- Email: [email protected]
Cyclic performance of steel moment-resisting connections with reduced beam sections — experimental analysis and finite element model simulation
Engineering Structures 32 (2010) 2683–2692
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Cyclic performance of steel moment-resisting connections with reduced beam sections — experimental analysis and finite element model simulation D.T. Pachoumis ∗ , E.G. Galoussis, C.N. Kalfas, I.Z. Efthimiou Steel Structures Laboratory, School of Civil Engineering, Democritus University of Thrace, Xanthi, 67100, Greece
article
info
Article history: Received 13 May 2009 Received in revised form 9 April 2010 Accepted 28 April 2010 Available online 16 June 2010 Keywords: Reduced beam section connection Dogbone Moment-resisting connection Cyclic loading Finite element analysis
abstract Reduced beam section (RBS) moment-resisting connections have been developed in order to provide a highly ductile response and reliable performance. Recommendations for the design and detailing of the RBS member were prescribed in EC8, Part 3. However, the effectiveness of these recommendations for a European profile is dubious, due to limited existing data from European research. An experimental program was performed in order to evaluate the proposed values of the geometrical characteristics of the RBS, and the results are presented in the present paper. Two full-scale subassemblages were tested under cyclic loading and the results are compared with those obtained from the theoretical model, using the finite element method. The analysis confirms the need for readjustment of the geometrical characteristics of the RBS in order to apply to European profiles. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The unexpected local brittle damage of beam-to-column connections of steel moment-resisting frames in the Northridge (1994) and Kobe (1995) earthquakes generated concerns regarding the reliability of the current design practise and detailing of connections. Rigorous post-earthquake investigations have revealed many factors contributing to the failure. The high stress concentration at the welded web and flanges and the vulnerability of the connection to the large ductility demand are considered to be two critical factors causing such failures. A natural way to solve the problem is to reduce the ductility demand on the welded areas and alleviate the stress concentration level. Numerous solutions to the moment frame connection problem have been proposed [1–4], many of which have been shown to exhibit satisfactory levels of ductility in numerous tests. One of these is the reduced beam section (RBS) configuration. Portions of the beam flanges are trimmed away in the region adjacent to the beam-to-column connection. The RBS can be viewed as a ductile fuse that forces the formation of the plastic hinge away from the joint so that much of ductility demand on beams may result from the RBS instead of the welded beam-to-column interface. Extensive experimental [5–7] and analytical [8–10] projects have been conducted proving the effectiveness of this solution. Apparently, the efficiency of the RBS in mitigating the problems relies on
∗
Corresponding author. Tel.: +30 6977135683; fax: +30 2541079821. E-mail address: [email protected] (D.T. Pachoumis).
0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.04.038
the proper design of the RBS, which includes the shape, the location and flange reduction ratio (the reduced flange area over the original flange area) of the RBS. Various shaped cutouts were proposed (constant, tapered or radius cut) to reduce the cross-sectional area. Experimental investigations have demonstrated that a curved RBS behaves with the highest rotational capacity with respect to polyline-shaped solutions [11]. The location of the RBS with a given flange reduction ratio may alter its efficiency. Besides, an RBS with small reduction in beam flanges might do little to reduce the stress in the column faces. However, an RBS with excessive reduction in the beam flanges may result in premature lateral–torsional buckling of the RBS. Some design parameters are recommended by FEMA 350 [1] and FEMA 351 [12] regarding the location and reduction rate of an RBS, based on the local performance of tested beam-to-column assemblies. In Europe, also, following the spirit of the abovementioned recommendations, in EC8, Part 3 [13] designs of such type of connection are presented. The proposals for the radius cut from FEMA 350, which prequalified this shape, and EC8, Part 3 are presented in Table 1. The values for the geometrical parameters recommended in EC8, Part 3 are the average of, or even the same as, those in FEMA 350, due to the lack of experimental studies on European profiles. So, the effectiveness of these recommendations is questionable. Recent experimental research [14] confirmed the need for readjustment of the geometrical characteristics for the design of a radius-cut RBS. This paper presents an investigation on the cyclic performance of steel moment-resisting connections with RBS, using European
2684
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
finite elements simulating the RBS connection with specimens similar to the experimental ones. The agreement between experimental and numerical results is obvious and so there is the need to readjust the geometrical characteristics of RBSs in order for them to be safely applied to European profiles.
