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GATE 2022 CE (CE2) – Question 39

Concrete Structures · Working stress and limit state design concepts · 2 marks · Multiple choice

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 mm2. 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

  1. 14.16 MPa
  2. 7.08 MPa
  3. 28.32 MPa
  4. 42.48 MPa

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Correct answer: (A) 14.16 MPa

Explanation

Each tendon force is $200(1500)=300000$ N and eccentricity is 225−125=100 mm. Concrete stress at tendon level from one tendon is $P/A+Pe^2/I$, where $A=450^2$ and $I=450^4/12$. This gives 2.3594 MPa.

The first tendon loses stress from two later tendons, the second from one, and the third from none. Average loss is $[(2+1+0)/3](6)(2.3594)=\mathbf{14.16}$ MPa, **A**.