The design criterion for laterally supported steel beams with respect to crippling recommends that the maximum permissible bearing stress should NOT exceed _______ times of the yield stress of steel (fy).
- A0.80
- B0.40
- C0.75Correct
- D0.66
Solution
Concept
Under the working stress method (IS 800:1984), the bearing stress in the web at the root of the flange, where a concentrated load or reaction acts, is limited to 0.75 fy.
Formula
σp = F / [(b + n2) tw] ≤ 0.75 fy, where n2 = 2.5 × (flange thickness + root radius) for 1:2.5 dispersion
Step-by-step solution
1. Web crippling is local yielding of the thin web under a concentrated load or support reaction. 2. The load spreads through the flange into the web at a slope of 1:2.5. 3. Bearing length = b + n2, where b is the stiff bearing length. 4. Bearing stress = Load / (bearing length × web thickness). 5. Under the working stress method, this stress must not exceed 0.75 fy. 6. So the answer is 0.75, option (C).
Explanation
Crippling means the web crushes or buckles locally under a heavy point load or reaction. To prevent this, the code limits the bearing stress in the web to 0.75 times the yield stress. If the stress is higher, bearing stiffeners must be provided.
Why the other options are wrong
(A) 0.80 is not the code limit for web bearing. (B) 0.40 is close to the permissible average shear stress (0.4 fy), not bearing stress. (D) 0.66 is the permissible bending stress (0.66 fy), not bearing stress.
Shortcut
In WSM, remember: bending 0.66 fy, average shear 0.4 fy, bearing 0.75 fy.
Common mistake
Students often pick 0.66 fy because it is the permissible bending stress.
Correct answer: C) 0.75