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Experimental study on beam-to-column clip angle bolted connection
Thin-Walled Structures 141 (2019) 540–553
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Full length article
Experimental study on beam-to-column clip angle bolted connection Vijayakumar Natesan, Mahendrakumar Madhavan
T
∗
Department of Civil Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, 502 285, Telangana, India
ARTICLE INFO
ABSTRACT
Keywords: Cold-formed steel Clip angle bolted connection Beam-to-column Reliability Shear resistance
The effectiveness of the clip angle bolted connection between CFS (Cold-formed steel) beam-to-column under shear is investigated in the present study. A total of thirty-one specimens were tested under four-point bending configuration to study the behavior of beam-to-column clip angle connection using bolts. The parameters considered in the experimental study are clip angle thickness and aspect ratio of the clip angle leg connected to the column. The test results indicate that the aspect ratio (L/B) of the clip angle leg plays a significant role in governing the ultimate strength, stiffness and failure mode of the connection. Two different failure modes were observed namely (i) local buckling failure at an aspect ratio (L/B) less than 0.8 and (ii) distortional buckling failure at an aspect ratio (L/B) greater than 0.8 in the clip angle leg connected to the column. An improved design equation for the clip angle bolted connection is proposed and validated with the previous studies from the literature. The proposed design equations for clip angle bolted connection were conservative compared with experimental test results. In addition, a shift in the anchor point (compact limit) i.e., reduction in the slenderness ratio (λ) is suggested for limiting the shear resistance of clip angle bolted connection. Further, reliability studies were carried out to determine the resistance and safety factors for the connections not listed in Table F1 of AISI S100-12 based on the current study and test results from the literature. The suggested design method will be applicable and conservative for the material yield strength up to 550 MPa.
1. Introduction Cold-formed steel (CFS) sections are widely used due to various advantages over the hot rolled steel such as (i) lightweight, (ii) higher strength to weight ratio, (iii) reduced construction time, and (iv) ease in fabrication and installation. Two shapes of CFS sections commonly used are C and Z type with the section depth typically ranging from 100 to 350 mm and the thickness from 1.2 to 3.0 mm. The yield strength of the material varies between 250 and 550 MPa. Design recommendations on CFS connections primarily depend on the type of fasteners such as bolts, screws, and welds. These fastener designs are considered important when two CFS sections are connected directly as shown in Fig. 1a. Few researchers have studied the connection between beam-to-column connections as shown in Fig. 1a. Ahamed and Mahendran [1] investigated the bolted moment connection between CFS beam-to-column with four different configurations. The observed that the failure was due to local buckling in the beam section and the failure location depends on the connection type. In addition, the research revealed that the strength and ductility of the connection depending on the connection type and the depth of section. A similar mode of failure was observed by Lim and Nethercot ([9,10]) for moment connection at apex
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joint between the CFS sections using bolts. However, this type of failure mode is not anticipated when the CFS members are connected through CFS connector such as a clip angle (see Fig. 1b) using a bolt. Bolted connections possess inherent advantages over other fastener types such as welded and self-drilling screw connections due to its ability to quickly assemble and dismantle structural steel members without the need for skilled labor. It is also worth mentioning that the welded connection is difficult in CFS due to its smaller thickness. The selfdrilling screw in CFS connection between beam-to-beam and beam-tocolumn failed due to shearing and pull-out of the clip angle (Chung and Lawson [4]). Similar failure mode (shear failure of the screw) in selfdrilling screw between two CFS rafter through CFS connector in the knee joint was observed by Mills and Laboube [11]. In addition, past studies by Fox [5] indicate that clip angles failed due to compression when acting as a bearing stiffener between two CFS sections. In general, when two CFS members are directly connected (Fig. 1a) through bolt without a connector, the failure occurs in one or both the members. Whereas if the member is connected through clip angle (Fig. 1b), the failure can be either in the clip angle or in the fastener depending on the clip angle thickness or the fastener type (screw or bolt). Typically, screw connections exhibit pull through/pull out and or
Corresponding author. E-mail addresses: [email protected] (V. Natesan), [email protected] (M. Madhavan).
https://doi.org/10.1016/j.tws.2019.04.048 Received 30 August 2018; Received in revised form 7 March 2019; Accepted 24 April 2019 Available online 29 May 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.
Thin-Walled Structures 141 (2019) 540–553
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Fig. 1. (a) Direct beam-to-column connection using bolt; (b) Beam-to-column connection through clip angle using a bolt.
ratios of clip angle (L/B) under shear load. (ii) to suggest an improved design equation for clip angles with material yield strength up to 550 MPa with realistic beam-to-column bolted connections.
shear for higher clip angle thickness. However, when the fastener is a bolt, the possibility of failure (local/distortional buckling) of the clip angle is higher since the bolts are typically much stronger than the parent member and the clip angle. Yu et al. [12] investigated the behavior of clip angle subjected to shear load and formulated the design equations for predicting the service load and ultimate load valid within the range of parameters (i) material yield strength (227–350 MPa) (ii) aspect ratio of the clip angle (0.18–1.4) and (iii) thickness of clip angle (0.8–2.46 mm). In addition, it should be noted that the study carried out by Yu et al. [12] was on self-drilling screws which is typically used for connecting the sheathing (Gypsum, wooden board or CFS sheet with 0.45 mm thickness) while fabricating wall panels and is considered as a non-structural member compared to connection between two CFS members with thickness up to 2.0 mm. However, the present study was on connecting two structural members using bolts through the use of clip angle. Yu et al. [13] and Zhang et al. [15] investigated the behavior of clip angle subjected to compression and tension respectively and proposed design equations for service limit. It should be noted that the literature study has a couple of drawbacks: (i) the yield stress of the material was confined to 350 MPa (ii) experimental test set-up does not reflect the realistic beam-to-column bolted connection. In the current study, an attempt is made to investigate clip angle with material yield strength up to 550 MPa with realistic beam-to-column bolted connection. In general practice for a given clip angle dimension the connected beam can have any depth depending upon the structural demand and ease of construction. The sizes of the clip angle in the present study however, was chosen such that the depth of clip angle should at least be equal to 50% of the beam depth or higher (but 20 mm less than the beam depth for clearance) to effectively transfer the shear load. Therefore, the present study was focused on studying the clip angle behavior for a constant beam depth of 200 mm for three different clip angles with the depth of 100 mm, 150 mm and 180 mm.
2. Experimental program 2.1. Material properties In this study, the clip angles with three different thicknesses (1.5 mm, 2.0 mm and 2.5 mm) were used. Three coupon samples were prepared for each thickness as per E8/E8M-13a [3] and Huang and Young [7]. All the coupon samples were tested in a displacement control mode at a rate of 0.01 mm/s using a servo-controlled hydraulic cyclic testing machine of 100 kN capacity. The material properties such as elastic modulus, yield strength, ultimate strength and percentage of elongation were determined from the coupon test. The test setup is shown in Fig. 2a and tested coupon samples are shown in Fig. 2b. The stress-strain behavior for three different thickness, 1.5 mm and 2.0 mm and 2.5 mm is shown in Fig. 3a, Fig. 3b and c respectively. The material properties of the tested coupon samples are presented in Table 1. 2.2. Details of clip angle configuration and fabrication of test specimen The geometric layout of the clip angle bolted connection between CFS beam-to-column is shown in Fig. 4. The sectional details of the beam and column members are kept constant for all experiments as shown in Fig. 5. For all the test specimens, two bolts were used for connecting clip angle leg to the column web and four bolts for connecting the clip angle leg to the beam. This type of test configuration is selected to hold more focus on strength and failures in the clip angle leg connected to CFS column. The weak link in the connection system was designed such that the failure was anticipated in the clip angle to observe its mode of failure when subjected to shear loading. Hence, the present study did not account for the interaction between beam and clip angle end rotations although it is quite possible that the results may be different if the beam is significantly more flexible. The two main parameters included in this study are (i) aspect ratio of the clip angle leg connected to the column and (ii) thickness of the clip angle. The aspect ratio is defined as the ratio of the flat distance (L) between the centerline of fasteners and bend line of clip angle leg to the depth of clip angle leg (B) connected to the column (Yu et al. [12]). The dimension details of clip angle configuration are given in Table 2. A minimum
1.1. Research motivation and objectives In recent times, the use of high strength steel for structural construction has become prominent. However, design provisions for material (connectors) with a yield strength of more than 350 MPa are not available. The objective of this study is (i) to understand the behavior of clip angle bolted connection between beam to column in terms of ultimate strength for different parameters such as thickness and aspect 541
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Fig. 2. (a) Test setup of coupon test; (b) Tested coupon samples.
edge distance (1.5d) and pitch distance (3d) are recommended by AISI S 100-12 [2] for bolted connection. In the present study, a constant edge distance of 25 mm was maintained for the use of 12 mm diameter in all the clip angle configurations. The pitch distance (P) of clip angle
increased with the increase in the depth of clip angle since only two bolts were provided in the clip angle leg connected to the column. The specimen configuration ending with “R” denotes the repeat tests carried out for clip angle bolted specimen to ensure consistency in
Fig. 3. Stress vs strain plot: (a) 1.5 mm thick clip angle; (b) 2.0 mm thick clip angle; (c) 2.5 mm thick clip angle. 542
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and the other two columns connected on either side of the beam member using a clip angle bolted connection. All the clip angles and CFS channel sections were drilled using a drill bit of 12.8 mm diameter for the provision of 12 mm diameter bolt. Two wooden blocks acting as stiffeners were placed between the flange elements of the beam (CFS channel) under the loading points (400 mm c/c) to avoid the local buckling of beam (CFS channel) section as shown in Fig. 5 (Wang and Young [14]). The bottom end of both the CFS columns was made rigid using a 12 mm thick hot rolled steel (HRS) plate by the application of fillet weld. To ensure consistency in the application of a torque for each bolted connection, an impact torque wrench was used for tightening of bolted clip angle. A maximum torque of 25 N-m was applied based on the recommendation of Fastenal industrial and construction supplies [6] for an M12 bolt of 4.6 grade.
Table 1 Material properties. Sample No
Thickness of clip angle TC (mm)
Yield strength fy (N/mm2)
Ultimate strength fu (N/mm2)
Elastic modulus E (N/mm2)
Percentage of elongation
1 2 3 Mean 1 2 3 Mean 1 2 3 Mean
1.5
564.49 581.57 537.21 561.09 406.81 400.36 399.79 402.32 368.42 377.05 383.15 376.21
575.12 597.41 547.21 573.25 434.59 433.33 420.82 429.58 421.93 436.79 438.34 432.35
207293 212248 201078 206873 216223 214193 215691 215369 200517 202302 210088 204302
11.26 12.18 10.12 11.19 18.90 17.91 18.36 18.39 20.66 20.67 20.66 20.66
2.0
2.5
2.3. Experimental test setup A universal flexural test frame with a hydraulic load cell of 300 kN capacity was used to perform a four-point bending test. All specimens were tested in displacement control mode at a rate of 0.01 mm/s. Fig. 6 shows the overall test setup and instrumentation details to study the behavior of the clip angle bolted connection between CFS beam to column subjected to shear under four-point bending test. In general, clip angle is designed to carry the shear load between beam-to-beam and beam to column connection at the web. The shear resistance of clip angle was studied by Chung and Lawson [4] for the connection between the beam-to-beam and beam-to-column at the web using three different types of the fasteners (self-drilling screws, bolts, and rivets) with load eccentricity of 250 mm. Chung and Lawson [4] observed the clip angle leg connected to the unloaded/supported member of beam-to-beam and beam-to-column has experienced out-of-plane bending due to the thinness of the clip angle. In the current study, the load was applied at a distance of approximately 230 mm from the column web and the clip angle leg connected to beam was predominantly subjected to shear. To prevent the web crippling and local buckling at the point of load application, a small channel fabricated using HRS plates was placed below the actuator to convert the line load to a patch load. In addition, HRS was used to fabricate rigid support (base beam) over which the CFS column is fillet welded to ensure a rigid support condition. The HRS base plate connected with the base beam using a bolted connection threaded rod. Further, the base beam is also fixed to the FTM frame using the bolted connection by means of a threaded rod. The vertical displacement at the mid-span was measured using the NCDT (Noncontact differential transducer) with a measuring range of 300 mm to capture the large deformation exhibited by the specimen. Moreover, two more LVDTs (linear variable differential transducer) were used to measure the displacement of the loaded CFS channel close to the clip angle connection. 3. Result and discussion Table 3 shows the observed values of the ultimate shear load for clip angle connection at one end (half of the tested load) and failure mode of clip angle bolted connection under four-point bending test. The test results indicate that there is not much difference between the boundary conditions imposed by a beam attached to a column compared to direct pull-out of the clip angle connected to the column. This indicates that the realistic connection configuration provided by the beam connected to one end of the clip angle did not significantly alter the boundary conditions compared to the loading condition where the clip angle was directly subjected to a shear load. Fig. 7a classifies the failure mode of the specimen based on the aspect ratio of the clip angle leg connected to the column.
