Civil Engineering > GATE 2026 SET-1 > Section Properties
The cross-section of a steel T-beam is shown in the figure where all dimensions are in mm.
Flange: width = 100 mm, thickness = 20 mm
Web: height = 100 mm, thickness = 20 mm
The plastic section modulus of the given cross-section is _________ × 104 mm3 (in integer).
Web: height = 100 mm, thickness = 20 mm
The plastic section modulus of the given cross-section is _________ × 104 mm3 (in integer).
Correct : 12
The plastic section modulus Zp equals the sum of first moments of area of each half about the Plastic Neutral Axis (PNA), which divides the section into two equal areas.
Total area = 100×20 + 20×100 = 2000 + 2000 = 4000 mm². Half area = 2000 mm².
The flange alone has area = 2000 mm² = exactly half the total. So the PNA lies at the bottom of the flange, 20 mm from the top.
First moment of upper half (flange) about PNA:
Qtop = 2000 × 10 = 20,000 mm³ (centroid of flange is 10mm above PNA)
First moment of lower half (web) about PNA:
Qbottom = 2000 × 50 = 100,000 mm³ (centroid of web is 50mm below PNA)
Zp = 20,000 + 100,000 = 120,000 mm³ = 12 × 10⁴ mm³
Correct answer: 12 × 10⁴ mm³
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