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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 187.5mm2. Take modulus of elasticity of steel and concrete as 2.1 x 105 MPa and 3.0 x 104 MPa respectively. The percentage loss of stress in the pre-stressing steel due to elastic deformation of concrete is

A
8.75
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B
6.125
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C
4.81
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D
2.19
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Solution

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
σc=PA+(Pe).eI

=150×103120×200+(150×103×20)×20120×(200)312
=7MPa

Loss in stress of steel bar =m. σc

=EsEc.σc=2.1×1053×104×7=49 MPa

Initial stress in steel bar

=ForceArea=150×103187.5=800 MPa

%loss of stress =49800×100=6.125

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