Fig. 4. Geometric layout of clip angle configuration.
test results. In total, 31 specimens were tested including four repeat test specimen configurations of clip angle by varying test parameters such as clip angle thickness and aspect ratios (L/B) of leg connected to the column. The cross section details of CFS beam and column are shown in Fig. 5. Each specimen consists of three CFS members; one loaded beam
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Fig. 5. Typical view of the fabricated specimen before the test.
3.1. Ultimate shear strength of clip angle bolted connection and its failure modes
to a column. The magnitude of ultimate shear strength increases with the thickness but reduces with the increase in aspect ratio of clip angle for all the specimens (Fig. 7a). The variation in the bolt configuration was not considered in the present study since the bolt failure was not observed in the two bolt configuration from the experimental results. It
The ultimate shear strength of clip angle bolted connections depends on the thickness and aspect ratio of the clip angle leg connected Table 2 Clip angle configuration for experimental program. Specimen configuration TC-B-P-W
Thickness of clip angle TC (mm)
1.5-100-50-40 1.5 1.5-100-50-40 R 1.5 1.5-150-100-40 1.5 1.5-180-130-40 1.5 1.5-180-130-40 R 1.5 1.5-100-50-70 1.5 1.5-150-100-70 1.5 1.5-180-130-70 1.5 1.5-100-50-100 1.5 1.5-150-100-100 1.5 1.5-180-130-100 1.5 1.5-180-130-100 R 1.5 2.0-100-50-40 2.0 2.0-100-50-40 R 2.0 2.0-150-100-40 2.0 2.0-180-130-40 2.0 2.0-100-50-70 2.0 2.0-150-100-70 2.0 2.0-180-130-70 2.0 2.0-100-50-100 2.0 2.0-150-100-100 2.0 2.0-180-130-100 2.0 2.5-100-50-40 2.5 2.5-150-100-40 2.5 2.5-180-130-40 2.5 2.5-100-50-70 2.5 2.5-150-100-70 2.5 2.5-180-130-70 2.5 2.5-100-50-100 2.5 2.5-150-100-100 2.5 2.5-180-130-100 2.5 R -Indicates the configuration of clip angle specimen
Depth of clip angle B (mm)
Pitch distance of clip angle P (mm)
Distance between the center of bolt line and outer to the end of the bend line W (mm)
Total width of clip angle leg connected to column A (mm)
100 100 150 180 180 100 150 180 100 150 180 180 100 100 150 180 100 150 180 100 150 180 100 150 180 100 150 180 100 150 180 repeated test
50 50 100 130 130 50 100 130 50 100 130 130 50 50 100 130 100 100 130 50 100 130 50 100 130 50 100 130 50 100 130
40 40 40 40 40 70 70 70 100 100 100 100 40 40 40 40 70 70 70 100 100 100 40 40 40 70 70 70 100 100 100
65 65 65 65 65 95 95 95 125 125 125 125 65 65 65 65 95 95 95 125 125 125 65 65 65 95 95 95 125 125 125
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Fig. 6. Overall experimental test setup.
should be noted that the maximum experimental shear load on either side of the clip angle (with two bolt configuration) did not exceed the 50 kN (see Table 3). Since the shear load capacity of two bolts provided in the clip angle leg connected to the column web is 72 kN (36 kN for each bolt for 12 mm diameter of the bolt with 4.6 grade), this study chose to focus on the variation in the thickness and the aspect ratio of the clip angle to better understand the clip angle behavior. The bolts in the present study were provided such that they maintain the minimum edge distance and the minimum pitch as per AISI S100-12 [2]. However, AISI S100-12 [2] does not provide a specified maximum limit on the pitch distance. Therefore, the current study did not account for the maximum pitch distance. In addition, the design provisions provided by Yu et al. [12] also did not include the pitch distance but rather included the clip angle depth. While it is intuitive to think that the pitch is more valuable parameter than the depth, the results from the experiments provided a specific trend with a compelling argument to consider the depth of the clip angle compared to the pitch as can be observed from Fig. 7b. Nevertheless, a plot with a pitch distance as a parameter was considered in the present study shown in Fig. 7b does indicate that the pitch does matter for smaller clip angle thicknesses. Fig. 7b indicates that there is a decrease in ultimate load capacity with the increase in pitch distance for lower thickness (1.5 mm) of the clip angle. The decrease in thickness with a larger pitch distance increases the plate slenderness (high P/t) thereby increasing the vulnerability of the clip angle plate to local buckling. The local buckling failure of the clip angle leads to a reduction in the ultimate capacity for thin clip angle plates with large pitch distance. Two types of failure modes were observed in the clip angle bolted connection between CFS beam-to-column under four-point bending test. When the aspect ratio (L/B) of the clip angle leg connected to column web is less than 0.8, the mode of failure observed was local buckling (Fig. 8a) whereas for aspect ratios greater than 0.8 the observed mode of failure was distortional buckling (Fig. 8b). Similar failure modes for clip angle subjected to shear load were observed by Yu et al. [12]. In addition, the bearing deformation was observed in the bolt hole of the clip angle leg connected to the column as shown in
Table 3 Observed experimental ultimate shear load and failure modes. Specimen configuration TC-B-P-W
L/B ratio
* Ultimate shear load Vexp (kN)
Failure modes
1.5-100-50-40 1.5-100-50-40 R 1.5-150-100-40 1.5-180-130-40 1.5-180-130-40 R 1.5-100-50-70 1.5-150-100-70 1.5-180-130-70 1.5-100-50-100 1.5-150-100-100 1.5-180-130-100 1.5-180-130-100 R 2.0-100-50-40 2.0-100-50-40 R 2.0-150-100-40 2.0-180-130-40 2.0-100-50-70 2.0-150-100-70 2.0-180-130-70 2.0-100-50-100 2.0-150-100-100 2.0-180-130-100 2.5-100-50-40 2.5-150-100-40 2.5-180-130-40 2.5-100-50-70 2.5-150-100-70 2.5-180-130-70 2.5-100-50-100 2.5-150-100-100 2.5-180-130-100
0.363 0.363 0.242 0.201 0.201 0.663 0.442 0.368 0.963 0.642 0.535 0.535 0.350 0.350 0.233 0.194 0.650 0.433 0.361 0.950 0.633 0.528 0.338 0.225 0.188 0.638 0.425 0.354 0.938 0.625 0.521
24.525 24.492 37.235 33.453 35.270 17.164 24.277 25.819 5.825 9.894 16.402 15.990 27.715 27.876 40.830 43.176 16.681 21.407 32.489 9.180 15.635 24.838 31.958 46.385 48.159 17.120 32.122 32.771 11.321 16.498 28.325
LB LB LB LB LB LB LB LB DB LB LB LB LB LB LB LB LB LB LB DB LB LB LB LB LB LB LB LB DB LB LB
Note: * The ultimate shear load is halved between each single clip angle. LB and DB are local and distortional buckling of clip angle leg connected to column respectively.
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Fig. 7. (a) Experimental shear load vs L/B (or) L/P; (b) Experimental shear load vs depth of clip angle (B).
Fig. 8c. Such type of deformation was not reported by Yu et al. [12] since self-drilling screws were used as fasteners compared to bolts in the present study. In general, the bearing deformation is a common mode of failure in the bolted connection. In the current study, the bearing deformations of the bolt hole are higher in the clip angle leg connected to column compared to clip angle leg connected to beam due to the presence of a minimum number of bolts. Moreover, the bearing deformation of the clip angle depends on the L/B ratio and the thickness of the clip angle. The L/B ratio is similar to the unbraced length and the thickness of the clip angle to the slenderness of the connected leg. An increase in L/B and a decrease in clip angle thickness results in a decrease in the buckling resistance offered by the clip angle against the applied shear load.
thickness such as 1.5 mm, 2.0 mm and 2.5 mm from the recorded data during the test as shown in Figs. 9–11. In addition, Fig. 12 shows that the difference in the magnitudes of the displacements between the midspan (using NCDT), loading point (using 50 mm LVDT's) and at the clip angle connection location (using 100 mm LVDTs) are insignificant. This indicates that the beam and the leg of clip angle connected to beam were predominantly subjected to shear. However, the leg which was connected to the column experienced out-of-plane bending due to the eccentricity in loading. The following observations are made from the load vs deflection plot. 1. For 100 mm and 150 mm depth sections, a reduction in initial stiffness was observed when the distance between the center line of bolts and bend line (W) of clip angle (leg connected to column web) increases from 40 mm to 100 mm for both 1.5 mm and 2.0 mm thick clip angle. This may be attributed to the increase in L/B ratio due to the increase in W resulting in a higher aspect ratio of the clip angle leading to out-of-plane bending in the clip angle leg connected to the column.
3.2. Load-deflection behavior The load versus applied deflection is plotted for clip angle bolted connection between CFS beam-to-column for three different clip angle
Fig. 8. Failure modes: (a) Local buckling of specimen 1.5-180-130-40; (b) Distortional buckling of specimen 2.0-100-50-100; and (c) Local buckling of specimen 2.5100-50-40. 546
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Fig. 9. Load vs deflection plot for 1.5 mm thick clip angle: (a) D = 100 mm depth; (b) D = 150 mm depth; (c) D = 180 mm depth.
2. For 180 mm depth clip angle, no significant increase in stiffness can be observed for 1.5 mm, 2.0 mm and 2.5 mm compared to 100 mm and 150 mm. This indicates that an optimum depth is reached when the depth of the clip angle approaches the depth of the parent member. 3. In general, the load vs deflection plot becomes stiffer with increased depth and thickness of the clip angle. Similarly, in the current study, the load-deflection plot of specimens with higher clip angle thickness (2.5 mm) is stiffer than the load-deflection plot of specimens with other two thickness of clip angle (1.5 mm and 2.0 mm). 4. In addition, with an increase in thickness, the specimens exhibited more ductility as can be observed in the large rotation prior to attaining the ultimate load. On the contrary, for specimens with lesser clip angle thickness, initiation of buckling took place at lower loads followed by distortion (see Fig. 8) at ultimate as can be observed in the failure behavior of the specimens.
=
k = 2.569
k 2E 12(1 µ2) L B
2.569
slenderness ratio;Fcr t B
2
critical buckling stress
buckling coefficient;Vy = 0.6Fy B t;
t = design thickness of clip angle; B = depth of clip angle; L = flat width of clip angle; distance the between the center of the first line of screws to the bend line. Eq. (1) is valid within the following range of parameters:
• Clip angle design thickness: 0.84–2.46 mm. • Clip angle design yield strength: 227–345 MPa. • L/B ratio: 0.18–1.40 Since the above equation (Eq. (1)) is recommended for the material yield strength up to 345 MPa, that is a need to validate or improve the design equation for higher yield strength values. Table 4 shows the test results for bolted clip angle loaded in shear along with a comparison of design equation provided by Yu et al. [12]. The average ratio of test results compares well (Vexp/Vn = 1.036) with Eq. (1). However, it can be observed that more than 50% of the tested specimens (16 specimens) had a reduced shear capacity compared to Eq. (1). In particular, the experimental results indicate that few specimens (see Fig. 13) do not satisfy the limiting shear resistance (0.583 Vy) for the slenderness ratio
In the current study, two different aspect ratios such as (i) L/B and (ii) L/P were investigated for the design of clip angle. Yu et al. [12] proposed an equation for calculating the nominal shear capacity of the clip angle without considering its deformation as given by Eq. (1) based on the depth of the clip angle. 0.8V y
Vcr
Vcr = 0.6Fcr B t
3.3. Comparison of test results with Yu et al. [12] Using aspect ratios L/B and L/P
Vn = 0.231
Vy
Where, =
(1) 547
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Fig. 10. Load vs deflection plot for 2.0 mm thick clip angle: (a) D = 100 mm depth; (b) D = 150 mm depth; (c) D = 180 mm depth.
