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Development of cold-formed steel elements for earthquake resistant moment frame buildings
Thin-Walled Structures 53 (2012) 99–108
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Development of cold-formed steel elements for earthquake resistant moment frame buildings Alireza Bagheri Sabbagh a,n, Mihail Petkovski a, Kypros Pilakoutas a, Rasoul Mirghaderi b a b
Department of Civil and Structural Engineering, University of Sheffield, Sheffield S1 3JD, UK Department of Civil Engineering, University of Tehran, Tehran, Iran
a r t i c l e i n f o
abstract
Article history: Received 29 September 2011 Accepted 4 January 2012 Available online 31 January 2012
The development of thin-walled cold-formed steel (CFS) sections as energy dissipative elements for seismic moment-resisting multi-storey frame buildings is presented through FE analysis and experimental work. Studies on different structural levels are undertaken. At the element level, increasing the number of flange bends enhances both the elastic and inelastic behavior, and beams with an infinite number of bends (with curved flanges) show the highest strength, stiffness and ductility. At the connection level, different configurations of CFS beam-to-column connections using through plates are investigated numerically and verified experimentally. In web bolted connections without out-of-plane stiffeners, premature web buckling results in early loss of strength. A minimum of two pairs of vertical stiffeners are identified as essential in the connection region to delay web and flange buckling and produce relatively high moment strength and ductility. This investigation is validated by beam-tocolumn connection tests using through plates and curved flange beams with different types of out-ofplane stiffeners in the connection region. The results show that the envelope of the hysteretic curves obtained in the tests of the CFS connections can be predicted by the FE analysis. The use of out-of-plane stiffeners can increase the seismic energy dissipation capacity by up to 90%, the moment strength by up to 35% and the ductility by up to 75% when compared with connections without stiffeners. Correspondingly the use of the two minimum pairs of the vertical stiffeners can increase the seismic energy dissipation capacity by 30%, the moment strength by 28% and the ductility by 50%. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Cold-formed steel sections Beam–column connections Moment-resisting frames Seismic behavior
1. Introduction The use of cold-formed steel sections (CFS sections) as main structural components in buildings is mainly limited to stud-wall frames with low seismic energy dissipation capacity [1–5]. The deficiencies of CFS sections are typically a result of premature local failures and low strength and stiffness of beam–column connections. The research of monotonic and cyclic behavior of components and elements of CFS moment-resisting frames (MRFs) is relatively limited [6–15]. In a recently developed CFS moment-resisting frame with bolted connections, restricted to single-storey dwellings [6–9], the ductility is mainly provided by the connections while the beams and columns remain elastic. For seismic design of multi-storey buildings, however, there is a need to develop plasticity in the beams instead of just yielding the material around the bolt holes in the connections. Other investigations have shown that by using appropriate connection details, such as gusset or through plates, relatively high moment
n
Corresponding author. Tel.: þ44 114 222 5724; fax: þ 44 114 222 5700. E-mail addresses: [email protected], a.sabbagh@sheffield.ac.uk (A. Bagheri Sabbagh). 0263-8231/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2012.01.004
resistance can be developed in CFS beams [10–13]. The general view is that frames with thin-walled elements cannot create plastic hinges in CFS beams, and hence cannot produce sufficient ductility for high seismic resistance [16–18]. In some recent studies conventional double back-to-back channel sections were shown to possess a degree of ductile capacity in dissipating seismic energy [13,14], but they do not satisfy the required width/thickness limits of design codes [16–18] which aim to delay local buckling after yielding. If CFS beams are used as main dissipative elements in earthquake resistant frame buildings, their ductility needs to be significantly improved by delaying local buckling and allowing development of large plastic deformations. This can be achieved by optimizing the shapes of CFS sections and using appropriate details and stiffeners in the beam– column connections. This paper presents analytical and experimental investigations that underpin the development of thin-walled CFS sections as energy dissipative elements for moment-resisting multi-storey buildings in seismic regions. Both beam and connection elements are examined. A numerical study on the buckling and postbuckling behavior of curved flange beams with different dimensions and flange angles was presented in a previous work by the authors [15].
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1 1
A
1
1
1 1
1
1
1
A 1
1 2 hw/2
1 1
1 1 2
section A-A
1 1
section A-A
1
1
A section A-A
1
1 1
1
section A-A
1
section A-A
1 1
section A-A
1
A
Through plate end section
A
A
2
hw
Optimum stiffener
1.2
Optimum stiffener Other stiffeners
1
M/Mp
0.8 0.6 Without stiffener
0.4 0.2 0 0
0.02
0.04
0.06
θ (rad.) Fig. 1. Different out-of-plane stiffener configurations for the CFS beam–column connections, M–y curves and local buckling deformation of beam without stiffener and beam with optimum stiffener [15].
In addition, the moment–rotation (M–y) behavior of CFS beam– column connections with different types of out-of-plane stiffener configurations were compared [15]. These included stiffening the flanges in the connection region by horizontal plates and angles, stiffening the webs by long horizontal plates and vertical plates tied to the webs and finally a combination of vertical plates tied to entire section and horizontal plates between them (Fig. 1). The FE simulations showed that the latter produced the best M–y behavior as shown in Fig. 1 [15]. This paper takes a step back and begins by presenting the evolutionary development that led to the curved flange beams, starting from the simplest shape of CFS double back-to-back channel section. The minimum number of vertical stiffeners in CFS beam–column connections that can delay premature buckling is then determined by examining the M–y behavior of different combinations. The FE predictions, which can suppose the development of design guidelines, are validated by experimental work on different beam–column connection configurations.
2. Evolutionary development of CFS beams The width/thickness ratios of compression elements of hotrolled steel sections are restricted by codes of practice to certain limits to avoid local buckling before yielding [16,17]. Greater restrictions are applied when higher ductility is required for seismic design [18]. These width/thickness ratio limits are almost
impossible to achieve by common structural CFS sections, such as flat flange channels. CFS sections are commonly formed from a single sheet, so all the sectional elements have the same thickness. Therefore, instead of modifying the thickness, the critical elements should be stiffened by other means. Sectional stiffeners and out-of-plane stiffeners are the two types that are used in practice. Sectional stiffeners are more common for CFS sections since they can be created during the forming process. Out-of-plane stiffeners are more common in hotrolled sections and can be welded or bolted at different locations along the span depending on demand. Sectional stiffeners are examined in the first instance, because they are easier to implement in CFS sections than the out-of-plane stiffeners. Flexural behavior is normally dominant in MRF beams, although shear forces should also be checked. For flexural behavior, the flanges attract the largest normal stresses, whereas the webs are subjected to gradient stresses. Therefore, flanges are more critical and are considered first. However, the width/thickness ratio of the webs should also be limited to delay web buckling and to avoid interaction of the buckling modes between web and flanges. The flanges can be stiffened by increasing the number of bends as shown in Fig. 2. According to the design codes [16–18], the width/thickness ratio of the flat flanges is highly restricted, so the optimum solution is arrived when the elements of the flat portions of the flange approach zero length, leading to a curved flange section (section C in Fig. 2).
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101
Fig. 2. Evolution of CFS sections toward more buckling resistant flanges (the weight of the section remains unchanged).
Fixed end in x, y& z directions
Tied lines between the sections Bracing lines in x direction
Loading points in y direction
Fig. 3. Boundary conditions, loading points and constraints of cantilever beams.