Nomenclature RBS a b bf db E fy fu G g l M M–ϕ P r s ti
δy ν ϕ
Reduced beam section Distance of the beginning of the RBS from the column face Length of the RBS Flange width Beam depth Modulus of elasticity Yield strength Ultimate strength Shear modulus Depth of the flange cut The distance between the load axis and the column face axis Bending moment Moment versus rotation Load Radius of the cuts in both top and bottom flanges at the RBS Distance of the intended plastic hinge at the centre of the RBS from the column face Thickness of element i Displacement at the yield point Poisson’s ratio in the elastic stage Rotation of the joint
2. Design of specimens The specimen geometry and overall test set-up are shown in Fig. 1. The geometry of the test specimens was chosen to model the exterior connection of a multi-storey steel frame. Two types of specimen were studied, designated as RBSa and RBSb . Each one consisted of one HE 300B column and one HE 180A beam (Table 2). A strong panel zone was produced using double web plates and continuity plates, equal in thickness to the beam’s flange thickness, at the column (Table 3), forcing the formation of the plastic hinge in the weakening zone. The typical geometry and seismic moment profile for the design of the radius-cut RBS are shown in Figs. 2 and 3. The material properties for the beams was obtained from threepoint bending coupon tests performed for this study. The resulting values were as follows: Young’s modulus E = 209 000 N/mm2 , yield stress fy = 310 N/mm2 and ultimate stress fu = 430 N/mm2 (Fig. 4). The same properties were also given to the weld material. The RBS design did not follow the recommendations proposed by EC8, Part 3 [13]. The resulting dimensions for the RBS region are given in Table 4. 3. Finite element modelling
profiles (Fig. 1). The RBS connections were not designed according to the recommendations proposed by EC8, Part 3. Two experiments were conducted investigating the key parameters for the design adopted by EC8, Part 3. A theoretical model was also created with
1000
In the present project, the finite element package ABAQUS [15] was used to predict the structural behaviour of RBS momentresisting connections subjected to cyclic loading. Two types of analysis were conducted having almost identical results. For the first one, two-dimensional four-noded thin shell elements with
200
1200
Fig. 1. Test set-up.
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
2685
Table 1 Geometrical characteristics of the reduced beam section. FEMA 350 [1]/351 [12]
EC 8, Part 3 [13]
a = 0.50 − 0.75bf b = 0.65 − 0.85db c ≤ 0.25bf s = a + b/2 r = 4c 2 + b2 /8c
a = 0.60bf b = 0.75db g ≤ 0.25bf s = a + b/2 r = 4g 2 + b2 /8g
Fig. 5. View of the finite element mesh of the RBS connection (element S4R). Fig. 2. Typical geometry of a radius-cut reduced beam section.
Fig. 3. Seismic moment profile for reduced beam section design. Fig. 6. View of the finite element mesh of the RBS connection (element C3D8R).
with reduced integration (element C3D8R in ABAQUS) were employed to model the beams and columns flanges (Fig. 6). All the other components were modelled according to the previous analysis. Based on the results of the coupon tests, a true stress–strain curve with reduced strength at large strain after yielding, that is strength degradation, was adopted. A more refined mesh was applied at the regions near the RBS. The mesh was formed with the ratio elementx : elementy : element thickness = 1:1:1, and with the ratio 1–2 for the remaining areas. Due to the biaxial symmetry of the specimens, only one half was modelled to reduce the computational time and for better viewing of the results, with the appropriate boundary conditions imposed. The analyses were conducted by applying cyclic variable amplitude displacement at the top of the beam at a distance of 1.00 m from the face of the column. The cyclic displacement amplitude followed the loading protocol in the AISC Seismic Provisions (AISC 2002), which is the same as the SAC loading protocol 1997. The loading protocol is shown in Fig. 7 and in Table 5.
Fig. 4. Specimen material three-point bending coupon stress–strain curve.
reduced integration (element S4R in ABAQUS) were employed to model all the components of a typical RBS connection (Fig. 5). For the second one, three-dimensional eight-noded solid elements Table 2 European beams in accordance with Euronorm 53–62. Designation
HE 180A HE 300B
Depth of section h (mm)
171 300
Width of section b (mm)
180 300
Thickness
Root radius r (mm)
of web, tw (mm)
of flange, tf (mm)
6 11
9.5 19
15 27
Area of section A (cm2 )
45.3 149
Mass per metre G (kg/m)
35.5 117
Second moment of area
Axis y–y Iy (cm4 )
Axis z–z Iz (cm4 )
2 510 25 170
925 8563
2686
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692 Table 5 Loading protocol. Load step
Peak deformation, δy
Number of cycles, n
1 2 3 4 5 6 7
0.375 0.50 0.75 1.00 1.50 2.00 3.00
2 2 2 4 2 2 2
Continue with increments in δy of 1.00 δy , and perform two cycles at each step.
Number of cycles
Fig. 7. Loading protocol.
Table 3 Specifications of specimens. Specimens
Column
Beam
Doubler plate thickness (mm)
Continuity plate thickness (mm)
RBSa RBSb
HE 300B HE 300B
HE 180A HE 180A
12 12
10 10
Several complete loading cycles were applied to each specimen with displacement amplitudes in multiples of δy , the displacement expected to yield the specimen. In order to determine this yield displacement, a nonlinear analysis using ABAQUS finite element software under monotonic loading was conducted before the tests. 4. Experimental study The experimental procedure was carried out at the Steel Structures Laboratory of the Civil Engineering Department of Democritus University of Thrace. An overall view of the test set-up is shown in Fig. 8. The specimens were in full agreement with the theoretical models in the overall external dimensions, while the column and beam dimensions were examined and found to be in full agreement with the nominal ones. The geometrical external dimensions are 1797 mm for the vertical member, acting as the column, and 1200 mm for the horizontal member, behaving as the beam. Continuity plates were used at all connections with the thickness chosen to be equal to the beam’s flange thickness (10 mm). Doubler web plates with thickness (12 mm) bigger than that of the column’s web were also used. A thick end plate (tp = 20 mm) was used at the beam’s free end in order to avoid the end effects and to simulate the beam’s continuity. The supports were considered as fixed, constructed of extended end plate connections. An identical ‘twin’ subassemblage was placed at the ring, providing lateral restraint at a distance of 1.00 m from the column’s face (Fig. 9). Each beam flange and web was welded at the face of the column using welds. It should be noted that there were no web access holes. The welds’ throats were 8 mm for all the specimens. The welds’ throats and
Fig. 8. An overall view of the test set-up.
