GATE 2026 CE (CE2) – Question 48
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$^2$.
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 $\pi = 3.14$
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Correct answer: 85.77 to 86.63
Explanation
The prestressing force is $P = 4 \times \frac{3.14 \times 14^2}{4} \times 700 = 430\,808$ N $= 430.8$ kN. The tendons are $300 - 200 = 100$ mm below the centroid, so $e = 100$ mm. The section has $A = 250 \times 600 = 150\,000$ mm$^2$ and $Z = \frac{250 \times 600^2}{6} = 15 \times 10^6$ mm$^3$. The prestress gives a compression at the soffit of $\frac{P}{A} + \frac{Pe}{Z} = 2.872 + 2.872 = 5.744$ N/mm$^2$. The applied moment can cancel this without causing tension: $M = 5.744 \times 15 \times 10^6 = 86.2 \times 10^6$ N·mm $= 86.2$ kN·m.