2.1. FE analysis for predicting buckling and postbuckling behavior in CFS beams For FEM, 2 m long cantilever beams were selected representing a 4 m beam span in a laterally loaded moment frame. Nonlinear inelastic postbuckling analysis (using Abaqus [19]) was performed by using the standard RIKS arc-length method, which takes into account stiffness degradation due to buckling [19]. The boundary conditions, loading points and constraints are shown in Fig. 3. Other parameters of the FE models were: element type: 8-noded standard quadratic, reduced integration, homogenous shell element (S8R in Abaqus FE package), mesh sizes: 20 mm 20 mm and material: bi-linear stress-strain behavior with Fy ¼275 MPa (yield stress), Fu ¼445 MPa (tensile stress), E¼210 GPa, (modulus of elasticity), Es ¼E/100 (second modulus) and u ¼0.33 (Poisson’s ratio). Abaqus was used in FE analyses by other researchers [20–23] and it was shown to predict well the load bearing capacity of CFS sections and their buckling behavior. Various sectional stiffening methods were used for developing double back-to-back channel sections. Fig. 4 shows the modified sections and their corresponding buckling shapes obtained in the FEA. All the beam sections have the same amount of material with a thickness t ¼3 mm, web depth h¼200 mm and total flange width (including the stiffeners) b¼125 mm. The fixed end moment plotted against tip rotation (M/Mp–y) obtained in the FEA is shown in Fig. 5. The moments are normalized by the full plastic moment capacity Mp ¼58 kNm of the flat flange section without stiffeners (F0 in Fig. 4), without taking into account the local buckling effects. Due to premature flange buckling, beam F0 only achieved 0.76 Mp (F0 in Fig. 5). A conventional step in stiffening CFS sections is to add a lip at the end of flat flanges (F1 in Fig. 4). This increases significantly the moment and ductility capacity of the double back-to-back channel section beam (compare the M/Mp–y curves of F0 and F1 beams in Fig. 5). It can be seen that, there is still a sudden loss of strength for beam F1 at a rotation of less than 0.02 rad. To improve further the ductility capacity of such beams, an intermediate stiffener has been added (beam F2 in Fig. 4). This prevents the sudden loss of strength in the moment–rotation
curve of beam F2 (Fig. 5). Another alternative introduces a further bend in the flanges (beam F3 in Fig. 4). This solution not only increases the moment strength and ductility of the double backto-back channel section beam, but also increases the initial stiffness, which can be of importance for MRFs (compare F1, F2 and F3 curves in Fig. 5). Increasing the number of flange bends increases the moment strength and the initial stiffness even more (F4 curve in Fig. 5). An infinite number of bends i.e. a curved flange section, results in the highest moment strength and initial stiffness (beam C in Fig. 5). The bent elements of curved flanges can support each other by producing in-plane stiffness when out-of-plane deformations (local buckling) are initiated. This arching action delays local buckling.
3. Development of CFS moment frames at connection level A web bolted moment resistant type of connection is adopted in this study for CFS beam–column connections. This type of connection is mainly used for lapped connections [22–29]. FEA and experimental work has shown that long lap length connections are stiffer and stronger than short lap length connections and typical section failure is observed at the ends of the lapped connections [22–29]. The main component of the beam–column MR connection comprises welded cross through-plates which can be bolted to separate beam and column sections, as shown in Fig. 6. Previous studies by the authors [15,30] indicate that in this type of connection, if designed properly, the column and through plate remain elastic without large deformations or local buckling. Large deformation and local buckling only take place in the beams (Fig. 1). The following section examines the impact of vertical stiffeners on connection performance. 3.1. FE analysis for predicting buckling and postbuckling behavior of CFS beam–column connections Nonlinear inelastic postbuckling analysis was performed by employing the standard RIKS arc-length method [19], with FE
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F0
F1
F2
F3
C
F4
Fig. 4. Different sectional stiffeners for double back-to-back channel sections and their buckling shapes.
C
1.4 F4
C
1.2
F4
F3
M/Mp
1
F2
F3
0.8 F1
0.6
F2
F0
2000
0.4
F1
Rotation
0.2 0 0
0.01
F
0.02 θ(rad)
F0
0.03
0.04
Fig. 5. Moment–rotation curves of the beams with the dimensions in Fig. 4.
Fig. 6. CFS beam–column connections: diamond column, cross through-plates and curved flange beam.
model parameters similar to those shown in Section 2.1, except the reduced mesh sizes of 13 mm 13 mm were used for beams (to accommodate the curves) and through-plates and mesh sizes of 19 mm 19 mm were used for columns. The boundary conditions and loading points are shown in Fig. 7a and the tied points in Fig. 7b. The investigation on the effectiveness of various vertical stiffener combinations was performed on a connection comprising a beam of L¼2000 mm length and a column of L¼3000 mm length. Other dimensions of the beam section, column section and the through plate are shown in Fig. 7c. The peak moment of the beam–column connection without stiffener (Fig. 1) was around 25% less than that of the same beam with the theoretical fixed-end moment connection (Fig. 5—beam C). This is due to premature web buckling (see Fig. 1) as a result of force concentration at the first line of bolts. To mitigate this loss, one approach is to increase the bolt-group length, as investigated
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103
Fig. 7. FE models used in the analysis: (a) boundary conditions and loading points, (b) tied points of connection elements and parts of the beam and column and (c) beam, column and through plate dimensions.
by Lim and Nethercot [23] for moment connections of portal frames. The ratio of the bolt-group length to the web height of the beam used here was 1.5. Increasing the bolt-group length cannot always be efficient for MR beam-to-column connections since it increases the moment demand on the column. Moreover, this approach can make frame erection more difficult. Therefore, the approach adopted in this investigation is to delay the premature web buckling of the beam by employing out-of-plane stiffeners. Different configurations of stiffeners were examined (Fig. 1), each introducing a gradual improvement in ductility and strength to the proposed moment resisting connections [15]. The moment–rotation curve of the best of the examined connections (see Fig. 1, optimum stiffener) showed a significant increase in both strength ( 40%) and ductility ( 100%) in comparison with the connection without stiffeners (Fig. 1). The optimum stiffener configuration delayed the local buckling in the web thus maintaining the flange stiffness and postponing the web-flange local buckling interaction. The generalized configuration of the optimum stiffener (Fig. 1) comprised vertical stiffeners positioned one pair at the end of the beam, one pair at hw/2 before the end of the through plate, one pair just at the end of the through plate and one pair at hw after the end of the through plate, welded to the inside of the beams, where hw is the beam web height. The horizontal stiffeners were welded (tied) to the 2nd, 3rd and 4th pairs of the vertical stiffeners and not to the beam web. The minimum number of vertical stiffeners was determined by examining the M–y behavior of six different combinations as shown in Fig. 8 (curves 1–6) and Table 1 (1–6). The M/Mp–y curve of the connection without horizontal stiffeners (Table 1(1)) showed lower ductility than the connection with full vertical and horizontal stiffeners (Fig. 8, curves 1 and optimum stiffener). This is because the vertical stiffeners are laterally restrained by the horizontal stiffeners, which delays the local buckling of the beam section between the vertical stiffeners. The M/Mp–y curve of the connection without the pair of vertical stiffeners at the end of the through plate (Table 1(2)) showed sharp loss of strength (Fig. 8, curve 2) due to interaction of web and flange buckling. Therefore, using of the pair of vertical stiffeners at this location (V3) is essential. The local buckling deformation of the connection without the pair of vertical stiffeners at the beam end extended inside the connection (Table 1(3)), which may affect the frictional resistance of the bolts in actual connections. This combination of vertical stiffeners showed a lower level of moment resistance (Fig. 8,
curve 3) than the other combinations comprising beam-end stiffeners, thus this pair of vertical stiffeners (V1) is also essential. The M/Mp–y curve of the connection with the pairs V1, V3 and V4 vertical stiffeners (Table 1(4)) resulted in the higher moment resistance and ductility (Fig. 8, curve 4) than the connections without either V1 or V3 and the local buckling deformation extended outside the connection (Table 1(4)). Among the connections with combinations of three vertical stiffeners, the highest moment strength and ductility was achieved by using the pairs V1, V2 and V3 (Table 1(5)), including the essential stiffeners (V1 and V3) (Fig. 8, curve 5). The buckling deformation was at the critical section (through plate end) and extended along the beam outside the connection (Table 1(5)). The connection with the two most essential pairs of vertical stiffeners (V1 and V3) (Table 1(6)) can also produce high moment strength and a good degree of ductility (Fig. 8, curve 6), higher than other connections with three pairs of vertical stiffeners but without either of the essential pairs (V1 or V3). Therefore, stiffeners V1 and V3 (considered as minimum stiffeners) can be used instead of the optimum stiffener (shown in Fig. 1) for connections where very high ductility demand is not essential. It can be seen from the M–y curves in Fig. 8 that, in combination with other pairs of vertical stiffeners, the pair of vertical stiffeners at the beam-end (V1) mainly improves the moment resistance and that at the through plate end (V3) increases the ductility of the connection. These minimum pairs of vertical stiffeners (V1 and V3) were used in the beams for the test connections along with the beams without stiffener and with optimum stiffener (shown in Fig. 1).