quality were measured and checked during the constructional process. The load was imposed through two hydraulic jacks of 1000 kN capacity each. Whitewash was painted in the connection region, with the finite element model (FEM) mesh arrangement drawing to monitor yielding (Fig. 10). The test specimens were instrumented with a combination of displacement transducers and strain gauges to measure the global and local responses. 5. Results The beam moment–rotation hysteretic responses of the subassemblies resulting from the experimental study are compared with those of the finite element analysis (Figs. 11 and 12). The FEM used in this work was thoroughly verified by comparing the simulated response to experimental results for moment-resisting subassemblages. Reasonable correlation between the analysis and experimental results is evident in both figures, especially in the elastic region where the divergences are negligible. As is observed,
Table 4 RBS region dimensions. Specimens
RBSa RBSb
bf (mm)
180 180
db (mm)
171 171
a
b
g
%bf
(mm)
%db
(mm)
%bf
(mm)
80 40
144 72
75 60
128.25 102.6
40 25
36 22.5
s (mm)
r (mm)
208.125 123.3
75.11 69.73
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
2687
Fig. 9. The arrangement of ‘twin’ subassemblages.
Fig. 10. The FEM mesh drawing in specimens.
there is a pretty good qualitative correlation between the FEM behaviour and the experimental RBS model behaviour. All the characteristics of bending moments discussed hereafter are computed for M = Pl, where l is the distance between load axis and the column face axis. The beam’s deflections were measured at the RBS, near the face of the column (4 cm) and at a distance 60 cm and 75 cm from the face of the column, in order to examine the effectiveness of the radius cut with EC8 and FEMA geometrical characteristics. Each point rotation was computed by dividing its deflection by the points distance from the face of the column. Specimen RBSa exhibited excellent performance under cyclic loading, although the value of the geometrical parameter a was greater (80%bf ) than the upper limits recommended by EC8 or FEMA. A real plastic hinge developed at the RBS area. The ductility, in terms of rotation, was greater than the 0.03 rad, a rotation which is sometimes considered as the upper limit of the ϕ required in practice. Initial yielding occurred during the first cycle at 1.0δy , with yielding observed at the bottom flange. It should be noted that during that cycle the beam-to-column interface remained in the elastic area. Progressing through the loading history, yielding started to propagate along the RBS bottom flange. During the second cycle at 2.0δy , yielding was also observed at the top flange of the RBS. Due to the limitation of the test set-up, after the second cycle at
Table 6 Connection’s strength. Specimens
Mpl,Rd,beam (nominal) (kN m)
Mpl,Rd,RBS (nominal) (kN m)
Mpl,Rd,FEM (kN m)
Mpl,Rd,Experiment (kN m)
RBSa RBSb
100.75 100.75
66.50 79.35
74 80
76 86
3.0δy , the test was continued monotonically. During that loading, local buckling of the bottom flange developed, which became more pronounced with each successive loading. Initiation of web buckling appeared close to the yielded bottom flange. It should be noted here that the bottom flange and web buckling was not accompanied by a significant deterioration in the hysteresis loops. Specimen RBSa reached 0.11 rad rotation without observing any failure in the vicinity of welds and at the face of the column. The test stopped when the available limits of the ring was reached. Photographs of the specimen during the test are shown in Figs. 13 and 14. Severe local buckling occurred in the bottom flange and the portion of the web next to the bottom flange, as shown in Fig. 14. The length of the buckle extended over the entire length of the RBS. As is observed from Fig. 15, there is a very good qualitative correlation between the FEM behaviour and the experimental RBS model behaviour.
2688
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
Fig. 11. Experimental moment–rotation curves (RBSa ).
The strength of the connection calculated according to EC3 for the full section of the beam and for the reduced beam section compared with those measured from the FEM analysis and from the experiment in Table 6. In summary, the excellent performance of specimen RBSa under cyclic loading was confirmed from the plastic hinge formation at the RBS region, with extensive yielding occurring in the beam flanges as well as the web. Specimen RBSa developed 0.11 rad of plastic rotation and showed no sign of distress at the face of the column.
