The extreme stress at the top and bottom edges of a prestressed beam when tendons are placed along the longitudinal axis of the beam are

This question was previously asked in

MPSC AE CE Mains 2017 Official (Paper 1)

Option 1 : \(\frac{P}{A} \pm \frac{M}{Z}\)

**Concept:**

**Prestressed Beam:**

- Prestressed beam concrete is a form of concrete used in construction.
- In a prestressed concrete member, the internal stresses are introduced in a planned manner so that. the stresses resulting from the superimposed loads are counteracted to the desired degree.

**Stress distribution:**

According to the figure,

Extreme stress the top edges = \(\frac{P}{A} + \frac{M}{Z}\)

Extreme stress the bottom edges = \(\frac{P}{A} - \frac{M}{Z}\)

__Additional Information__

Assumptions:

- Concrete is
**homogenous, elastic, material.** - Stress variation in steel due to external load is negligible.
**Hooke's law is valid.**- The plane section before bending remains plane after bending.
- Stress in reinforcement does not change along with the member.