Question

A prestressing force of \(300\,\mathrm{kN}\) is applied to a concrete member of cross-sectional area \(15000\,\mathrm{mm^2}\). Due to losses, \(20\%\) of the prestress is lost. The effective compressive stress in concrete is

• A. \(12\,\mathrm{MPa}\)
• B. \(14\,\mathrm{MPa}\)
• C. \(16\,\mathrm{MPa}\)
• D. \(18\,\mathrm{MPa}\)

Hint:

Prestress after losses: \[ \boxed{P_e=P(1-\text{Loss Fraction})} \] and \[ \boxed{\sigma=\frac{P_e}{A}.} \]

Answer 1

The Correct Option is C

Step 1: Calculate the effective prestressing force. Loss of prestress \[ =20\%. \] Hence, \[ P_e=300(1-0.20)=240\,\mathrm{kN}. \]

Step 2: Calculate the effective compressive stress. \[ \sigma=\frac{P_e}{A} =\frac{240\times10^3}{15000} =16\,\mathrm{N/mm^2} =16\,\mathrm{MPa}. \] Hence, \[ \boxed{16\,\mathrm{MPa}} \] is the correct answer.