The response of specimen RBSb is shown in Fig. 16. Initial yielding occurred during the fourth cycle at 1.0δy , with significant yielding observed at the bottom flange. Progressing through the loading history, yielding started to propagate along the RBS bottom flange. Web buckling was not noted. During the first cycle at 1.5δy , yielding was also observed at the top flange of the RBS. During the cycle at 3.0δy , severe flange local buckling developed, which became more pronounced with each successive loading cycle. After the second cycle at 4.0δy , the test was continued monotonically until the specimen reached the 0.12 rad rotation. Testing was stopped
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
2689
Fig. 12. Experimental moment–rotation curves (RBSb ).
at this point due to the limitations in the test set-up. No failure occurred in specimen RBSb . Photographs of the specimen during the test are shown in Fig. 17. Specimen RBSb exhibited excellent performance under cyclic loading, although the values of the geometrical parameter a (40%bf ) and b (60%db ) were not according to the recommendations proposed by EC8 or FEMA. A plastic hinge was formed at the RBS region;, therefore specimen RBSb developed 0.12 rad of plastic rotation without showing any sign of distress at the face of the column or any failure in the vicinity of the welds. As is observed from Fig. 18, there is a very good qualitative correlation between the FEM behaviour and the experimental RBS model behaviour.
Table 6 shows the strength of the connection measured from the FEM analysis and from the experiment, compared with those calculated according to EC3 for the full and for the reduced beam section. 6. Conclusions Two full-scale moment-resisting connection specimens that employed a reduced beam section (RBS) were tested. The test variables included the limit values for the geometrical parameters a and b of the radius cut. Experiments and analysis on the RBS specimens have provided the following conclusions.
2690
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
RBS
RBS
RBS
Fig. 13. Beam’s bottom flange (left) and web buckling (right) of specimen RBSa at 0.03 rad moment rotation.
RBS
RBS
RBS
Fig. 14. Beam’s bottom flange buckling of specimen RBSa at 0.09 rad (left) and 0.11 rad (right) moment rotation.
Fig. 15. Correlation between the experimental model and the FEM (RBSa ).
• Both the experimental and numerical specimens exhibited
• The RBS can be viewed as a ductile ‘fuse’ that forces yielding to
satisfactory levels of connection ductility required of special moment-resisting frames. Although the values of the geometrical parameters were not according to the recommendations proposed, the plastic rotation exceeded the acceptable 0.03 rad without any weld fracture or any sign of distress at the face of the column, on both specimens RBSa and RBSb . • Plastification of the RBS developed in same way. • The cyclic performance of the RBS moment-resisting connection is excellent when the plastic hinge is formed at the RBS area.
occur within the reduced section of the beam, an area that can sustain large inelastic strains while at the same time limiting the stress in the less ductile region near the face of the column.
• Specimens RBSa and RBSb , which were not designed according to the proposed recommendations, exhibited excellent performance when subjected to cyclic loading. The key parameters for the design of an RBS with radius cut that were adopted by EC8 should be readjusted in order to be more safely applicable to European profiles.
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
2691
RBS RBS
RBS
RBS
RBS
Fig. 16. Progress of beam’s bottom flange buckling of specimen RBSb .
RBS
RBS RBS
RBS
RBS
Fig. 17. Beam’s bottom flange buckling of specimen RBSb at 0.12 rad moment rotation.
2692
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
Fig. 18. Correlation between the experimental model and the FEM (RBSb ).
References [9] [1] FEMA 350. Recommended seismic design criteria for new steel moment-frame buildings. Washington (DC); 2000. [2] Engelhardt MD, Husain AS. Cyclic-loading performance of welded flangebolted web connections. J Struct Eng 1993;119(12):3537–49. [3] Tsai KC, Shun W, Popov E. Experimental performance of seismic steel beam–column moment joints. J Struct Eng 1995;121(6):925–31. [4] Plumier A. Behaviour of connections. J Constr Steel Res 1994;29:95–119. [5] Moore KO, Malley J, Engelhardt M. Design of reduced beam section moment frame connection. Structural steel educational council: technical information and product service. CA; 1999. [6] Chen SJ, Chu JM, Chou ZL. Dynamic behavior of steel frames with beam flanges shaved around connection. J Constr Steel Res 1997;42(1):49–70. [7] Popov E, Blondet M, Stepanov L. Application of dog bones for improvement of seismic behavior of steel connections. Report no UCB/EERC 96/05. USA; 1996. [8] Anastasiadis A, Gioncu V. Influence of joint details on the local ductility of steel
[10]
[11]
[12] [13] [14]
[15]
