Question

A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is ________.

• A. 40

Answer 1

The correct option is A 40

$\theta$ is small so, assume

$sin\theta =tan\theta$

For load balancing.

$2Psin\theta =12$

$2\times 600\times tan\theta =12$

$tan\theta =0.01$

From fig.

$tan\theta =\frac{e}{L/2}=\frac{2e}{L}=0.01$

$\Rightarrow e=\frac{0.01\times 8}{2}$

$\Rightarrow e=0.04m$

$e=40mm$