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: Find the stress before any losses.
\[ \sigma_{initial} = \frac{P}{A} = \frac{300 \times 10^3}{15000} = 20\,\mathrm{N/mm^2} = 20\,\mathrm{MPa}. \]
Step 2: Apply the 20 percent loss straight to the stress.
Since stress is directly proportional to the prestressing force for a fixed area, a 20 percent drop in force means a 20 percent drop in stress too.
Step 3: Calculate the effective stress.
\[ \sigma_{eff} = \sigma_{initial}(1 - 0.20) = 20 \times 0.8 = 16\,\mathrm{MPa}. \]
\[ \boxed{16\,\mathrm{MPa}} \]