moment resisting frames. In: Proceedings of 3rd national Greek conference on steel structures. 1998. p. 311–19. Anastasiadis A, Gioncu V, Mazzolani FM. New upgrading procedures to improve the ductility of steel MR-frames. In: XVII CTA Congress. 1999. p. 193–204. Faggiano B, Landolfo R. Seismic analysis of steel MR frames with dog bone connections. In: Proceedings of 12th European conference on earthquake engineering. 2002. Paper reference. 309. Engelhardt MD, Sabol TA. Seismic-resistant steel moment connections: developments since the 1994 Northridge earthquake. J Prog Struct Eng Mater 1997; 1(1):68–77. FEMA 351. Recommended seismic evaluation and upgrade criteria for existing welded steel moment frame buildings. Washington (DC); 2000. EC 8. Part 3: design of structures for earthquake resistance. Assessment and retrofitting of buildings. EN 1998-3: June 2005E. Pachoumis DT, Galoussis EG, Kalfas CN, Christitsas AD. Reduced beam section moment connections subjected to cyclic loading: experimental analysis and FEM simulation. J Eng Struct 2009;31:216–23. ABAQUS/PRE. Users manual. Hibbit. Karlsson and Sorensen Inc.; 1997.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Cyclic performance of steel moment-resisting connections with reduced beam sections — experimental analysis and finite element model simulation D.T. Pachoumis ∗ , E.G. Galoussis, C.N. Kalfas, I.Z. Efthimiou Steel Structures Laboratory, School of Civil Engineering, Democritus University of Thrace, Xanthi, 67100, Greece
article
info
Article history: Received 13 May 2009 Received in revised form 9 April 2010 Accepted 28 April 2010 Available online 16 June 2010 Keywords: Reduced beam section connection Dogbone Moment-resisting connection Cyclic loading Finite element analysis
abstract Reduced beam section (RBS) moment-resisting connections have been developed in order to provide a highly ductile response and reliable performance. Recommendations for the design and detailing of the RBS member were prescribed in EC8, Part 3. However, the effectiveness of these recommendations for a European profile is dubious, due to limited existing data from European research. An experimental program was performed in order to evaluate the proposed values of the geometrical characteristics of the RBS, and the results are presented in the present paper. Two full-scale subassemblages were tested under cyclic loading and the results are compared with those obtained from the theoretical model, using the finite element method. The analysis confirms the need for readjustment of the geometrical characteristics of the RBS in order to apply to European profiles. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The unexpected local brittle damage of beam-to-column connections of steel moment-resisting frames in the Northridge (1994) and Kobe (1995) earthquakes generated concerns regarding the reliability of the current design practise and detailing of connections. Rigorous post-earthquake investigations have revealed many factors contributing to the failure. The high stress concentration at the welded web and flanges and the vulnerability of the connection to the large ductility demand are considered to be two critical factors causing such failures. A natural way to solve the problem is to reduce the ductility demand on the welded areas and alleviate the stress concentration level. Numerous solutions to the moment frame connection problem have been proposed [1–4], many of which have been shown to exhibit satisfactory levels of ductility in numerous tests. One of these is the reduced beam section (RBS) configuration. Portions of the beam flanges are trimmed away in the region adjacent to the beam-to-column connection. The RBS can be viewed as a ductile fuse that forces the formation of the plastic hinge away from the joint so that much of ductility demand on beams may result from the RBS instead of the welded beam-to-column interface. Extensive experimental [5–7] and analytical [8–10] projects have been conducted proving the effectiveness of this solution. Apparently, the efficiency of the RBS in mitigating the problems relies on
∗
Corresponding author. Tel.: +30 6977135683; fax: +30 2541079821. E-mail address: [email protected] (D.T. Pachoumis).
0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.04.038
the proper design of the RBS, which includes the shape, the location and flange reduction ratio (the reduced flange area over the original flange area) of the RBS. Various shaped cutouts were proposed (constant, tapered or radius cut) to reduce the cross-sectional area. Experimental investigations have demonstrated that a curved RBS behaves with the highest rotational capacity with respect to polyline-shaped solutions [11]. The location of the RBS with a given flange reduction ratio may alter its efficiency. Besides, an RBS with small reduction in beam flanges might do little to reduce the stress in the column faces. However, an RBS with excessive reduction in the beam flanges may result in premature lateral–torsional buckling of the RBS. Some design parameters are recommended by FEMA 350 [1] and FEMA 351 [12] regarding the location and reduction rate of an RBS, based on the local performance of tested beam-to-column assemblies. In Europe, also, following the spirit of the abovementioned recommendations, in EC8, Part 3 [13] designs of such type of connection are presented. The proposals for the radius cut from FEMA 350, which prequalified this shape, and EC8, Part 3 are presented in Table 1. The values for the geometrical parameters recommended in EC8, Part 3 are the average of, or even the same as, those in FEMA 350, due to the lack of experimental studies on European profiles. So, the effectiveness of these recommendations is questionable. Recent experimental research [14] confirmed the need for readjustment of the geometrical characteristics for the design of a radius-cut RBS. This paper presents an investigation on the cyclic performance of steel moment-resisting connections with RBS, using European
2684
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
finite elements simulating the RBS connection with specimens similar to the experimental ones. The agreement between experimental and numerical results is obvious and so there is the need to readjust the geometrical characteristics of RBSs in order for them to be safely applied to European profiles.
