GATE CE 2022 Set 2 — Question 39
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Structural Engineering → Slabs, Columns & Prestressed → Losses in Prestress
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Question
A post-tensioned concrete member of span 15 m and cross-section of 450 mm 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 mm. The tendons are tensioned one after another to a stress of 1500 MPa. All the tendons are straight and located at 125 mm from the bottom of the member. Assume the prestress to be the same in all tendons and the modular ratio to be 6. The average loss of prestress, due to elastic deformation of concrete, considering all three tendons is
Correct answer
(A) 14.16 MPa
Solution
Given data:
Span m
Cross-section mm 450 mm
Area of concrete mm
Moment of Inertia mm
Number of tendons
Area of each tendon mm
Initial stress MPa
Prestressing force per tendon N
Eccentricity mm
Modular ratio Stress in concrete at the level of steel due to one tendon:
MPaIn post-tensioning, when tendons are tensioned sequentially:
Average loss = MPa MPa.Hence, the correct option is (A).
Span m
Cross-section mm 450 mm
Area of concrete mm
Moment of Inertia mm
Number of tendons
Area of each tendon mm
Initial stress MPa
Prestressing force per tendon N
Eccentricity mm
Modular ratio Stress in concrete at the level of steel due to one tendon:
MPaIn post-tensioning, when tendons are tensioned sequentially:
- Tendon 1 (tensioned first) suffers loss when Tendon 2 and Tendon 3 are tensioned. Total loss = MPa
- Tendon 2 (tensioned second) suffers loss when Tendon 3 is tensioned. Total loss = MPa
- Tendon 3 (tensioned last) suffers no loss due to elastic shortening. Loss = 0
Average loss = MPa MPa.Hence, the correct option is (A).
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