4. Experimental verification The beam-to-column connection configurations of the test Specimens A1, A2 and A3 used in the experimental investigation are presented in Table 2. The difference between the FE models and the test specimens is that the column was made up of two hot-rolled back-to-back channels instead of CFS columns. This was easier to manufacture and fit into the testing rig. Since no plastic action was detected in the CFS columns in the FE analyses this change is justified. Dimensions of the beam and through plate for the specimens were the same as those used in the FE model, shown in Fig. 7c. For all specimens, the connections were designed based on the requirements for slip-critical joints of
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Fig. 8. M/Mp–y curves for beams without stiffener, with optimum stiffener (Fig. 1) and 6 different combinations of vertical stiffeners (1–6) (Table 1). Table 1 Local buckling deformation of the CFS connection with the specifications as shown in Fig. 7 and with six different combinations of vertical stiffeners (1–6). (1) 4 Pairs of vertical stiffeners at 0, 300, 400 and 600 mm from the beam end
V1
V2 V3
A
V4
(2) 3 Pairs of vertical stiffeners at 0, 300 and 600 mm (3) 3 Pairs of vertical stiffeners at 300, 400 and from the beam end 600 mm from the beam end
V1
V2
A
V3
A
(5) 3 Pairs of vertical stiffeners at 0, 300 and 400 mm (6) 2 Pairs of vertical stiffeners at 0 and 400 mm from from the beam end the beam end
V1
V4
section A-A
V1
V4
section A-A
section A-A (4) 3 Pairs of vertical stiffeners at 0, 400 and 600 mm from the beam end
V2 V3
V4
V2 V3
A
V3
A section A-A
section A-A
section A-A Specification for Structural Joints [31]. Full description of the test configurations, set up, instrumentation as well as the test observations and results are given elsewhere [30,32]. A presentation of the experimental work validating the results of the FE analysis (Section 3) is presented in this section.
V1
The connection with full set of stiffeners (used for Specimen A3) was the configuration that provided the highest resistance and ductility in the FE simulations (Figs. 1 and 8, optimum stiffener) and the connection with partial stiffeners (used for Specimen A2) was the configuration with the minimum stiffeners
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V1 and V3 (Table 1(6)). The connection without stiffeners (Specimen A1) was used for bench marking and comparison purposes. 4.1. Test setup and loading cycles The test column was bolted to a reaction frame (see Fig. 9a). Cyclic loading was applied through a hinge connection at the end of the beams (Fig. 9a) using a loading protocol given in section S6.2 of AISC Seismic Provisions [18] for qualifying beam–column moment connections in special and intermediate moment frames. For the definition of beam maximum moment, M, and rotation, y, the middle section of the plastic hinge region of the beams is assumed to be at the end of the through plate (see Fig. 9b). Two lateral brace frames Table 2 The specimens configurations. Specimens
Connection stiffeners
Connection type
A1 A2 A3
Without stiffeners Partial (minimum) stiffeners Full (optimum) stiffeners
Slip-critical Slip-critical Slip-critical
105
were used to avoid premature global instability (Fig. 9a). This is in accordance with the AISC Seismic Provisions [18], which require that both flanges of beams shall be laterally braced near plastic hinges and regions with concentrated forces.
4.2. Test results The normalized moment–rotation (M/Mp–y) hysteretic curves for Specimens A1-3 are shown in Fig. 10. Mp is the nominal plastic moment of the beam sections equal to 67 kNm for the nominal yield stress of 275 MPa (the mean yield stress of the plate was found to be 310 MPa). For all the specimens, the beam sustained 80% of the maximum moment at a rotation equal to 0.04 rad (for Specimen A1) or greater than 0.04 rad (for Specimens A2 and A3) which is the rotation required for special moment frames (SMF) [18]. The local buckling deformation of the beam of Specimen A1 without stiffeners (Fig. 10) was dominated by web buckling at the end of the through plate accompanied by opening of the beam flanges inside the connection, similar to the prediction of the FE analysis for the model without stiffeners (see Fig. 1). The beam reached only M/ Mp ¼0.85 and showed abrupt loss of strength (see Fig. 10, A1) which
Reaction frame
Actuator
Test specimen
Lateral restraints
Hinge connection
Cyclic loading
M Moment diagram
1811
150.0
Rotation
Actuator deformation (mm)
200.0
100.0 50.0 (1)
(2)
(3)
(4)
(5)
θ
(6)
(7)
(8)
(9)
(11) (10)
(12)
0.0 -50.0
(1) 6 cycles at = 0.00375 rad
-100.0
(2) 6 cycles at = 0.00500 rad
-150.0
(3) 6 cycles at = 0.00750 rad
-200.0
(4) 4 cycles at = 0.010 rad (5) 2 cycles at = 0.015 rad
(6) 2 cycles at = 0.02 rad
cycles
(7) 2 cycles at = 0.03 rad (8) 2 cycles at = 0.04 rad Continue every 2 cycles at increments of = 0.01
Fig. 9. (a) Test setup photo and (b) loading cycles.
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1 0.8 0.6
M/Mp
0.4 0.2 0 -0.2 -0.4 -0.6 FE without stiffener Experiment
-0.8 -1 -0.08 -0.06 -0.04 -0.02
0
0.02
0.04
0.06
0.08
M/Mp
θ (rad) 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -0.08 -0.06 -0.04 -0.02
FE with minimum stiffener Experiment
0
0.02
0.04
0.06
0.08
M/Mp
θ (rad) 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4 -0.08 -0.06 -0.04 -0.02
FE with optimum stiffener Experiment
0
0.02
0.04
0.06
0.08
θ (rad) Fig. 10. M/Mp–y hysteretic curves and local buckling deformation of Specimens A1–3 and envelope M/Mp–y curves of FE predictions.
