Structural Strength of Lapped Cold-Formed Steel Z-Shaped Purlin Connections with Vertical Slotted Holes

Transcription

1 Missouri University of Science and Technology Scholars' Mine International Specialty Conference on Cold- Formed Steel Structures (2014) - 22nd International Specialty Conference on Cold-Formed Steel Structures Nov 6th - Structural Strength of Lapped Cold-Formed Steel Z-Shaped Purlin Connections with Vertical Slotted Holes J. Liu L. Xu S. Fox Follow this and additional works at: Part of the Structural Engineering Commons Recommended Citation Liu, J.; Xu, L.; and Fox, S., "Structural Strength of Lapped Cold-Formed Steel Z-Shaped Purlin Connections with Vertical Slotted Holes" (2014). International Specialty Conference on Cold-Formed Steel Structures This Article - Conference proceedings is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in International Specialty Conference on Cold-Formed Steel Structures by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu.

2 Twenty-Second International Specialty Conference on Cold-Formed Steel Structures St. Louis, Missouri, USA, November 5 & 6, 2014 Structural Strength of Lapped Cold-Formed Steel Z-shaped Purlin Connections with Vertical Slotted Holes J. Liu 1,L. Xu 2 and S. Fox 3 Abstract: Lapped joints of cold-formed steel (CFS) Z-shaped purlins are extensively used in metal building roof systems. The research that has been carried out so far for these lapped connections is primarily focused on connections with round holes. However, the lapped connections with vertical slotted holes are extensively used in current construction practice to simplify the erection of continuous Z-shaped roof purlins. There are no design guidelines or recommendations available for CFS Z-purlin lapped connections with vertical slotted holes. Presented in this paper are the results of an experimental study on the structural strength behaviour of lapped CFS Z-shaped purlin connections with vertical slotted holes. A total of 42 flexural tests were performed on lapped CFS Z- shaped purlins with vertical slotted holes in different lap lengths, purlin depths, thicknesses and spans. The flexural strength and deflection of each specimen were measured. The characteristics of moment resistance were computed. The test results indicate that the characteristics of moment resistance in the slotted connections are dependent on the ratio of lap length to purlin depth and ratio of purlin depth to purlin thickness. Based on the results, design recommendations for evaluating the moment resistance of lapped slotted connections are proposed. 1. Introduction Cold-formed steel (CFS) Z-shaped purlins have been extensively used as a primary component in metal roof systems for low-rise industrial and commercial 1 Research assistant, the Canadian Cold-Formed Steel Research Group, University of Waterloo, Canada, ( j238liu@uwaterloo.ca) 2 Corresponding author, Professor, the Department of Civil and Environmental Engineering, University of Waterloo, Canada, ( lxu@uwaterloo.ca) 3 General Manager, the Canadian Sheet Steel Building Institute, Canada 697

3 698 buildings around the world. Lapped joints with bolted connections are one of the most popular design solutions for providing the continuity of purlins in multispan roof systems. The long-standing design practice for CFS Z-purlins focused primarily on the behaviour of individual members. The strength and stiffness of the lapped section is often assumed to be double that of a single section. However, this assumption could lead to unsafe design because it neglects or oversimplifies the effects of the connections. In recent years, the structural behaviour of lapped Z-purlins with bolted connections has been extensively investigated by the work of Ho and Chung (Ho and Chung 2004, Chung and Ho 2005). The semi-continuity of lapped purlins was shown to depend on the stress level, the connection configuration, and on the lap length-to-section depth ratio. It was also found that the failure mode of such purlins is governed by the combined bending and shear at the single sections at the end of the lapped connection. Some recent tests and numerical analysis also confirmed that the critical section is at the end of the lap section of the connection (Zhang and Tong 2008, Dan and Viorel 2010, Pham, Davis and Emmett 2014). However, the research that has been carried out so far is primarily focused on lapped purlins with unequal top and bottom flange widths, and connections with round holes. In current construction practice vertical slotted holes are extensively used in this connection. The extra erection tolerance at the connections allows two identical purlins with the same top and bottom flange width to nest together. It simplifies the fabrication, provides more effective stacking to lower the transportation and storage cost, and also expedites the erection of continuous Z-shaped roof purlins. However, there are no explicit design guidelines or recommendations available for CFS Z-purlin lapped connections with vertical slotted holes. Presented in this paper are the results of an experimental study on the structural strength of lapped CFS Z-shaped purlins with vertical slotted connections. Based on the results, design recommendations for evaluating the moment resistance of lapped slotted connections are proposed. 2. Experiments on Lapped Z-section with Vertical Slotted Holes 2.1. Test Program Figure 1 demonstrates the general arrangement of lapped Z-shaped purlins for a multi-span system. The simplified analysis method is used for testing lapped purlins under one point load instead of carrying out full-scale tests on multi-span purlin systems.

