Question

A steel beam is subjected to a bending moment of \(60\,\mathrm{kN\!-\!m}\). If the allowable bending stress is \(150\,\mathrm{MPa}\), the required section modulus is

• A. \(2\times10^5\,\mathrm{mm^3}\)
• B. \(3\times10^5\,\mathrm{mm^3}\)
• C. \(4\times10^5\,\mathrm{mm^3}\)
• D. \(5\times10^5\,\mathrm{mm^3}\)

Hint:

For bending, \[ \boxed{ Z=\frac{M}{\sigma_b}. } \] Always convert the bending moment into \(\mathrm{N\,mm}\).

Answer 1

The Correct Option is C

Step 1: Use the bending equation. The required section modulus is \[ Z=\frac{M}{\sigma_b}, \] where \[ M=60\,\mathrm{kN\!-\!m} =60\times10^6\,\mathrm{N\,mm}, \] and \[ \sigma_b=150\,\mathrm{N/mm^2}. \]

Step 2: Calculate the section modulus. \[ Z = \frac{60\times10^6}{150} = 4\times10^5\,\mathrm{mm^3}. \] Hence, \[ \boxed{4\times10^5\,\mathrm{mm^3}} \] is the correct answer. Therefore, \[ \boxed{(C)} \] is the correct answer.