GATE CE 2026 Set 2 — Question 48
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Structural Engineering → Slabs, Columns & Prestressed → Prestressed Concrete Beams
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Question
A 250 mm wide 600 mm deep rectangular concrete beam is prestressed by means of 4 high-tensile tendons, each of 14 mm diameter. The centre of the tendons is 200 mm from the soffit of the beam. The effective stress in each tendon is 700 N/mm.The maximum bending moment (in kN-m), that can be applied to the section without causing tension at the soffit of the beam due to prestressing only, is ______ (rounded off to one decimal place).Use
Correct answer
85.5 to 87.6
Solution
Given data:
Width mm
Depth mm
Number of tendons
Diameter of each tendon mm
Effective stress N/mm
Distance of tendons from soffit = 200 mmStep 1: Calculate geometric properties.
Area of cross-section mm
Section modulus mm
Neutral axis is at mm from soffit.
Eccentricity mmStep 2: Calculate prestressing force .
Area of steel mm
Prestressing force N = 430.808 kNStep 3: Apply the condition for no tension at the soffit.
Stress at the bottom fiber (soffit) due to prestress and external moment must be .Rounding to one decimal place, we get 86.2.
Width mm
Depth mm
Number of tendons
Diameter of each tendon mm
Effective stress N/mm
Distance of tendons from soffit = 200 mmStep 1: Calculate geometric properties.
Area of cross-section mm
Section modulus mm
Neutral axis is at mm from soffit.
Eccentricity mmStep 2: Calculate prestressing force .
Area of steel mm
Prestressing force N = 430.808 kNStep 3: Apply the condition for no tension at the soffit.
Stress at the bottom fiber (soffit) due to prestress and external moment must be .Rounding to one decimal place, we get 86.2.
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