came1pt3 - the plane of the joint are P.cos θ and P.sin θ...

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Question1.3: A square prismatic bar of cross-sectional area is composed of two pieces of wood glued together along the x’ plane, which makes an angle θ with the axial direction. The normal and the shearing stresses acting simultaneously on the joint are limited to 20 and 10 Mpa, respectively, and on the bar itself, to 56 and 28 Mpa respectively. Determine the maximum allowable axial load that the bar can carry and the corresponding value of angle θ . Y Solution Y’ X’ X θ P P Let us denote the axial force applied by “P”, the cross-sectional area of the bar by “A”, σ , σ ’, τ , τ ’ be the normal and shear stresses on the normal cross-section of the bar and the joint respectively. Cross-section of the joint, ) cos( A A' q = ………………. by geometry. Now the stresses developed on the joint are ' joint on the force Normal ' A = s ' joint on the force shear ' A = t Since the axial load on the bar is P, the normal and shear components of this load onto
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