고체역학 (Gere) — Axially Loaded Members: Problem 2.6-16

2.6-16 Two boards are joined by gluing along a scarf joint, as shown in the figure. For purposes of cutting and gluing, the angle \(\alpha\) between the plane of the joint and the faces of the boards must be between \(10^\circ\) and \(40^\circ\). Under a tensile load \(P\), the normal stress in the boards is 4.9 MPa. (a) What are the normal and shear stresses acting on the glued joint if \(\alpha = 20^\circ\)? (b) If the allowable shear stress on the joint is 2.25 MPa, what is the largest permissible value of the angle \(\alpha\)? (c) For what angle \(\alpha\) will the shear stress on the glued joint be numerically equal to twice the normal stress on the joint?