GATE 2024 CE (CE2) – Question 33
The steel angle section shown in the figure has elastic section modulus of 150.92 cm$^3$ about the horizontal X−X axis, which passes through the centroid of the section.
[Figure: an L-shaped angle section with a vertical leg of 15 cm overall height and thickness 3 cm, and a horizontal leg of 12 cm overall width and thickness 3 cm at the bottom. The axis X-X passes through the centroid.]
The shape factor of the section is ________ (rounded off to 2 decimal places).
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Show answer and explanation
Correct answer: 1.78 to 1.80
Explanation
The area is $15 \times 3 + 9 \times 3 = 72$ cm², so the plastic neutral axis divides it into two areas of 36 cm². The bottom flange $12 \times 3$ has exactly 36 cm², so the plastic neutral axis lies at the top of the flange, 3 cm above the base. Above it is the part of the vertical leg from 3 to 15 cm (12 cm tall, 3 cm wide, area 36 cm²), with its centroid at 9 cm, that is 6 cm above the axis. Below it is the flange with its centroid 1.5 cm below the axis. The plastic modulus is $Z_p = 36 \times 6 + 36 \times 1.5 = 270$ cm³. The shape factor is $\frac{Z_p}{Z_e} = \frac{270}{150.92} = 1.79$.