90000 80000 A3
70000 60000 E(Nm)
agrees with the FE analysis results (also shown in Fig. 10, FE without stiffeners). These results highlight the need for the use of out-of-plane stiffeners to delay the premature web buckling and to avoid extension of failure inside the connection. The local buckling deformation of Specimen A2 (Fig. 10, A2) was also predicted well by the FE analysis (for comparison see Table 1(6)). The beam reached M/Mp ¼ 1.09 and showed a degree of ductility (Fig. 10, A2) also predicted by the FE analysis (Fig. 10, FE with minimum stiffener). The local buckling deformation of Specimen A3 (Fig. 10, A3) occurred mainly between V2 and V3 stiffeners, whereas in the FE analysis (Fig. 1, connection with optimum stiffener) this occurred between V3 and V4 stiffeners. The beam reached M/Mp ¼1.15 (Fig. 10, A3), but with a degree of ductility lower than that of the FE prediction (Fig. 10, FE with optimum stiffener).
50000
A2
40000 30000 20000
A1
10000 0 0
0.02
0.04
0.06
0.08
0.1
θ(rad) Fig. 11. Hysteretic energy dissipation curves of test Specimens A1–3.
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1.4
5
1.2
4
1 3
M/M p
Ductility Factor
107
2 A1-3 1
0.8 0.6 A1-3
0.4 0.2 0
0 0
2 4 Number of pairs of vertical stiffeners
0
2 4 Number of pairs of vertical stiffeners
Fig. 12. (a) Ductility factors and (b) normalized bending moment strength of test Specimens A1–3.
The differences between the experimental results and the FE predictions can be due to imperfections, differences between the material properties of the test and the FE model and also actual dimensions of the test specimens. In addition, connection slip and cyclic loading effects were not taken into account by the FE analysis at this stage. These can affect the buckling mode shape, the M–y behavior and in particular the strength degradation thus, they should be incorporated in the analyses of updated FE models [30,33]. The cumulative energy dissipation curves derived from these hysteretic curves at each cycle are shown in Fig. 11. Specimen A1 without any stiffeners dissipated the lowest amount of energy. The use of partial (minimum) stiffeners in Specimen A2 increased the hysteretic energy at each cycle. The use of full (optimum) stiffeners in Specimen A3 increased the hysteretic energy further at each cycle and allowed the specimen to reach larger rotations by delaying local failures. The beams of Specimens A2 and A3 (with partial or full stiffeners) were able to mobilize the full plastic moment (M/ Mp 41) and sustain high moment resistance even at large rotations. Therefore, they can be placed in the Class 1 category of cross sections in Eurocode 3 [16], as sections with an ability of forming plastic hinges and providing rotational capacity required from plastic analysis without resistance degradation. The use of partial (minimum) stiffeners (2 pairs of vertical stiffeners) and full (optimum) stiffeners (4 pairs of vertical and 2 pairs of horizontal stiffeners) in the connection resulted in a significant increase in both ductility factor (determined at 0.8 M/Mp) and M/Mp ratio (see Fig. 12). The stiffeners constrained both flanges and webs and increased the transverse stiffness of the sectional elements, delaying the web and flange buckling.
5. Conclusions The research presented in this paper shows that thin-walled cold-formed steel (CFS) elements can be used as dissipative elements for moment frames in highly seismic areas. The investigation presented here was carried out at two structural levels: element and connection.
5.1. FE analysis at the element level Curved flange beam sections evolved from the gradual increase of resistance by introducing more bends in the flanges, a process ultimately leading to stiffening the flanges with an infinite number of bends. The bent flange elements support each other and produce arching action which delays local buckling and
increases strength and ductility compared with conventional flat flange sections. 5.2. FE analysis at the connection level The web bolted through-plate beam-to-column connection produced a lower level of ductility and strength than the theoretical fixed-end connection. Web buckling adjacent to the first line of bolts at the beam-through plate connection was identified as the main reason for the abrupt loss of strength. Therefore, out-ofplane stiffeners are needed to improve the bending strength and ductility of the connection. A minimum of two pairs of vertical stiffeners is recommended to be used inside the connection at the beam end and at the through plate end. 5.3. Experimental verification at the connection level The use of the minimum (partial) and the optimum (full) configuration of out-of-plane stiffeners for the beams in the connections improved (i) the moment strength by 28% and 35%, (ii) the ductility by 50% and 75% and (iii) the hysteretic energy dissipation capacity by 30% and 90%, respectively, compared with the connection without stiffeners. The hysteretic M–y behavior and the local buckling deformation obtained in the tests on CFS moment-resisting beam-to-column connections show a reasonable agreement with the FE predictions which is sufficient at the design stage. For more precise results, the presented FE analyses need to be updated by incorporating actual dimensions of the test specimens, imperfections of the beams, material properties achieved from tensile coupon tests and connection slip-bearing action through cyclic loading analysis. This work will be presented in the near future [33].
Acknowledgment The authors would like to express their gratitude to the University of Sheffield and Corus Research, Development & Technology for their financial support. References [1] Dubina D. Behavior and performance of cold-formed steel-framed houses under seismic action. Journal of Constructional Steel Research 2008;64: 896–913. [2] Moghimi H, Ronagh H. Performance of light-gauge cold-formed steel strapbraced stud walls subjected to cyclic loading. Engineering Structures 2009;31:69–83. [3] Casafont M, Arnedo A, Roure F, Rodrıguez-Ferran A. Experimental testing of joints for seismic design of lightweight structures. Part 1. Screwed joints in straps. Thin-Walled Structures 2006;44:197–210.
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[4] Casafont M, Arnedo A, Roure F, Rodrıguez-Ferran A. Experimental testing of joints for seismic design of lightweight structures. Part 2: Bolted joints in straps. Thin-Walled Structures 2006;44:677–91. [5] Casafont M, Arnedo A, Roure F, Rodrıguez-Ferran A. Experimental testing of joints for seismic design of lightweight structures. Part 3: gussets, corner joints, x-braced frames. Thin-Walled Structures 2007;45:637–59. [6] Sato A, Uang C-M. Seismic design procedure development for cold-formed steel-special bolted moment frames. Journal of Constructional Steel Research 2009;65:860–8. [7] Sato A, Uang C-M, ASCE M. Seismic performance factors for cold-formed steel special bolted moment frames. Journal of Structural Engineering 2010;136(8). [8] Uang C-M, ASCE M, Sato A, Hong J-K, Wood K. Cyclic testing and modeling of cold-formed steel special bolted moment frame connections. Journal of Structural Engineering 2010;136(8). [9] AISI S110. Standard for Seismic Design of Cold-Formed Steel Structural Systems—Special Bolted Moment Frames. Washington, DC: American Iron and Steel Institute; 2007. [10] Chung KF, Lau L. Experimental investigation on bolted moment connections among cold formed steel members. Engineering Structures 1999;21: 898–911. [11] Wong MF, Chung KF. Structural behaviour of bolted moment connections in cold-formed steel beam–column sub-frames. Journal of Constructional Steel Research 2002;58:253–74. [12] Yu WK, Chung KF, Wong MF. Analysis of bolted moment connections in coldformed steel beam–column sub-frames. Journal of Constructional Steel Research 2005;61:1332–52. [13] Bagheri Sabbagh A, Mirghaderi R, Petkovski M, Pilakoutas K. An integrated thin-walled steel skeleton structure (two full scale tests). Journal of Constructional Steel Research 2010;66:470–9. [14] Calderoni B, De Martino A, Formisano A, Fiorino L. Cold formed steel beams under monotonic and cyclic loading: experimental investigation. Journal of Constructional Steel Research 2009;65:219–27. [15] Bagheri Sabbagh A, Petkovski M, Pilakoutas K, Mirghaderi R. Ductile moment-resisting frames using cold-formed steel sections: an analytical investigation. Journal of Constructional Steel Research 2011;67:634–46. [16] Eurocode 3: design of steel structures: Part 1.1: general rules and rules for buildings, EN 1993-1-1; 2005. [17] ANSI/AISC 360-05. Specification for Structural Steel Buildings. Illinois: American Institute of Steel Construction; 2005.
