Question

A rectangular concrete beam 250 mm wide and 600 mm deep is pre-stressed by means of 16 high tensile wires, each of 7 mm diameter, located at 200 mm from the bottom face of the beam at a given section. If the effective pre-stress in the wires is 700 MPa, what is the maximum sagging bending moment (in kNm)(correct to 1-decimal place) due to live load that this section of the beam can withstand without causing tensile stress at the bottom face of the beam? Neglect the effect of dead load of beam .______

• A. 86.16

Answer 1

The correct option is A 86.16

Area of pre-stressed steel
$=\frac{16\times \pi \times 7^2}{4}m{m}^2$

Force of prestress

$=\frac{16\times \pi \times 49\times 700N}{4}$

= 430.808 kN

The moment caused by prestress,
F x e = 43.0808 kNm

The various stress diagrams are; Taking tension (+)ve and compression (-)ve,



$F/A=\frac{430.808\times {10}^{3}N}{250\times 600}m{m}^2$

$=2.872N/m{m}^2$

Flexural stress due to moment caused by pre-stress i.e.,

M = 43.0808 kN-m

$f_{max}=\frac{M}{z}$,

$\left[\begin{array}{c}z=\frac{I}{y}=\frac{1}{12}\times \frac{250\times (600{)}^3}{300}m{m}^3\\ =15\times {10}^{6}m{m}^3\end{array}\right]$

$=2.872N/m{m}^2$

The net stress diagram;



The additional sagging moment that can be applied without causing tensile stress at the bottom face of the beam should generate the maximum tensile stress of 5.744 MPa.

$\Rightarrow M=f\times z$

$=5.744N/m{m}^2\times 15\times {10}^{6}m{m}^3$

M = 86.16 kN-m