4 699 Figure 1: Multi-span CFS Z-shaped Purlin System (Detail 1: Courtesy of Metal Roofing Industries PTY Ltd.) A total of 42 one-point load tests were performed for lapped Z-shaped purlins with vertical slotted holes for three different purlin depths and thicknesses. Purlins with section depths of 8 inch (203mm) and 10 inch (254mm) were tested for 10 gauge (0.135 inch or 3.429mm), 13 gauge (0.090 inch or 2.286mm) and 16 gauge (0.060 inch or 1.524mm) thicknesses with lap lengths of 34 inch (0.864m) and 60 inch (1.524m). The 12 inch (305mm) purlins were tested for 10 gauge (0.135 inch or 3.429mm), 12 gauge (0.105 inch or 2.667mm) and 14 gauge (0.075 inch or 1.905mm) thicknesses with lap lengths of 34 inch (0.864m), 48 inch (1.219m) and 60 inch (1.524m). For each section depth a specified span of specimen was used, i.e. 10 ft (3.048m) for 8 inch (203mm) purlins, 15 ft (4.572m) for 10 inch (254mm) purlins and 20 ft (6.096m) for 12 inch (305mm) purlins Mechanical Properties and Section Properties Mechanical properties of CFS Z-shaped purlins were determined based on the standard tensile coupon tests as per ASTM standard E8 (ASTM, 2011). All coupons were cut from the coils used for making the test specimens and the galvanized coating was removed prior to the tensile test. Section properties were calculated based on the AISI S100 North American Specification for the Design of Cold-Formed Steel Structural Members (AISI 2012).

5 Connection Configuration and Bolt Holes A common connection configuration for lapped purlins in the North American metal building industry was chosen and detailed in Figure 2. Six bolts connected the webs of lapped Z-shaped purlins, where the four outer bolts were used to resist the flexural bending and shear whereas the two inner bolts at the centerline of the lap were used to connect the web cleat of the loading plate to resist lateral loads. The web cleat at the loading plate simulated the connection over the rafter as shown in Detail 1 of Figure 1. Vertical slotted holes with dimensions of 9/16 inch (14.3mm) x 7/8 inch (22.2mm) were used in the lapped section for connecting the webs of Z-sections. Standard holes with diameters of 9/16 inch (14.3mm) were used for bolts at end reaction supports and internal braces. Figure 2: Test Specimen Assembles Details 2.4. Specimen Assemblies and Test Setup Each test specimen consisted of two pairs of identical lapped CFS Z-sections with top flanges facing inwards and a 1/2 inch (12.7mm) clearance between them. In order to prevent the latreral-torsional bucking and instability, a lateral restraint system similar to those used Ho and Chung (Ho and Chung, 2004) was adopted as shown in View A-A of Figure 2. The lateral restraint system consisted of two bracing plates connected at both top and bottom flanges, and an internal brace connecting the webs of the two purlins. The lateral restraint system was located at intervals of one-sixth of the span length to prevent tipping and lateral defection of either flange in either direction at the intermediate braces. At the end supports, web cleats were also used to prevent the lateral deformation and twisting during the tests. All specimens were simply supported at the ends and loaded with a single point load applied at mid-span with a constant rate of displacement of 0.24 inch (6.1mm) per minute until failure was detected. Mid-

6 701 span vertical deflections of the specimens were recorded using linear motion transducers (LMT) Test Results and Data Analysis The failure location of all tests was just outside the end of lapped connections caused by combined shear and bending. The top flange buckling was found to always initiate the failure as shown in Figure 3. The top flange was subjected to compression stress due to the bending. The applied load dropped rapidly once the top flange buckled, then the failure extended to webs. The shear buckling of the web section was also observed just outside the end of the lapped connections. Significant cross-section distortion of Z-sections occurred at the end of lap at large deformation. The failure mode is consistent with the test results for standard holes carried out by Ho and Chung (2004). In the research conducted by Dubina and Ungureanu (2010), it was suggested that the web crippling should be checked instead of the shear buckling of the web at the failure of the section. However, there was no web crippling observed at the failure of the section for any test, only shear buckling. After examining the dissembled tested specimens, no bearing deformation was found at the bolt holes. Figure 3: Typical Failure Mode at the End of Lapped Connection 3.1. Flexural Strength of Lapped Purlins with Vertical Slotted Holes For lapped purlins with slotted holes, the tested ultimate load (P t ) was determined for each specimen. The tested maximum flexural strength (M t ) was evaluated at mid-span of the test specimen and compared to the calculated nominal section strength (M n ) of non-lapped purlins. According to the AISI S100 (AISI 2012), the nominal section strength (M n ) was calculated using equation (1) on the basis of initiation of yielding of the effective section. M n = S e F y (Eq. 1)

