Advances in Steel Structures - part 27 doc

240 A.T. Wheeler et al. ferent end plate thicknesses (12 mm, 16 mm and 20 mm) were all within 3 percent, an average stress- strain relationship was used for all plate thicknesses. This average stress-strain curve was based on a yield stress of 351 MPa and an ultimate tensile strength of 492 MPa. Bolts In many cases, the ultimate strength of the connection was limited by tensile fracture of the bolts rather than end plate or section failure. Therefore, to simulate the connection behaviour accurately, each bolt was modelled as a separate entity using the nominal cross-sectional areas and measured material properties. Reflecting the experimental behaviour of a bolt in tension, in the finite element analyses the bolts were deemed to fracture when the strain reached 3 percent (Wheeler, 1998). The interaction (i.e. contact and separation) between the bolt and the end plate was modelled using the INTER4 cubic interface elements (HKS, 1995). These assemblages were positioned between the underside of the bolt head and the end plate, and also between the bolt hole in the end plate and the bolt shank. The interface elements between the underside of the bolt head and the end plate were im- plemented as a "rough" interface to prevent slipping between the surfaces. The assemblages of inter- face elements between the bolt shank and the bolt hole modelled a frictionless interface to prevent the "penetration" of the bolt into the end plate at high rotations. Weld The connection between the tubular section and the end plate consisted of a combination butt-fillet weld. The weld was modelled as an individual component using eight noded linear brick elements (C3D8) and six noded linear triangular prism elements (C3D6) to encompass the butt and fillet por- tions, respectively. The specified nominal material properties of the weld metal (fy = 428 MPa, fu = 528 MPa) exceed those of the tubular section and the end plate. Initial Stresses and End Plate Deformations The cold-formed tubular sections used in the end plate connections contain residual stresses as a re- sult of the manufacturing process. Welding the end plate to the tubular section induces residual stresses and bowing deformations in the end plate. Bolt pre-tensioning introduces further initial stresses in the connection. These heat induced distortions and the consequent initial stresses in the end plate may have a significant effect on the stiffness of the connection as the subsequent bolt pre- tensioning induces stresses into the end plate through the clamping action. In the finite element analyses, the heat-induced deformations of the end plate were modelled by sim- ply displacing the initial geometry as shown in Figure 4. The internal residual stress state resulting from welding was not modelled. An initial transverse displacement of 80, the magnitude of which depends on the end plate thickness and is based on measurements of test specimens, is applied to all four edges of the end plate with a linear variation to zero initial displacement at the flanges and webs. Although initial end plate deformations were incorporated in the finite element model, verification studies have shown that the initial deformations have only a minor effect on the overall moment- rotation response for the eight-bolt connections (Wheeler, 1998). End Plate Thickness tp (ram) 12 16 20 Initial Deformation 80 (mm) 2.0 1.0 0.75 Figure 4: Imposed initial end plate deformations Finite Element Modelling of Bolted Moment End Plate Connections 241 Loading To model the complete behaviour of the connection, the loading was carried out in five steps as shown in Figure 5. In the first two steps, displacements are applied to close the nominal gap between the solid elements and the appropriate rigid surfaces. In the third step, a concentrated load was ap- plied to the end of the bolts to produce the pre-tension of 145 kN as specified in AS4100 for a fric- tion grip connection employing high strength bolts (SA, 1998). In the fourth step, the bolts ends were fixed in their pre-tensioned position and equilibrium re-established. In the fifth and final step, the rigid end cap was rotated, thus applying a moment to the beam section and the connection. Initial State Step 1 Close bolt rigid surfaces Step 2 Close end plate rigid surfaces Step 3 Pre-tension bolts (load P) IF Step 4 Fix bolt ends in pre-tensioned position Rotate end cap Figure 5: Schematic representation of loading procedure SIMULATION OF CONNECTIONS The experimental and numerical results for the eight-bolt connections are given in Table 1. Graphical comparisons for all tests are presented in Wheeler (1998). When comparing the results, it should be noted that in the experimental study the tests were terminated when either a punching shear failure had occurred (Wheeler et al., 1999), when the load cells indicated a drop in bolt load, or when the section formed a plastic hinge. In the numerical analysis, the