Topic: Strength of Materials
A massless beam has a loading pattern as shown in the figure. The beam is of rectangular cross section with a width of 30 mm and height of 100 mm. The maximum magnitude of bending stress (in MPa) is given by
- A. 60.0
- B. 67.5
- C. 200
- D. 225
Answer: B. 67.5
Explanation: First, take moments about point C to find the reaction at A: $R_A \times 4 = 6000$, yielding $R_A = 1500$ N. The maximum bending moment occurs where shear force is zero. Setting $\frac{dM}{dx} = 1500 - 3000(x-2) = 0$ gives $x = 2.5$ m. The maximum bending moment is $M = 1500(2.5) - 3000(0.5^2/2) = 3375$ Nm. The section modulus is $Z = \frac{bd²}{6} = \frac{30 \times 100^2}{6} = 50000$ mm$^3 = 5 \times 10^{-5}$ m$^3$. Maximum bending stress $\sigma_{max} = \frac{M_{max}}{Z} = \frac{3375}{5 \times 10^{-5}} = 67.5$ MPa.