7 702 Where F y is the yield stress of the steel and S e is the elastic section modulus of the effective section calculated relative to extreme compression fiber at F y. It should be noted that all calculations were based on a single purlin. Measured mechanical properties obtained from standard coupon tests were used in the calculation of the flexural strength (M n ) of all purlins. All data is summarized in Table 1. For all calculations, the lap length (L p ) of the connection was taken as the distance between the center of the outer bolts of the lapped section instead of the actual edge to edge distance. It can be observed from Table 1 that the moment resistance ratio (M t /M n ) lies between 0.77 and 1.69 while the lap length to section depth ratio (L P /D) ranges from 2.67 to The moment resistance ratios are directly related to the lap length to section depth ratios for lapped purlins with vertical slotted holes. The findings are similar to the test of lapped purlins with standard holes carried out by Ho and Chung (2004). Ho and Chung suggested that a unity moment resistance ratio may be achieved with a minimum lap length to section depth ratio of 2.0 for lapped purlins with standard holes. For the reason of comparison, the moment resistance ratios (M t /M n ) vs. lap length to section depth ratios (L P /D) were plotted as shown in Figure 4. This figure shows the unity moment resistance ratio can be achieved with a minimum lap length to section depth ratio of 3.0 for lapped purlins with vertical slotted holes. This result confirmed the design criteria given in AISI S100 (AISI 2012). Moment Resistance Ratio (Mt / Mn) ga 10 ga 12 ga 13 ga 14 ga Lap Length to Section Depth Ratio (Lp/D) Figure 4: Moment Resistance Ratio vs. Lap Length to Section Depth Ratio Figure 4 also shows that the moment resistance ratios vary for the same lap length to section depth ratio, and the moment resistance ratios of lighter gauge

8 703 purlins are always lower than that of thicker gauge purlins. Therefore, the section depth to web thickness ratios (D/t) were compared to the moment resistance ratios (M t /M n ), and the results were plotted in Figure 5. Results indicate that the lowest M t /M n ratios occurred for the lapped purlins with large D/t ratios even when the lap length exceeded the three times of the section depth. As shown in Figure 4, the M t /M n ratios decrease as the D/t ratios increase. The best trend line of the test data reaches the M t /M n ratio at 1.0 when the D/t ratio approximately equals to 155. It suggests that the maximum section depth to thickness ratios (D/t) of 155 should be met in order to achieve the unity moment resistance ratio for lapped purlins with vertical slotted holes. Moment Resistance Ratio (Mt / Mn) Lp / D = 2.67 Lp / D = 3.20 Lp / D = 3.83 Lp / D = 4.00 Lp / D = 4.83 Lp / D = 5.80 Lp / D = Web Slenderness (D/t) Figure 5: Moment Resistance Ratio vs. Section Depth to Web Thickness Ratio 3.2. Force Distributions at the Lapped Connection All moment resistances used for the comparison above were the maximum moment evaluated at mid-span of the specimens. However, all section failures were observed at the end of the lapped sections. A static analysis was performed to determine all the internal forces at the lap connections under applied loads. The analysis method was proposed by Chung and Hoon for lapped purlins with standard holes and well explained in their paper (Chung and Ho 2005). Similar findings were also discovered from these tests on the lapped purlins with vertical slotted holes. 1. The critical section is found at the end of lap, which is the cross-section of the purlin containing the vertical slotted holes.

9 The moment just outside of the critical section at the end of lap is always found to be the largest moment along the individual length of purlin. The moment just inside of the critical section at the end of lap is slightly less than that just outside of the critical section. The moment at the mid-span of the test specimen, which is distributed on the individual piece, is found to be relatively less than the moment at the critical section. 3. The shear force just inside of the critical section is considerably larger than the shear force just outside of the critical section for short lap length. When the lap length increases to 4.8 times of the section depth, the shear forces at these two locations become the same. The maximum shear force is found at the mid-span of the test specimen. Therefore, the combined bending and shear should be checked near the critical section at the end of lap. Theoretically, the shear buckling strength of the section at the mid-span of the test specimen should be compared with the maximum shear force. However, the webs of two nested purlins are bolted together and connected to the web cleats of the loading plate at this location. When one web intends to buckle, the other web and the web cleat may act against it and prevent it from buckling. Furthermore, the corresponding moment at the mid-span is relatively small. Therefore, instead of checking the combined bending and shear, only the shear yielding at the cross-section with vertical slotted holes at the midspan of the specimen should be checked, as well as the bearing strength at the vertical slotted holes Design Checks for Shear, Bearing and Combined Bending and Shear The shear strength of a CFS Z-section is governed by either yielding or buckling calculated according to clause C3.2.1 of AISI S100 (AISI 2012). For shear yielding, the nominal shear strength (V ny ) is determined by V ny = 0.60F y ht (Eq. 2) where h is the net section depth of flat portion of web for the section with web holes, t is web thickness, and F y is the design yield stress. For shear buckling strength, the nominal shear strength (V n ) can be evaluated as: V n = A w F v (Eq. 3)

