An I-section has flanges 100 mm wide × 20 mm thick and a web 80 mm high × 20 mm thick. The shear stress at point P (in the flange, just above the flange–web junction) is 12 MPa. The shear stress at point Q (in the web, just below the junction) is:
Try it first: pick an option, then read the explanation.
Correct answer: B. 60 MPa
Asked in SSC JE 03/03/2017 (Morning)
Detailed Explanation
Points P and Q are at the same level, just on either side of the change in width. The area above, its ȳ, the shear force and I are identical for both — only the width b differs.
\[ \tau = \frac{VA\bar y}{Ib} \Rightarrow \tau_P\,b_f = \tau_Q\,b_w \Rightarrow \tau_Q = 12\times\frac{100}{20} = 60\ \text{MPa} \]
Why “60 MPa” Is Correct
The web is five times narrower than the flange, so the stress jumps five-fold: 60 MPa.
Why the Other Options Are Wrong
- A. indeterminable due to incomplete data: The ratio of widths is all that is needed.
- C. 18 MPa: 18 MPa does not follow from the width ratio.
- D. 12 MPa: τ is not continuous at a sudden change in width.
Key Point
At a sudden change in width: τ₁b₁ = τ₂b₂ (shear flow is continuous).
Key Concepts for Students
- Shear flow q = τb is continuous across a width change.
- The web stress rises further to the N.A.
- Point stresses at re-entrant corners are smoothed by fillets in rolled sections.
Practice more: this is question 56 in Bending and Shear Stress MCQs – Part 4. Try the whole set and check every answer instantly.