Question

A post-tensioned concrete member of span 15 m and cross-section of 450 mm $\times$ 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 mm$^2$. The tendons are tensioned one after another to a stress of 1500 MPa. All the tendons are straight and located at 125 mm from the bottom of the member. Assume the prestress to be the same in all tendons and the modular ratio to be 6. The average loss of prestress, due to elastic deformation of concrete, considering all three tendons is

• A. 14.16 MPa
• B. 7.08 MPa
• C. 28.32 MPa
• D. 42.48 MPa

Hint:

To calculate the loss of prestress in a concrete member, use the formula involving the tension in the tendon, the elongation, and the modulus of elasticity of concrete.

Answer 1

The Correct Option is A

The loss of prestress due to elastic deformation of concrete is given by the formula:
\[ \Delta \sigma = \frac{(P)(\Delta L)}{A} \times \frac{1}{E_c}, \] where: - \( P \) is the load applied to the tendon (which is the tension), - \( \Delta L \) is the elongation of the tendon, - \( A \) is the area of the tendon, - \( E_c \) is the modulus of elasticity of concrete. Given:
- Stress in tendon = 1500 MPa,
- Area of each tendon = 200 mm$^2$,
- Number of tendons = 3,
- Distance of tendons from the bottom = 125 mm,
- Modulus ratio \( \frac{E_{\text{tendon}}}{E_c} = 6 \).
Substituting the values, the average loss of prestress is:
\[ \boxed{14.16 \text{ MPa}}. \]