Solved Problems

Problem: A simply supported rectangular timber beam is 4 m long, 200 mm wide, and 300 mm deep. It carries a uniformly distributed load of 10 kN/m over its entire length. Determine the maximum flexural stress.

Problem: Using the same beam as Example 1, determine the maximum shearing stress.

Problem: A T-beam has a flange width of 100 mm, flange thickness of 20 mm, web thickness of 20 mm, and total depth of 120 mm. The web depth is $120 - 20 = 100$ mm. If the vertical shear force $V = 10$ kN, determine the shear stress at the junction of the flange and the web.

Problem: A W-shape steel beam (W410x60) is subjected to a maximum bending moment of $250 \text{ kN}\cdot\text{m}$. From the steel manual, the section properties are: depth $d = 407 \text{ mm}$, moment of inertia $I_x = 216 \times 10^6 \text{ mm}^4$. Calculate the maximum bending stress and state whether it exceeds an allowable stress of $165 \text{ MPa}$.