270 K.H. Ip and K.F. Chung design codes 1-3, however, may be inappropriate for CFS sections with high yield strength but low ductility (< 5%). Consequently, a close examination on the resistance and the associated failure modes of bolted connections with high strength low ductility CFS strip is essential before the established design codes can be applied with confidence. With the advent of computer hardware and software, numerical simulation has drawn the attention of researchers in many areas of engineering and science. In the field of solid mechanics, finite element (FE) method is perhaps the one having the greatest impact. The method is particularly useful in solving boundary value problems where large strains, nonlinear materials and contact surfaces are involved. Results from FE analysis provide a clear picture on the stress and the strain distributions in a structure, which is not easily obtained from physical tests. Besides, extensive parametric studies can be carried out to reveal the effects of geometrical and material properties on the performance of a structure. The present study 4 concerns with finite element simulation on bolted connections between CFS strips and HRS plates under static shear loading. Emphasis is given to predict the possible failure modes, namely, (i) the bearing failure, (ii) the shear-out failure and (iii) the net-section failure aider calibration. Parametric runs will be carried out to reveal the effects of geometrical and material properties on the resistances of different failure modes. The results are then compared with design values to reveal the applicability of codified design rules 5. FINITE ELEMENT ANALYSIS The ANSYS (ver 4.3) finite element package is used to predict the load-extension curves of bolted connections between cold-formed steel strips and hot rolled steel plates under static shear loading. As the connection contains a plane of symmetry, the half model shown in Figure 1 is sufficient, where the edge distance Se and the specimen width W are indicated. The CFS strip, the HRS plate and the bolt-washer assembly are represented three-dimensionally by eight-node iso-parametic solid elements SOLID45, as they allow both geometric and material nonlinearities. Contact between the various components is accomplished by employing contact elements CONTACT49. The contact stiffness and the friction coefficient for all interfaces are assigned the values of 2 x 103 N/mm and 0.2, respectively. In a typical FE model, there are 1878 nodes, 1197 solid elements and 981 contact elements. Plasticity in the CFS strip is considered by incorporating the von Mises yield criterion, the Prandtl-Reuss flow rule together with isotropic hardening rule. However, for simplicity, the bolt-washer assembly is linear elastic with Young's modulus, E, at 205 kN/mm 2 and Poisson's ratio v at 0.3. Shear load is applied to the FE model by imposing incremental displacements to the end of the CFS strip, along the longitudinal direction of the specimen. Throughout the course of loading, the HRS plate and the root of the bolt are fixed in space. As the model is highly nonlinear, the full Newton-Raphson (N-R) procedure is employed to obtain the solution atter each displacement increment. Failure M octes oj t~olted Cold-Formed Steel Connections 271 Figure 1 Finite element model of a bolted connection between CFS strip and HRS plate Figure 2 True Strain (%) Proposed stress-strain curves for cold-formed steel strips RESULTS AND DISCUSSIONS The FE model is first calibrated with the results from lap shear tests. Both G300 and G550 cold-formed steel strips of different yield strengths py and thicknesses t are considered. Their material curves as deduced from standard coupon tests and they are presented in Figure 2. A negative slope is appended to each curve to simulate the effect of strength degradation at high tensile or compressive strains. The CFS strip is bolted to the HRS plate by a grade 8.8 bolt of 12mm diameter. Comparison between the predicted and the measured load-extension curves associated with bearing failure is given in Figure 3. Close agreement between the experimental and simulation results indicates the accuracy of the finite element model as well as the proposed material curves. 