10 705 Where A w = ht, the gross area of web element, h is the depth of flat portion of web, t is web thickness, and F v is the nominal shear stress. For Ek v F y < h t 1.51 Ek v F y, F v = 0.60 Ek v F y (h t) (Eq. 4) π For h t > 1.51 Ek v F y, F v = 2 Ek v 12(1 μ 2 )(h t) 2 (Eq. 5) Where μ = 0.3 is the Poisson s ratio, k v is the shear buckling coefficient for webs with restraint elements. k v = (a/h) 2 (Eq. 6) Where a is the clear distance between transverse stiffeners of reinforced web elements which is conservatively taken as the distance from the centerline of the web cleat at loading plate to the centerline of the first adjacent internal brace. The bearing strength of the CFS Z-section web at bolt holes was calculated by using the method indicated in the clause E3.3.1 of AISI S100 (AISI 2012), as follows. P n = Cm f dtf u (Eq. 7) where d is the nominal bolt diameter, t is the web thickness, F u is the tensile strength, C is the bearing factor which is taken as 3.0 since d t < 10 for all specimens, m f is the modification factor for type of bearing connection which is conservatively taken as 1.00 since washers under both bolt head and nut are used for all specimens. As previously discussed, the calculated shear yielding strength (V ny ) at the crosssection with vertical slotted holes and the bearing strength (P n ) at the bolts holes were both compared to the maximum shear force V max at mid-span from the tests, and the results were summarized in Table 2. The results show that the maximum V max /V ny ratio is 0.44, while the maximum V max /P n ratio is It can be concluded that the cross-section at mid-span is not critical in term of shear. This agrees with the test observations where the shear failures never occur at the midspan and the bearing deformation was not observed at bolt holes. For checking the critical section subjected to combined bending and shear, the following interaction equation from clause C3.3.2 of AISI S100 (AISI 2012) was used.

11 706 M 2 + V (Eq. 8) M n V n Where M is the required flexural strength, M n is the nominal flexural strength, V is the required shear force, and V n is the nominal shear strength. It should be noted that the nominal flexural strength (M n ) is based on the local buckling strength (M nl ) calculated based on equation (Eq. 1). The nominal shear strength (V n ) at the critical section is always governed by the shear buckling strength for all test specimens; therefore, the gross area of the web section was used to determine V n through equations (Eq. 2) to (Eq. 6). M and V are the critical pair of moment, M t, and shear, V t, obtained from the tests near the critical section. The governing pair of (M t /M n ) and (V t /V n ) ratios are summarized in Table 2, and plotted in Figure 6 together with the interaction equation (Eq. 8). It can be seen from Figure 6 that most of the test results are located below the interaction curve (Eq. 8). Most of the (V t /V n ) ratios are smaller than 0.6 whereas the (M t /M n ) ratios range from 0.6 to 1, which indicates that shear has less effect than bending. When two identical CFS Z-shaped purlins lap together, the purlins cannot nest properly as shown in Figure 7(a). There is always a gap between the two Z- sections. The vertical slotted holes made at the same location on each purlin are offset and provide the extra tolerance at the connections compared to the standard holes. Once the loading applies, the loads are transferred through the bolts at the connections and the two top flanges. It pulls the upper purlin down until the two vertical slotted holes align each other and bear together as shown in Figure 7(b). Two purlins are forced to fit each other, and the cross-section distortions are initiated. The loading also causes the top flange of the upper purlin to immediately bear down to the top flange of the lower purlin. The bearing stress acting on the top flange of lower purlin is concentrated at the edge of the lapped section due to the connection rotation between two purlins. It initiates the premature buckling of the top flange, and induces the shear buckling of the web of the lower purlins at the end of lap. Thus, the capacities of the lapped Z-shaped purlins are reduced due to the presence of vertical slotted holes at the connections. This is consistent with the observations that all the failures occurred at the lower purlins just outside the end of the lapped connection. Hence, new interaction equations are proposed for checking the CFSZ-shaped purlins with vertical slotted connections subjected to combined bending and shear.

