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A rectangular concrete beam of width 120 mm and depth 200 mm is pre-stressed by pre-tensioning to a force of 150 kN at an eccentricity of 20 mm. The cross sectional area of the prestressing steel is 187.5 mm2. Take modulus of elasticity of steel and concrete as 2.1 × 105 MPa and 3.0 × 104 MPa respectively. The percentage loss of stress in the prestressing steel due to elastic deformation of concrete is
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- 8.75
- 6.125
- 4.81
- 2.19
Correct Option: B
Initial direct stress
| = | = | |||
| A | bd |
| = | = 6.25 N/mm2 | 120 × 200 |
| = | ||||
| I | y |
| ∴ f = | × e | I |
| = | × 20 | ||
| × 120 × (200)3 | |||
| 12 | |||
= 0.75 N/mm2
Max. compression in concrete = 6.25 + 0.75
= 7 N/mm2
strain in concrete
| = | = | |||
| Es | 3 × 104 |
= 2.33 ×10-4
loss of tensile stress = 2.33 × 10-4 × 2.1 × 105 = 40 N/mm2
| Initial stress = | = 800 N/mm2 | 187.5 |
| % loss = | = 6.125% | 800 |
