Limit state design per IS 456: Unfactored bending moments at a beam section from frame analysis are 50, 80, 120, and 180 kNm due to dead, live, wind, and earthquake loads respectively. What is the design (factored) moment for collapse in flexure?

Introduction / Context:
IS 456 (limit state method) specifies load combinations and partial safety factors to obtain design actions. For beams, the governing factored moment is the maximum among prescribed combinations including gravity plus wind or earthquake, and combined cases (1.2 combination) when lateral loads act with gravity.

Given Data / Assumptions:

• M(D) = 50 kNm, M(L) = 80 kNm, M(W) = 120 kNm, M(E) = 180 kNm (unfactored).
• Use IS 456 load combinations for ultimate limit state.
• Consider both wind and earthquake combinations.

Concept / Approach:

Relevant combinations include: 1.5(D+L); 1.5(D+W) or 1.5(D+E); 1.2(D+L+W) or 1.2(D+L+E); and 0.9D ± 1.5W or 0.9D ± 1.5E for stability. The design moment is the maximum absolute value from these combinations at the section.

Step-by-Step Solution:

Verification / Alternative check:

Since earthquake governs over wind here, the 1.2(D+L+E) combination produces the highest value; check opposite signs if applicable at other sections.

Why Other Options Are Wrong:

• 195 from 1.5(D+L), 250/255 not governing, 345 from 1.5(D+E) is lower, 315 from 0.9D + 1.5E is lower.

Common Pitfalls:

• Ignoring the 1.2 combination which often governs when lateral loads are large.
• Forgetting the 0.9D combinations meant for stability checks.

Final Answer:

372