GATE 2026 CE (CE1) – Question 52

Steel Structures · Plastic analysis of beams and portal frames · 2 marks · Numerical answer

The cross-section of a steel T-beam is shown in the figure where all dimensions are in mm.

The plastic section modulus of the given cross-section is _________ $\times 10^4$ mm$^3$ (*in integer*).

A T-section with a flange 100 mm wide and 20 mm thick, and a web 20 mm wide and 100 mm deep hanging below the flange.

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Correct answer: 12

Explanation

The flange area is $100 \times 20 = 2000$ mm$^2$ and the web area is $20 \times 100 = 2000$ mm$^2$, so each half of the 4000 mm$^2$ section has 2000 mm$^2$. The plastic neutral axis is at the junction of the flange and the web. The centroid of the flange is 10 mm above it and the centroid of the web is 50 mm below it. So $Z_p = 2000 \times 10 + 2000 \times 50 = 120{,}000$ mm$^3$, which is $12 \times 10^4$ mm$^3$.