 0.25 in the present study. [23–25].
100 A36 steel
0 0
0.02
0.04
0.06
0.08
strain
4. Boundary conditions and applied loads Fig. 7. Stress–strain curve for A36 steel [30].
out in Refs. [21,22], nuts and bolt heads are modeled as hexahedral which are similar to the real shape. According to the sensitivity studies carried out by the first author, the value of 0.25
Since the geometry of the connection is symmetric, just onefourth of the connection was modeled and the displacements perpendicular to the symmetric plane were closed. It is noted that since the beams of the connections were compact sections,
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55
8S1
36
moment (kNm)
moment (kNm)
45
27 18 TEST FE Citipitioglu et al
9
8S2
44 33 22 TEST FE Citipitioglu et al
11 0
0 0
5
10
15
20
25
30
0
5
50
8S3
30 moment (kNm)
moment (kNm)
40 30 20 TEST FE Citipitioglu et al
10
20
25
30
8S4
24 18 12 TEST FE Citipitioglu et al
0 0
5
10
15
20
25
30
0
8
rotation (mrad) 40 moment (kNm)
40 30 20 TEST FE Citipitioglu et al
10
16
24
32
40
rotation (mrad)
8S5
50 moment (kNm)
15
6
0
8S6
32 24 16 TEST FE Citipitioglu et al
8
0
0 0
8
16
24
32
40
0
8
45
8S7
24
32
40
8S8
50 moment (kNm)
36 27 18 TEST FE Citipitioglu et al
9
16
rotation (mrad)
rotation (mrad)
moment (kNm)
10
rotation (mrad)
rotation (mrad)
40 30 20 TEST FE
10
0
0 0
8
16
24
32
40
0
5
65
85
8S9 moment (kNm)
52 39 26 TEST FE Citipitioglu et al
13
10
15
20
25
30
rotation (mrad)
rotation (mrad)
moment (kNm)
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8S10
68 51 34 TEST FE Citipitioglu et al
17
0
0 0
8
16
24
rotation (mrad)
32
40
0
5
10
15
20
rotation (mrad)
Fig. 8. Comparison between the results of finite element and experimental test.
25
30
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the local buckling instabilities occur in the inelastic range or high stress levels. The Von Mises stress distribution in FE models clarifies that the beam remains nearly elastic and so the local buckling failure mode can be ignored in the FE models. For the specimens tested at ambient temperature, 50 mm vertical displacement was applied monotonically on the nodes located at the end of beam to apply the moment on the connections. This displacement at the end of the beam causes an approximately 0.03 rad rotation. The amount of bending moment and relative rotation of connection can be computed by Eqs. (1) and (2): M ¼ PL R¼
e1 e2 h
ð1Þ ð2Þ
where M is the applied connection moment, P is the summation of the reaction forces of the applied displacement on beam end nodes, L corresponds to beam length, R is relative rotation of connection, h is beam depth, e1 and e2 are the top and bottom flange horizontal displacements, respectively. In the tests carried out at elevated temperatures, the specified concentrated force was first applied at a distance 200 cm from the column flange, in order to create the necessary moment in the connection. A uniform temperature in the neighborhood of the connections was then gradually increased to the desired level to study the effect of temperature on the structural behavior of the beam–column configuration. The column is assumed to be fixed at the bottom, since no displacements were expected to take place at nodes far away from the connections, and was free to move at the top, in order to reflect the experimental test set-up. The beam was allowed to deflect downward only, while horizontal movement was restrained to prevent any possibility of premature failure of the beam by lateral torsional buckling. The beam was also allowed to expand freely along the longitudinal axis, thus ensuring no thermal stresses were generated. Only the area around the connection was subjected to the full temperature regime whereas sections away from the connection were subjected to ambient temperature in order to simulate the
Fig. 9. Deformation of the connection S5 from the experimental tests.
experimental tests. In the tests conducted on these series of connections at elevated temperatures, the temperature of furnace is increased according to the curves provided by ASTME119 and ISO834 [26,27]. As a result of increase in the temperature of furnace, the temperature of specimens is also increased and is recorded by thermocouples connected to each specimen. The average values of recorded thermocouple temperatures for each specimen are presented in Refs. [19,20]. In the present study, these values are used as input temperatures for the software. Fig. 6 shows the average temperature of each specimen. The rotational degrees of freedom were not active for solid elements in ANSYS; therefore, the vertical deflection was determined at a certain point along the beam from which the connection rotation, j, can be estimated using the following equation [28]:
j ¼ tan1 ðu=LÞ
Fig. 10. Predicted deformation of the connection S5.
ð3Þ
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where u is the vertical deflection of the point along the beam, and L is the distance from the connection centerline to the point where the deflection was taken.
5. Material properties Different material properties were used for the two series of tests performed at ambient and elevated temperatures. 5.1. Material properties of specimens conducted by Azizinamini (ambient temperature) The stress–strain relation for all connection components, except for bolts, was represented using a three linear constitutive model. An isotropic hardening rule with a Von Mises yielding criterion was used to simulate plastic deformations of connection components, and fracture of material was not considered.