Nomenclature RBS a b bf db E fy fu G g l M M–ϕ P r s ti
δy ν ϕ
Reduced beam section Distance of the beginning of the RBS from the column face Length of the RBS Flange width Beam depth Modulus of elasticity Yield strength Ultimate strength Shear modulus Depth of the flange cut The distance between the load axis and the column face axis Bending moment Moment versus rotation Load Radius of the cuts in both top and bottom flanges at the RBS Distance of the intended plastic hinge at the centre of the RBS from the column face Thickness of element i Displacement at the yield point Poisson’s ratio in the elastic stage Rotation of the joint
2. Design of specimens The specimen geometry and overall test set-up are shown in Fig. 1. The geometry of the test specimens was chosen to model the exterior connection of a multi-storey steel frame. Two types of specimen were studied, designated as RBSa and RBSb . Each one consisted of one HE 300B column and one HE 180A beam (Table 2). A strong panel zone was produced using double web plates and continuity plates, equal in thickness to the beam’s flange thickness, at the column (Table 3), forcing the formation of the plastic hinge in the weakening zone. The typical geometry and seismic moment profile for the design of the radius-cut RBS are shown in Figs. 2 and 3. The material properties for the beams was obtained from threepoint bending coupon tests performed for this study. The resulting values were as follows: Young’s modulus E = 209 000 N/mm2 , yield stress fy = 310 N/mm2 and ultimate stress fu = 430 N/mm2 (Fig. 4). The same properties were also given to the weld material. The RBS design did not follow the recommendations proposed by EC8, Part 3 [13]. The resulting dimensions for the RBS region are given in Table 4. 3. Finite element modelling
profiles (Fig. 1). The RBS connections were not designed according to the recommendations proposed by EC8, Part 3. Two experiments were conducted investigating the key parameters for the design adopted by EC8, Part 3. A theoretical model was also created with
1000
In the present project, the finite element package ABAQUS [15] was used to predict the structural behaviour of RBS momentresisting connections subjected to cyclic loading. Two types of analysis were conducted having almost identical results. For the first one, two-dimensional four-noded thin shell elements with
200
1200
Fig. 1. Test set-up.
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
2685
Table 1 Geometrical characteristics of the reduced beam section. FEMA 350 [1]/351 [12]
EC 8, Part 3 [13]
a = 0.50 − 0.75bf b = 0.65 − 0.85db c ≤ 0.25bf s = a + b/2 r = 4c 2 + b2 /8c
a = 0.60bf b = 0.75db g ≤ 0.25bf s = a + b/2 r = 4g 2 + b2 /8g
Fig. 5. View of the finite element mesh of the RBS connection (element S4R). Fig. 2. Typical geometry of a radius-cut reduced beam section.
Fig. 3. Seismic moment profile for reduced beam section design. Fig. 6. View of the finite element mesh of the RBS connection (element C3D8R).
with reduced integration (element C3D8R in ABAQUS) were employed to model the beams and columns flanges (Fig. 6). All the other components were modelled according to the previous analysis. Based on the results of the coupon tests, a true stress–strain curve with reduced strength at large strain after yielding, that is strength degradation, was adopted. A more refined mesh was applied at the regions near the RBS. The mesh was formed with the ratio elementx : elementy : element thickness = 1:1:1, and with the ratio 1–2 for the remaining areas. Due to the biaxial symmetry of the specimens, only one half was modelled to reduce the computational time and for better viewing of the results, with the appropriate boundary conditions imposed. The analyses were conducted by applying cyclic variable amplitude displacement at the top of the beam at a distance of 1.00 m from the face of the column. The cyclic displacement amplitude followed the loading protocol in the AISC Seismic Provisions (AISC 2002), which is the same as the SAC loading protocol 1997. The loading protocol is shown in Fig. 7 and in Table 5.
Fig. 4. Specimen material three-point bending coupon stress–strain curve.
reduced integration (element S4R in ABAQUS) were employed to model all the components of a typical RBS connection (Fig. 5). For the second one, three-dimensional eight-noded solid elements Table 2 European beams in accordance with Euronorm 53–62. Designation
HE 180A HE 300B
Depth of section h (mm)
171 300
Width of section b (mm)
180 300
Thickness
Root radius r (mm)
of web, tw (mm)
of flange, tf (mm)
6 11
9.5 19
15 27
Area of section A (cm2 )
45.3 149
Mass per metre G (kg/m)
35.5 117
Second moment of area
Axis y–y Iy (cm4 )
Axis z–z Iz (cm4 )
2 510 25 170
925 8563
2686
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692 Table 5 Loading protocol. Load step
Peak deformation, δy
Number of cycles, n
1 2 3 4 5 6 7
0.375 0.50 0.75 1.00 1.50 2.00 3.00
2 2 2 4 2 2 2
Continue with increments in δy of 1.00 δy , and perform two cycles at each step.
Number of cycles
Fig. 7. Loading protocol.
Table 3 Specifications of specimens. Specimens
Column
Beam
Doubler plate thickness (mm)
Continuity plate thickness (mm)
RBSa RBSb
HE 300B HE 300B
HE 180A HE 180A
12 12
10 10
Several complete loading cycles were applied to each specimen with displacement amplitudes in multiples of δy , the displacement expected to yield the specimen. In order to determine this yield displacement, a nonlinear analysis using ABAQUS finite element software under monotonic loading was conducted before the tests. 4. Experimental study The experimental procedure was carried out at the Steel Structures Laboratory of the Civil Engineering Department of Democritus University of Thrace. An overall view of the test set-up is shown in Fig. 8. The specimens were in full agreement with the theoretical models in the overall external dimensions, while the column and beam dimensions were examined and found to be in full agreement with the nominal ones. The geometrical external dimensions are 1797 mm for the vertical member, acting as the column, and 1200 mm for the horizontal member, behaving as the beam. Continuity plates were used at all connections with the thickness chosen to be equal to the beam’s flange thickness (10 mm). Doubler web plates with thickness (12 mm) bigger than that of the column’s web were also used. A thick end plate (tp = 20 mm) was used at the beam’s free end in order to avoid the end effects and to simulate the beam’s continuity. The supports were considered as fixed, constructed of extended end plate connections. An identical ‘twin’ subassemblage was placed at the ring, providing lateral restraint at a distance of 1.00 m from the column’s face (Fig. 9). Each beam flange and web was welded at the face of the column using welds. It should be noted that there were no web access holes. The welds’ throats were 8 mm for all the specimens. The welds’ throats and
Fig. 8. An overall view of the test set-up.
