Question

A simply supported prestressed concrete beam of span 30 m. The initial stress is 1000 MPa. The slip in the jack during tensioning has been 3 mm. If $E_s = 200$ GPa, the loss of prestress due to anchorage is:

• A. 10%
• B. 2%
• C. 12%
• D. 6%

Hint:

Anchorage slip loss is a fixed magnitude of shortening. Therefore, the percentage loss is much higher for shorter beams than for longer beams. For very long spans, this loss often becomes negligible.

Answer 1

The Correct Option is B

Concept: In post-tensioned members, when the jack is released, the wedges move slightly into the anchorage before they can grip the wires. This shortening of the tendon results in a loss of prestress known as anchorage slip loss.

Step 1: Calculate the reduction in stress due to slip.
The loss of stress ($\Delta f_s$) is given by the formula: \[ \Delta f_s = \frac{\Delta L}{L} \times E_s \] Where:
• $\Delta L = 3 \text{ mm}$ (Anchorage slip)
• $L = 30 \text{ m} = 30,000 \text{ mm}$ (Span length)
• $E_s = 200 \text{ GPa} = 200,000 \text{ MPa}$ \[ \Delta f_s = \frac{3}{30,000} \times 200,000 = \frac{1}{10,000} \times 200,000 = 20 \text{ MPa} \]

Step 2: Calculate the percentage loss.
The initial stress is $1000 \text{ MPa}$. \[ \text{Percentage loss} = \left( \frac{\text{Loss of stress}}{\text{Initial stress}} \right) \times 100 \] \[ \text{Percentage loss} = \left( \frac{20}{1000} \right) \times 100 = 2% \]