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GATE 2022 CE (CE2) – Question 38

Steel Structures · Plastic analysis of beams and portal frames · 2 marks · Multiple choice

For the square steel beam cross-section shown in the figure, the shape factor about z−z axis is S and the plastic moment capacity is MP. Consider yield stress fy = 250 MPa and a = 100 mm. The values of S and MP (rounded-off to one decimal place) are

Square HIJK oriented as a diamond, side a, with horizontal bending axis z–z through H and J. See the attached source image.
  1. S = 2.0, MP = 58.9 kN-m
  2. S = 2.0, MP = 100.2 kN-m
  3. S = 1.5, MP = 58.9 kN-m
  4. S = 1.5, MP = 100.2 kN-m

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Correct answer: (A) S = 2.0, MP = 58.9 kN-m

Explanation

About the diagonal axis, $I=a^4/12$ and extreme-fibre distance is $a/\sqrt2$, so $Z_e=\sqrt2a^3/12$. Integrating the triangular half-section gives $Z_p=\sqrt2a^3/6$.

Thus S=Zₚ/Zₑ=2. With a=100 mm and fᵧ=250 MPa, $M_p=f_yZ_p=58.9256$ kNm. **2.0 and 58.9 kNm (A)**.