Question

A pre-tensioned concrete member of section 200 mm x 250 mm contains tendons of area 500 mm ${}^2$ at centre of gravity of the section. The pre-stress in the tendons is 1000 N/mm${}^2$. Assuming modular ratio as 10, the stress (N/mm${}^2$) in concrete is

• A. 11
• B. 9
• C. 7
• D. 5

Answer 1

The correct option is B 9

Area of cross section
$=200\times 250=5\times {10}^{4}m{m}^2$

Moment of inertia
$I=\frac{b{d}^3}{12}=\frac{200\times {250}^3}{12}=260.415\times {10}^{6}m{m}^4$

Modular ratio, m =10
Prestress in tendon = 1000 N/mm${}^2$
Area of tendon, $A_s=500m{m}^2$
Prestressing force, P$=1000\times 500=5\times {10}^{5}N$

Stress in concrete at the level of steel

$\sigma =\frac{P}{A}+\frac{M.y}{I}=\frac{5\times {10}^5}{5\times {10}^4}+0=10N/m{m}^2$

Loss of prestress due to elastic shortening of concrete ,

$\Delta \sigma =m\sigma =10\times 10=100N/m^2$

$\therefore$ Stress in wire after loss = 1000 - 100 = 900 N/mm${}^2$
Stress in concrete corresponding to 1000 N/mm${}^2$ prestress = 10 N/mm${}^2$

Stress in concrete corresponding to 900 N/mm${}^2$ prestress

$=\frac{10}{1000}\times 900=9N/m{m}^2$