In a previous paper we examined the applicability of Timoshenko's bending theory, which describes the effect of shearing force in bending deflection, when measuring the shear modulus of wood, and found that it is difficult to obtain the shear modulus by Timoshenko's theory because of the distorted shear stress condition around the loading point. When the deflection is measured at the point distant from the loading point, we thought that the shear modulus would be obtained by Timoshenko's theory properly. Here, we conducted the three-point bending tests with measuring the deflection at the midpoint between the loading point and a support, and examined whether Young's and shear moduli can be measured properly.
Akamatsu (Japanese red pine. Pinus densiflora D.Don) and balsa (Ochroma lagopus Sw.) were used for the testing materials. First the Young's modulus and the shear modulus were measured by free-free flexural vibration tests. Then the three-point static bending tests with varying the depth/span ratios were simulated by the finite element method (FEM). From the FEM analyses , the load-deflection behavior is effectively described by Timoshenko's bending theory when the deflection is measured at the opposite point against the loading point. Finally the static bending tets were conducted with a dial gage set below the specimen to measure the deflection at the opposite point against the loading point, and the Young's and shear moduli were calculated by Timoshenko's bending equation.
From the testing results, we concluded that it is difficult to obtain the shear modulus properly by original Timoshenko's theory even when the measured points of dflections were variously changed, and that the modification of the original equation should be needed.