GATE CE 2017 Set 2 — Question 40
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Structural Engineering → Slabs, Columns & Prestressed → Prestressed Concrete Beams
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Question
A simply supported rectangular concrete beam of span has to be prestressed with a force of . The tendon is of parabolic profile having zero eccentricity at the supports. The beam has to carry an external uniformly distributed load of intensity . Neglecting the self-weight of the beam, the maximum dip (in meters, up to two decimal places) of the tendon at the mid-span to balance the external load should be __________
Correct answer
0.14 to 0.16
Solution
According to the load balancing concept in prestressed concrete, a parabolic tendon with a dip and prestressing force over a span exerts an equivalent upward uniformly distributed load given by:To balance the external uniformly distributed load , we equate the two:Substituting the given values (, ):Thus, the maximum dip required at the mid-span is .
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