Solved Problems

Problem: A steel rod with a cross-sectional area of 200 mm$^2$ and a length of 5 m is subjected to an axial tensile load of 50 kN. Determine the elongation of the rod. Assume $E = 200$ GPa.

Problem: Two plates are connected by a single 20 mm diameter bolt in a lap joint. If a tensile force of 100 kN is applied to the plates, determine the average shear stress in the bolt.

Problem: A steel bar is rigidly held between two unyielding supports at 20°C. If the temperature is raised to 60°C, determine the thermal stress developed in the bar. Assume $\alpha = 11.7 \times 10^{-6} /^\circ\text{C}$ and $E = 200$ GPa.

Problem: A light fixture weighing 500 kg is supported by a vertical steel rod. If the allowable tensile stress is 100 MPa, determine the minimum required diameter of the rod. (Use $g = 9.81 \text{ m/s}^2$)

Problem: A heavy uniform vertical steel rod of length $L = 10 \text{ m}$, cross-sectional area $A = 500 \text{ mm}^2$, and density $\rho = 7850 \text{ kg/m}^3$ hangs freely from the ceiling. Determine the total elongation due to its own weight. Assume $E = 200 \text{ GPa}$ and $g = 9.81 \text{ m/s}^2$.

Problem: A tie rod is intended to support a tensile load of 40 kN. It is made of a steel alloy with a yield strength of 250 MPa and an ultimate strength of 400 MPa. If a factor of safety of 2.0 with respect to the yield strength is required, determine the minimum diameter of the rod. What is the Margin of Safety with respect to ultimate failure?