고체역학 (Gere) — Applications of Plane Stress: Problem 8.4-8

8.4-8 Solve the preceding problem for the following data: \(P = 160\text{ kN}, N = 200\text{ kN}, L = 2\text{ m}, b = 95\text{ mm}, h = 300\text{ mm}\), and \(d = 200\text{ mm}\). Reference Problem 8.4-7: A cantilever beam (\(L = 2\text{ m}\)) with a rectangular cross section supports an upward load \(P\) at its free end. (a) Find the state of stress (\(\sigma_x, \sigma_y\), and \(\tau_{xy}\) in MPa) on a plane-stress element at \(L/2\) that is \(d = 200\text{ mm}\) up from the bottom of the beam. Find the principal normal stresses and maximum shear stress. Show these stresses on sketches of properly oriented elements. (b) Repeat part (a) if an axial compressive centroidal load \(N\) is added at the free end.