Question

A post-tensioned concrete beam of 100 mm x 300 mm rectangular section is having cable with zero eccentricity at the supports and an eccentricity of 50 mm at the centre of span. The cross sectional area of the cable is $200m{m}^2$ and initial stress in the cable is $1200N/m{m}^2$, If the ultimate creep strain is $30\times {10}^{-6}$ mm/mm per $N/m{m}^2$ of stress and modulus of elasticity of steel is $210kN/m{m}^2$ then the loss of stress in steel only due to creep of concrete is______ $N/m{m}^2$.

• A. 62

Answer 1

The correct option is A 62
Area, A = $300\times 100=30000m{m}^2$

P = $200\times 1200=240000N$

$I=\frac{100\times {300}^3}{12}=225\times {10}^{6}m{m}^4$

e = 50 mm

Stress in concrete at the level of steel,

Direct stress = $\frac{P}{A}=\frac{240000}{30000}=8N/m{m}^2$

Flexural stress = $\frac{M}{I}y=\frac{(24\times {10}^4\times 50)\times 50}{225\times {10}^6}=2.667N/m{m}^2$

$\therefore$ Average stress at the level of steel,
$f_c=8+\frac{2}{3}\times 2.667\approx 9.8N/m{m}^2$

$\therefore$ Loss of stress in the cable due to creep of concrete

$={\epsilon }_{cc}{f}_c{E}_s,$
$=30\times {10}^{-6}\times 9.8\times 210\times {10}^3$

$=61.74N/m{m}^2\simeq 62N/m{m}^2$