ultimate load was deemed to occur when the bolts reached their predefined fracture strain (3 percent) or when the section failed plasti- cally. Consequently, punching shear failure was not considered in the finite element model. The agreement between the experimental (Mcu) and numerical (ABAQUS) (mab) ultimate moments is excellent as indicated in Table 1, with the mean and standard deviation of the experimental-to- numerical ratio (mcu/Mab) being 0.96 and 0.07, respectively. Furthermore, if the tests that failed as a result of punching shear are ignored in the comparisons (Tests 2, 5, 8, 9, and 10), the mean and stan- dard deviation are improved to 1.01 and 0.03, respectively. The comparison of experimental and nu- merical overall moment-rotation responses was generally good for the RHS (see Figures 6 and 7), but only fair for the SHS. The numerical predictions of the theoretical model (Mth) which considers yield line analysis, the stub tee analogy, beam section plasticity and punching shear (Wheeler et al., 1999), are also given in Table 1. With a mean theoretical-to-experimental ratio (Mcu/Mth) of 1.03 and a stan- dard deviation of 0.05, the theoretical model is evidently very effective (Wheeler et al., 1999). 242 A.T. Wheeler et al. TABLE 1 COMPARISON OF EXPERIMENTAL, NUMERICAL AND THEORETICAL ULTIMATE MOMENTS Test 1 (SHS) 2 (RHS) 3 (SHS) 4 (SHS) 5 (RHS) 6 (RHS) 7 (SHS) 8 (SHS) 9 (RHS) 10 (RHS) Test Mcu (kNm) 116.0 (S) 124.5 (P) 93.9 (B) 116.0 (S) 92.7 (P) 136.7 (S) 113.2 (B) 97.6 (P) 133.0 (P) 119.3 (P) ABAQUS Mab (kNm) 110.8 131.5 95.7 111.9 114.7 137.4 115.1 105.6 136.0 133.3 (P) = Punching shear failure (S) = Section capacity failure (B) = Failure by yield line formation and bolt fracture Theoretical Mth (~qrn) 116.3 (S) 116.8 (P) 92.8 (B) 116.3 (S) 87.6 (P) 128.4 (S) 116.3 (S) 104.9 (B) 123.2 (P) 110.0 (P) Mean S.D. Mcu/Mab 1.05 0.95 0.98 1.04 0.81 0.99 0.98 0.92 0.98 0.89 0.96 0.07 MeulMth 1.00 1.07 1.01 1.00 1.06 1.06 0.97 0.93 1.08 1.08 1.03 0.05 Figure 6: Effect of variation in end plate thickness for RHS connections The numerical analyses demonstrate that the flexibility and strength of the connection depends on the flexibility of the end plate. This flexibility is a function of the thickness of the end plate and the posi- tion of the bolts relative to the section perimeter. The effect of varying the end plate thickness is shown in Figure 6, in which the connection moment- rotation behaviour is presented for Tests 5, 2 and 6 which comprise end plate thicknesses of 12 mm, 16 mm and 20 mm, respectively. These three tests differ only in end plate thickness. A significant increase in the overall stiffness and strength is observed with an increase in the end plate thickness. In both the physical test and the ABAQUS model, the 20 mm end plate connection (Test 6) failed through the attainment of full plasticity in the beam section rather than the failure occurring in the connection itself. Conversely, the 16 mm and 12 mm end plate connections (Tests 2 and 5) failed through punching shear in the physical experiments, but are predicted to fail as a result of the bolts attaining their assumed fracture strain of 3 percent in the ABAQUS model. The ramifications of the inability of the ABAQUS model to consider the punching shear failure mode are particularly appar- ent for Test 5 (12 mm end plate) as indicated in Figure 6. Finite Element Modelling of Bolted Moment End Plate Connections 243 Figure 7: Effect of bolt position on moment-rotation behaviour for RHS connections The stiffening effect of the position of the bolts relative to the section perimeter is illustrated in Fig- ure 7. The three simulations presented in this figure have a constant end plate thickness of 16 mm, with the distance to the perimeter of the section (So) being varied. Increasing the value of So reduces the stiffness of the end plate, thus resulting in a more flexible moment-rotation response and lower ultimate strength (compare Tests 10 and 2 for which So = 45 mm and 35 mm, respectively). As can be seen in Figures 6 and 7, the finite element analysis is reasonably effective in simulating the experimental moment-rotation response for the RHS connections. Generally the computed response is marginally stiffer than the experimentally measured one. However, the SHS connections (Tests 1, 3, 4, 7 and 8) are generally significantly stiffer in the finite element simulations than in the tests (Wheeler, 1998). It is believed that the additional stiffness in the SHS connections is associated with inadequate modelling of the bolts and their interaction with the end plate. The bolts in the SHS con- nection are positioned such that they restrain the comers of the section (i.e. the line of restraint be- tween adjacent bolts passes through the comer of the section). Conversely, the positioning of the bolts in the RHS connections offers less restraint to the comers of the section, thus enabling a greater degree of flexibility within the end plate. As