Results comparison between analytical and experimental investigations
Experimental results (Serrette et al, 2002; Rogers et al 2004a; Fulop and Dubina 2004a) are used to validate the accuracy of the proposed analytical method of evaluating the ultimate lateral strength of SWP. The accuracy of the evaluated strengths are generally correlated with the material properties and the geometric dimensions of the components. As not all properties are reported in the foregoing literature, the material properties adopted in the evaluation may not be matched with those of the tested materials. In this study, both the material and geometric properties of steel studs were based on the values published by the Steel Stud Manufacturers Association (SSMA, 2001), and the material properties of sheathing being used in the calculation will be discussed in each individual case.
Rogers et al (2004) conducted a series of experimental investigations on SWP with three different sheathing materials, Oriented Strand Board (OSB), Douglas Fir Plywood (DFP), and Canadian Softwood Plywood (CSP). The cold formed steel studs were 92S41-1.12mm (358S158-44mils), spaced 610mm (24in) at the center, and double studs were placed at the chords. The sheathing was fastened with No. 8 screws (diameter = 4.06mm) on one-side of the panel. Screw spacing was 305mm (12in) in the field, and the edge spacing varied from 152mm (6in) to 76mm (3in). The length and height of the SWP were 1219mm (4ft) and 2438mm (8ft), respectively. The ultimate lateral strengths shown in Table 1 are the average values obtained from three specimens.
The following material properties are used to evaluate the ultimate lateral strengths of the foregoing SWP. The shear modulus of elasticity for OSB, DFP and CSP are 925MPa, 825MPa, and 497MPa, respectively (Okasha, 2004), while the modulus of elasticity associated with OSB (OSB, 1995), DFP and CSP (CANPLY, 2003) are 9917MPa, 10445MPa, and 7376MPa, respectively. The comparison between the analytical and test results is presented in Table 1.
Table 2 shows the comparison between the results of the proposed method and those of the experimental investigation conducted by Serrette et al (2002). The framing steel studs used in the two tests were 89S41 (350S158) with thicknesses of 1.37mm (54 mils) and 1.73mm (68 mils). The studs were spaced 610mm (24in) at the center, and double studs were placed at the chords. The sheathing material was OSB, and sheathing was presented on one side of the panel. The screw spacings on the edge and in the field of the panel were 51mm (2in) and 305mm (12in), respectively. The SWP dimensions were 1219mm (4ft) by 2438mm (8ft). The ultimate lateral strengths shown in Table 2 are the average values obtained from two specimens. The foregoing material properties associated with OSB sheathing are used to evaluate the strength of the SWP.
Presented in Table 3 is the comparison between the result of the proposed method and that of the experimental investigation conducted by Fulop and Dubina (2004a). The framing steel studs were 152S44-1.57mm (600S175-62mils) with 610 mm (24in) spacing. OSB sheathing was presented
Table 1. Comparison between analytical and tested results (Rogers et al, 2004a)
Table 2. Comparison between analytical and tested results (Serrette et al, 2002)
Table 3. Comparison between analytical and tested results (Fulop and Dubina, 2004a)
on one side of the panel. The screw diameter was 4.6mm and the screw spacings were 102mm (4in) on the edge and 254mm (10in) in the field of the panel. Different from the foregoing two experimental investigations, the dimensions of the panel were 3600mm (~ 12ft) by 2440mm (8ft). The ultimate lateral strengths shown in Table 3 are obtained from one specimen. As the material properties of sheathing were not available from the literature, the foregoing properties of OSB are employed in the analytical evaluation.
Figure 1. Fastener arrangement notation
The utilization of shear wall panels constructed with cold-formed steel and wood sheathing is becoming common practice for low – and mid-rise residential construction. However, analytical methods of evaluating the ultimate lateral strengths of the panels are needed to be developed in order to make cold formed steel systems more attractive to design practitioners. The method presented in this paper is comprehensive and can be used to evaluate the ultimate lateral strengths of SWP with different sheathing and framing materials, as well as panel dimensions and construction details such as fastener spacing. The comparisons made on the results obtained from the proposed method and the experimental investigations have shown good agreement between the evaluated and tested results. Therefore, the proposed method is recommended for engineering practice.
The first author would like to express his appreciation to the Mexican National Council for Science and Technology (Consejo Nacional de Ciencia y Tecnologia) for its financial support. The authors are in debt to Dr. C. Rogers for providing experimental data.
AISI (2004). Standard for Cold-Formed Steel Framing-Lateral Design, American Iron and Steel Institute.
Brandt, G. D. (1982). Rapid Determination of Ultimate Strength of Eccentrically Loaded Bolt Groups, Engineering Journal, American Institute of Steel Construction.
Brockenbrough, R. L. & Associates (1998). Shear Wall Design Guide, American Iron and Steel Institute, Technical Data, RG-9804.