(λ) less than 0.32. This is primarily due to the location of the anchor point (λ = 0.32) determined based on the 345 MPa clip angle steel sections tested by Yu et al. [12]. Therefore, a new slenderness limit is required for clip angles with higher yield strength for the conservative design of clip angle bolted connection. For better clarity, the geometrical aspect ratios L/P were implemented in Eq. (1) instead of L/B as shown in Fig. 13 to design the clip angle. As can be observed from Fig. 13, it becomes obvious that the depth of the clip angle provides more consistent results compared to the pitch distance. Hence, the depth of the clip angle is used to formulate the design provisions based on the experimental results for the limited set of parameters considered. In addition, Table 5 shows the experimental shear load and calculated shear values of Eq. (1) using the geometrical aspect ratios L/P instead of L/B. The mean, standard deviation, and coefficient of variation are presented for the ratio between the experimental shear load (Vexp) and calculated shear values of Eq. (1). The results from Table 5 shows a high degree of conservativeness due to the use of pitch distance as can be observed by comparing the mean value of the ratio between experimental shear load (Vexp) to the calculated shear values obtained from Eq. (1). It should be noted that when the pitch distance is implemented replacing the depth as given in Eq. (1), the mean value of the ratio is higher (1.709) for pitch distance compared to the depth (1.036) as shown in Table 4. Similarly, the standard deviation and coefficient of variation are also more when the pitch distance is considered compared to the depth of the clip angle. This indicates that the efficacy of Eq. (1) decreases when pitch distance p is replaced with clip angle depth B leading to the highly conservative design value.
3.4. Improved ultimate shear design equation for CFS clip angle bolted connection Fig. 13 shows the plot for Vexp/Vy versus λ for all the tested specimens. In the current study, an improved design equation was proposed with a realistic beam-column connection through clip angle using bolts based on experimental observations. The procedure proposed by Yu et al. [12] is adopted for determining the slenderness (λ) values. However, the design equation (see Eq. (2)) has been modified and the maximum slenderness limit for attaining the limiting shear resistance (0.583 Vy) was shifted to the left (towards the origin) based on the experimental results.
Vn = 0.222
0.6V y
(2)
Eq. (2) shall be valid within the following range of parameters:
• Clip angle design thickness: 1.5 mm−2.5 mm; • L/B ratio: 0.188–0.963; • Maximum depth of beam is 200 mm; • Clip angle design yield strength: 376–561 MPa; • Minimum two number of bolts should be present in the column web. The maximum slenderness value was shifted to 0.2 such that the maximum shear strength was limited to 0.583 Vy. Table 6 presents the calculated nominal shear capacity using Eq. (2) for corresponding values of λ and Vy. The mean, standard deviation, and coefficient of variation are presented in Table 6 for the ratio between experimental shear resistances (Vexp) to the values of the improved nominal shear 548
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Fig. 11. Load vs deflection plot for 2.5 mm thick clip angle: (a) D = 100 mm depth; (b) D = 150 mm depth; (c) D = 180 mm depth.
strength (Vnsb) of the bolted clip angle connection between CFS beamto-column. The mean value is 1.112 for the ratio between experimental shear resistance (Vexp) to the calculated nominal shear strength using Eq. (2) and this value is higher than the mean value of the ratio between experimental shear resistances (Vexp) to the calculated nominal shear strength using Eq. (1). This indicates that Eq. (2) is more conservative compared to the nominal shear Eq. (1). In addition, the standard deviation is 0.247 and 0.227 for the ratio between the experimental shear resistances (Vexp) to the calculated nominal shear strength using Eqs. (2) and (1) respectively. However, the corresponding coefficient of variation is 0.219 and 0.222 indicating that the percentage of error is almost
the same when using both Eqs. (1) and (2) for the design of clip angle. Fig. 14 shows the combined results from the present investigation along with the test data from Yu et al. [12] superimposed with Eq. (2). The mean, standard deviation, and coefficient of variation for the ratio between the combined experimental results (present investigation and Yu et al. [12]) to the calculated nominal shear strength using Eq. (2) are 1.091, 0.212, and 0.194 respectively (Table 7). These statistical values are very much similar to the values obtained from Eq. (1) indicating that the use of Eq. (2) can be extended for the design of beam-column clip angle leg with material yield strength up to 550 MPa.
Fig. 12. Load vs deflection using LVDTs (100 mm and 50 mm) and NCDT for the specimen configuration 1.5–100-50-70. 549
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Table 4 Comparison of experimental shear load value with Yu et al. [12] using aspect ratio L/B. Specimen configuration TC-B-P-W
Vexp (kN)
1.5-100-50-40 24.525 1.5-100-50-40 R 24.492 1.5-150-100-40 37.235 1.5-180-130-40 33.453 1.5-180-130-40 R 35.270 1.5-100-50-70 17.164 1.5-150-100-70 24.277 1.5-180-130-70 25.819 1.5-100-50-100 5.825 1.5-150-100-100 9.894 1.5-180-130-100 16.402 1.5-180-130-100 R 15.990 2.0-100-50-40 27.715 2.0-100-50-40 R 27.876 2.0-150-100-40 40.830 2.0-180-130-40 43.176 2.0-100-50-70 16.681 2.0-150-100-70 21.407 2.0-180-130-70 32.489 2.0-100-50-100 9.180 2.0-150-100-100 15.635 2.0-180-130-100 24.838 2.5-100-50-40 31.958 2.5-150-100-40 46.385 2.5-180-130-40 48.159 2.5-100-50-70 17.120 2.5-150-100-70 32.122 2.5-180-130-70 32.771 2.5-100-50-100 11.321 2.5-150-100-100 16.498 2.5-180-130-100 28.325 Mean Standard deviation Coefficient of variation
Vy (kN) 50.498 50.498 75.747 90.897 90.897 50.498 75.747 90.897 50.498 75.747 90.897 90.897 48.278 48.278 72.418 86.901 48.278 72.418 86.901 48.278 72.418 86.901 56.432 84.647 101.577 56.432 84.647 101.577 56.432 84.647 101.577
=
0.578 0.578 0.555 0.544 0.544 1.122 1.077 1.058 1.693 1.625 1.595 1.595 0.346 0.346 0.332 0.326 0.684 0.657 0.645 1.039 0.997 0.979 0.264 0.253 0.249 0.532 0.510 0.501 0.813 0.780 0.766
Vy Vcr
Table 5 Comparison of experimental shear load value with Yu et al. [12] using aspect ratio L/P.
Vn = 0.231 λ−0.8 Vy (kN)
Vexp/Vn
Specimen configuration TC-B-P-W
18.086 18.086 28.025 34.173 34.173 10.639 16.489 20.071 7.655 11.866 14.453 14.453 26.068 26.068 40.416 49.211 15.112 23.410 28.509 10.816 16.769 20.418 32.900 49.349 59.219 21.598 33.509 40.788 15.384 23.853 29.042
1.360 1.350 1.330 0.980 1.030 1.610 1.470 1.290 0.760 0.830 1.130 1.110 1.060 1.070 1.010 0.880 1.100 0.910 1.140 0.850 0.930 1.220 0.971 0.940 0.813 0.790 0.960 0.800 0.740 0.690 0.980 1.036 0.227 0.219
1.5-100-50-40 24.525 1.5-100-50-40 R 24.492 1.5-150-100-40 37.235 1.5-180-130-40 33.453 1.5-180-130-40 R 35.270 1.5-100-50-70 17.164 1.5-150-100-70 24.277 1.5-180-130-70 25.819 1.5-100-50-100 5.825 1.5-150-100-100 9.894 1.5-180-130-100 16.402 1.5-180-130-100 R 15.990 2.0-100-50-40 27.715 2.0-100-50-40 R 27.876 2.0-150-100-40 40.830 2.0-180-130-40 43.176 2.0-100-50-70 16.681 2.0-150-100-70 21.407 2.0-180-130-70 32.489 2.0-100-50-100 9.180 2.0-150-100-100 15.635 2.0-180-130-100 24.838 2.5-100-50-40 31.958 2.5-150-100-40 46.385 2.5-180-130-40 48.159 2.5-100-50-70 17.120 2.5-150-100-70 32.122 2.5-180-130-70 32.771 2.5-100-50-100 11.321 2.5-150-100-100 16.498 2.5-180-130-100 28.325 Mean Standard deviation Coefficient of variation
Vexp (kN)
Vy (kN) 25.249 25.249 50.498 65.648 65.648 25.249 50.498 65.648 25.249 50.498 65.648 65.648 24.139 24.139 48.278 62.762 48.278 48.278 62.762 24.139 48.278 62.762 28.216 56.432 73.361 28.216 56.432 73.361 28.216 56.432 73.361
=
0.620 0.620 0.578 0.563 0.563 1.204 1.122 1.093 1.816 1.693 1.649 1.649 0.371 0.371 0.346 0.337 0.684 0.684 0.666 1.114 1.039 1.012 0.283 0.264 0.257 0.570 0.532 0.518 0.872 0.813 0.792
Vy Vcr
Vn = 0.231 λ−0.8 Vy (kN)
Vexp/Vn
8.553 8.553 18.092 24.024 24.024 5.029 10.637 14.125 3.619 7.655 10.165 10.165 12.324 12.324 26.069 34.615 15.112 15.112 20.066 5.114 10.818 14.365 17.884 37.828 50.231 10.214 21.604 28.687 7.272 15.382 20.425
2.867 2.864 2.058 1.392 1.468 3.413 2.282 1.828 1.610 1.292 1.614 1.573 2.249 2.262 1.566 1.247 1.104 1.417 1.619 1.795 1.445 1.729 1.787 1.226 0.959 1.676 1.487 1.142 1.557 1.073 1.387 1.709 0.562 0.329
4. Analysis of resistance and safety factor A reliability analysis was carried out for Eq. (2) to calculate the shear resistance of the clip angle bolted connection. The reliability analysis can be carried out in two ways; (i) calculate the AISI target reliability value for a given resistance factor for LRFD (Load and resistance factor design) and LSD (Limit state design) methods and safety factor for ASD (Allowable strength design) method, or (ii) calculate the resistance and safety factors of a fixed target reliability value by AISI method. The present study was carried out using the second approach. In this reliability study, the resistance factors for the LRFD and LSD methods and the safety factor for the ASD method were calculated for the shear resistance considering the connection type as not listed in Table F1 of chapter F in AISI S100-12 [2]. The target reliability value was taken as 3.5 and 4.0 for LRFD and LSD method respectively according to AISI S100-12 [2]. This approach was previously employed by Yu et al. [12] and Teh and Clements [8] where the resistance and safety factors were back-calculated for AISI target reliability (β0 = 3.5 and 4.0). In the present study, the resistance and safety factor analysis were similarly carried out to achieve the target reliability index (β0) value as per AISI limit. The resistance factor ɸ was calculated using Eq. (3) [Eqn. F1.1-2 of AISI S100-12 [2]] in which VP and PM were taken from Table 6, and all the remaining values were obtained from the chapter F of AISI S100-12 [2].
Fig. 13. Comparison of test results using the geometrical aspect ratios of L/B and L/P in Eq. (1).
