Further Studies in Combined Bending and Tension Strength of Structural 2 By 4 Lumber

One hundred specimens of machine-graded west coast hemlock 2 by 4 structural lumber were loaded in combined bending and tension. The members were loaded on edge at quarter-points over an eight-foot span with a constant tensile stress (0, 500, 1000, 1500, 2000, 2500, or 2750 psi) and then additionally loaded in bending to failure. The bending load at failure was found to be nearly independent of the applied tensile load. A counter-moment, caused by the deflection of the path of the internal tensile forces, opposes the bending moment in a beam to substantially reduce the effective stress due to moment. As a consequence, the combined stress due to simultaneously applied bending and tensile loads is made up of three separate components: a tensile stress, and bending stress due to the bending load, and a bending stress due to the tensile load acting on the deflected beam. Since the two bending stresses counter-act each other, the combined stress is the algebraic sum of its three components. If the bending stress due to the counter-moment, which was always greater in magnitude than the applied tensile, stress, is assumed to be equal in magnitude to the tensile stress, a conservative design equation may be derived.

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