can be seen in Figure 8, the yield mechanisms in the end plates vary depending on the shape of the beam section (SHS or RHS), which defines the positions of the bolts. For both the SHS and RHS, the pitch of the four bolts above and below the axis of bending is approximately constant. The dis- tance between the bolts adjacent to the section webs varies according to the depth of the section. This distance was generally either 90 mm for the SHS or 170 mm for the RHS. The close proximity of the bolts in the SHS models causes high concentrations of stresses to form around the perimeter of the section and between the tensile bolts (Figure 8a). On the other hand, the additional spacing between the bolts in the RHS allows the formation of a horizontal yielded zone in the end plate at mid-depth (Figure 8b). These areas of high stress concentration observed in the finite element results are con- sistent with the yield line patterns observed experimentally and determined theoretically (Wheeler, 1998). CONCLUSIONS A numerical study of the behaviour of tubular bolted moment end plate connections has been de- scribed in this paper. The analyses were conducted using the commercially available finite element package ABAQUS. Brick elements were chosen to form the basis of the models used for this study as 244 A.T. Wheeler et al. Figure 8: Von Mises stresses (MPa) illustrating end plate yield line patterns this type of element is easily adapted to model the interfaces between the connecting surface and the end plates and bolts. Overall, the models simulated the behaviour of the eight-bolt connections well, with the mean and standard deviation of the ratio of the experimental and numerical ultimate moments being 0.96 and 0.07. Comparisons of the experimental and numerical moment-rotation responses of the connections were excellent for the eight-bolt connections comprising the RHS. The eight-bolt connections utilis- ing the SHS were generally predicted to be stiffer than the corresponding test results. Although not fully investigated in this paper due to time constraints, it is thought that this additional stiffness may be due to the inadequate modelling of the bolts. Although the predicted ultimate loads generally corresponded well with the experimental results, the numerical analyses did not specifically model the effects of punching shear (although the effects of shear yielding were of course modelled in the nonlinear material behaviour). The deformation and yielding patterns developed in the models correlated well with the experimental results and the yield line analyses developed in the corresponding theoretical models (Wheeler et al., 1999). REFERENCES AISC (1997). Hollow Structural Sections Connections Manual, American Institute of Steel Construction, Inc. Bursi, O. S. and Jaspart, J. P. (1997a). Benchmarks for Finite Element Modelling of Bolted Steel Connections. Journal of Constructional Steel Research, Elsevier, 43:1, 17-42. Bursi, O. S. and Jaspart, J. P. (1997b). Calibration of a Finite Element Model for Isolated Bolted End Plate Steel Connec- tions. Journal of Constructional Steel Research, Elsevier, 44:3, 225-262. HKS (1995). ABAQUS/Standard Users Manual, Version 5.5, Hibbitt, Karlsson and Sorensen, Inc. PDA Engineering (1994). PATRAN 3, PDA Engineering, Costa Mesa, California. SA (1998). AS 4100-1998: Steel Structures, Standards Australia, Sydney. Syam, A. A. and Chapman, B. G., (1996). Design of Structural Steel Hollow Section Connections. Volume 1: Design Models, 1 st Edition, Australian Institute of Steel Construction, Sydney. Wheeler, A. T. (1998). The Behaviour of Bolted Moment End Plate Connections in Rectangular Hollow Sections Sub- jected to Flexure. PhD Thesis, Department of Civil Engineering, The University of Sydney. Wheeler, A. T., Clarke, M.J. and Hancock, G.J. (1995). Tests of Bolted Flange Plate Connections Joining Square and Rectangular Hollow Sections. Proceedings, Fourth Pacific Structural Steel Conference, Singapore, 97-104. Wheeler A. T., Clarke M. J. and Hancock G. J. (1999). Analytical Model for Eight-Bolt Rectangular Hollow Section Bolted Moment End Plate Connections. Proceedings, Second International Conference on Advances in Steel Structures, Hong Kong, December. FINITE ELEMENT MODELLING OF DOUBLE BOLTED CONNECTIONS BETWEEN COLD-FORMED STEEL STRIPS UNDER STATIC SHEAR LOADING K.F.Chung 1 and K.H.Ip 2 t Department of Civil and Structural Engineering; 2 Department of Mechanical Engineering, the Hong Kong Polytechnic University, Hung Horn, Hong Kong. ABSTRACT In a complementary paper 1, it was reported that a finite element model with three- dimensional solid elements was successfully established to investigate the bearing failure of bolted connections between cold-formed steel strips and hot rolled steel plates under static shear loading. Non-linear material geometrical and contact analysis was carried out to predict the load-extension curves of bolted connections with cold-formed steel strips of high yield strength and low ductility. The predicted load-extension curves were found to follow closely the measured load-extension curves, and both the maximum load carrying capacities and the initial extensional stiffness were satisfactorily predicted In this paper, the finite element model is further extended to examine the structural behaviour of bolted connections with two bolts, or double bolted connections between cold-formed steel strips and hot rolled steel plates under static shear loading. The effects of strength degradation, hole clearance and bolt spacing on the load carrying capacity of double bolted connections are discussed. Comparison on the predicted load carrying capacity of the finite element model with the bearing resistances given by the design rules from both BS5950: Part 5 2 and Eurocode 3: Part 1.3 3 is also presented. KEYWORDS Cold-formed steel, bearing failure, double bolted connections, high strength steel with low ductility. INTRODUCTION Galvanized cold-formed steel strips are commonly used in building construction, such as sections for secondary steel frames and purlins, and sheetings for roof cladding and floor decking. Cold-formed steel sections and sheetings are effective construction materials due to their high strength to weight ratio, high buildability during construction and also long-term durability against environmental attack. In building construction, cold-formed steel sections are usually bolted to hot rolled steel plates or members to form simple and moment connections. With the development of material technology, high strength cold-formed steel products are available for building applications, but concern has been raised on the reduced ductility of the high strength steel (< 5%). Existing codified design rules 2-5 may not be necessarily 245 246 K.F. Chung and K.H. Ip applicable for high strength low ductility steel, as the design rules are developed with low strength high ductility steel 6,7. Consequently, a close examination s on the resistance and the associated failure modes of bolted connections with high strength low ductility steel strip was carded out. Three distinct failure modes were identified 1 from the finite element modelling, namely, (i) the bearing failure, (ii) the shear-out failure, and (iii) the net-section failure. Parametric runs 9 were also carded out to reveal the effects of geometrical and material properties on the resistances of different failure modes. It is found that while the existing design rules are sufficient for bolted connections with low strength steels, such as steel with yield strength at 280 N/mm 2 and 350 N/ram 2, they may not be conservative when applying to high strength low ductility steel. In this paper, the finite element model is further extended to examine the structural behaviour of bolted connections with two bolts, i.e. double bolted connections between cold-formed steel strips and hot rolled steel plates under static shear loading as shown in Figure 1. The effects of strength degradation, hole clearance and bolt spacing on the load carrying capacity of typical double bolted connections are presented. The predicted load carrying capacity of the finite element model is also compared with the bearing resistances given by the design rules from both BS5950: Part 5 and Eurocode 3: Part 1.3; comparison with test data 10 is also presented. FINITE ELEMENT MODELLING The finite element package ANSYS (Verison 5.3) is used to predict the bearing behaviour in double bolted connections between cold-formed steel strips and hot rolled steel plates under static shear loading, and the following areas of interest are examined in detail: a) Stress-strain curves Two different stress-strain curves are proposed for the model as illustrated in Figure 2: 9 bi-linear elastro-plastic curve for low strength high ductility steel, designated as FEA- Pr, 9 multi-linear elastro-plastic curve with strength degradation at large strain for high strength low ductility steel, designated as FEA-pr. b) Deformation Sequences Due to the presence of clearance in bolt holes for easy installation, it is possible that the two bolts may not always come into contact with the cold-formed steel strips at the same time. The bolts may have a hole clearance of 1 mm to 2 mm typically. In order to examine the effect of hole clearance to the structural performance of the double bolted connection, three deformation sequences are considered as follows: 9 Deformation sequence IA where Bolt 1 is always in direct contact with the cold- formed steel strip while Bolt 2 only comes into contact with the cold-formed steel strip aRer I mm (or 2 mm) extension. 