272 K.H. Ip and K.F. Chung Figure 3 Theoretical and experimental load-extension curves for bolted connections with 12mm diameter bolts By changing the dimensions of the CFS model, i.e. the edge distance Se and the specimen width W, three distinct failure modes are identified: (i) Bearing failure It prevails for strips having sufficiently large Se and W, as shown in Figure 4(a). The yield zone emerges from the bearing edge of the CFS strip owing to highly localized compressive stresses. O0 Shear-out failure It occurs when the edge distance Se of the specimen is small, as shown in Figures 4(b). Such failure is characterized by large shear stresses between the hole and the edge of the strip. Protrusion of the edge of the strip can be observed. (iii) Net-section failure It takes place for narrow specimens as shown in Figure 4(c). In contrast to bearing failure, the yield zone is developed from the tensile edges of the hole, accompanied by necking of the net-section. The deformed meshes of each failure mode are also presented in Figure 5 for comparison. Failure Modes of Bolted Cold-Formed Steel Connections 273 Figure 4 Failure modes of G550 CFS strip at 3ram extension (t - 1.60 mm with 12mm diameter bolts) 274 K.H. Ip and K.F. Chung Figure 5 Deformed meshes of G550 CFS strip at 3mm extension (t = 1.60 mm with 12mm diameter bolts) Failure Modes of Bolted Cold-Formed Steel Connections 275 A strength coefficient is established to compare the resistances of a bolted connections from finite element models to basic resistances of the connections, and the strength coefficient is defined as follows: Resis tan ce at 3ram Strength coefficient = (1) tdU s Through parametric runs, the effects of Se and W on the normalized resistance of the FE model are summarized in Figures 6 and 7 for the G300 and G550 strips, respectively. These figures also present the capacities of the connections based on the design formulae in Section 8.2 in BS5950: Part 5 [1 ]. A glance at these plots reveals that the FE predictions exhibit a similar trend with the design values. Maximum connection resistance is found to occur in the bearing mode. The results also demonstrate the independence of bearing resistance to Se and W when the bolt hole is sufficiently far from the sides of the strip. Inspection of Figure 6 shows that the design rules is conservative for predicting the resistance of G300 strips under net- section and bearing failures. In the FE model, transitions from the shear-out and the net-section failures to the bearing failure are found to occur at larger Se / d and W/d. In other words, sufficient distances, say Se / d > 4 and W/d > 5, should be provided for the CFS strip in order to secure the maximum connection resistance. Refer to Figure 7 for G550 strips, the design formulae are unsafe when applying to high strength steels. Figure 6 Strength coefficient of bolted connection with G300 CFS strip ( t = 1.50 mm and d = 12 mm ) Figure 7 Strength coefficient of bolted connection with G550 CFS strip ( t = 1.60 mm and d = 12 mm ) 276 CONCLUSIONS K.H. Ip and K.F. Chung A finite element model was employed to determine the resistance of bolted connections between cold-formed steel (CFS) strips and hot rolled steel (HRS) plates subject to static shear loading. By incorporating both solid and contact elements, the model is able to capture nonlinearities associated with geometry, materials and boundary conditions. The von Mises stress distributions in the CFS strips under different types of connection failure are also predicted. Results from parametric runs indicate that the existing design formulae are sufficient only for bolted connections with low strength steels, such as 280N/mm 2 and 350N/mm 2. However, the existing codified design rules may not to conservative when applying to high strength low ductility steel. 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. BS5950: Structural use of steelwork in buildings: Part 5 Code of practice for the design of cold-formed sections, British Standards Institution, London, 1998. 2. Cold-formed steel structure code AS/NZ 4600: 1996, Standard Australia/Standards New Zealand, Sydney, 1996. 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. 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). 5. 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. DESIGN MOMENT RESISTANCE OF END PLATE CONNECTIONS* Yongjiu Shi Jun Jing Department of Civil Engineering, Tsinghua University, Beijing 100084, China ABSTRACT The end plate connection, either flush end plate or extended end plate, bolted with high strength friction fasteners, is one of the moment resistant connections recommended for steel portal frame design, and can be used for rafter to column connection or rafter splice. Current design rules specify that the tension force produced by the bending moment is triangularly distributed among the bolt rows in tension zone, if the end plate is stiff enough and its deformation is negligible. The engineering practice demonstrates that the end plate thickness usually varies from 12 to 36mm and its flexible deformation can not be neglected. In this paper, a finite element model is constructed to analyze connection behaviour under the applied bending moment and the model is verified by the available test results. The bolt tension force distribution and end plate deformation for connections with different configurations are compared. Finally, a modified design method is proposed. KEY WORDS Steel structures, End plate connection, High strength fastener, Portal frame design INTRODUCTION In