= C (MM FM PM ) e
2 VM + VP2+ CP VP2+ VQ2
(3)
Where, Cɸ - calibration coefficient = 1.52 for LRFD method and 1.42 for LSD method; MM -mean value of the material factor = 1.10; FMmean value of fabrication factor = 1.0; VQ - coefficient of variation of 550
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Table 6 Comparison of experimental shear load value with improved design equation. Specimen configuration TC-B-P-W
Vexp (kN)
Vy (kN)
Vexp/Vy
1.5-100-50-40 1.5-100-50-40 R 1.5-150-100-40 1.5-180-130-40 1.5-180-130-40 R 1.5-100-50-70 1.5-150-100-70 1.5-180-130-70 1.5-100-50-100 1.5-150-100-100 1.5-180-130-100 1.5-180-130-100 R 2.0-100-50-40 2.0-100-50-40 R 2.0-150-100-40 2.0-180-130-40 2.0-100-50-70 2.0-150-100-70 2.0-180-130-70 2.0-100-50-100 2.0-150-100-100 2.0-180-130-100 2.5-100-50-40 2.5-150-100-40 2.5-180-130-40 2.5-100-50-70 2.5-150-100-70 2.5-180-130-70 2.5-100-50-100 2.5-150-100-100 2.5-180-130-100 Mean Standard deviation Coefficient of variation
24.525 24.492 37.235 33.453 35.270 17.164 24.277 25.819 5.825 9.894 16.402 15.990 27.715 27.876 40.830 43.176 16.681 21.407 32.489 9.180 15.635 24.838 31.958 46.385 48.159 17.120 32.122 32.771 11.321 16.498 28.325
50.498 50.498 75.747 90.897 90.897 50.498 75.747 90.897 50.498 75.747 90.897 90.897 48.278 48.278 72.418 86.901 48.278 72.418 86.901 48.278 72.418 86.901 56.432 84.647 101.577 56.432 84.647 101.577 56.432 84.647 101.577
0.486 0.485 0.492 0.368 0.388 0.340 0.321 0.284 0.115 0.131 0.180 0.176 0.574 0.577 0.564 0.497 0.346 0.296 0.374 0.190 0.216 0.286 0.566 0.548 0.474 0.303 0.379 0.323 0.201 0.195 0.279
=
Vy Vcr
0.578 0.578 0.555 0.544 0.544 1.122 1.077 1.058 1.693 1.625 1.595 1.595 0.346 0.346 0.332 0.326 0.684 0.657 0.645 1.039 0.997 0.979 0.264 0.253 0.249 0.532 0.510 0.501 0.813 0.780 0.766
Vnsb = 0.222 λ−0.6 Vy (kN)
Vexp/Vnsb
16.208 16.208 24.912 30.255 30.255 10.887 16.736 20.299 8.505 13.076 15.867 15.867 21.082 21.082 32.417 39.328 14.006 21.524 26.116 10.899 16.759 20.331 28.985 44.602 54.037 19.037 29.287 35.523 14.76 22.697 27.534
1.513 1.511 1.495 1.106 1.166 1.577 1.451 1.272 0.685 0.757 1.034 1.008 1.315 1.322 1.260 1.098 1.191 0.995 1.244 0.842 0.933 1.222 1.103 1.040 0.891 0.899 1.097 0.923 0.767 0.727 1.029 1.112 0.247 0.222
Table 7 Resistant factor and safety factors for improved shear Eq. (2). Parameter in the statistical analysis
Parameter values for current test results
Parameter values for combined test results of current test data and test data of Yu et al. [12]
Quantity Mean, PM Standard deviation, σ Co-efficient of variation, VP MM VM FM CP VF VQ βo (LRFD) βo (LSD) ϕ (LRFD) ϕ (LSD) Ω (ASD)
31.00 1.112 0.247 0.222
64.00 1.091 0.212 0.194
1.10 0.10 1.00 1.106 0.15 0.21 3.50 3.00 0.52 0.41 3.06
1.10 0.10 1.00 1.049 0.15 0.21 3.50 3.00 0.55 0.44 2.91
m = n-1 = 30, Vp - coefficient of variation of the ratio between the experimental and predicted shear strength. The predicted resistance and safety factors are presented in Table 7 for Eq. (2). The resistance factors were calculated as 0.52 and 0.41 for LRFD and LSD methods respectively and safety factor as 3.06 for the ASD method. The obtained resistance factor value is lower than the resistance factor value of Yu et al. [12] in both LRFD and LSD methods and the safety factor was higher when compared to the safety factor value of Yu et al. [12] in the ASD method. In addition, the reliability studies for Eq. (2) were also carried out
Fig. 14. Comparison of current test results and test results of Yu et al. [12] with improved Eq. (2).
load effect = 0.21 for LRFD; βo - target reliability index = 3.5 for LRFD method; PM - mean professional factor calculated as the mean value of ratio between the experimental shear resistance and the improved design of shear value of bolted clip angle connection; CP - correction factor = (1 + 1/n) (m/m-2) = 1.106, where, n - number of shear test = 31, 551
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for the combined test data (data from present investigation and Yu et al. [12]). The resistance factors for the combined data are 0.55 and 0.44 for LRFD and LSD methods respectively and the safety factor as 2.74 for the ASD method. This indicates that Eq. (2) is conservative for both current test results and test results of Yu et al. [12] as can be observed from Fig. 14. Therefore, Eq. (2) can be considered for the design of clip angle from 227 MPa to 561 MPa. The design example is given in the Annexure A for clip angle leg connected to the column.
• • •
5. Summary and conclusions
•
A series of experiments on the CFS clip angle bolted connections between CFS beam-to-column were conducted to investigate the behavior in terms of load - deflection and failure modes. The specimens were tested under four-point bending for different configuration such as aspect ratio (L/B) and thickness of the clip angle. An improved design equation for the clip angle connection has been proposed and compared with the experiments. In addition, a detailed reliability analysis was performed. The following conclusions that can be drawn from this work:
•
• The strength and load vs deflection behavior depend largely on the
•
clip angle increases due to the increase in W due to out-of-plane bending effects. The geometrical aspect ratio L/B is more reliable than the L/P when compared with the design equation of literature study. Based on test results, an improved design equation is suggested for the beam-to-column connection using a bolt through clip angle for materials with yield strength up to 561 MPa. The maximum slenderness (λ) limit is shifted to 0.2 (Eq. (2)) from 0.32 (Eq. (1)) to attain the limiting shear resistance value of 0.583 Vy in Eq. (2). The LRFD, LSD resistance factors and the ASD safety factors were calculated for improved shear equation by following the Chapter F in AISI S100-12. The suggested values of resistant and safety factor can be applied for the design of clip angle since the target reliability index value associated CFS connection by considering the connection not listed in Table F1 of Chapter F in AISI S100-12. In the current study, two number of the bolt was used in the clip angle leg connected to the column web. However, the bearing deformation of the bolt hole can be reduced by increasing the number of bolts in clip angle leg connected to the column web for higher depth of clip angle.
Acknowledgments
aspect ratio (L/B) of clip angle and thickness of clip angle. When the aspect ratio (L/B) of the clip angle connected to the column web is less than 0.8, the dominant mode of failure was local buckling. However, clip angles with an aspect ratio (L/B) greater than 0.8 exhibited failure due to distortional buckling. In addition, bearing deformation of the bolt hole was observed in all the test specimens. The stiffness of the clip angle reduces as the aspect ratio (L/B) of the
The first author would like to acknowledge the fellowship from the Ministry of Human Resource Development (MHRD) India. The authors would like to gratefully acknowledge Pennar Engineered Building Systems Ltd., Hyderabad for their help in fabricating the test specimens required for experimental investigation.
Annexure A Design Example Fig. A shows the dimension of the clip angle. The corner radius is assumed to be 3.0 mm. The thickness of the clip angle is 2.0 mm. The yield strength and elastic modulus of clip angle were 350 N/mm2 and 205300 N/mm2 respectively. Calculate the nominal and design shear strength of clip angle.
Fig A. Dimension of the clip angle.
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V. Natesan and M. Madhavan
Solution: L = 75 - 25–2.0–3.0 = 45 mm
k = 2.569 Fcr =
L B
2.202
k 2E 12(1 µ2 )
=
Vy Vcr
=
Vnsb = 0.222
= 2.569
t B
2
=
2.202
45 150
36.4 x 12(1
2
= 36.4
x 205300 0. 32)
2.0 150
2
= 1200.73 N / mm2
0.6 x 350x 150 x 2.0 = 0.42 1200.73 x 150 x 2.0 0.6
Vy = 0.222
0.42
0.6
x 0.6 x 350 x 150 x 2.0 = 23.54 kN
< 0.583 x 0.6 x 350x 150 x 2.0 = 36.73 kN Design shear strength of clip angle.
Vdsb =
x Vnsb for LRFD and LSD methods
Vdsb = 0.55 x 23.54 = 12.95 kN for LRFD method Vdsb = 0.44 x 23.54 = 10.36 kN for LSD method Vdsb = Vnsb/
for ASD method
Vdsb = 23.54/2.91 = 8.09 kN for ASD method
References
Notations
[1] H. Ahamed, M. Mahendran, Bolted Beam-Column Moment Connections between Cold-Formed Steel Members, (ACMSM 21), Victoria University, Melbourne, 2010. [2] AISI S100-12: North American Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC, 2012. [3] ASTM, Standard Test Methods for Tension Testing of Metallic Materials”, ASTM, West Conshohocken, PA, 2013 ASTM E8/E8M-13a. [4] K.F. Chung, R.M. Lawson, Structural performance of shear resisting connections between cold-formed steel sections using web cleats of cold-formed steel strip, Eng. Struct. 22 (2000) 1350–1366. [5] S. Fox, Strength of CFS floor assemblies with clip angle bearing stiffeners, AISI Research Rep PR0vols. 5–6 American Iron and Steel Institute, Washington, DC, 2005. [6] Fastenal Industrial, Construction Supplies, ReVision vol. 9, (2005) A-8 s7028. [7] Y. Huang, B. Young, The art of coupon tests, J. Constr. Steel Res. 96 (2014) 159–174. [8] Lip H. Teh, Drew D.A. Clements, Block shear capacity of bolted connections in coldreduced steel sheets, J. Struct. Eng. 138 (4) (2012) 459–467. [9] J.B.P. Lim, D.A. Nethercot, Ultimate strength of bolted moment-connections between cold-formed steel members, Thin-Walled Struct. 41 (2003) 1019–1039. [10] J.B.P. Lim, D.A. Nethercot, Stiffness prediction for bolted moment-connections between cold-formed steel members, J. Constr. Steel Res. 60 (2004) 85–107. [11] J. Mills, R. LaBoube, Self-drilling screw joints for cold-formed channel portal frames, J. Struct. Eng. 130 (11) (2004) 1799–1806. [12] C. Yu, M. Yousof, M. Mahdavian, W. Zhang, Behavior and design of thin-walled cold-formed steel clip angles subjected to shear load, J. Struct. Eng. 142 (7) (2016) 1–9 04016040. [13] C. Yu, M. Yousof, M. Mahdavian, W. Zhang, Design of cold-formed steel clip angles in compression, J. Struct. Eng. 143 (6) (2017) 1–8 04017030. [14] L. Wang, B. Young, Behavior of cold-formed steel built-up sections with intermediate stiffeners under bending. I: tests and numerical validation”, J. Struct. Eng. 142 (3) (2016) 1–9 04015150. [15] W. Zhang, M. Mahdavian, M. Yousof, C. Yu, Testing and design of cold-formed steel clip angles in tension: pull-over and serviceability, Thin-Walled Struct. 124 (2018) 13–19.
