GATE CE 2023 Set 1 — Question 38
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Structural Engineering → Connections & Plastic Analysis → Shape Factor & Collapse Load
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Question
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?
Correct answer
(B) 1.7
Solution
The cross-section is a cross shape composed of five squares of side .
Total Area .
Due to symmetry, the centroidal axis (X-X) passes through the center of the middle square. 1. Moment of Inertia ():
The section can be seen as a central vertical rectangle () and two side squares ().Elastic Section Modulus .2. Plastic Section Modulus ():
for the area above the equal area axis. Upper half area . It consists of:
Total Area .
Due to symmetry, the centroidal axis (X-X) passes through the center of the middle square. 1. Moment of Inertia ():
The section can be seen as a central vertical rectangle () and two side squares ().Elastic Section Modulus .2. Plastic Section Modulus ():
for the area above the equal area axis. Upper half area . It consists of:
- Top square: Area , distance from centroidal axis to its own centroid .
- Upper half of middle horizontal bar: Area , distance from centroidal axis to its own centroid .
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