[18] ANSI/AISC 341-05. Seismic Provisions for Structural Steel Buildings. Illinois: American Institute of Steel Construction (AISC); 2005. [19] Abaqus/CAE User’s Manual, Version 6.7, USA; 2007. [20] Pham CH, Hancock GJ. Numerical simulation of high strength cold-formed purlins in combined bending and shear. Journal of Constructional Steel Research 2010;66:1205–17. [21] Wang H, Zhang Y. Experimental and numerical investigation on cold-formed steel C-section flexural members. Journal of Constructional Steel Research 2009;65:1225–35. [22] Lim JBP, Nethercot DA. Stiffness prediction for bolted moment-connections between cold-formed steel members. Journal of Constructional Steel Research 2004;60:85–107. [23] Lim JBP, Nethercot DA. Ultimate strength of bolted moment-connections between cold-formed steel members. Thin-Walled Structures 2003;41: 1019–39. [24] Ho HC, Chung KF. Experimental investigation into the structural behaviour of lapped connections between cold-formed steel Z sections. Thin-Walled Structures 2004;42:1013–33. [25] Ho HC, Chung KF. Structural behaviour of lapped cold-formed steel Z sections with generic bolted configurations. Thin-Walled Structures 2006;44:466–80. [26] Dan Dubina, Ungureanu V. Behaviour of multi-span cold-formed Z-purlins with bolted lapped connections. Thin-Walled Structures 2010;48:866–71. [27] Chung KF, Ho HC. Analysis and design of lapped connections between coldformed steel Z sections. Thin-Walled Structures 2005;43:1071–90. [28] Zhang Lei Tong. Gengshu, moment resistance and flexural rigidity of lapped connections in multi-span cold-formed Z purlin systems. Thin-Walled Structures 2008;46:551–60. [29] Ho HC, Chung KF. Analytical prediction on deformation characteristics of lapped connections between cold-formed steel Z sections. Thin-Walled Structures 2006;44:115–30. [30] Bagheri Sabbagh A. Cold-formed steel elements for earthquake resistant moment frame buildings, The University of Sheffield, PhD thesis; 2011. [31] Specification for structural joints using ASTM A325 or A490 bolts. Chicago, Illinois: American Institute of Steel Construction; 2004. [32] Bagheri Sabbagh A, Petkovski M, Pilakoutas K, Mirghaderi R. Experimental work on cold-formed steel elements for earthquake resilient moment frame buildings, under review. [33] Bagheri Sabbagh A, Petkovski M, Pilakoutas K, Mirghaderi R. Cyclic behavior of bolted cold-formed steel moment connections; FE modelling including slip, in preparation.
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Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Development of cold-formed steel elements for earthquake resistant moment frame buildings Alireza Bagheri Sabbagh a,n, Mihail Petkovski a, Kypros Pilakoutas a, Rasoul Mirghaderi b a b
Department of Civil and Structural Engineering, University of Sheffield, Sheffield S1 3JD, UK Department of Civil Engineering, University of Tehran, Tehran, Iran
a r t i c l e i n f o
abstract
Article history: Received 29 September 2011 Accepted 4 January 2012 Available online 31 January 2012
The development of thin-walled cold-formed steel (CFS) sections as energy dissipative elements for seismic moment-resisting multi-storey frame buildings is presented through FE analysis and experimental work. Studies on different structural levels are undertaken. At the element level, increasing the number of flange bends enhances both the elastic and inelastic behavior, and beams with an infinite number of bends (with curved flanges) show the highest strength, stiffness and ductility. At the connection level, different configurations of CFS beam-to-column connections using through plates are investigated numerically and verified experimentally. In web bolted connections without out-of-plane stiffeners, premature web buckling results in early loss of strength. A minimum of two pairs of vertical stiffeners are identified as essential in the connection region to delay web and flange buckling and produce relatively high moment strength and ductility. This investigation is validated by beam-tocolumn connection tests using through plates and curved flange beams with different types of out-ofplane stiffeners in the connection region. The results show that the envelope of the hysteretic curves obtained in the tests of the CFS connections can be predicted by the FE analysis. The use of out-of-plane stiffeners can increase the seismic energy dissipation capacity by up to 90%, the moment strength by up to 35% and the ductility by up to 75% when compared with connections without stiffeners. Correspondingly the use of the two minimum pairs of the vertical stiffeners can increase the seismic energy dissipation capacity by 30%, the moment strength by 28% and the ductility by 50%. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Cold-formed steel sections Beam–column connections Moment-resisting frames Seismic behavior
1. Introduction The use of cold-formed steel sections (CFS sections) as main structural components in buildings is mainly limited to stud-wall frames with low seismic energy dissipation capacity [1–5]. The deficiencies of CFS sections are typically a result of premature local failures and low strength and stiffness of beam–column connections. The research of monotonic and cyclic behavior of components and elements of CFS moment-resisting frames (MRFs) is relatively limited [6–15]. In a recently developed CFS moment-resisting frame with bolted connections, restricted to single-storey dwellings [6–9], the ductility is mainly provided by the connections while the beams and columns remain elastic. For seismic design of multi-storey buildings, however, there is a need to develop plasticity in the beams instead of just yielding the material around the bolt holes in the connections. Other investigations have shown that by using appropriate connection details, such as gusset or through plates, relatively high moment
n
Corresponding author. Tel.: þ44 114 222 5724; fax: þ 44 114 222 5700. E-mail addresses: [email protected], a.sabbagh@sheffield.ac.uk (A. Bagheri Sabbagh). 0263-8231/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2012.01.004
resistance can be developed in CFS beams [10–13]. The general view is that frames with thin-walled elements cannot create plastic hinges in CFS beams, and hence cannot produce sufficient ductility for high seismic resistance [16–18]. In some recent studies conventional double back-to-back channel sections were shown to possess a degree of ductile capacity in dissipating seismic energy [13,14], but they do not satisfy the required width/thickness limits of design codes [16–18] which aim to delay local buckling after yielding. If CFS beams are used as main dissipative elements in earthquake resistant frame buildings, their ductility needs to be significantly improved by delaying local buckling and allowing development of large plastic deformations. This can be achieved by optimizing the shapes of CFS sections and using appropriate details and stiffeners in the beam– column connections. This paper presents analytical and experimental investigations that underpin the development of thin-walled CFS sections as energy dissipative elements for moment-resisting multi-storey buildings in seismic regions. Both beam and connection elements are examined. A numerical study on the buckling and postbuckling behavior of curved flange beams with different dimensions and flange angles was presented in a previous work by the authors [15].
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1 1
A
1
1
1 1
1
1
1
A 1
1 2 hw/2
1 1
1 1 2
section A-A
1 1
section A-A
1
1
A section A-A
1
1 1
1
section A-A
1
section A-A
1 1
section A-A
1
A
Through plate end section
A
A
2
hw
Optimum stiffener
1.2
Optimum stiffener Other stiffeners
1
M/Mp
0.8 0.6 Without stiffener
0.4 0.2 0 0
0.02
0.04
0.06
θ (rad.) Fig. 1. Different out-of-plane stiffener configurations for the CFS beam–column connections, M–y curves and local buckling deformation of beam without stiffener and beam with optimum stiffener [15].
