📘 mechanics of materials

1. **Problem Statement:** Determine the reactions at supports A and B for an A-36 steel rod of diameter 50 mm, initially at temperature $T_1=80^\circ C$, cooled to $T_2=20^\circ C$

1. **Problem Statement:** Determine the normal stress in cables AB, CD, EF and cable A, and the extension of point E for a rigid bar ACE supported by three steel cables AB, CD, EF.

1. **Problem Statement:** Calculate the maximum shear stress developed in the steel shaft in regions CF and BC.

1. **Problem Statement:** Calculate the maximum shear stresses $\tau_{max}$ at points A and B on the cross section of a cantilevered round peg subjected to a force $F=50000$ N and

1. **Problem Statement:** Determine the internal forces and average normal stresses in the aluminium and steel rods subjected to a 50 kN load at point B.

1. **Problem statement:** A wire DE made of A-36 steel with diameter 5 mm supports a beam with a man of mass 80 kg sitting at seat C. We need to find the elongation of wire DE due

1. **Stating the problem:** We need to determine the magnitude of the average normal stress developed in rods AB, CD, and EF. Rods AB and CD are made of C83400 copper, and rod EF i

1. **State the problem:** We have a bar with cross-sectional area $A = 1385$ mm$^2$ under a compressive load $P = 60000$ N (since 60 kN = 60000 N). The bar is cut at an angle $B =

1. **State the problem:** Calculate the direct axial stress at point A on the top of a rectangular beam with breadth $b=0.03$ m, depth $d=0.21$ m, subjected to an axial compressive

1. **Problem Statement:** Calculate the maximum shear stress in the hollow shaft segment CD subjected to a torque $T_C = 28$ kNm, with inner radius $R_i = 22$ mm and outer radius $

1. **Problem Statement:** Determine the maximum normal stress in bar ABCD with cross-sectional area $600\ \text{mm}^2$ under applied loads 25 kN at B, 20 kN at C, and 30 kN at D.

1. **Problem 01:** Calculate average shear stress in two 20 mm diameter bolts in single shear carrying 150 kN. Formula: Average shear stress $\tau = \frac{F}{A}$ where $F$ is force

1. **Problem Statement:** Determine the minimum width $b$ of a beam subjected to a distributed load of 2000 N/m over 4 m total length, a point load of 5000 N at 1 m from the left s

1. **Problem Statement:** A steel I-section has flange dimensions 200 mm by 12 mm and web dimensions 376 mm by 8 mm. It is subjected to a pure torque. The maximum shear stress allo

1. **Problem Statement:** A rigid bar ABC is supported by two aluminum cables CE and BD, each with diameter $d = \frac{1}{2}$ inches and modulus of elasticity $E = 10000$ ksi. A do

1. **Problem statement:** A thin cylinder with internal diameter $d_i=800$ mm, length $L=5$ m, wall thickness $t=5$ mm is subjected to internal pressure $p=50$ MN/m². Given Poisson

1. **State the problem:** We have a composite cylindrical shaft with an aluminum core radius $r_a = 30$ mm and a steel shell outer radius $r_s = 40$ mm. A torque $T$ is applied at