quality were measured and checked during the constructional process. The load was imposed through two hydraulic jacks of 1000 kN capacity each. Whitewash was painted in the connection region, with the finite element model (FEM) mesh arrangement drawing to monitor yielding (Fig. 10). The test specimens were instrumented with a combination of displacement transducers and strain gauges to measure the global and local responses. 5. Results The beam moment–rotation hysteretic responses of the subassemblies resulting from the experimental study are compared with those of the finite element analysis (Figs. 11 and 12). The FEM used in this work was thoroughly verified by comparing the simulated response to experimental results for moment-resisting subassemblages. Reasonable correlation between the analysis and experimental results is evident in both figures, especially in the elastic region where the divergences are negligible. As is observed,
Table 4 RBS region dimensions. Specimens
RBSa RBSb
bf (mm)
180 180
db (mm)
171 171
a
b
g
%bf
(mm)
%db
(mm)
%bf
(mm)
80 40
144 72
75 60
128.25 102.6
40 25
36 22.5
s (mm)
r (mm)
208.125 123.3
75.11 69.73
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
2687
Fig. 9. The arrangement of ‘twin’ subassemblages.
Fig. 10. The FEM mesh drawing in specimens.
there is a pretty good qualitative correlation between the FEM behaviour and the experimental RBS model behaviour. All the characteristics of bending moments discussed hereafter are computed for M = Pl, where l is the distance between load axis and the column face axis. The beam’s deflections were measured at the RBS, near the face of the column (4 cm) and at a distance 60 cm and 75 cm from the face of the column, in order to examine the effectiveness of the radius cut with EC8 and FEMA geometrical characteristics. Each point rotation was computed by dividing its deflection by the points distance from the face of the column. Specimen RBSa exhibited excellent performance under cyclic loading, although the value of the geometrical parameter a was greater (80%bf ) than the upper limits recommended by EC8 or FEMA. A real plastic hinge developed at the RBS area. The ductility, in terms of rotation, was greater than the 0.03 rad, a rotation which is sometimes considered as the upper limit of the ϕ required in practice. Initial yielding occurred during the first cycle at 1.0δy , with yielding observed at the bottom flange. It should be noted that during that cycle the beam-to-column interface remained in the elastic area. Progressing through the loading history, yielding started to propagate along the RBS bottom flange. During the second cycle at 2.0δy , yielding was also observed at the top flange of the RBS. Due to the limitation of the test set-up, after the second cycle at
Table 6 Connection’s strength. Specimens
Mpl,Rd,beam (nominal) (kN m)
Mpl,Rd,RBS (nominal) (kN m)
Mpl,Rd,FEM (kN m)
Mpl,Rd,Experiment (kN m)
RBSa RBSb
100.75 100.75
66.50 79.35
74 80
76 86
3.0δy , the test was continued monotonically. During that loading, local buckling of the bottom flange developed, which became more pronounced with each successive loading. Initiation of web buckling appeared close to the yielded bottom flange. It should be noted here that the bottom flange and web buckling was not accompanied by a significant deterioration in the hysteresis loops. Specimen RBSa reached 0.11 rad rotation without observing any failure in the vicinity of welds and at the face of the column. The test stopped when the available limits of the ring was reached. Photographs of the specimen during the test are shown in Figs. 13 and 14. Severe local buckling occurred in the bottom flange and the portion of the web next to the bottom flange, as shown in Fig. 14. The length of the buckle extended over the entire length of the RBS. As is observed from Fig. 15, there is a very good qualitative correlation between the FEM behaviour and the experimental RBS model behaviour.
2688
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
Fig. 11. Experimental moment–rotation curves (RBSa ).
The strength of the connection calculated according to EC3 for the full section of the beam and for the reduced beam section compared with those measured from the FEM analysis and from the experiment in Table 6. In summary, the excellent performance of specimen RBSa under cyclic loading was confirmed from the plastic hinge formation at the RBS region, with extensive yielding occurring in the beam flanges as well as the web. Specimen RBSa developed 0.11 rad of plastic rotation and showed no sign of distress at the face of the column.
The response of specimen RBSb is shown in Fig. 16. Initial yielding occurred during the fourth cycle at 1.0δy , with significant yielding observed at the bottom flange. Progressing through the loading history, yielding started to propagate along the RBS bottom flange. Web buckling was not noted. During the first cycle at 1.5δy , yielding was also observed at the top flange of the RBS. During the cycle at 3.0δy , severe flange local buckling developed, which became more pronounced with each successive loading cycle. After the second cycle at 4.0δy , the test was continued monotonically until the specimen reached the 0.12 rad rotation. Testing was stopped
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
2689
Fig. 12. Experimental moment–rotation curves (RBSb ).
at this point due to the limitations in the test set-up. No failure occurred in specimen RBSb . Photographs of the specimen during the test are shown in Fig. 17. Specimen RBSb exhibited excellent performance under cyclic loading, although the values of the geometrical parameter a (40%bf ) and b (60%db ) were not according to the recommendations proposed by EC8 or FEMA. A plastic hinge was formed at the RBS region;, therefore specimen RBSb developed 0.12 rad of plastic rotation without showing any sign of distress at the face of the column or any failure in the vicinity of the welds. As is observed from Fig. 18, there is a very good qualitative correlation between the FEM behaviour and the experimental RBS model behaviour.
