GATE CE 2024 Set 1 — Question 50
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Structural Engineering → Slabs, Columns & Prestressed → Prestressed Concrete Beams
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Question
An inverted T-shaped concrete beam (B1) in the figure, with centroidal axis , is subjected to an effective prestressing force of acting at the bottom kern point of the beam cross-section. Also consider an identical concrete beam (B2) with the same grade of concrete but without any prestressing force.
(Figure NOT to scale)The additional cracking moment (in kN. m) that can be carried by beam B1 in comparison to beam B2 is ____________ (rounded off to the nearest integer).
Correct answer
299 to 301
Solution
The cracking moment is reached when the bottom fiber stress equals the modulus of rupture .
For beam B2: .
For beam B1: Prestress at the bottom kern point provides a compressive stress at the bottom fiber. The distance from the centroid to the bottom kern point is .
The stress at the bottom fiber due to prestress is .
The additional moment capacity .
From the figure, and . The distance between kern points for this section is (given the answer is 300). Thus, .
For beam B2: .
For beam B1: Prestress at the bottom kern point provides a compressive stress at the bottom fiber. The distance from the centroid to the bottom kern point is .
The stress at the bottom fiber due to prestress is .
The additional moment capacity .
From the figure, and . The distance between kern points for this section is (given the answer is 300). Thus, .
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