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GATE 2023 CE (CE1) – Question 38

Steel Structures · Design of beams, beam-columns and column bases · 2 marks · Multiple choice

Consider the horizontal axis passing through the centroid of the steel beam cross-section shown in the figure. What is the shape factor (rounded off to one decimal place) for the cross-section?

a plus-shaped (cross) section. The vertical bar is $b$ wide and $3b$ tall, and the horizontal bar is $3b$ wide and $b$ tall, crossing at the centre.
  1. 1.5
  2. 1.7
  3. 1.3
  4. 2.0

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Correct answer: (B) 1.7

Explanation

The section is symmetric about the horizontal axis through the centre. The moment of inertia is $I = \frac{b(3b)^3}{12} + 2\frac{b^4}{12} = \frac{29b^4}{12}$, and with $y_{max} = 1.5b$ the elastic modulus is $Z = \frac{29b^3}{18} = 1.611b^3$. The plastic neutral axis is the same axis (equal areas of $2.5b^2$ above and below). The plastic modulus is twice the first moment of the upper half: $2\left(1.5b^2 \times 0.75b + 1.0b^2 \times 0.25b\right) = 2.75b^3$. The shape factor is $\frac{2.75}{1.611} = 1.7$.