A: length of clip angle leg connected to the column B: depth of clip angle Bnc: number of bolts provided on leg clip angle connected to the column Bnb: number of bolts provided on leg clip angle connected to the beam CP: correction factor Cф: calibration coefficient d: diameter of the bolt E: Young's modulus of the material Fcr: critical buckling stress FM: mean value of fabrication factor Fy: yield strength of the material Fu: ultimate strength material K: buckling coefficient L: flat width of clip angle leg; distance between the center of the bolt line to the bend line MM: mean value of the material factor n: number of shear test p: pitch distance between two bolts along the depth of clip angle PM: mean professional factor calculated as the mean value of the ratio between the experimental shear value to the calculated shear value of improved design equation TC or t: thickness of clip angle Vy: yield shear strength Vcr: critical shear strength W: distance between the center of bolt line and outer to the end of the bend line Vnsb: nominal shear strength of clip angle by improved design equation Vp: coefficient of variation of the ratio between the experimental shear value to the calculated shear value of improved shear equation Vn: nominal shear strength of clip angle of Yu et al. [12] method VQ: coefficient of variation of load effect ɸ: resistance factor λ: slenderness ratio β0: target reliability index Ω: safety factor σ: standard deviation of the ratio between the experimental shear resistance to the calculated shear value of nominal shear equation
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Full length article
Experimental study on beam-to-column clip angle bolted connection Vijayakumar Natesan, Mahendrakumar Madhavan
T
∗
Department of Civil Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, 502 285, Telangana, India
ARTICLE INFO
ABSTRACT
Keywords: Cold-formed steel Clip angle bolted connection Beam-to-column Reliability Shear resistance
The effectiveness of the clip angle bolted connection between CFS (Cold-formed steel) beam-to-column under shear is investigated in the present study. A total of thirty-one specimens were tested under four-point bending configuration to study the behavior of beam-to-column clip angle connection using bolts. The parameters considered in the experimental study are clip angle thickness and aspect ratio of the clip angle leg connected to the column. The test results indicate that the aspect ratio (L/B) of the clip angle leg plays a significant role in governing the ultimate strength, stiffness and failure mode of the connection. Two different failure modes were observed namely (i) local buckling failure at an aspect ratio (L/B) less than 0.8 and (ii) distortional buckling failure at an aspect ratio (L/B) greater than 0.8 in the clip angle leg connected to the column. An improved design equation for the clip angle bolted connection is proposed and validated with the previous studies from the literature. The proposed design equations for clip angle bolted connection were conservative compared with experimental test results. In addition, a shift in the anchor point (compact limit) i.e., reduction in the slenderness ratio (λ) is suggested for limiting the shear resistance of clip angle bolted connection. Further, reliability studies were carried out to determine the resistance and safety factors for the connections not listed in Table F1 of AISI S100-12 based on the current study and test results from the literature. The suggested design method will be applicable and conservative for the material yield strength up to 550 MPa.
1. Introduction Cold-formed steel (CFS) sections are widely used due to various advantages over the hot rolled steel such as (i) lightweight, (ii) higher strength to weight ratio, (iii) reduced construction time, and (iv) ease in fabrication and installation. Two shapes of CFS sections commonly used are C and Z type with the section depth typically ranging from 100 to 350 mm and the thickness from 1.2 to 3.0 mm. The yield strength of the material varies between 250 and 550 MPa. Design recommendations on CFS connections primarily depend on the type of fasteners such as bolts, screws, and welds. These fastener designs are considered important when two CFS sections are connected directly as shown in Fig. 1a. Few researchers have studied the connection between beam-to-column connections as shown in Fig. 1a. Ahamed and Mahendran [1] investigated the bolted moment connection between CFS beam-to-column with four different configurations. The observed that the failure was due to local buckling in the beam section and the failure location depends on the connection type. In addition, the research revealed that the strength and ductility of the connection depending on the connection type and the depth of section. A similar mode of failure was observed by Lim and Nethercot ([9,10]) for moment connection at apex
∗
joint between the CFS sections using bolts. However, this type of failure mode is not anticipated when the CFS members are connected through CFS connector such as a clip angle (see Fig. 1b) using a bolt. Bolted connections possess inherent advantages over other fastener types such as welded and self-drilling screw connections due to its ability to quickly assemble and dismantle structural steel members without the need for skilled labor. It is also worth mentioning that the welded connection is difficult in CFS due to its smaller thickness. The selfdrilling screw in CFS connection between beam-to-beam and beam-tocolumn failed due to shearing and pull-out of the clip angle (Chung and Lawson [4]). Similar failure mode (shear failure of the screw) in selfdrilling screw between two CFS rafter through CFS connector in the knee joint was observed by Mills and Laboube [11]. In addition, past studies by Fox [5] indicate that clip angles failed due to compression when acting as a bearing stiffener between two CFS sections. In general, when two CFS members are directly connected (Fig. 1a) through bolt without a connector, the failure occurs in one or both the members. Whereas if the member is connected through clip angle (Fig. 1b), the failure can be either in the clip angle or in the fastener depending on the clip angle thickness or the fastener type (screw or bolt). Typically, screw connections exhibit pull through/pull out and or
Corresponding author. E-mail addresses: [email protected] (V. Natesan), [email protected] (M. Madhavan).
https://doi.org/10.1016/j.tws.2019.04.048 Received 30 August 2018; Received in revised form 7 March 2019; Accepted 24 April 2019 Available online 29 May 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.
Thin-Walled Structures 141 (2019) 540–553
V. Natesan and M. Madhavan
Fig. 1. (a) Direct beam-to-column connection using bolt; (b) Beam-to-column connection through clip angle using a bolt.
ratios of clip angle (L/B) under shear load. (ii) to suggest an improved design equation for clip angles with material yield strength up to 550 MPa with realistic beam-to-column bolted connections.
shear for higher clip angle thickness. However, when the fastener is a bolt, the possibility of failure (local/distortional buckling) of the clip angle is higher since the bolts are typically much stronger than the parent member and the clip angle. Yu et al. [12] investigated the behavior of clip angle subjected to shear load and formulated the design equations for predicting the service load and ultimate load valid within the range of parameters (i) material yield strength (227–350 MPa) (ii) aspect ratio of the clip angle (0.18–1.4) and (iii) thickness of clip angle (0.8–2.46 mm). In addition, it should be noted that the study carried out by Yu et al. [12] was on self-drilling screws which is typically used for connecting the sheathing (Gypsum, wooden board or CFS sheet with 0.45 mm thickness) while fabricating wall panels and is considered as a non-structural member compared to connection between two CFS members with thickness up to 2.0 mm. However, the present study was on connecting two structural members using bolts through the use of clip angle. Yu et al. [13] and Zhang et al. [15] investigated the behavior of clip angle subjected to compression and tension respectively and proposed design equations for service limit. It should be noted that the literature study has a couple of drawbacks: (i) the yield stress of the material was confined to 350 MPa (ii) experimental test set-up does not reflect the realistic beam-to-column bolted connection. In the current study, an attempt is made to investigate clip angle with material yield strength up to 550 MPa with realistic beam-to-column bolted connection. In general practice for a given clip angle dimension the connected beam can have any depth depending upon the structural demand and ease of construction. The sizes of the clip angle in the present study however, was chosen such that the depth of clip angle should at least be equal to 50% of the beam depth or higher (but 20 mm less than the beam depth for clearance) to effectively transfer the shear load. Therefore, the present study was focused on studying the clip angle behavior for a constant beam depth of 200 mm for three different clip angles with the depth of 100 mm, 150 mm and 180 mm.
2. Experimental program 2.1. Material properties In this study, the clip angles with three different thicknesses (1.5 mm, 2.0 mm and 2.5 mm) were used. Three coupon samples were prepared for each thickness as per E8/E8M-13a [3] and Huang and Young [7]. All the coupon samples were tested in a displacement control mode at a rate of 0.01 mm/s using a servo-controlled hydraulic cyclic testing machine of 100 kN capacity. The material properties such as elastic modulus, yield strength, ultimate strength and percentage of elongation were determined from the coupon test. The test setup is shown in Fig. 2a and tested coupon samples are shown in Fig. 2b. The stress-strain behavior for three different thickness, 1.5 mm and 2.0 mm and 2.5 mm is shown in Fig. 3a, Fig. 3b and c respectively. The material properties of the tested coupon samples are presented in Table 1. 2.2. Details of clip angle configuration and fabrication of test specimen The geometric layout of the clip angle bolted connection between CFS beam-to-column is shown in Fig. 4. The sectional details of the beam and column members are kept constant for all experiments as shown in Fig. 5. For all the test specimens, two bolts were used for connecting clip angle leg to the column web and four bolts for connecting the clip angle leg to the beam. This type of test configuration is selected to hold more focus on strength and failures in the clip angle leg connected to CFS column. The weak link in the connection system was designed such that the failure was anticipated in the clip angle to observe its mode of failure when subjected to shear loading. Hence, the present study did not account for the interaction between beam and clip angle end rotations although it is quite possible that the results may be different if the beam is significantly more flexible. The two main parameters included in this study are (i) aspect ratio of the clip angle leg connected to the column and (ii) thickness of the clip angle. The aspect ratio is defined as the ratio of the flat distance (L) between the centerline of fasteners and bend line of clip angle leg to the depth of clip angle leg (B) connected to the column (Yu et al. [12]). The dimension details of clip angle configuration are given in Table 2. A minimum
1.1. Research motivation and objectives In recent times, the use of high strength steel for structural construction has become prominent. However, design provisions for material (connectors) with a yield strength of more than 350 MPa are not available. The objective of this study is (i) to understand the behavior of clip angle bolted connection between beam to column in terms of ultimate strength for different parameters such as thickness and aspect 541
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Fig. 2. (a) Test setup of coupon test; (b) Tested coupon samples.
edge distance (1.5d) and pitch distance (3d) are recommended by AISI S 100-12 [2] for bolted connection. In the present study, a constant edge distance of 25 mm was maintained for the use of 12 mm diameter in all the clip angle configurations. The pitch distance (P) of clip angle
increased with the increase in the depth of clip angle since only two bolts were provided in the clip angle leg connected to the column. The specimen configuration ending with “R” denotes the repeat tests carried out for clip angle bolted specimen to ensure consistency in
Fig. 3. Stress vs strain plot: (a) 1.5 mm thick clip angle; (b) 2.0 mm thick clip angle; (c) 2.5 mm thick clip angle. 542
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and the other two columns connected on either side of the beam member using a clip angle bolted connection. All the clip angles and CFS channel sections were drilled using a drill bit of 12.8 mm diameter for the provision of 12 mm diameter bolt. Two wooden blocks acting as stiffeners were placed between the flange elements of the beam (CFS channel) under the loading points (400 mm c/c) to avoid the local buckling of beam (CFS channel) section as shown in Fig. 5 (Wang and Young [14]). The bottom end of both the CFS columns was made rigid using a 12 mm thick hot rolled steel (HRS) plate by the application of fillet weld. To ensure consistency in the application of a torque for each bolted connection, an impact torque wrench was used for tightening of bolted clip angle. A maximum torque of 25 N-m was applied based on the recommendation of Fastenal industrial and construction supplies [6] for an M12 bolt of 4.6 grade.
Table 1 Material properties. Sample No
Thickness of clip angle TC (mm)
Yield strength fy (N/mm2)
Ultimate strength fu (N/mm2)
Elastic modulus E (N/mm2)
Percentage of elongation
1 2 3 Mean 1 2 3 Mean 1 2 3 Mean
1.5
564.49 581.57 537.21 561.09 406.81 400.36 399.79 402.32 368.42 377.05 383.15 376.21
575.12 597.41 547.21 573.25 434.59 433.33 420.82 429.58 421.93 436.79 438.34 432.35
207293 212248 201078 206873 216223 214193 215691 215369 200517 202302 210088 204302
11.26 12.18 10.12 11.19 18.90 17.91 18.36 18.39 20.66 20.67 20.66 20.66
2.0
2.5
2.3. Experimental test setup A universal flexural test frame with a hydraulic load cell of 300 kN capacity was used to perform a four-point bending test. All specimens were tested in displacement control mode at a rate of 0.01 mm/s. Fig. 6 shows the overall test setup and instrumentation details to study the behavior of the clip angle bolted connection between CFS beam to column subjected to shear under four-point bending test. In general, clip angle is designed to carry the shear load between beam-to-beam and beam to column connection at the web. The shear resistance of clip angle was studied by Chung and Lawson [4] for the connection between the beam-to-beam and beam-to-column at the web using three different types of the fasteners (self-drilling screws, bolts, and rivets) with load eccentricity of 250 mm. Chung and Lawson [4] observed the clip angle leg connected to the unloaded/supported member of beam-to-beam and beam-to-column has experienced out-of-plane bending due to the thinness of the clip angle. In the current study, the load was applied at a distance of approximately 230 mm from the column web and the clip angle leg connected to beam was predominantly subjected to shear. To prevent the web crippling and local buckling at the point of load application, a small channel fabricated using HRS plates was placed below the actuator to convert the line load to a patch load. In addition, HRS was used to fabricate rigid support (base beam) over which the CFS column is fillet welded to ensure a rigid support condition. The HRS base plate connected with the base beam using a bolted connection threaded rod. Further, the base beam is also fixed to the FTM frame using the bolted connection by means of a threaded rod. The vertical displacement at the mid-span was measured using the NCDT (Noncontact differential transducer) with a measuring range of 300 mm to capture the large deformation exhibited by the specimen. Moreover, two more LVDTs (linear variable differential transducer) were used to measure the displacement of the loaded CFS channel close to the clip angle connection. 3. Result and discussion Table 3 shows the observed values of the ultimate shear load for clip angle connection at one end (half of the tested load) and failure mode of clip angle bolted connection under four-point bending test. The test results indicate that there is not much difference between the boundary conditions imposed by a beam attached to a column compared to direct pull-out of the clip angle connected to the column. This indicates that the realistic connection configuration provided by the beam connected to one end of the clip angle did not significantly alter the boundary conditions compared to the loading condition where the clip angle was directly subjected to a shear load. Fig. 7a classifies the failure mode of the specimen based on the aspect ratio of the clip angle leg connected to the column.