In addition, the moment–rotation (M–y) behavior of CFS beam– column connections with different types of out-of-plane stiffener configurations were compared [15]. These included stiffening the flanges in the connection region by horizontal plates and angles, stiffening the webs by long horizontal plates and vertical plates tied to the webs and finally a combination of vertical plates tied to entire section and horizontal plates between them (Fig. 1). The FE simulations showed that the latter produced the best M–y behavior as shown in Fig. 1 [15]. This paper takes a step back and begins by presenting the evolutionary development that led to the curved flange beams, starting from the simplest shape of CFS double back-to-back channel section. The minimum number of vertical stiffeners in CFS beam–column connections that can delay premature buckling is then determined by examining the M–y behavior of different combinations. The FE predictions, which can suppose the development of design guidelines, are validated by experimental work on different beam–column connection configurations.
2. Evolutionary development of CFS beams The width/thickness ratios of compression elements of hotrolled steel sections are restricted by codes of practice to certain limits to avoid local buckling before yielding [16,17]. Greater restrictions are applied when higher ductility is required for seismic design [18]. These width/thickness ratio limits are almost
impossible to achieve by common structural CFS sections, such as flat flange channels. CFS sections are commonly formed from a single sheet, so all the sectional elements have the same thickness. Therefore, instead of modifying the thickness, the critical elements should be stiffened by other means. Sectional stiffeners and out-of-plane stiffeners are the two types that are used in practice. Sectional stiffeners are more common for CFS sections since they can be created during the forming process. Out-of-plane stiffeners are more common in hotrolled sections and can be welded or bolted at different locations along the span depending on demand. Sectional stiffeners are examined in the first instance, because they are easier to implement in CFS sections than the out-of-plane stiffeners. Flexural behavior is normally dominant in MRF beams, although shear forces should also be checked. For flexural behavior, the flanges attract the largest normal stresses, whereas the webs are subjected to gradient stresses. Therefore, flanges are more critical and are considered first. However, the width/thickness ratio of the webs should also be limited to delay web buckling and to avoid interaction of the buckling modes between web and flanges. The flanges can be stiffened by increasing the number of bends as shown in Fig. 2. According to the design codes [16–18], the width/thickness ratio of the flat flanges is highly restricted, so the optimum solution is arrived when the elements of the flat portions of the flange approach zero length, leading to a curved flange section (section C in Fig. 2).
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101
Fig. 2. Evolution of CFS sections toward more buckling resistant flanges (the weight of the section remains unchanged).
Fixed end in x, y& z directions
Tied lines between the sections Bracing lines in x direction
Loading points in y direction
Fig. 3. Boundary conditions, loading points and constraints of cantilever beams.
2.1. FE analysis for predicting buckling and postbuckling behavior in CFS beams For FEM, 2 m long cantilever beams were selected representing a 4 m beam span in a laterally loaded moment frame. Nonlinear inelastic postbuckling analysis (using Abaqus [19]) was performed by using the standard RIKS arc-length method, which takes into account stiffness degradation due to buckling [19]. The boundary conditions, loading points and constraints are shown in Fig. 3. Other parameters of the FE models were: element type: 8-noded standard quadratic, reduced integration, homogenous shell element (S8R in Abaqus FE package), mesh sizes: 20 mm 20 mm and material: bi-linear stress-strain behavior with Fy ¼275 MPa (yield stress), Fu ¼445 MPa (tensile stress), E¼210 GPa, (modulus of elasticity), Es ¼E/100 (second modulus) and u ¼0.33 (Poisson’s ratio). Abaqus was used in FE analyses by other researchers [20–23] and it was shown to predict well the load bearing capacity of CFS sections and their buckling behavior. Various sectional stiffening methods were used for developing double back-to-back channel sections. Fig. 4 shows the modified sections and their corresponding buckling shapes obtained in the FEA. All the beam sections have the same amount of material with a thickness t ¼3 mm, web depth h¼200 mm and total flange width (including the stiffeners) b¼125 mm. The fixed end moment plotted against tip rotation (M/Mp–y) obtained in the FEA is shown in Fig. 5. The moments are normalized by the full plastic moment capacity Mp ¼58 kNm of the flat flange section without stiffeners (F0 in Fig. 4), without taking into account the local buckling effects. Due to premature flange buckling, beam F0 only achieved 0.76 Mp (F0 in Fig. 5). A conventional step in stiffening CFS sections is to add a lip at the end of flat flanges (F1 in Fig. 4). This increases significantly the moment and ductility capacity of the double back-to-back channel section beam (compare the M/Mp–y curves of F0 and F1 beams in Fig. 5). It can be seen that, there is still a sudden loss of strength for beam F1 at a rotation of less than 0.02 rad. To improve further the ductility capacity of such beams, an intermediate stiffener has been added (beam F2 in Fig. 4). This prevents the sudden loss of strength in the moment–rotation
curve of beam F2 (Fig. 5). Another alternative introduces a further bend in the flanges (beam F3 in Fig. 4). This solution not only increases the moment strength and ductility of the double backto-back channel section beam, but also increases the initial stiffness, which can be of importance for MRFs (compare F1, F2 and F3 curves in Fig. 5). Increasing the number of flange bends increases the moment strength and the initial stiffness even more (F4 curve in Fig. 5). An infinite number of bends i.e. a curved flange section, results in the highest moment strength and initial stiffness (beam C in Fig. 5). The bent elements of curved flanges can support each other by producing in-plane stiffness when out-of-plane deformations (local buckling) are initiated. This arching action delays local buckling.
3. Development of CFS moment frames at connection level A web bolted moment resistant type of connection is adopted in this study for CFS beam–column connections. This type of connection is mainly used for lapped connections [22–29]. FEA and experimental work has shown that long lap length connections are stiffer and stronger than short lap length connections and typical section failure is observed at the ends of the lapped connections [22–29]. The main component of the beam–column MR connection comprises welded cross through-plates which can be bolted to separate beam and column sections, as shown in Fig. 6. Previous studies by the authors [15,30] indicate that in this type of connection, if designed properly, the column and through plate remain elastic without large deformations or local buckling. Large deformation and local buckling only take place in the beams (Fig. 1). The following section examines the impact of vertical stiffeners on connection performance. 3.1. FE analysis for predicting buckling and postbuckling behavior of CFS beam–column connections Nonlinear inelastic postbuckling analysis was performed by employing the standard RIKS arc-length method [19], with FE
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F0
F1
F2
F3
C
F4
Fig. 4. Different sectional stiffeners for double back-to-back channel sections and their buckling shapes.
C
1.4 F4
C
1.2
F4
F3
M/Mp
1
F2
F3
0.8 F1
0.6
F2
F0
2000
0.4
F1
Rotation
0.2 0 0
0.01
F
0.02 θ(rad)
F0
0.03
0.04
Fig. 5. Moment–rotation curves of the beams with the dimensions in Fig. 4.
