Q.24 A beam cross section has shape of an angle section. Which of the following cross sections has the same nature of shear stress distribution as that of the angle section?
- AT-SectionCorrect
- BTriangular
- CI-Section
- DCross-Section
Solution
Concept
An angle section and a T-section both have one wide flange and one thin web, so their shear stress diagrams have the same shape.
Formula
τ = (F × A × ȳ) / (I × b)
Step-by-step solution
1. Use τ = F A ȳ / (I b). Shear stress is inversely proportional to the width b. 2. In an angle section, the width changes suddenly from the flange width to the web thickness at the junction. 3. So the shear stress jumps suddenly at the junction. The maximum shear stress is at the neutral axis, which lies in the web. 4. The angle is unsymmetrical about the neutral axis, so the neutral axis is not at mid-depth. 5. A T-section has the same features: one flange, one web, a sudden jump at the junction, and an off-centre neutral axis. 6. Answer is (A) T-section.
Explanation
Both the angle section and the T-section have one flange and one web. At the flange-web junction the width changes suddenly, so the shear stress jumps there, and the maximum value is at the neutral axis in the web. The I-section and cross-section are symmetrical, and the triangle has no sudden jump.
Why the other options are wrong
(B) Triangular: the curve is a smooth parabola, maximum at mid-height, with no jump. (C) I-Section: it has two flanges and is symmetrical, so there are two jumps and a symmetric diagram. (D) Cross-section: it is symmetrical, and the jump goes the opposite way (width increases at the centre).
Shortcut
Angle = half of a T (one flange, one web), so its shear diagram is like a T-section.
Common mistake
Choosing the I-section only because it also has flange-web jumps, without noticing that it is symmetrical.
Correct answer: A) T-Section