Question

For the square steel beam cross-section shown in the figure, the shape factor about \(z - z\) axis is \(S\) and the plastic moment capacity is \(M_P\). Consider yield stress \(f_y = 250 \, \text{MPa}\) and \(a = 100 \, \text{mm}\). The values of \(S\) and \(M_P\) (rounded-off to one decimal place) are:

• A. \(S = 2.0, \, M_P = 58.9 \, \text{kN-m}\)
• B. \(S = 2.0, \, M_P = 100.2 \, \text{kN-m}\)
• C. \(S = 1.5, \, M_P = 58.9 \, \text{kN-m}\)
• D. \(S = 1.5, \, M_P = 100.2 \, \text{kN-m}\)

Hint:

To calculate the shape factor and plastic moment capacity, use the standard formulas for section moduli and apply the yield stress to get the moment capacity.

Answer 1

The Correct Option is A

The shape factor \(S\) for a given section is the ratio of the plastic section modulus \(Z_P\) to the elastic section modulus \(Z_E\). For a square section, the shape factor is given by: \[ S = \frac{Z_P}{Z_E} \] For the square section, the plastic moment \(M_P\) is determined by the plastic section modulus and yield stress, i.e., \[ M_P = Z_P \cdot f_y \] Substitute the values:
- The yield stress \(f_y = 250 \, \text{MPa} = 250 \, \text{N/mm}^2\),
- The dimension \(a = 100 \, \text{mm}\).
After performing the calculations for the section modulus and using the standard formulas for the plastic section modulus and elastic section modulus, we get: - \(S = 2.0\),
- \(M_P = 58.9 \, \text{kN-m}\).
Thus, the correct answer is (A).