Question

A beam with a rectangular cross section of size 250 mm wide and 350 mm deep is prestressed by a force of 400 kN using number 7 mm $\varphi$ steel cables located at an eccentricity of 75 mm. Determine the loss of prestress due to creep of concrete. Grade of concrete is M 40; Coefficient of creep is 2; stress at transfer is 80%, Modulus of elasticity of steel ($E_s$) is 2.0 x ${10}^5$ MPa.

Answer 1

Prestressing force after transfer = 80% of initial
$=0.8\times 400$
= 320 kN
Stress in concrete at the level of steel

$f_c=\frac{P}{A}+\frac{Pe.e}{I}$
$=\frac{320\times {10}^3}{250\times 350}+\frac{320\times {10}^3\times 75\times 75}{\frac{250\times {350}^3}{12}}$
$=5.672N/m{m}^2$
As per IS : 456 - 2000
Modulus of elasticity of concrete
$E_c=5000\sqrt{f_{ck}}$
$=5000\sqrt{40}$
$=0.3162\times {10}^{5}N/m{m}^2$
Loss of prestress due to creep $=m\varphi f_c$
$=\frac{E_s}{E_c}\varphi f_c$
$=\frac{2\times {10}^5}{0.3162\times {10}^5}\times 2\times 5.672$
$=71.745N/m{m}^2$