Prestressed Concrete MCQ with answer and solution

Concept

Initial Prestressing Force and Prestress Loss

Formula

P_initial = P_final / (1 - Loss percentage)

Step-by-step solution

1. Identify the given values: P_final = 300 kN and Loss percentage = 25% (or 0.25). 2. Substitute the values into the formula: P_initial = 300 / (1 - 0.25) = 300 / 0.75. 3. Calculate the final value: P_initial = 400 kN.

Explanation

The final prestressing force represents 75% of the initial force after a 25% loss (100% - 25% = 75%). Dividing the final force of 300 kN by 0.75 gives the initial prestressing force of 400 kN.

Shortcut

Initial Force = Final Force ÷ Remaining Fraction. For a 25% loss, 75% (3/4) remains, so multiply the final force by 4/3 (or add 1/3 of the final force: 300 + 100 = 400 kN).

Common mistake

Calculating 25% of the final force (300 kN) to get 75 kN and adding it to 300 kN to choose 375 kN (Option C), rather than calculating the 25% loss relative to the initial prestressing force.