Fig. 4. Geometric layout of clip angle configuration.
test results. In total, 31 specimens were tested including four repeat test specimen configurations of clip angle by varying test parameters such as clip angle thickness and aspect ratios (L/B) of leg connected to the column. The cross section details of CFS beam and column are shown in Fig. 5. Each specimen consists of three CFS members; one loaded beam
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Fig. 5. Typical view of the fabricated specimen before the test.
3.1. Ultimate shear strength of clip angle bolted connection and its failure modes
to a column. The magnitude of ultimate shear strength increases with the thickness but reduces with the increase in aspect ratio of clip angle for all the specimens (Fig. 7a). The variation in the bolt configuration was not considered in the present study since the bolt failure was not observed in the two bolt configuration from the experimental results. It
The ultimate shear strength of clip angle bolted connections depends on the thickness and aspect ratio of the clip angle leg connected Table 2 Clip angle configuration for experimental program. Specimen configuration TC-B-P-W
Thickness of clip angle TC (mm)
1.5-100-50-40 1.5 1.5-100-50-40 R 1.5 1.5-150-100-40 1.5 1.5-180-130-40 1.5 1.5-180-130-40 R 1.5 1.5-100-50-70 1.5 1.5-150-100-70 1.5 1.5-180-130-70 1.5 1.5-100-50-100 1.5 1.5-150-100-100 1.5 1.5-180-130-100 1.5 1.5-180-130-100 R 1.5 2.0-100-50-40 2.0 2.0-100-50-40 R 2.0 2.0-150-100-40 2.0 2.0-180-130-40 2.0 2.0-100-50-70 2.0 2.0-150-100-70 2.0 2.0-180-130-70 2.0 2.0-100-50-100 2.0 2.0-150-100-100 2.0 2.0-180-130-100 2.0 2.5-100-50-40 2.5 2.5-150-100-40 2.5 2.5-180-130-40 2.5 2.5-100-50-70 2.5 2.5-150-100-70 2.5 2.5-180-130-70 2.5 2.5-100-50-100 2.5 2.5-150-100-100 2.5 2.5-180-130-100 2.5 R -Indicates the configuration of clip angle specimen
Depth of clip angle B (mm)
Pitch distance of clip angle P (mm)
Distance between the center of bolt line and outer to the end of the bend line W (mm)
Total width of clip angle leg connected to column A (mm)
100 100 150 180 180 100 150 180 100 150 180 180 100 100 150 180 100 150 180 100 150 180 100 150 180 100 150 180 100 150 180 repeated test
50 50 100 130 130 50 100 130 50 100 130 130 50 50 100 130 100 100 130 50 100 130 50 100 130 50 100 130 50 100 130
40 40 40 40 40 70 70 70 100 100 100 100 40 40 40 40 70 70 70 100 100 100 40 40 40 70 70 70 100 100 100
65 65 65 65 65 95 95 95 125 125 125 125 65 65 65 65 95 95 95 125 125 125 65 65 65 95 95 95 125 125 125
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Fig. 6. Overall experimental test setup.
should be noted that the maximum experimental shear load on either side of the clip angle (with two bolt configuration) did not exceed the 50 kN (see Table 3). Since the shear load capacity of two bolts provided in the clip angle leg connected to the column web is 72 kN (36 kN for each bolt for 12 mm diameter of the bolt with 4.6 grade), this study chose to focus on the variation in the thickness and the aspect ratio of the clip angle to better understand the clip angle behavior. The bolts in the present study were provided such that they maintain the minimum edge distance and the minimum pitch as per AISI S100-12 [2]. However, AISI S100-12 [2] does not provide a specified maximum limit on the pitch distance. Therefore, the current study did not account for the maximum pitch distance. In addition, the design provisions provided by Yu et al. [12] also did not include the pitch distance but rather included the clip angle depth. While it is intuitive to think that the pitch is more valuable parameter than the depth, the results from the experiments provided a specific trend with a compelling argument to consider the depth of the clip angle compared to the pitch as can be observed from Fig. 7b. Nevertheless, a plot with a pitch distance as a parameter was considered in the present study shown in Fig. 7b does indicate that the pitch does matter for smaller clip angle thicknesses. Fig. 7b indicates that there is a decrease in ultimate load capacity with the increase in pitch distance for lower thickness (1.5 mm) of the clip angle. The decrease in thickness with a larger pitch distance increases the plate slenderness (high P/t) thereby increasing the vulnerability of the clip angle plate to local buckling. The local buckling failure of the clip angle leads to a reduction in the ultimate capacity for thin clip angle plates with large pitch distance. Two types of failure modes were observed in the clip angle bolted connection between CFS beam-to-column under four-point bending test. When the aspect ratio (L/B) of the clip angle leg connected to column web is less than 0.8, the mode of failure observed was local buckling (Fig. 8a) whereas for aspect ratios greater than 0.8 the observed mode of failure was distortional buckling (Fig. 8b). Similar failure modes for clip angle subjected to shear load were observed by Yu et al. [12]. In addition, the bearing deformation was observed in the bolt hole of the clip angle leg connected to the column as shown in
Table 3 Observed experimental ultimate shear load and failure modes. Specimen configuration TC-B-P-W
L/B ratio
* Ultimate shear load Vexp (kN)
Failure modes
1.5-100-50-40 1.5-100-50-40 R 1.5-150-100-40 1.5-180-130-40 1.5-180-130-40 R 1.5-100-50-70 1.5-150-100-70 1.5-180-130-70 1.5-100-50-100 1.5-150-100-100 1.5-180-130-100 1.5-180-130-100 R 2.0-100-50-40 2.0-100-50-40 R 2.0-150-100-40 2.0-180-130-40 2.0-100-50-70 2.0-150-100-70 2.0-180-130-70 2.0-100-50-100 2.0-150-100-100 2.0-180-130-100 2.5-100-50-40 2.5-150-100-40 2.5-180-130-40 2.5-100-50-70 2.5-150-100-70 2.5-180-130-70 2.5-100-50-100 2.5-150-100-100 2.5-180-130-100
0.363 0.363 0.242 0.201 0.201 0.663 0.442 0.368 0.963 0.642 0.535 0.535 0.350 0.350 0.233 0.194 0.650 0.433 0.361 0.950 0.633 0.528 0.338 0.225 0.188 0.638 0.425 0.354 0.938 0.625 0.521
24.525 24.492 37.235 33.453 35.270 17.164 24.277 25.819 5.825 9.894 16.402 15.990 27.715 27.876 40.830 43.176 16.681 21.407 32.489 9.180 15.635 24.838 31.958 46.385 48.159 17.120 32.122 32.771 11.321 16.498 28.325
LB LB LB LB LB LB LB LB DB LB LB LB LB LB LB LB LB LB LB DB LB LB LB LB LB LB LB LB DB LB LB
Note: * The ultimate shear load is halved between each single clip angle. LB and DB are local and distortional buckling of clip angle leg connected to column respectively.
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Fig. 7. (a) Experimental shear load vs L/B (or) L/P; (b) Experimental shear load vs depth of clip angle (B).
Fig. 8c. Such type of deformation was not reported by Yu et al. [12] since self-drilling screws were used as fasteners compared to bolts in the present study. In general, the bearing deformation is a common mode of failure in the bolted connection. In the current study, the bearing deformations of the bolt hole are higher in the clip angle leg connected to column compared to clip angle leg connected to beam due to the presence of a minimum number of bolts. Moreover, the bearing deformation of the clip angle depends on the L/B ratio and the thickness of the clip angle. The L/B ratio is similar to the unbraced length and the thickness of the clip angle to the slenderness of the connected leg. An increase in L/B and a decrease in clip angle thickness results in a decrease in the buckling resistance offered by the clip angle against the applied shear load.
thickness such as 1.5 mm, 2.0 mm and 2.5 mm from the recorded data during the test as shown in Figs. 9–11. In addition, Fig. 12 shows that the difference in the magnitudes of the displacements between the midspan (using NCDT), loading point (using 50 mm LVDT's) and at the clip angle connection location (using 100 mm LVDTs) are insignificant. This indicates that the beam and the leg of clip angle connected to beam were predominantly subjected to shear. However, the leg which was connected to the column experienced out-of-plane bending due to the eccentricity in loading. The following observations are made from the load vs deflection plot. 1. For 100 mm and 150 mm depth sections, a reduction in initial stiffness was observed when the distance between the center line of bolts and bend line (W) of clip angle (leg connected to column web) increases from 40 mm to 100 mm for both 1.5 mm and 2.0 mm thick clip angle. This may be attributed to the increase in L/B ratio due to the increase in W resulting in a higher aspect ratio of the clip angle leading to out-of-plane bending in the clip angle leg connected to the column.
3.2. Load-deflection behavior The load versus applied deflection is plotted for clip angle bolted connection between CFS beam-to-column for three different clip angle
Fig. 8. Failure modes: (a) Local buckling of specimen 1.5-180-130-40; (b) Distortional buckling of specimen 2.0-100-50-100; and (c) Local buckling of specimen 2.5100-50-40. 546
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Fig. 9. Load vs deflection plot for 1.5 mm thick clip angle: (a) D = 100 mm depth; (b) D = 150 mm depth; (c) D = 180 mm depth.
2. For 180 mm depth clip angle, no significant increase in stiffness can be observed for 1.5 mm, 2.0 mm and 2.5 mm compared to 100 mm and 150 mm. This indicates that an optimum depth is reached when the depth of the clip angle approaches the depth of the parent member. 3. In general, the load vs deflection plot becomes stiffer with increased depth and thickness of the clip angle. Similarly, in the current study, the load-deflection plot of specimens with higher clip angle thickness (2.5 mm) is stiffer than the load-deflection plot of specimens with other two thickness of clip angle (1.5 mm and 2.0 mm). 4. In addition, with an increase in thickness, the specimens exhibited more ductility as can be observed in the large rotation prior to attaining the ultimate load. On the contrary, for specimens with lesser clip angle thickness, initiation of buckling took place at lower loads followed by distortion (see Fig. 8) at ultimate as can be observed in the failure behavior of the specimens.
=
k = 2.569
k 2E 12(1 µ2) L B
2.569
slenderness ratio;Fcr t B
2
critical buckling stress
buckling coefficient;Vy = 0.6Fy B t;
t = design thickness of clip angle; B = depth of clip angle; L = flat width of clip angle; distance the between the center of the first line of screws to the bend line. Eq. (1) is valid within the following range of parameters:
• Clip angle design thickness: 0.84–2.46 mm. • Clip angle design yield strength: 227–345 MPa. • L/B ratio: 0.18–1.40 Since the above equation (Eq. (1)) is recommended for the material yield strength up to 345 MPa, that is a need to validate or improve the design equation for higher yield strength values. Table 4 shows the test results for bolted clip angle loaded in shear along with a comparison of design equation provided by Yu et al. [12]. The average ratio of test results compares well (Vexp/Vn = 1.036) with Eq. (1). However, it can be observed that more than 50% of the tested specimens (16 specimens) had a reduced shear capacity compared to Eq. (1). In particular, the experimental results indicate that few specimens (see Fig. 13) do not satisfy the limiting shear resistance (0.583 Vy) for the slenderness ratio
In the current study, two different aspect ratios such as (i) L/B and (ii) L/P were investigated for the design of clip angle. Yu et al. [12] proposed an equation for calculating the nominal shear capacity of the clip angle without considering its deformation as given by Eq. (1) based on the depth of the clip angle. 0.8V y
Vcr
Vcr = 0.6Fcr B t
3.3. Comparison of test results with Yu et al. [12] Using aspect ratios L/B and L/P
Vn = 0.231
Vy
Where, =
(1) 547
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Fig. 10. Load vs deflection plot for 2.0 mm thick clip angle: (a) D = 100 mm depth; (b) D = 150 mm depth; (c) D = 180 mm depth.