9 Deformation sequence IB which is similar to that of Deformation sequence 1,4 but with reverse order of bolts in contact, i.e. where Bolt 2 is always in direct contact with the cold-formed steel strip while Bolt 1 only comes into contact with the cold-formed steel strip after 1 mm (or 2 mm ) extension. Finite Element Modelling of Double Bolted Connections 247 9 Deformation sequence 11where both Bolts 1 and 2 always come into contact with the cold-formed steel strip together. c) Bolt spacing In BS5950: Part 5, the minimum bolt spacing Sp is recommended to be not less than 3 d, and the total load carrying capacity of a connection with multiple bolts may be obtained directly as the sum of the bearing resistances of all the bolts. No adverse interaction between bolts should be allowed for and this design method seems satisfactory for low strength high ductility steel. However, for high strength low ductility steel, it is necessary to investigate the minimum bolt spacing to avoid any adverse interaction of yield zones of the two bolts. As the connection contains a plane of symmetry, the half model shown in Figure 3 is incorporated. The cold-formed steel strip, the hot rolled steel plate and the two bolt-washer assemblies are represented three-dimensionally by eight-node iso-parametic solid elements SOLID45, as they allow both geometric and material non-linearities. Contact between the various components is accomplished by employing contact elements CONTACT49. Shear load is applied to the finite element model by imposing incremental displacement to the end of the cold-formed steel strip, along the longitudinal direction of the model. Throughout the entire deformation range, the hot rolled steel plate and the root of the bolt are fixed in space. At present, only the bearing failure of double bolted connections is considered. In typical fmite element models, there are over 3724 nodes, 2422 solid elements and 2022 contact elements. As the model is highly non-linear, the full Newton-Raphson procedure is employed to obtain solution after each displacement increment. For detail of the finite element model, see Reference 8. RESULTS AND DISCUSSIONS The load-extension curves for the double bolted connection with different stress-strain curves, deformation sequences and bolt spacings are presented in Figure 4. The von Mises stress distribution of the double bolted connections at various extensions are presented in Figure 5 while the deformed mesh of the double bolted connection is presented in Figure 6. a) Stress-strain curves With Sp = 3 d and Deformation sequence 11, the load carrying capacity of the connection is estimated to be 31.10 kN with material curve FEA-py, and 28.08 kN with material curve FEA-pr, as illustrated in Figure 4a. It is thus shown that the strength of the connection may be reduced by 10% when strength degradation is considered in high strength low ductility steel. b) Deformation sequences In Figure 4b, it is shown that the load-extension curves derived from both Deformation sequences IA and 1B follow each other fairly closely along the entire deformation range. By plotting the load-extension curve derived from Deformation sequence 11 on the same graph for direct comparison, it is shown that both the load carrying capacity and the extensional stiffness of the connection will be reduced approximately by half if only one bolt is in contact with the cold-formed steel strip. However, at 3 mm extension, the load 248 K.F. Chung and K.H. Ip carrying capacity with Deformation sequences IA and IB are found to be 26.69 kN with 1 mm gap and 24.10 kN with a 2 mm gap, corresponding to a strength reduction of 0.95 and 0.85 respectively. c) Bolt spacing In Figure 4c, it is shown that with Deformation sequence 11, the load carrying capacity of the double bolted connection is found to be increased from 28.08 kN at Sp = 3 d or 36 mm to 31.82 kN at Sp = 4 d or 48 mm, i.e. an increase of 13% in strength. A close examination on the von Mises stress distribution of the cold-formed steel strip in Figure 5 reveals that under low applied loads, the yield zones in the cold-formed steel for both bolts are fairly localized around the bolt holes. However, under large applied load at 3 mm extension, it is evident that the yield zones of both bolts overlap, leading to significant reduction to the total load carrying capacity of the connection. Consequently, in bolted connections with high strength low ductility steel, it is recommended that the minimum bolt spacing should be 4 d. COMPARISON WITH DESIGN RULES In order to provide simple design rules in assessing the bearing resistance, Pb, of double bolted connections with high strength low ductility steel, a number of existing design rules are examined as follows: Pb = (1.64 + 0.45 t) t dpy = 2.5tdpy = (4-0.1 d/t) tdpy from clause 8.2.5.2 of BS5950:Part 5 (A) from clause 8.4(4) with Table 8.4, EC3: Part 1.3 03) from page 133 & Table 4.12, Volume 1 of Reference 10 (C) Substituting the numerical values of t = 0.99 mm, d = 12 mm and replacing py with f~ = 592 N/mm" (where py and f~ are the yield strength and the tensile strength respectively) into the above design rules, the beating resistances are summarized in Table 1 together with the f'mite element results. Based on the results from the