On Bending Tests of Five - Ply

K-factor has Ions been used as a modifier of section modulus In the calculation of bending moment for plywood beams. No comparable modification of moment ot inertia is included In current reoommendatioDS for calculating plywood deflection at span-depth ratios of 30: 1 or greater. Results of limited testing lend support 'to the authors' contention that, where "shear" strains are signifIcant, the same K value would be appropriate for predicting both the deflection and beDdiDI moment of plywood. If these results are confirmed by further investigation. a method tor determining an appropriate value tor K based on separate calculations of deflections due to shear and bendiDg is suggested. E = modulus of elasticity in bendinl of parallelstressed plies (psi) 1 = effective moment of inertia (in..) = Z(l. + 1/35 I,,) Although calculation of deflection by this method appears to ignore shea,r, it should be noted that the usual shear effect encountered in standard testing of solid wood beams with a spanldepth ratio of 14:1 (on the order of 10 percent of total deflection) is included in the value for modulus of elasticity when this value is taken from standard sources. For the normal span-depth ratios of 30:1 to 50:1 at which plywood sheathing is most commonly used, equations ignoring any additional effect of shear are usually considered ad~e (1). This conclusion appears to be based on extensive tests conducted more than 30 years ago at the Forest Products Laboratory (6), although those tests were limited to a span-depth ratio of 48:1 when outer plies were stressed parallel to grain. Section modulus (S), nolmally calculated u II", where" is the distance from the neutml plane to the outermost fiber, is modified still further in the case of plywood beams. Limiting consideration here to plywood in whid1 the ooter plies are stressed parallel to the grain. effective section modulus (KS) involves a reduction factor K u well u effective I in the expression II"; KS = KII". For the loading condition just described, talw~ted values for KS appearing in the Plywood Design Specifiation (1) incorporate a value of 0.85 fac K based on experimental results obtained, as noted in the preceding paragraph. at the Forest Produds LaOOratory (6). The test data were evaluated at the proportiooallimit level u well u at the level of failure. This val~ for K, appliable to aln11stioo of bending moment for plywood through the relationship M = (KI/c or fKS [2] CUUENT DESK;N ROCEDURES for plywood loaded in bending are based 00 an "effective" moment of inertia (1) and an "effective" section modulus (KS). These section properties are deflOed in current design specifiations published by the American Plywood Association (1). Due to the lower modulus of elasticity of plies stressed perpendicular to the grain, the effective moment of inertia of a plywood section is less than that of a section com~d of all parallel-laminated plies of the same material. The effectiveness of a plywood section is accounted for by calculating its 1 as the summation of the 1 of the plies stressed-parallel-to-grain a d 1/3.5 I of the perpendicular plies, all taken ~ the neutral axis of the section. The Plywood Design Specification includes tabulated values for effective I for standard plywood constructions (1). Deflection of a plywood be-.m is calml.t~ by incorporating the effective 1 into ~ of the usual engineering formulas. For example, deflection (in.) of a simple beam supporting a center load P is calcu1ated as pp The authoR are, resDeCtivelY, Department Head, Graduate Student, and Graauate Research A881staJ1t, Department of Forest and Wood Sciences, Collese of Forestry and Natural Resoun:es, Colorado State Univenity, Fort Collins. Colo. This paper was received for publication in April 1972. [I] A=48£1 where P = load (lb.) r = span (in.) Reprinted fr~ FOREST PRODUCTS JOURNAL Vol. 23. No.4 55 and D grade inner and back plies corresponding to CD grade plywood. Engelmann sproce specimens were made with a C grade face and inner plies and D grade back, representative of a mill ron consisting of approximately 80 percent C grade and 20 percent D grade veneer. Layups ,of both species were hot-pressed in two series using an interior type glue line in one and an exterior type in the other. Bending specimens were 12 inches wide and 20 inches long and were tested by center loading over a 16-inch span. Rate of crosshead travel of the testing machine was standard for a one-halfinch deep beam at this span. The resulting span-depth ratio of 32:1 is in the range of recommended spans for this thickness of plywood. Average results obtain~ from te$ting approximately 25 specimens of each type are shown in Tables 1 and 2. Values in these tables have been calculated as follows for plywood: