고체역학 (Gere) — Applications of Plane Stress: Problem 8.3-14

8.3-14 A pressurized steel tank is constructed with a helical weld that makes an angle \(\alpha = 55^\circ\) with the longitudinal axis (see figure). The tank has radius \(r = 0.6\) m, wall thickness \(t = 18\) mm, and internal pressure \(p = 2.8\) MPa. Also, the steel has modulus of elasticity \(E = 200\) GPa and Poisson’s ratio \(\nu = 0.30\). Determine the following quantities for the cylindrical part of the tank. (a) The circumferential and longitudinal stresses. (b) The maximum in-plane and out-of-plane shear stresses. (c) The circumferential and longitudinal strains. (d) The normal and shear stresses acting on planes parallel and perpendicular to the weld (show these stresses on a properly oriented stress element).