In a pre-stressed beam carrying an external load W with a bent tendon is having angle of inclination θ and pre-stressed load P. The net downward load at the centre is

The net downward load at the center of the beam is:

W - 2P sin(α)

This is because the pre-stressed load P is acting in the opposite direction to the external load W, and the angle of inclination α affects the vertical component of the pre-stressed load.

Here's the breakdown:

- W is the external load acting downward
- 2P sin(α) is the upward component of the pre-stressed load, where:
- 2P is the total pre-stressed load (acting in both directions)
- sin(α) is the vertical component of the pre-stressed load, due to the angle of inclination α

So, the net downward load at the center is the external load minus the upward component of the pre-stressed load.