Solved Problems

Problem: A concrete column of cross-section $300 \text{ mm} \times 500 \text{ mm}$ carries a compressive load of 600 kN applied with an eccentricity of 100 mm from the centroid along the strong axis ($y$-axis). Determine the maximum and minimum stresses in the section.

Problem: An element is subjected to $\sigma_x = 80$ MPa (Tension), $\sigma_y = -40$ MPa (Compression), and $\tau_{xy} = 30$ MPa (Counter-clockwise on X-face). Determine the Principal Stresses and Max Shear Stress.

Problem: A solid steel shaft of diameter 50 mm is subjected to a bending moment $M = 1.5$ kN$\cdot$m and a torque $T = 2.0$ kN$\cdot$m. Determine the maximum principal stress.

Problem: An element is subjected to a state of plane stress where $\sigma_x = 50 \text{ MPa}$ (tension), $\sigma_y = 10 \text{ MPa}$ (compression), and $\tau_{xy} = 40 \text{ MPa}$. Find the principal stresses and the maximum shear stress.

Problem: A solid cylindrical shaft with a diameter of $50 \text{ mm}$ is subjected to an axial tensile force $P = 20 \text{ kN}$, a bending moment $M = 300 \text{ N}\cdot\text{m}$, and a torque $T = 400 \text{ N}\cdot\text{m}$. Determine the state of stress ($\sigma_x, \sigma_y, \tau_{xy}$) at the topmost fiber of the shaft's cross-section (the point furthest from the neutral axis under bending).