Question

A rectangular concrete beam of width 120 mm and depth 200 mm is prestressed by pre-tensioning to a force of 150 kN at an eccentricity of 20 mm. The cross-sectional area of the pre-stressing steel is 187.5mm${}^2$. Take modulus of elasticity of steel and concrete as 2.1 x 10${}^5$ MPa and 3.0 x 10${}^4$ MPa respectively. The percentage loss of stress in the pre-stressing steel due to elastic deformation of concrete is

• A. 8.75
• B. 6.125
• C. 4.81
• D. 2.19

Answer 1

The correct option is B 6.125

Pretensioning force
P = 150 kN
Eccentricity, e = 20 mm
Cross sectional area of beam
= 120 mm x 200 mm
Stress in concrete at the level of steel bar
${\sigma }_c=\frac{P}{A}+\frac{\left(Pe\right).e}{I}$

$=\frac{150\times {10}^3}{120\times 200}+\frac{(150\times {10}^3\times 20)\times 20}{120\times \frac{(200{)}^3}{12}}$
$=7MPa$

Loss in stress of steel bar$=m.{\sigma }_c$

$=\frac{E_s}{E_c}.{\sigma }_c=\frac{2.1\times {10}^5}{3\times {10}^4}\times 7=49MPa$

Initial stress in steel bar

$=\frac{Force}{Area}=\frac{150\times {10}^3}{187.5}=800MPa$

$\%lossofstress=\frac{49}{800}\times 100=6.125$