(λ) less than 0.32. This is primarily due to the location of the anchor point (λ = 0.32) determined based on the 345 MPa clip angle steel sections tested by Yu et al. [12]. Therefore, a new slenderness limit is required for clip angles with higher yield strength for the conservative design of clip angle bolted connection. For better clarity, the geometrical aspect ratios L/P were implemented in Eq. (1) instead of L/B as shown in Fig. 13 to design the clip angle. As can be observed from Fig. 13, it becomes obvious that the depth of the clip angle provides more consistent results compared to the pitch distance. Hence, the depth of the clip angle is used to formulate the design provisions based on the experimental results for the limited set of parameters considered. In addition, Table 5 shows the experimental shear load and calculated shear values of Eq. (1) using the geometrical aspect ratios L/P instead of L/B. The mean, standard deviation, and coefficient of variation are presented for the ratio between the experimental shear load (Vexp) and calculated shear values of Eq. (1). The results from Table 5 shows a high degree of conservativeness due to the use of pitch distance as can be observed by comparing the mean value of the ratio between experimental shear load (Vexp) to the calculated shear values obtained from Eq. (1). It should be noted that when the pitch distance is implemented replacing the depth as given in Eq. (1), the mean value of the ratio is higher (1.709) for pitch distance compared to the depth (1.036) as shown in Table 4. Similarly, the standard deviation and coefficient of variation are also more when the pitch distance is considered compared to the depth of the clip angle. This indicates that the efficacy of Eq. (1) decreases when pitch distance p is replaced with clip angle depth B leading to the highly conservative design value.
3.4. Improved ultimate shear design equation for CFS clip angle bolted connection Fig. 13 shows the plot for Vexp/Vy versus λ for all the tested specimens. In the current study, an improved design equation was proposed with a realistic beam-column connection through clip angle using bolts based on experimental observations. The procedure proposed by Yu et al. [12] is adopted for determining the slenderness (λ) values. However, the design equation (see Eq. (2)) has been modified and the maximum slenderness limit for attaining the limiting shear resistance (0.583 Vy) was shifted to the left (towards the origin) based on the experimental results.
Vn = 0.222
0.6V y
(2)
Eq. (2) shall be valid within the following range of parameters:
• Clip angle design thickness: 1.5 mm−2.5 mm; • L/B ratio: 0.188–0.963; • Maximum depth of beam is 200 mm; • Clip angle design yield strength: 376–561 MPa; • Minimum two number of bolts should be present in the column web. The maximum slenderness value was shifted to 0.2 such that the maximum shear strength was limited to 0.583 Vy. Table 6 presents the calculated nominal shear capacity using Eq. (2) for corresponding values of λ and Vy. The mean, standard deviation, and coefficient of variation are presented in Table 6 for the ratio between experimental shear resistances (Vexp) to the values of the improved nominal shear 548
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Fig. 11. Load vs deflection plot for 2.5 mm thick clip angle: (a) D = 100 mm depth; (b) D = 150 mm depth; (c) D = 180 mm depth.
strength (Vnsb) of the bolted clip angle connection between CFS beamto-column. The mean value is 1.112 for the ratio between experimental shear resistance (Vexp) to the calculated nominal shear strength using Eq. (2) and this value is higher than the mean value of the ratio between experimental shear resistances (Vexp) to the calculated nominal shear strength using Eq. (1). This indicates that Eq. (2) is more conservative compared to the nominal shear Eq. (1). In addition, the standard deviation is 0.247 and 0.227 for the ratio between the experimental shear resistances (Vexp) to the calculated nominal shear strength using Eqs. (2) and (1) respectively. However, the corresponding coefficient of variation is 0.219 and 0.222 indicating that the percentage of error is almost
the same when using both Eqs. (1) and (2) for the design of clip angle. Fig. 14 shows the combined results from the present investigation along with the test data from Yu et al. [12] superimposed with Eq. (2). The mean, standard deviation, and coefficient of variation for the ratio between the combined experimental results (present investigation and Yu et al. [12]) to the calculated nominal shear strength using Eq. (2) are 1.091, 0.212, and 0.194 respectively (Table 7). These statistical values are very much similar to the values obtained from Eq. (1) indicating that the use of Eq. (2) can be extended for the design of beam-column clip angle leg with material yield strength up to 550 MPa.
Fig. 12. Load vs deflection using LVDTs (100 mm and 50 mm) and NCDT for the specimen configuration 1.5–100-50-70. 549
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Table 4 Comparison of experimental shear load value with Yu et al. [12] using aspect ratio L/B. Specimen configuration TC-B-P-W
Vexp (kN)
1.5-100-50-40 24.525 1.5-100-50-40 R 24.492 1.5-150-100-40 37.235 1.5-180-130-40 33.453 1.5-180-130-40 R 35.270 1.5-100-50-70 17.164 1.5-150-100-70 24.277 1.5-180-130-70 25.819 1.5-100-50-100 5.825 1.5-150-100-100 9.894 1.5-180-130-100 16.402 1.5-180-130-100 R 15.990 2.0-100-50-40 27.715 2.0-100-50-40 R 27.876 2.0-150-100-40 40.830 2.0-180-130-40 43.176 2.0-100-50-70 16.681 2.0-150-100-70 21.407 2.0-180-130-70 32.489 2.0-100-50-100 9.180 2.0-150-100-100 15.635 2.0-180-130-100 24.838 2.5-100-50-40 31.958 2.5-150-100-40 46.385 2.5-180-130-40 48.159 2.5-100-50-70 17.120 2.5-150-100-70 32.122 2.5-180-130-70 32.771 2.5-100-50-100 11.321 2.5-150-100-100 16.498 2.5-180-130-100 28.325 Mean Standard deviation Coefficient of variation
Vy (kN) 50.498 50.498 75.747 90.897 90.897 50.498 75.747 90.897 50.498 75.747 90.897 90.897 48.278 48.278 72.418 86.901 48.278 72.418 86.901 48.278 72.418 86.901 56.432 84.647 101.577 56.432 84.647 101.577 56.432 84.647 101.577
=
0.578 0.578 0.555 0.544 0.544 1.122 1.077 1.058 1.693 1.625 1.595 1.595 0.346 0.346 0.332 0.326 0.684 0.657 0.645 1.039 0.997 0.979 0.264 0.253 0.249 0.532 0.510 0.501 0.813 0.780 0.766
Vy Vcr
Table 5 Comparison of experimental shear load value with Yu et al. [12] using aspect ratio L/P.
Vn = 0.231 λ−0.8 Vy (kN)
Vexp/Vn
Specimen configuration TC-B-P-W
18.086 18.086 28.025 34.173 34.173 10.639 16.489 20.071 7.655 11.866 14.453 14.453 26.068 26.068 40.416 49.211 15.112 23.410 28.509 10.816 16.769 20.418 32.900 49.349 59.219 21.598 33.509 40.788 15.384 23.853 29.042
1.360 1.350 1.330 0.980 1.030 1.610 1.470 1.290 0.760 0.830 1.130 1.110 1.060 1.070 1.010 0.880 1.100 0.910 1.140 0.850 0.930 1.220 0.971 0.940 0.813 0.790 0.960 0.800 0.740 0.690 0.980 1.036 0.227 0.219
1.5-100-50-40 24.525 1.5-100-50-40 R 24.492 1.5-150-100-40 37.235 1.5-180-130-40 33.453 1.5-180-130-40 R 35.270 1.5-100-50-70 17.164 1.5-150-100-70 24.277 1.5-180-130-70 25.819 1.5-100-50-100 5.825 1.5-150-100-100 9.894 1.5-180-130-100 16.402 1.5-180-130-100 R 15.990 2.0-100-50-40 27.715 2.0-100-50-40 R 27.876 2.0-150-100-40 40.830 2.0-180-130-40 43.176 2.0-100-50-70 16.681 2.0-150-100-70 21.407 2.0-180-130-70 32.489 2.0-100-50-100 9.180 2.0-150-100-100 15.635 2.0-180-130-100 24.838 2.5-100-50-40 31.958 2.5-150-100-40 46.385 2.5-180-130-40 48.159 2.5-100-50-70 17.120 2.5-150-100-70 32.122 2.5-180-130-70 32.771 2.5-100-50-100 11.321 2.5-150-100-100 16.498 2.5-180-130-100 28.325 Mean Standard deviation Coefficient of variation
Vexp (kN)
Vy (kN) 25.249 25.249 50.498 65.648 65.648 25.249 50.498 65.648 25.249 50.498 65.648 65.648 24.139 24.139 48.278 62.762 48.278 48.278 62.762 24.139 48.278 62.762 28.216 56.432 73.361 28.216 56.432 73.361 28.216 56.432 73.361
=
0.620 0.620 0.578 0.563 0.563 1.204 1.122 1.093 1.816 1.693 1.649 1.649 0.371 0.371 0.346 0.337 0.684 0.684 0.666 1.114 1.039 1.012 0.283 0.264 0.257 0.570 0.532 0.518 0.872 0.813 0.792
Vy Vcr
Vn = 0.231 λ−0.8 Vy (kN)
Vexp/Vn
8.553 8.553 18.092 24.024 24.024 5.029 10.637 14.125 3.619 7.655 10.165 10.165 12.324 12.324 26.069 34.615 15.112 15.112 20.066 5.114 10.818 14.365 17.884 37.828 50.231 10.214 21.604 28.687 7.272 15.382 20.425
2.867 2.864 2.058 1.392 1.468 3.413 2.282 1.828 1.610 1.292 1.614 1.573 2.249 2.262 1.566 1.247 1.104 1.417 1.619 1.795 1.445 1.729 1.787 1.226 0.959 1.676 1.487 1.142 1.557 1.073 1.387 1.709 0.562 0.329
4. Analysis of resistance and safety factor A reliability analysis was carried out for Eq. (2) to calculate the shear resistance of the clip angle bolted connection. The reliability analysis can be carried out in two ways; (i) calculate the AISI target reliability value for a given resistance factor for LRFD (Load and resistance factor design) and LSD (Limit state design) methods and safety factor for ASD (Allowable strength design) method, or (ii) calculate the resistance and safety factors of a fixed target reliability value by AISI method. The present study was carried out using the second approach. In this reliability study, the resistance factors for the LRFD and LSD methods and the safety factor for the ASD method were calculated for the shear resistance considering the connection type as not listed in Table F1 of chapter F in AISI S100-12 [2]. The target reliability value was taken as 3.5 and 4.0 for LRFD and LSD method respectively according to AISI S100-12 [2]. This approach was previously employed by Yu et al. [12] and Teh and Clements [8] where the resistance and safety factors were back-calculated for AISI target reliability (β0 = 3.5 and 4.0). In the present study, the resistance and safety factor analysis were similarly carried out to achieve the target reliability index (β0) value as per AISI limit. The resistance factor ɸ was calculated using Eq. (3) [Eqn. F1.1-2 of AISI S100-12 [2]] in which VP and PM were taken from Table 6, and all the remaining values were obtained from the chapter F of AISI S100-12 [2].
Fig. 13. Comparison of test results using the geometrical aspect ratios of L/B and L/P in Eq. (1).