Fig. 6. CFS beam–column connections: diamond column, cross through-plates and curved flange beam.
model parameters similar to those shown in Section 2.1, except the reduced mesh sizes of 13 mm 13 mm were used for beams (to accommodate the curves) and through-plates and mesh sizes of 19 mm 19 mm were used for columns. The boundary conditions and loading points are shown in Fig. 7a and the tied points in Fig. 7b. The investigation on the effectiveness of various vertical stiffener combinations was performed on a connection comprising a beam of L¼2000 mm length and a column of L¼3000 mm length. Other dimensions of the beam section, column section and the through plate are shown in Fig. 7c. The peak moment of the beam–column connection without stiffener (Fig. 1) was around 25% less than that of the same beam with the theoretical fixed-end moment connection (Fig. 5—beam C). This is due to premature web buckling (see Fig. 1) as a result of force concentration at the first line of bolts. To mitigate this loss, one approach is to increase the bolt-group length, as investigated
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103
Fig. 7. FE models used in the analysis: (a) boundary conditions and loading points, (b) tied points of connection elements and parts of the beam and column and (c) beam, column and through plate dimensions.
by Lim and Nethercot [23] for moment connections of portal frames. The ratio of the bolt-group length to the web height of the beam used here was 1.5. Increasing the bolt-group length cannot always be efficient for MR beam-to-column connections since it increases the moment demand on the column. Moreover, this approach can make frame erection more difficult. Therefore, the approach adopted in this investigation is to delay the premature web buckling of the beam by employing out-of-plane stiffeners. Different configurations of stiffeners were examined (Fig. 1), each introducing a gradual improvement in ductility and strength to the proposed moment resisting connections [15]. The moment–rotation curve of the best of the examined connections (see Fig. 1, optimum stiffener) showed a significant increase in both strength ( 40%) and ductility ( 100%) in comparison with the connection without stiffeners (Fig. 1). The optimum stiffener configuration delayed the local buckling in the web thus maintaining the flange stiffness and postponing the web-flange local buckling interaction. The generalized configuration of the optimum stiffener (Fig. 1) comprised vertical stiffeners positioned one pair at the end of the beam, one pair at hw/2 before the end of the through plate, one pair just at the end of the through plate and one pair at hw after the end of the through plate, welded to the inside of the beams, where hw is the beam web height. The horizontal stiffeners were welded (tied) to the 2nd, 3rd and 4th pairs of the vertical stiffeners and not to the beam web. The minimum number of vertical stiffeners was determined by examining the M–y behavior of six different combinations as shown in Fig. 8 (curves 1–6) and Table 1 (1–6). The M/Mp–y curve of the connection without horizontal stiffeners (Table 1(1)) showed lower ductility than the connection with full vertical and horizontal stiffeners (Fig. 8, curves 1 and optimum stiffener). This is because the vertical stiffeners are laterally restrained by the horizontal stiffeners, which delays the local buckling of the beam section between the vertical stiffeners. The M/Mp–y curve of the connection without the pair of vertical stiffeners at the end of the through plate (Table 1(2)) showed sharp loss of strength (Fig. 8, curve 2) due to interaction of web and flange buckling. Therefore, using of the pair of vertical stiffeners at this location (V3) is essential. The local buckling deformation of the connection without the pair of vertical stiffeners at the beam end extended inside the connection (Table 1(3)), which may affect the frictional resistance of the bolts in actual connections. This combination of vertical stiffeners showed a lower level of moment resistance (Fig. 8,
curve 3) than the other combinations comprising beam-end stiffeners, thus this pair of vertical stiffeners (V1) is also essential. The M/Mp–y curve of the connection with the pairs V1, V3 and V4 vertical stiffeners (Table 1(4)) resulted in the higher moment resistance and ductility (Fig. 8, curve 4) than the connections without either V1 or V3 and the local buckling deformation extended outside the connection (Table 1(4)). Among the connections with combinations of three vertical stiffeners, the highest moment strength and ductility was achieved by using the pairs V1, V2 and V3 (Table 1(5)), including the essential stiffeners (V1 and V3) (Fig. 8, curve 5). The buckling deformation was at the critical section (through plate end) and extended along the beam outside the connection (Table 1(5)). The connection with the two most essential pairs of vertical stiffeners (V1 and V3) (Table 1(6)) can also produce high moment strength and a good degree of ductility (Fig. 8, curve 6), higher than other connections with three pairs of vertical stiffeners but without either of the essential pairs (V1 or V3). Therefore, stiffeners V1 and V3 (considered as minimum stiffeners) can be used instead of the optimum stiffener (shown in Fig. 1) for connections where very high ductility demand is not essential. It can be seen from the M–y curves in Fig. 8 that, in combination with other pairs of vertical stiffeners, the pair of vertical stiffeners at the beam-end (V1) mainly improves the moment resistance and that at the through plate end (V3) increases the ductility of the connection. These minimum pairs of vertical stiffeners (V1 and V3) were used in the beams for the test connections along with the beams without stiffener and with optimum stiffener (shown in Fig. 1).
4. Experimental verification The beam-to-column connection configurations of the test Specimens A1, A2 and A3 used in the experimental investigation are presented in Table 2. The difference between the FE models and the test specimens is that the column was made up of two hot-rolled back-to-back channels instead of CFS columns. This was easier to manufacture and fit into the testing rig. Since no plastic action was detected in the CFS columns in the FE analyses this change is justified. Dimensions of the beam and through plate for the specimens were the same as those used in the FE model, shown in Fig. 7c. For all specimens, the connections were designed based on the requirements for slip-critical joints of
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Fig. 8. M/Mp–y curves for beams without stiffener, with optimum stiffener (Fig. 1) and 6 different combinations of vertical stiffeners (1–6) (Table 1). Table 1 Local buckling deformation of the CFS connection with the specifications as shown in Fig. 7 and with six different combinations of vertical stiffeners (1–6). (1) 4 Pairs of vertical stiffeners at 0, 300, 400 and 600 mm from the beam end
V1
V2 V3
A
V4
(2) 3 Pairs of vertical stiffeners at 0, 300 and 600 mm (3) 3 Pairs of vertical stiffeners at 300, 400 and from the beam end 600 mm from the beam end
V1
V2
A
V3
A
(5) 3 Pairs of vertical stiffeners at 0, 300 and 400 mm (6) 2 Pairs of vertical stiffeners at 0 and 400 mm from from the beam end the beam end
V1
V4
section A-A
V1
V4
section A-A
section A-A (4) 3 Pairs of vertical stiffeners at 0, 400 and 600 mm from the beam end
V2 V3
V4
V2 V3
A
V3
A section A-A
section A-A
section A-A Specification for Structural Joints [31]. Full description of the test configurations, set up, instrumentation as well as the test observations and results are given elsewhere [30,32]. A presentation of the experimental work validating the results of the FE analysis (Section 3) is presented in this section.
V1
The connection with full set of stiffeners (used for Specimen A3) was the configuration that provided the highest resistance and ductility in the FE simulations (Figs. 1 and 8, optimum stiffener) and the connection with partial stiffeners (used for Specimen A2) was the configuration with the minimum stiffeners
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V1 and V3 (Table 1(6)). The connection without stiffeners (Specimen A1) was used for bench marking and comparison purposes. 4.1. Test setup and loading cycles The test column was bolted to a reaction frame (see Fig. 9a). Cyclic loading was applied through a hinge connection at the end of the beams (Fig. 9a) using a loading protocol given in section S6.2 of AISC Seismic Provisions [18] for qualifying beam–column moment connections in special and intermediate moment frames. For the definition of beam maximum moment, M, and rotation, y, the middle section of the plastic hinge region of the beams is assumed to be at the end of the through plate (see Fig. 9b). Two lateral brace frames Table 2 The specimens configurations. Specimens
Connection stiffeners
Connection type
A1 A2 A3
Without stiffeners Partial (minimum) stiffeners Full (optimum) stiffeners
Slip-critical Slip-critical Slip-critical
105
were used to avoid premature global instability (Fig. 9a). This is in accordance with the AISC Seismic Provisions [18], which require that both flanges of beams shall be laterally braced near plastic hinges and regions with concentrated forces.