present research project, it is shown that a) Existing design rules tend to over-estimate the bearing resistances of bolted connections with high strength low ductility steel up to 30 % for both single and double bored connections when compared with test results. b) The results from the finite element models are found to be conservative when compared with test results. c) R is necessary to allow for adverse interaction of yield zones around boR holes indouble bored connections. At a boR spacing of 3 d, the reduction factor is estimated to be 27.13 / (2 x 14.43) or 0.94 based on test results, or 26.72 / (2 x 14.54) or 0.92 based on finite element results. Thus, a value of 0.90 is recommended for design purpose. Alternatively, the minimum boR spacing, Sp, for no adverse interaction should be increased and Sp = 4 d is recommended as appropriate. CONCLUSIONS A finite element model is presented to examine the structural performance of the bearing failure in double bolted connections between cold-formed steel strips and hot rolled steel plates under static shear loading. By incorporating bolt solid and contact elements, the model Finite Element Modelling of Double Bolted Connections 249 is demonstrated to able to capture non-linearities associated with geometry, material and contact (boundary) conditions. It is shown that existing design rules may not be applicable for high strength low ductility steel and new design rules are required to ensure structural adequacy. The bearing resistances of double bolted connections may be reduced by 10 % to 30 % due to strength degradation, hole clearance, and also adverse interaction of yield zones. ACKNOWLEDGEMENT The research project leading to the publication of this paper is supported by the Hong Kong Polytechnic University Research Committee (Project A/C code G-$565). REFERENCES 1. Ip K.H. and Chung, K.F.: Failure modes of bolted cold-formed steel connections under static shear loading, Proceeding of the Second International Conference on Advances in Steel Structures, Hong Kong, December 1999. 2. BS5950: Structural use of steelwork in buildings: Part 5 Code of practice for the design of cold- formed sections, British Standards Institution, London, 1998. 3. Eurocode 3: Design of steel structures: Part 1.3: General rules - Supplementary rules for cold- formed thin gauge members and sheeting, ENV 1993-1-3, European Committee for Standardization. 4. Cold-formed steel structure code AS/NZ 4600: 1996, Standard Australia/Standards New Zealand, Sydney, 1996. 5. Toma, A.W., Sedlacek, G., and Weynand, K.: Connections in cold-formed steel, Thin Walled Structures, Vol. 16, pp219-237, 1993. 6. Holcomb, B.D., LaBoube, R.A., and Yu, W.W.: Tensile and bearing capacities of bolted connections, Final Summary Report, Civil Engineering Study 95-1, Cold Formed Steel Series, Centre for Cold Formed Steel Structures, Department of Civil Engineering, University of Missouri-Rolla, MO, U.S.A. 7. Rogers, C. A. and Hancock, G. J.: New bolted connection design formulae for G550 and G300 sheet steels less than 1.0 mm thick, Research Report No. R769, the Centre for Advanced Structural Engineering, University of Sydney, Sydney, Australia, 1998. 8. Chung, K.F. and Ip, K.H.: Finite element modelling of bolted connections between cold-formed steel strips and hot rolled steel plates under shear, Engineering Structures (to be published). 9. Chung K.F. and Ip, K.H.: Finite element modelling of cold-formed steel bolted connections, Proceedings of the Second European Conference on Steel Structures, Praha, May 1999, pp503 to 506. 10. Rogers, C. A.: Structural behaviour of thin sheet steels, Ph.D. dissertation, Department of Civil Engineering, the University of Sydney, Australia, 1998. Table 1 Summary of bearing resistances - Design rules vs Finite element analysis (A) Single bolts e~(w0 14.77 03) 17.58 (C) 19.61 Finite element model (15.90 1.36) = 14.54 +Test value, Pr I 14. 43 Pr/Pb 0.977 0.821 0.736 0.992 I - Double bolts Pb (ld~ Pr / Pb 29.54 0.918 35.16 0.772 39.21 0.692 (28.08-1.36) = 26.72 1.015 I 27.13 ] - Note: * The model incorporates FEA-pr stress-strain curve, Deformation sequence 11 and Sp at 3d. A frictional force of 1.36 kN at zero extension is deducted from the load carrying capacity of the predicted resistance for direct comparison. + Averaged values from three test data in Table B55, Page 331 of Volume 2, Reference 10. . cold-formed steel strips are commonly used in building construction, such as sections for secondary steel frames and purlins, and sheetings for roof cladding and floor decking. Cold-formed steel. of steel structures: Part 1.3: General rules - Supplementary rules for cold- formed thin gauge members and sheeting, ENV 199 3-1 -3 , European Committee for Standardization. 4. Cold-formed steel. and bowing deformations in the end plate. Bolt pre-tensioning introduces further initial stresses in the connection. These heat induced distortions and the consequent initial stresses in the