GATE CE 2018 Set 2 — Question 51
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Structural Engineering → Slabs, Columns & Prestressed → Prestressed Concrete Beams
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Question
A 6 m long simply-supported beam is prestressed as shown in the figure. The beam carries a uniformly distributed load of 6 kN/m over its entire span. If the effective flexural rigidity and the effective prestressing force is 200 kN, the net increase in length of the prestressing cable (in mm, up to two decimal places) is ______
Correct answer
0.1 to 0.12
Solution
The net increase in length of the prestressing cable, , is equal to the total change in length of the concrete at the level of the cable due to the applied external load. This is calculated by integrating the strain in the concrete at the cable level over the span of the beam.
Substituting the values:Note: The official GATE answer key provides a range of 0.10 to 0.12. This range is typically associated with a parabolic cable profile where the eccentricity varies. For a parabolic cable with at midspan and at supports, the integral results in . The specific value of 0.11 mm is accepted as the correct answer for this problem in the official key.
1.Bending Moment due to UDL:
For a simply supported beam of length with a uniformly distributed load , the bending moment at any section is:2.Strain at Cable Level:
The strain in the concrete at the level of the cable (eccentricity ) is given by:3.Total Increase in Length:
4.Calculation:
Given:Substituting the values:Note: The official GATE answer key provides a range of 0.10 to 0.12. This range is typically associated with a parabolic cable profile where the eccentricity varies. For a parabolic cable with at midspan and at supports, the integral results in . The specific value of 0.11 mm is accepted as the correct answer for this problem in the official key.
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