CANPLY (2003). Plywood Design Fundamentals, Canadian Plywood Association.
Fulop, L., & Dubina, D. (2004a). Performance of wall-stud cold-formed shear panels under monotic and cyclic loading Part I: Experimental research. Thin-Walled Structures, 42, 321-338.
Fulop, L., & Dubina, D. (2004b). Performance of wall-stud cold-formed shear panels under monotic and cyclic loading Part II: Numerical modelling and performance analysis. Thin – Walled Structures, 42, 339-349.
Gad, E. F., Chandler, A. M., Duffield, C. F., & Stark, G. (1999). Lateral Behaviour of Plasterboard-Clad residential Steel Frames. Journal of Structural Engineering, ASCE, January, 32-39.
Okasha, A. F. (2004). Performance of steel frame / wood sheathing screw connections subjected to monotonic and cyclic loading, Department of Civil Engineering and Applied Mechanics, University of McGill, Montreal, Master’s Thesis.
OSB (1995). OSB Design Manual, Design Rated Oriented Strand Board, Structural Board Association.
Rogers, C. A., Branston, A. E., Boudreault, F. A., & Chen, C. Y. (2004a). Light gauge steel frame / wood panel shear wall test data: summer 2003, Department of Civil Engineering and Applied Mechanics, University of McGill, Montreal, Progress Report.
Rogers, C. A., Branston, A. E., Boudreault, F. A., & Chen, C. Y. (2004b). Steel Frame / Wood Panel Shear Walls: Preliminary Design Information for Use with the 2005 NBCC, 13th Word Conference on Earthquake Engineering.
Serrette, R. L, Escalada, J., & Juadines, M. (1997). Static Racking Behavior of Plywood, OSB, gypsum, and Fiberbond Walls with Metal Framing, Journal of Structural Engineering, ASCE, August 1997, 1079-1086.
Serrette, R. L., Morgan, K. A., & Sorhouet, M. A. (2002). Performance of Cold-Formed SteelFramed Shear Walls: Alternative Configurations. Light Gauge Steel Research Group, Department of Civil Engineering, Santa Clara University, Final Report LGSRG-06-02.
SSMA (2001). Product technical information. Steel Stud Manufacturers Association. ICBO ER – 4943P, Retrieved January, 12, 2004, http://www. ssma. com
B. W. Schafer
Johns Hopkins University, Department of Civil Engineering
Latrobe Hall 210, Baltimore, MD 21218, USA
E-mail: schafer@jhu. edu
Budapest University of Technology and Economics, Department of Structural Mechanics
1111 Budapest, Muegyetem rkp. 3., Hungary
E-mail: sadany@epito. bme. hu
This paper demonstrates how to decompose general stability solutions into useful subclasses of buckling modes through formal definition of the mechanical assumptions that underlie a class of buckling modes. For example, a thin-walled lipped channel column as typically used in cold-formed steel can have its buckling mode response decomposed into local, distortional, global, and other (transverse shear and extension) modes. The solution is performed by writing a series of constraint equations that are consistent with the mechanical assumptions of a given buckling class. The mechanical assumptions that defined the buckling classes were determined so as to be consistent with those used in Generalized Beam Theory (see e. g., Silvestre and Camotim 2002a, b) The resulting constraint equations may be used to constrain the solution before analysis, and thereby provide the opportunity to perform significant model reduction, or may be employed after the analysis to identify the buckling classes that participate in a given buckling mode. This paper shows the framework for this process in the context of the finite strip method (building off of Adany and Schafer 2004, 2005a, b) and discusses some of the interesting outcomes that result from the application of this approach. Of particular interest, and discussed here, is the definition of global buckling modes, and the treatment of members with rounded corners – each of which provide certain challenges with respect to traditional definitions of the buckling classes. Examples are provided to illustrate the technique and challenges. The long-term goal of the work is to implement the procedures in general purpose finite element codes and thus enable modal decomposition to become a widely available tool for analyzing thin-walled member cross-section stability.
Understanding cross-section stability of thin-walled members is critical to successful design. Inherently, or explicitly, design methods rely on prediction and separation of the cross-section stability modes. Different post-buckling behavior and strength are associated with each of the modes. For example, in the case of a cold-formed steel lipped channel column, typically three buckling modes are identified: local, distortional, and global. Local buckling modes are most typically handled by effective width methods which empirically include the potential for post-buckling reserve. Global buckling modes, such as flexural-torsional buckling, are handled through empirical column curves and are combined with the local post-buckling result in some fashion to account for local-global interaction. Distortional buckling is treated by modified effective width’s or a modified column curve. Regardless of the design approaches employed, a fundamental first step is identification and prediction of the elastic cross-section stability modes.