4.2. Test results The normalized moment–rotation (M/Mp–y) hysteretic curves for Specimens A1-3 are shown in Fig. 10. Mp is the nominal plastic moment of the beam sections equal to 67 kNm for the nominal yield stress of 275 MPa (the mean yield stress of the plate was found to be 310 MPa). For all the specimens, the beam sustained 80% of the maximum moment at a rotation equal to 0.04 rad (for Specimen A1) or greater than 0.04 rad (for Specimens A2 and A3) which is the rotation required for special moment frames (SMF) [18]. The local buckling deformation of the beam of Specimen A1 without stiffeners (Fig. 10) was dominated by web buckling at the end of the through plate accompanied by opening of the beam flanges inside the connection, similar to the prediction of the FE analysis for the model without stiffeners (see Fig. 1). The beam reached only M/ Mp ¼0.85 and showed abrupt loss of strength (see Fig. 10, A1) which
Reaction frame
Actuator
Test specimen
Lateral restraints
Hinge connection
Cyclic loading
M Moment diagram
1811
150.0
Rotation
Actuator deformation (mm)
200.0
100.0 50.0 (1)
(2)
(3)
(4)
(5)
θ
(6)
(7)
(8)
(9)
(11) (10)
(12)
0.0 -50.0
(1) 6 cycles at = 0.00375 rad
-100.0
(2) 6 cycles at = 0.00500 rad
-150.0
(3) 6 cycles at = 0.00750 rad
-200.0
(4) 4 cycles at = 0.010 rad (5) 2 cycles at = 0.015 rad
(6) 2 cycles at = 0.02 rad
cycles
(7) 2 cycles at = 0.03 rad (8) 2 cycles at = 0.04 rad Continue every 2 cycles at increments of = 0.01
Fig. 9. (a) Test setup photo and (b) loading cycles.
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1 0.8 0.6
M/Mp
0.4 0.2 0 -0.2 -0.4 -0.6 FE without stiffener Experiment
-0.8 -1 -0.08 -0.06 -0.04 -0.02
0
0.02
0.04
0.06
0.08
M/Mp
θ (rad) 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -0.08 -0.06 -0.04 -0.02
FE with minimum stiffener Experiment
0
0.02
0.04
0.06
0.08
M/Mp
θ (rad) 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4 -0.08 -0.06 -0.04 -0.02
FE with optimum stiffener Experiment
0
0.02
0.04
0.06
0.08
θ (rad) Fig. 10. M/Mp–y hysteretic curves and local buckling deformation of Specimens A1–3 and envelope M/Mp–y curves of FE predictions.
90000 80000 A3
70000 60000 E(Nm)
agrees with the FE analysis results (also shown in Fig. 10, FE without stiffeners). These results highlight the need for the use of out-of-plane stiffeners to delay the premature web buckling and to avoid extension of failure inside the connection. The local buckling deformation of Specimen A2 (Fig. 10, A2) was also predicted well by the FE analysis (for comparison see Table 1(6)). The beam reached M/Mp ¼ 1.09 and showed a degree of ductility (Fig. 10, A2) also predicted by the FE analysis (Fig. 10, FE with minimum stiffener). The local buckling deformation of Specimen A3 (Fig. 10, A3) occurred mainly between V2 and V3 stiffeners, whereas in the FE analysis (Fig. 1, connection with optimum stiffener) this occurred between V3 and V4 stiffeners. The beam reached M/Mp ¼1.15 (Fig. 10, A3), but with a degree of ductility lower than that of the FE prediction (Fig. 10, FE with optimum stiffener).
50000
A2
40000 30000 20000
A1
10000 0 0
0.02
0.04
0.06
0.08
0.1
θ(rad) Fig. 11. Hysteretic energy dissipation curves of test Specimens A1–3.
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1.4
5
1.2
4
1 3
M/M p
Ductility Factor
107
2 A1-3 1
0.8 0.6 A1-3
0.4 0.2 0
0 0
2 4 Number of pairs of vertical stiffeners
0
2 4 Number of pairs of vertical stiffeners
Fig. 12. (a) Ductility factors and (b) normalized bending moment strength of test Specimens A1–3.
The differences between the experimental results and the FE predictions can be due to imperfections, differences between the material properties of the test and the FE model and also actual dimensions of the test specimens. In addition, connection slip and cyclic loading effects were not taken into account by the FE analysis at this stage. These can affect the buckling mode shape, the M–y behavior and in particular the strength degradation thus, they should be incorporated in the analyses of updated FE models [30,33]. The cumulative energy dissipation curves derived from these hysteretic curves at each cycle are shown in Fig. 11. Specimen A1 without any stiffeners dissipated the lowest amount of energy. The use of partial (minimum) stiffeners in Specimen A2 increased the hysteretic energy at each cycle. The use of full (optimum) stiffeners in Specimen A3 increased the hysteretic energy further at each cycle and allowed the specimen to reach larger rotations by delaying local failures. The beams of Specimens A2 and A3 (with partial or full stiffeners) were able to mobilize the full plastic moment (M/ Mp 41) and sustain high moment resistance even at large rotations. Therefore, they can be placed in the Class 1 category of cross sections in Eurocode 3 [16], as sections with an ability of forming plastic hinges and providing rotational capacity required from plastic analysis without resistance degradation. The use of partial (minimum) stiffeners (2 pairs of vertical stiffeners) and full (optimum) stiffeners (4 pairs of vertical and 2 pairs of horizontal stiffeners) in the connection resulted in a significant increase in both ductility factor (determined at 0.8 M/Mp) and M/Mp ratio (see Fig. 12). The stiffeners constrained both flanges and webs and increased the transverse stiffness of the sectional elements, delaying the web and flange buckling.
5. Conclusions The research presented in this paper shows that thin-walled cold-formed steel (CFS) elements can be used as dissipative elements for moment frames in highly seismic areas. The investigation presented here was carried out at two structural levels: element and connection.
5.1. FE analysis at the element level Curved flange beam sections evolved from the gradual increase of resistance by introducing more bends in the flanges, a process ultimately leading to stiffening the flanges with an infinite number of bends. The bent flange elements support each other and produce arching action which delays local buckling and
increases strength and ductility compared with conventional flat flange sections. 5.2. FE analysis at the connection level The web bolted through-plate beam-to-column connection produced a lower level of ductility and strength than the theoretical fixed-end connection. Web buckling adjacent to the first line of bolts at the beam-through plate connection was identified as the main reason for the abrupt loss of strength. Therefore, out-ofplane stiffeners are needed to improve the bending strength and ductility of the connection. A minimum of two pairs of vertical stiffeners is recommended to be used inside the connection at the beam end and at the through plate end. 5.3. Experimental verification at the connection level The use of the minimum (partial) and the optimum (full) configuration of out-of-plane stiffeners for the beams in the connections improved (i) the moment strength by 28% and 35%, (ii) the ductility by 50% and 75% and (iii) the hysteretic energy dissipation capacity by 30% and 90%, respectively, compared with the connection without stiffeners. The hysteretic M–y behavior and the local buckling deformation obtained in the tests on CFS moment-resisting beam-to-column connections show a reasonable agreement with the FE predictions which is sufficient at the design stage. For more precise results, the presented FE analyses need to be updated by incorporating actual dimensions of the test specimens, imperfections of the beams, material properties achieved from tensile coupon tests and connection slip-bearing action through cyclic loading analysis. This work will be presented in the near future [33].
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