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Shear Design of Wood Beams: State of the Art

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Shear Design of Wood Beams: State of the Art United States Department of Agriculture Shear Design Forest Service Forest Products of Wood Beams Laboratory General Technical State of the Art Report FPL-GTR-56 Lawrence A. Soltis Terry D. Gerhardt Abstract Current shear design technology in the United States for lumber or glued-laminated beams is confusing. This report summarizes shear stress and strength research including both analytical and experimental approaches. Both checked and unchecked beams are included. The analytical work has been experimentally verified for only limited load conditions and span-to-depth ratios. Future research is required to better define the effects of beam size, load configuration, checks, and combined stresses on shear design. Keywords: Beams, design, shear strength, shear stress, shear tests, timber, lumber, glued laminated. March 1988 Soltis, Lawrence A.; Gerhardt, Terry D. 1988. Shear design of wood beams: State of the art. Gen. Tech. Rep. FPL-GTR-56. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 9 p. A limited number of free copies of this publication are available to the public from the Forest Products Laboratory, One Gifford Pinchot Drive, Madison, WI 53705-2398. Laboratory publications are sent to over 1,000 libraries in the United States and elsewhere. The Laboratory is maintained in cooperation with the University of Wisconsin. Shear Design of Wood Beams State of the Art Lawrence A. Soltis, Supervisory Research Engineer Forest Products Laboratory, Madison, WI Terry D. Gerhardt, Senior Research Associate Sonoco Products Co., Madison, WI Introduction Shear Stress Current shear design technology in the United States for Shear stresses (t) are local phenomena acting at a point in the lumber or glued laminated beams is not well founded, may be beam. The resultant shear force (V) is defined as the integral too conservative in some cases, and is frequently ignored by of t over a beam cross section: engineering designers. Shear design requirements (American Institute of Timber Construction (AITC) 1986, National (1) Forest Products Association (NFPA) 1986) are confusing and The distribution of V along the length of the beam is easily little understood. The objective of this report is to review the calculated from applied loads and reactions at each support. state of the art in shear design of rectangular wood beams. The shear stress distribution at a cross section away from a support is approximated by elementary beam theory and is Shear stresses and strengths must first be defined. Local shear dependent on V at that cross section. The shear stress stresses act at a point in the beam and are dependent on the distribution at a cross section near a support, however, cannot beam geometry and load configuration. Local shear failure be determined from elementary beam theory (Cowan 1962). occurs when the shear stresses parallel to the grain, i.e. shear These stresses can be computed using analytical or numerical stresses acting in the longitudinal-tangential (LT) or techniques (Liu and Cheng 1979). longitudinal-radial (LR) planes, exceed the shear strength of the beam. Cowan (1962) experimentally found that the maximum shear stress near a support is about 33 percent greater than the The shear strength of a wood member is difficult to quantify. maximum shear stress predicted by elementary beam theory. It depends on test method, member size, load configuration, The distribution of stress, however, is considerably different checks, splits or knots, grain slope, moisture content, and at a support than the parabolic distribution of elementary temperature. A pure local shear failure is difficult to attain beam theory for rectangular cross sections. since shear often interacts with bending and perpendicular- to-grain stresses. Additionally, the wood member may fail by Near supports, bending and perpendicular-to-grain stresses cracks propagating from end splits or side checks. also occur in addition to shear stresses (Liu and Cheng 1979). Shear forces, therefore, can be associated with nonshear-type For unchecked members, both shear stress and strength are failures. For example, Bickel (1983) documented bending dependent on member size and load configuration. This failures in floor trusses caused by shear reactions acting on complicates a generalized design procedure for all sizes and top chord bearing extensions. In that case, the bending failure configurations. For checked members, different failure modes was located quite close to the support. Such locations are further complicate a generalized procedure. usually associated with shear failures. Several orthotropic failure criteria have been investigated for combined stresses in wood members (Cowin 1979, Goodman and Bodig 1971, Keenan 1974, Liu 1984a, Norris 1950, Tsai and Wu 1971). These failure criteria require strength properties (discussed later) that are difficult to measure. Shear Strength The evolution of allowable shear strength values has been The shear strengths of timber beams have long been traced from 1906 (Ethington et al. 1979). The early research recognized as being lower than the shear strengths as summarized in that report recognized that flexural tests of measured in shear block tests. Wilson and Cottingham (1952) lumber resulted in lower shear strengths than found from tests tested glued-laminated wood beams (both horizontally and of small, clear, straight-grained specimens. That study traced vertically laminated) under two-point loading. The beams the evolution of adjustment factors based on experience and were 5- by 12-inch Douglas-fir and had a length-to-depth compromise. ratio, l /d, of 13.5. Longworth (1977) tested a number of sizes of Douglas-fir glued-laminated beams under two point Current shear strengths of small, clear specimens are given in loading. The beams had l /d ratios of approximately 5. American Society for Testing and Materials (ASTM) Keenan et al. (1985) tested small sizes of several species of Designation D 2555. Adjustments for strength ratio and splits glued-laminated beams under a concentrated midspan load and checks to visually graded lumber are given in ASTM with l /d ratios of 1.5 to 5. Results of average shear strengths Designation D 245. Standard methods of establishing from these three references are included in figure 1. glued-laminated timber values are given in ASTM Designation D 3737. Foschi and Barrett developed both a theory (1976) and a design procedure (1977) to predict the shear strengths of An ideal shear strength specimen would have a critical failure glued-laminated beams. The theory is based on finite element plane acted on exclusively by uniform shear stress. Such a simulations using quadratic isoparametric quadrilateral state of stress is difficult to achieve. Experimental stress elements (Zienkiewicz 1976) with nonlinear constitutive laws analysis of the standard test specimen ASTM D 143 has for compression parallel and perpendicular to the grain. From revealed a nonuniform shear stress distribution with a stress the numerical stress analyses, Foschi and Barrett (1976) concentration near the corner (Coker and Coleman 1935, concluded that: Radcliffe and Suddarth 1955). Keenan (1974) used wood tubes loaded in torsion to obtain a more uniform state of 1. The high shear stress near the support corners decays shear stress. It is difficult to fabricate wood specimens with rapidly and contributes only to bearing-type failures. proper grain orientation and without the development of residual stresses, which limits this approach. A 2. The maximum shear stress in regions removed from loads butterfly-shaped specimen has been used to measure shear and supports is conservatively estimated by the elementary strength (Arcan et al. 1978) and shear fracture properties beam equation. (Banks-Sills and Arcan 1983) of composite materials. Experimental results (Arcan et al. 1978) indicate a relatively Foschi and Barrett used the computed shear stresses in a two- uniform shear stress distribution in the failure plane. Liu parameter Weibull model to develop a strength theory that (1984b) recently measured the shear strength of Douglas-fir incorporates the effects of support, loading condition, and using this specimen. size. The Weibull parameters were calculated from data collected by Longworth (1977) for 5 beam configurations with The butterfly-shaped specimen appears promising for 30 replications of each. The parameters were calculated from measuring clear wood shear strength. However, setting a least squares procedure using only the mean values from allowable shear strength values for beams from these data each group. Foschi and Barrett (1976) then compared model present certain difficulties. To overcome these difficulties, predictions to shear failure loads for Griplam nail various researchers have considered the effects on shear connections (Foschi and Longworth 1975), torque tubes strength of the following: (Keenan 1974, Madsen 1972), and beams (Keenan 1974). 1. Member size (Keenan 1974, Longworth 1977, Madsen and In a subsequent paper, Foschi and Barrett (1977) developed a Nielsen 1978). design procedure by simplifying the analysis and incorporating the effects of support width. The final result 2. Moisture content and temperature (Gerhards 1982). was a set of tables for designing rectangular and tapered glued-laminated beams under various loading conditions for 3. Grain slope variation (Liu and Floeter 1984). shear strength. This design methodology is now prescribed in the Canadian Standards Association
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