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Since the steel properties of connection components is not clearly mentioned in Ref. [18], the properties that were assumed for Azizinamini tests by the Citipitioglu et al. [29] is used here that provide good results. The yield stress and ultimate strength of bolts were assumed based on nominal properties of A325 bolts. Bolt materials were modeled as bilinear with 634.3 MPa yield stress and an ultimate stress of 930 MPa at 8% strain. Modulus of elasticity and Poisson’s ratio were considered as 210 GPa and 0.3, respectively. Fig. 7 shows the stress–strain relation of A36 steel used for beam and angle materials in Citipitioglu et al.’s study. 5.2. Material properties of specimens tested by Saedi et al. (elevated temperatures) At elevated temperatures, the connection undergoes large plastic deformation; therefore, an elastic–plastic material model was adopted. Analytical models are considered as simplified models; however, it is sufficient to incorporate the main parameters (i.e.,
Fig. 11. Detail of deformation of the connection S5 components.
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stiffness and strength) representing the degradation of material properties with temperature. For this purpose, the stress–strain characteristics of structural steel at elevated temperatures are defined in the design codes BS5950, Part 8 [31] and EC3: Part 1.2. The equations for degradation of bolts steel were defined from these codes. The steel properties and bolt properties of the specimens are obtained from Ref. [20]. It should be noted that the results of Coupon test for each specimen is presented in Ref. [19] and just the results of Mill test is presented in Table 4.
6. Model verification In this section, the results of finite element models were compared to those of the experimental test conducted by Azizinamini at ambient temperatures. The models were then loaded according to the test carried out by Saedi et al., and the ability of the models to simulate the experimental behavior of connections at elevated temperatures was verified.
6.1. Verification of the models using the tests conducted by Azizinamini (ambient temperature) To evaluate the accuracy of the numerical models, 10 finite element models were developed according to the specimens tested by Azizinamini and the results were compared. In Fig. 8, moment–rotation curves obtained by analysis of finite element models were compared to those from the experimental tests conducted by Azizinamini and those obtained by Citipitiuglu using numerical methods. Fig. 8 shows that the results of the finite element models were in close agreement with the experimental test results. Differences between the numerical simulations and the experimental results may be due to several causes, such as numerical modeling simplification, test specimen defects, residual stress and contact surface interactions, frictional forces, and bolt pretensioning forces. Bolt pretension and the friction coefficient were two major factors that affect the behavior of the connections, especially in the nonlinear regime. These factors are difficult to
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estimate. Another major influence on connection behavior arises from the nonlinear constitutive laws for materials, especially for situations where only uniaxial values of the stress–strain curves are available. This is the cause for the increased difference between the curves in the nonlinear portion of the curve. As can be seen from Fig. 8, in specimens 8S3 and 8S4, the difference between the finite element modeling results and the test data was higher than for other specimens, while the two finite element results (the present study and that by Citipitioglu) were in close agreement. This difference is most likely due to test specimen defects such as geometrical measuring or bolt pretensions.
6.2. Verifying the models using the tests conducted by Saedi et al. (elevated temperatures) The FE results were compared with the experimental data generated by Saedi et al. in terms of temperature–rotation characteristics and failure modes of the connections. Figs. 9 and 10 show comparison between predicted deformations and real deformations for connection S5. Fig. 11 shows the deformation modes of the same
connection components in comparison with the real connection components deformations after the test. Fig. 9 shows a local deformation at the top and bottom angles, particularly around the top bolt, where it is subjected to the highest tensile stresses. Because of the high strength of columns used in the test, the columns were not deformed compared to the angles. The bolts used at the vertical leg of the top angle were subjected to the highest tensile stresses and failed. Distortion did not occur in the other bolts. This behavior was closely predicted by the FE model, as shown in Fig. 10. Fig. 11 shows the deformed shapes of each component of the connection assembly in comparison with the same component after the test, where damage in terms of permanent deformation takes place in the top and bottom angles. The critical stress at the end of bolt is clearly visible and the same thing can be seen in the real components of the connection. The column and beam have no significant deformation. In order to validate the results from the FE analysis, four elevated temperature tests were modeled. A comparison of the temperature–rotation response of the connections at different moments is shown in Fig. 12. The temperature–rotation response curves of the connections agree well with tests at the elastic and plastic stages. Differences between the numerical simulations and
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the test results may be due to several causes, such as numerical modeling simplification, test specimen defects, residual stress, contact surface interactions, frictional forces and bolt pretensions or nonlinear constitutive models of materials at elevated temperatures. As it can be clearly seen in Fig. 12, specimens 3 and 13 whose angle thickness is 10 mm failed significantly before the failure of specimens 9 and 5 whose angle thickness is 15 mm. As it can be seen in Table 3, the applied moment for all specimens is 8.5 kN m. This amount of moment is equal to 0.4 Mcc for specimen 5 whereas, it is 0.8 Mcc for specimen 13 that is similar to specimen 5 and the only difference is the thickness of angle that is 10 mm in specimen 13. As it can be concluded, although the moment applied to the specimens is the same, but the specimens are under different moment from the rotation capacity point of view. Now, it can be said that during the tests, the specimens are affected by two subjects, i.e. the moment applied by the jacks and the deterioration of steel stiffness and strength due to the increase of temperature and a combination of these two parameters leads to the failure of specimens. It can be seen that first, the specimens whose angle thickness is 10 mm are under greater moment from the rotation capacity point of view and this is an important reason for the premature failure of these specimens in comparison with the specimens whose angle thickness is 15 mm. Secondly, the stiffness and strength of specimens with smaller angle thickness deteriorate more quickly. Considering these two subjects, it is observed that the specimens with smaller angle thickness are in worse condition and the combination of these two subjects leads to the quicker failure of them in comparison to the time of failure of connections with thicker angle. One of the most important and applicable curves in connection design is the moment–rotation curve; this curve is shown in Fig. 13 for four types of connections at different temperatures using the finite element models. For all the tests, deterioration of connection characteristics due to temperature increase was predicted well by the models. Fig. 13 shows that the moment resistance of the connection was severely decreased. In general, these types of angle connections who have been made by usual constructional steel and bolts have no moment resistance at temperatures more than 800 1C.