design of steel portal frame, end plate connection is the most widely recommended economic moment-resistant joint with the advantage of fast erection and no field welding(Fig 1). The bolted end plate connection can be used for beam splice or beam to column connection and can be detailed as either flush or extended with or without stiffeners(CECS102:98, 1998). The moment resistance of end plate connections largely depends on the component behaviour in the tension zone, compression zone and shears zone, such as the bolt tension resistance, end plate yielding resistance and column web buckling resistance, etc. The traditional design guides(JGJ82 91,1992) suggest that the tension force produced by the bending moment is triangularly distributed among the bolt rows in tension zone under the assumption that both the flush and extended end plate is adequately stiff and its flexible deformation and prying force can be neglected(Fig. 2). The outermost row of bolts are assigned with the maximum "Supported by National Natural Science Foundation of China 277 278 Y. Shi and J. Jing tension and the forces resisted by any row of bolts can be given by Nti = Myi / E yi2 ( 1 ) It is required in Chinese code of practice that Nt~ should be limited to Na<~O.8P, where P is the bolt pretension. f(3 tit Figure 1: End plate connections for portal frame Ntl . v Figure 2: Traditional design model However, the end plate applied in the steel portal frame design may be just 20mm or less in thickness and the assumption described above may not be applicable. It is necessary to further investigate the design model that would be appropriate for connections in steel portal frame. In this paper, a finite element model is established to analyze the bolt force distribution for the beam to column connections. The contact pressure between end plate and column flange under different bending moment is also investigated. A revised design model is proposed for portal frame end plate connections. ANALYTICAL MODELING Traditionally, the T-stub or yielding line theory is used for analyzing the end plate deformation (Brown et al, 1996), and later, the 2D/3D finite element model was introduced(Sherbourne and Bahaari, 1994, Gebbeken et al, 1994). In this paper, a hybrid 2D/3D model was developed. The beam web and flange were modeled with plate element, while the end plate, bolt heads and nuts were represented by 3D block elements. A number of bar elements were adopted to simulate the bolt shank. The contact elements, which could resist compression but not tension, were used to simulate the interface between the end plate and the column flange. In establishing the finite element model, the bolt pretension were well simulated by temperature action, that is, a temperature stress were applied to the bolt shank, leading to the bolt to contract and subject to pretension. The established finite element model is shown in Fig. 3. The connection model is analyzed by loading increment method and the material properties are assumed remaining elastic. Figure 3. Finite element model Figure 4: Tested connection and result comparison To verify the finite element model, an end plate connection tested by Jenkins et al(1986) were analyzed again. The bolt tension force produced by the applied bending moment is compared in Fig. 4. It is noted that the finite element model simulates the tension force development very well, but gives higher value. Since calculated results are obtained in the elastic range of material properties, while partial plasticity Design Moment Res&tance of End Plate Connections 279 may be developed under large bending moment during the tests, it is understandable that the calculated tension is larger than the measured tension. Both the experiment and calculation reveal that the tension force on the first row of bolts is well below that on the second row of bolts. The traditional design model(Fig 2) is inappropriate to the extended end plate connection. PARAMETRIC STUDY Based on the establishedmodel, some typical joints with flush or extended end plates(Fig. 5a) were investigated. The end plate thickness varies from t = 10mm to t = 40mm, and the high strength bolts are M20, Grade 8.8 with pretension P = 110kN. The extended part can be stiffened or unstiffened. Figure 5: Bolt force versus applied bending moment . cold-formed steel strips and hot rolled steel plates under shear, Engineering Structures (to be published). 5. Chung~ K.F. and Ip, K.H.: Finite element modelling of cold-formed steel bolted. conservative for predicting the resistance of G300 strips under net- section and bearing failures. In the FE model, transitions from the shear-out and the net-section failures to the bearing failure are. cold-formed thin gauge members and sheeting, ENV 199 3-1 -3 , European Committee for Standardization. 4. Chung, K.F. and Ip, K.H.: Finite element modelling of bolted connections between cold-formed