GATE CE 2024 Set 2 — Question 33
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Structural Engineering → Connections & Plastic Analysis → Shape Factor & Collapse Load
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Question
The steel angle section shown in the figure has elastic section modulus of about the horizontal axis, which passes through the centroid of the section.
The shape factor of the section is ________ (rounded off to 2 decimal places).
Correct answer
1.75 to 1.85
Solution
1.Identify the dimensions of the angle section:
- Total height () =
- Total width () =
- Thickness of both legs () =
3.Locate the Plastic Neutral Axis (PNA):
The PNA divides the total area into two equal halves ().- Area of the horizontal leg = .
- Since this equals , the PNA lies exactly at the junction of the two legs, which is from the bottom edge.
is the sum of the first moments of area about the PNA.
- Area above PNA () = . Distance of its centroid from PNA () = .
- Area below PNA () = . Distance of its centroid from PNA () = .
5.Calculate the Shape Factor ():
Given elastic section modulus .Rounding off to 2 decimal places, the shape factor is 1.79.
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