7. Study of the connection failure mechanism using finite element model In this part, the verified finite element model presented above is used to study the failure mechanism of the 4 specimens and interpret the obtained results. The analysis results are presented as Von Mises stresses. The results showed that in specimens S3 and S13 whose angle thickness is 10 mm, critical stress is formed at the connection place of vertical and horizontal legs of top angle. This shows that the failure mechanism of these connections is the failure of top angle that is confirmed by the results of experimental test (Fig. 14a). Whereas, in the case of specimens S5 and S9 whose angle thickness is 15 mm, critical stress is formed at the bolts who connect the top angle to column and the failure mode is in the form of failure in these bolts (Fig. 14b). This result determines the weak points of connection that can be fortified to improve the connection behavior. For example, the angle thickness of connection S3 whose failure mode was the failure of top angle is increased from 10 to 15 mm and the connection is called S3 (1). The specimen is again analyzed and as it can be seen in Fig. 15, the specimen S3 (1) tolerated higher temperature and the failure mode is changed to failure of bolts. Besides, the main difference between specimens S3 and S3 (1) is the rotation capacity value, i.e., increasing the thickness of bolts and preventing the premature angle failure lead to higher rotations of
Fig. 14. Failure mechanism of connections.
the connection. In the next step, 10.9 bolts are used instead of 8.8 bolts to improve the behavior of connection (specimen S3 (2)). As it can be seen in Fig. 15, the temperature strength and rotation capacity are significantly increased, but the failure mode is still the failure of bolts. It should be noted that the results of numerical models about the effects of increasing the angle thickness and using 10.9 bolts instead of 8.8 bolts are confirmed by the results of experimental test of Ref. [20] and this shows the ability of numerical models to predict behavior of connection at elevated temperatures and improving the connection behavior. It should be noted that according to the results of Ref. [32], a problem which is observed in the behavior of angle bolted connections at elevated temperature is thread stripping in bolts and exiting of nut from bolt without failure of bolt. [32]. Since the finite element model
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present in the paper is not able to consider such mechanism, and the analysis of such mechanism is very time consuming, and besides, this new model should be verified again, the effects of thread stripping can be considered using safety factors in analysis to consider the decrease in temperature strength.
8. Conclusions Considering the high cost of experimental tests at elevated temperatures and the limitation in the number of parameters in tests for study the behavior of a specific connection at elevated temperatures, availability of an accurate numerical model that is able to accurately simulate the behavior of the connection at elevated temperature is of great importance. Without such a model, comprehensive investigation about the behavior of connections at elevated temperature is practically impossible. Besides, angle bolted connections are used widely in some countries as semi-rigid connections and numerical simulation is necessary to study the behavior of such connections at elevated temperatures. Since no previous research has been carried out before, the need for such study is felt twice. To do this, a 3-D finite element analysis was conducted to study the behavior of bolted top and bottom angle connections with and without web angles at elevated temperatures using the general purpose finite element software, ANSYS. The connection components were modeled using three-dimensional brick elements, while contacts between the components were modeled using contact elements based on the Coulomb friction law. Material nonlinearity was considered for both steel members and connection components. The whole stress–strain–temperature curves were incorporated in the model to simulate the degradation of the connection characteristics at elevated temperatures. Simulation results were compared with experimental data. The results obtained showed a good agreement between the predicted and measured responses in both the elastic and plastic ranges. This demonstrates that the FE technique is capable of predicting connection response at elevated temperatures to an acceptable degree of accuracy. The purpose of the present study is not just to investigate the feasibility of simulation of angle bolted connections. In more advanced step, the numerical model, whose accuracy has been verified by comparing to experimental test results at ambient and elevated temperatures, is used to study the connection failure mechanisms. According to
the type of failure, proper method is used to increase the temperature strength of the connections.
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