= C (MM FM PM ) e
2 VM + VP2+ CP VP2+ VQ2
(3)
Where, Cɸ - calibration coefficient = 1.52 for LRFD method and 1.42 for LSD method; MM -mean value of the material factor = 1.10; FMmean value of fabrication factor = 1.0; VQ - coefficient of variation of 550
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Table 6 Comparison of experimental shear load value with improved design equation. Specimen configuration TC-B-P-W
Vexp (kN)
Vy (kN)
Vexp/Vy
1.5-100-50-40 1.5-100-50-40 R 1.5-150-100-40 1.5-180-130-40 1.5-180-130-40 R 1.5-100-50-70 1.5-150-100-70 1.5-180-130-70 1.5-100-50-100 1.5-150-100-100 1.5-180-130-100 1.5-180-130-100 R 2.0-100-50-40 2.0-100-50-40 R 2.0-150-100-40 2.0-180-130-40 2.0-100-50-70 2.0-150-100-70 2.0-180-130-70 2.0-100-50-100 2.0-150-100-100 2.0-180-130-100 2.5-100-50-40 2.5-150-100-40 2.5-180-130-40 2.5-100-50-70 2.5-150-100-70 2.5-180-130-70 2.5-100-50-100 2.5-150-100-100 2.5-180-130-100 Mean Standard deviation Coefficient of variation
24.525 24.492 37.235 33.453 35.270 17.164 24.277 25.819 5.825 9.894 16.402 15.990 27.715 27.876 40.830 43.176 16.681 21.407 32.489 9.180 15.635 24.838 31.958 46.385 48.159 17.120 32.122 32.771 11.321 16.498 28.325
50.498 50.498 75.747 90.897 90.897 50.498 75.747 90.897 50.498 75.747 90.897 90.897 48.278 48.278 72.418 86.901 48.278 72.418 86.901 48.278 72.418 86.901 56.432 84.647 101.577 56.432 84.647 101.577 56.432 84.647 101.577
0.486 0.485 0.492 0.368 0.388 0.340 0.321 0.284 0.115 0.131 0.180 0.176 0.574 0.577 0.564 0.497 0.346 0.296 0.374 0.190 0.216 0.286 0.566 0.548 0.474 0.303 0.379 0.323 0.201 0.195 0.279
=
Vy Vcr
0.578 0.578 0.555 0.544 0.544 1.122 1.077 1.058 1.693 1.625 1.595 1.595 0.346 0.346 0.332 0.326 0.684 0.657 0.645 1.039 0.997 0.979 0.264 0.253 0.249 0.532 0.510 0.501 0.813 0.780 0.766
Vnsb = 0.222 λ−0.6 Vy (kN)
Vexp/Vnsb
16.208 16.208 24.912 30.255 30.255 10.887 16.736 20.299 8.505 13.076 15.867 15.867 21.082 21.082 32.417 39.328 14.006 21.524 26.116 10.899 16.759 20.331 28.985 44.602 54.037 19.037 29.287 35.523 14.76 22.697 27.534
1.513 1.511 1.495 1.106 1.166 1.577 1.451 1.272 0.685 0.757 1.034 1.008 1.315 1.322 1.260 1.098 1.191 0.995 1.244 0.842 0.933 1.222 1.103 1.040 0.891 0.899 1.097 0.923 0.767 0.727 1.029 1.112 0.247 0.222
Table 7 Resistant factor and safety factors for improved shear Eq. (2). Parameter in the statistical analysis
Parameter values for current test results
Parameter values for combined test results of current test data and test data of Yu et al. [12]
Quantity Mean, PM Standard deviation, σ Co-efficient of variation, VP MM VM FM CP VF VQ βo (LRFD) βo (LSD) ϕ (LRFD) ϕ (LSD) Ω (ASD)
31.00 1.112 0.247 0.222
64.00 1.091 0.212 0.194
1.10 0.10 1.00 1.106 0.15 0.21 3.50 3.00 0.52 0.41 3.06
1.10 0.10 1.00 1.049 0.15 0.21 3.50 3.00 0.55 0.44 2.91
m = n-1 = 30, Vp - coefficient of variation of the ratio between the experimental and predicted shear strength. The predicted resistance and safety factors are presented in Table 7 for Eq. (2). The resistance factors were calculated as 0.52 and 0.41 for LRFD and LSD methods respectively and safety factor as 3.06 for the ASD method. The obtained resistance factor value is lower than the resistance factor value of Yu et al. [12] in both LRFD and LSD methods and the safety factor was higher when compared to the safety factor value of Yu et al. [12] in the ASD method. In addition, the reliability studies for Eq. (2) were also carried out
Fig. 14. Comparison of current test results and test results of Yu et al. [12] with improved Eq. (2).
load effect = 0.21 for LRFD; βo - target reliability index = 3.5 for LRFD method; PM - mean professional factor calculated as the mean value of ratio between the experimental shear resistance and the improved design of shear value of bolted clip angle connection; CP - correction factor = (1 + 1/n) (m/m-2) = 1.106, where, n - number of shear test = 31, 551
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V. Natesan and M. Madhavan
for the combined test data (data from present investigation and Yu et al. [12]). The resistance factors for the combined data are 0.55 and 0.44 for LRFD and LSD methods respectively and the safety factor as 2.74 for the ASD method. This indicates that Eq. (2) is conservative for both current test results and test results of Yu et al. [12] as can be observed from Fig. 14. Therefore, Eq. (2) can be considered for the design of clip angle from 227 MPa to 561 MPa. The design example is given in the Annexure A for clip angle leg connected to the column.
• • •
5. Summary and conclusions
•
A series of experiments on the CFS clip angle bolted connections between CFS beam-to-column were conducted to investigate the behavior in terms of load - deflection and failure modes. The specimens were tested under four-point bending for different configuration such as aspect ratio (L/B) and thickness of the clip angle. An improved design equation for the clip angle connection has been proposed and compared with the experiments. In addition, a detailed reliability analysis was performed. The following conclusions that can be drawn from this work:
•
• The strength and load vs deflection behavior depend largely on the
•
clip angle increases due to the increase in W due to out-of-plane bending effects. The geometrical aspect ratio L/B is more reliable than the L/P when compared with the design equation of literature study. Based on test results, an improved design equation is suggested for the beam-to-column connection using a bolt through clip angle for materials with yield strength up to 561 MPa. The maximum slenderness (λ) limit is shifted to 0.2 (Eq. (2)) from 0.32 (Eq. (1)) to attain the limiting shear resistance value of 0.583 Vy in Eq. (2). The LRFD, LSD resistance factors and the ASD safety factors were calculated for improved shear equation by following the Chapter F in AISI S100-12. The suggested values of resistant and safety factor can be applied for the design of clip angle since the target reliability index value associated CFS connection by considering the connection not listed in Table F1 of Chapter F in AISI S100-12. In the current study, two number of the bolt was used in the clip angle leg connected to the column web. However, the bearing deformation of the bolt hole can be reduced by increasing the number of bolts in clip angle leg connected to the column web for higher depth of clip angle.
Acknowledgments
aspect ratio (L/B) of clip angle and thickness of clip angle. When the aspect ratio (L/B) of the clip angle connected to the column web is less than 0.8, the dominant mode of failure was local buckling. However, clip angles with an aspect ratio (L/B) greater than 0.8 exhibited failure due to distortional buckling. In addition, bearing deformation of the bolt hole was observed in all the test specimens. The stiffness of the clip angle reduces as the aspect ratio (L/B) of the
The first author would like to acknowledge the fellowship from the Ministry of Human Resource Development (MHRD) India. The authors would like to gratefully acknowledge Pennar Engineered Building Systems Ltd., Hyderabad for their help in fabricating the test specimens required for experimental investigation.
Annexure A Design Example Fig. A shows the dimension of the clip angle. The corner radius is assumed to be 3.0 mm. The thickness of the clip angle is 2.0 mm. The yield strength and elastic modulus of clip angle were 350 N/mm2 and 205300 N/mm2 respectively. Calculate the nominal and design shear strength of clip angle.
Fig A. Dimension of the clip angle.
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V. Natesan and M. Madhavan
Solution: L = 75 - 25–2.0–3.0 = 45 mm
k = 2.569 Fcr =
L B
2.202
k 2E 12(1 µ2 )
=
Vy Vcr
=
Vnsb = 0.222
= 2.569
t B
2
=
2.202
45 150
36.4 x 12(1
2
= 36.4
x 205300 0. 32)
2.0 150
2
= 1200.73 N / mm2
0.6 x 350x 150 x 2.0 = 0.42 1200.73 x 150 x 2.0 0.6
Vy = 0.222
0.42
0.6
x 0.6 x 350 x 150 x 2.0 = 23.54 kN
< 0.583 x 0.6 x 350x 150 x 2.0 = 36.73 kN Design shear strength of clip angle.
Vdsb =
x Vnsb for LRFD and LSD methods
Vdsb = 0.55 x 23.54 = 12.95 kN for LRFD method Vdsb = 0.44 x 23.54 = 10.36 kN for LSD method Vdsb = Vnsb/
for ASD method
Vdsb = 23.54/2.91 = 8.09 kN for ASD method
References
Notations
[1] H. Ahamed, M. Mahendran, Bolted Beam-Column Moment Connections between Cold-Formed Steel Members, (ACMSM 21), Victoria University, Melbourne, 2010. [2] AISI S100-12: North American Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC, 2012. [3] ASTM, Standard Test Methods for Tension Testing of Metallic Materials”, ASTM, West Conshohocken, PA, 2013 ASTM E8/E8M-13a. [4] K.F. Chung, R.M. Lawson, Structural performance of shear resisting connections between cold-formed steel sections using web cleats of cold-formed steel strip, Eng. Struct. 22 (2000) 1350–1366. [5] S. Fox, Strength of CFS floor assemblies with clip angle bearing stiffeners, AISI Research Rep PR0vols. 5–6 American Iron and Steel Institute, Washington, DC, 2005. [6] Fastenal Industrial, Construction Supplies, ReVision vol. 9, (2005) A-8 s7028. [7] Y. Huang, B. Young, The art of coupon tests, J. Constr. Steel Res. 96 (2014) 159–174. [8] Lip H. Teh, Drew D.A. Clements, Block shear capacity of bolted connections in coldreduced steel sheets, J. Struct. Eng. 138 (4) (2012) 459–467. [9] J.B.P. Lim, D.A. Nethercot, Ultimate strength of bolted moment-connections between cold-formed steel members, Thin-Walled Struct. 41 (2003) 1019–1039. [10] J.B.P. Lim, D.A. Nethercot, Stiffness prediction for bolted moment-connections between cold-formed steel members, J. Constr. Steel Res. 60 (2004) 85–107. [11] J. Mills, R. LaBoube, Self-drilling screw joints for cold-formed channel portal frames, J. Struct. Eng. 130 (11) (2004) 1799–1806. [12] C. Yu, M. Yousof, M. Mahdavian, W. Zhang, Behavior and design of thin-walled cold-formed steel clip angles subjected to shear load, J. Struct. Eng. 142 (7) (2016) 1–9 04016040. [13] C. Yu, M. Yousof, M. Mahdavian, W. Zhang, Design of cold-formed steel clip angles in compression, J. Struct. Eng. 143 (6) (2017) 1–8 04017030. [14] L. Wang, B. Young, Behavior of cold-formed steel built-up sections with intermediate stiffeners under bending. I: tests and numerical validation”, J. Struct. Eng. 142 (3) (2016) 1–9 04015150. [15] W. Zhang, M. Mahdavian, M. Yousof, C. Yu, Testing and design of cold-formed steel clip angles in tension: pull-over and serviceability, Thin-Walled Struct. 124 (2018) 13–19.
A: length of clip angle leg connected to the column B: depth of clip angle Bnc: number of bolts provided on leg clip angle connected to the column Bnb: number of bolts provided on leg clip angle connected to the beam CP: correction factor Cф: calibration coefficient d: diameter of the bolt E: Young's modulus of the material Fcr: critical buckling stress FM: mean value of fabrication factor Fy: yield strength of the material Fu: ultimate strength material K: buckling coefficient L: flat width of clip angle leg; distance between the center of the bolt line to the bend line MM: mean value of the material factor n: number of shear test p: pitch distance between two bolts along the depth of clip angle PM: mean professional factor calculated as the mean value of the ratio between the experimental shear value to the calculated shear value of improved design equation TC or t: thickness of clip angle Vy: yield shear strength Vcr: critical shear strength W: distance between the center of bolt line and outer to the end of the bend line Vnsb: nominal shear strength of clip angle by improved design equation Vp: coefficient of variation of the ratio between the experimental shear value to the calculated shear value of improved shear equation Vn: nominal shear strength of clip angle of Yu et al. [12] method VQ: coefficient of variation of load effect ɸ: resistance factor λ: slenderness ratio β0: target reliability index Ω: safety factor σ: standard deviation of the ratio between the experimental shear resistance to the calculated shear value of nominal shear equation
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