12 707 1 (Eq. 8) (Eq. 9) 0.8 M t /M n Z Z Z Z Z Z Z Z Z Z V t /V n Figure 6: Interaction between (M t /M n ) and (V t /V n ) a) Unloaded shape b) Loaded shape Figure 7:Cross-Section Distortion of Lapped Section 3.4. Proposed Interaction Equation for Checking Combined Bending and Shear An interaction equation is proposed to evaluate member strength at the critical location based on the nominal section strength and given below: M 0.907M n 2 + V V n (Eq. 9) The interaction equation is plotted in Figure 6 and based on the best-fit curve, which fits all the test data. The maximum design load (P design ) of the lapped purlins was calculated by using the proposed equation compared to the

13 708 maximum applied load ( P t ) obtained from the tests. The results were summarized in Table 2. The average P t /P design ratio is 1.00 with a coefficient of variance of The results indicate that Equation (9) provides an accurate and practical design solution for checking CFS Z-shaped purlins with vertical slotted connections subjected to combined bending and shear Conclusion 42 flexural tests were performed on lapped CFS Z-shaped purlins with vertical slotted connections. The test results indicate that the characteristics of moment resistances in the slotted connections are dependent on the ratios of lap length to purlin depth, and ratios of purlin depth to purlin web thickness. In order to achieve the full flexural strength of continuous purlins, the lap length of connection should be at least three times of the purlin depth, and maximum purlin depth to purlin web thickness ratios should be limited to 155. The section failures of all tests occurred at the end of lapped connections through combined shear and bending. The lapped sections are not critical in terms of shear and combined shear and bending due to the mutual restraint of the connected parts and the restraint of the rafter connection. The shear yielding at the cross-section with vertical slotted holes and the bearing deformation at the bolts holes never occurred. The moment capacities of the lapped Z-shaped purlins are reduced at the end of the lap due to the initial cross-section distortion and the concentrated bearing stress at the edge of slotted connection. The traditional interaction equation for checking the section subjected to combined bending and shear may not be applicable and may be conservative for lapped connection with slotted holes. Therefore, a new interaction equation is proposed. The characteristics of flexural stiffness for CFS Z-shaped lapped purlins with slotted holes were also studied and will be presented in detail in a complementary paper.

14 709 Appendix - References AISI. (2012). North American Specification for the Design of Cold-Formed Steel Structural Members, AISI S Washington, D.C.: American Iron and Steel Institute. ASTM.(2011). Standard Test Methods for Tension Testing of Metallic Materials, ASTM E West Conshohocken, P.A.: American Society for Testing and Materials. Chung, K. F., &Ho, H. C. (2005). Analysis and design of lapped connections between cold-formed steel Z sections. Thin-Walled Structures, 43(7), Dubina, D., & Ungureanu, V. (2010). Behaviour of multi-span cold-formed Z- purlins with bolted lapped connections. Thin-Walled Structures, 48(10-11), Ho, H. C., & Chung, K. F. (2004). Experimental investigation into the structural behaviour of lapped connections between cold-formed steel Z sections. Thin-Walled Structures, 42(7), Pham, C. H., Davis, A. F., & Emmett, B. R. (2014). Numerical investigation of cold-formed lapped Z purlins under combined bending and shear. Journal of Constructional Steel Research, 95, Zhang, L., & Tong, G. (2008). Moment resistance and flexural rigidity of lapped connections in multi-span cold-formed Z purlin systems. Thin-Walled Structures, 46(5),

15 710 Table 1: Test Strength Result Summary P t Test * L p /D D/t (kip) (kip in) (kip in) M t /M n 08Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Mean 1.15 Metric Conversion: 1 kip = kn,1 kip in = 0.112kN m Std. Dev 0.22 COV 0.19 * Test destination: For example, 08Z designates 8 inch (203mm) Z-shaped purlins, 13 gauge (0.09 inch or 2.286mm) thickness, with 34 inch (0.864m) edge to edge lap length, test #2. M t M n

16 711 Table 2: Summary of Design Checks and Calculated Design Load Test * V max V 3 M t V t P t (Eq. 9) V ny P n M n V n P design 08Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Mean 1.00 Std. Dev COV * Test destination: For example, 08Z designates 8 inch (203mm) Z-shaped purlins, 13 gauge (0.09 inch or 2.286mm) thickness, with 34 inch (0.864m) edge to edge lap length, test #2.