Table 6 shows the strength of the connection measured from the FEM analysis and from the experiment, compared with those calculated according to EC3 for the full and for the reduced beam section. 6. Conclusions Two full-scale moment-resisting connection specimens that employed a reduced beam section (RBS) were tested. The test variables included the limit values for the geometrical parameters a and b of the radius cut. Experiments and analysis on the RBS specimens have provided the following conclusions.
2690
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
RBS
RBS
RBS
Fig. 13. Beam’s bottom flange (left) and web buckling (right) of specimen RBSa at 0.03 rad moment rotation.
RBS
RBS
RBS
Fig. 14. Beam’s bottom flange buckling of specimen RBSa at 0.09 rad (left) and 0.11 rad (right) moment rotation.
Fig. 15. Correlation between the experimental model and the FEM (RBSa ).
• Both the experimental and numerical specimens exhibited
• The RBS can be viewed as a ductile ‘fuse’ that forces yielding to
satisfactory levels of connection ductility required of special moment-resisting frames. Although the values of the geometrical parameters were not according to the recommendations proposed, the plastic rotation exceeded the acceptable 0.03 rad without any weld fracture or any sign of distress at the face of the column, on both specimens RBSa and RBSb . • Plastification of the RBS developed in same way. • The cyclic performance of the RBS moment-resisting connection is excellent when the plastic hinge is formed at the RBS area.
occur within the reduced section of the beam, an area that can sustain large inelastic strains while at the same time limiting the stress in the less ductile region near the face of the column.
• Specimens RBSa and RBSb , which were not designed according to the proposed recommendations, exhibited excellent performance when subjected to cyclic loading. The key parameters for the design of an RBS with radius cut that were adopted by EC8 should be readjusted in order to be more safely applicable to European profiles.
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
2691
RBS RBS
RBS
RBS
RBS
Fig. 16. Progress of beam’s bottom flange buckling of specimen RBSb .
RBS
RBS RBS
RBS
RBS
Fig. 17. Beam’s bottom flange buckling of specimen RBSb at 0.12 rad moment rotation.
2692
D.T. Pachoumis et al. / Engineering Structures 32 (2010) 2683–2692
Fig. 18. Correlation between the experimental model and the FEM (RBSb ).
References [9] [1] FEMA 350. Recommended seismic design criteria for new steel moment-frame buildings. Washington (DC); 2000. [2] Engelhardt MD, Husain AS. Cyclic-loading performance of welded flangebolted web connections. J Struct Eng 1993;119(12):3537–49. [3] Tsai KC, Shun W, Popov E. Experimental performance of seismic steel beam–column moment joints. J Struct Eng 1995;121(6):925–31. [4] Plumier A. Behaviour of connections. J Constr Steel Res 1994;29:95–119. [5] Moore KO, Malley J, Engelhardt M. Design of reduced beam section moment frame connection. Structural steel educational council: technical information and product service. CA; 1999. [6] Chen SJ, Chu JM, Chou ZL. Dynamic behavior of steel frames with beam flanges shaved around connection. J Constr Steel Res 1997;42(1):49–70. [7] Popov E, Blondet M, Stepanov L. Application of dog bones for improvement of seismic behavior of steel connections. Report no UCB/EERC 96/05. USA; 1996. [8] Anastasiadis A, Gioncu V. Influence of joint details on the local ductility of steel
[10]
[11]
[12] [13] [14]
[15]
moment resisting frames. In: Proceedings of 3rd national Greek conference on steel structures. 1998. p. 311–19. Anastasiadis A, Gioncu V, Mazzolani FM. New upgrading procedures to improve the ductility of steel MR-frames. In: XVII CTA Congress. 1999. p. 193–204. Faggiano B, Landolfo R. Seismic analysis of steel MR frames with dog bone connections. In: Proceedings of 12th European conference on earthquake engineering. 2002. Paper reference. 309. Engelhardt MD, Sabol TA. Seismic-resistant steel moment connections: developments since the 1994 Northridge earthquake. J Prog Struct Eng Mater 1997; 1(1):68–77. FEMA 351. Recommended seismic evaluation and upgrade criteria for existing welded steel moment frame buildings. Washington (DC); 2000. EC 8. Part 3: design of structures for earthquake resistance. Assessment and retrofitting of buildings. EN 1998-3: June 2005E. Pachoumis DT, Galoussis EG, Kalfas CN, Christitsas AD. Reduced beam section moment connections subjected to cyclic loading: experimental analysis and FEM simulation. J Eng Struct 2009;31:216–23. ABAQUS/PRE. Users manual. Hibbit. Karlsson and Sorensen Inc.; 1997.