Bending moments due to dead load, live load, wind load and seismic load at service conditions on a RC beam are 10 kNm, 5 kNm, 12 kNm and 15 kNm respectively. The design load under limit state collapse is
- A22.5 kNm
- B36 kNm
- C37.5 kNmCorrect
- D45 kNm
Solution
Concept
Load Combinations in Limit State Design
Formula
Mu = max(1.5(DL + LL), 1.5(DL + WL/EL), 1.2(DL + LL + WL/EL))
Step-by-step solution
- Calculate 1.5 × (DL + LL) = 1.5 × (10 + 5) = 22.5 kNm - Calculate 1.5 × (DL + EL) = 1.5 × (10 + 15) = 37.5 kNm using the larger of wind/seismic load - Calculate 1.2 × (DL + LL + EL) = 1.2 × (10 + 5 + 15) = 36 kNm - Take the maximum value: 37.5 kNm
Explanation
As per IS 456, we calculate the limit state of collapse load combinations to find the maximum design bending moment:1. DL + LL: 1.5 × (10 + 5) = 22.5 kNm 2. DL + WL/EL: 1.5 × (10 + 15) = 37.5 kNm (using the larger of wind load 12 kNm or seismic load 15 kNm) 3. DL + LL + WL/EL: 1.2 × (10 + 5 + 15) = 36 kNmThe maximum critical design moment among these combinations is 37.5 kNm, which corresponds to option C.
Common mistake
A common mistake is applying a load factor of 1.5 instead of 1.2 when combining three load cases (DL + LL + EL), leading to 1.5 × (10 + 5 + 15) = 45 kNm (Option D), or choosing Option B (36 kNm) under the assumption that the three-load combination always governs, forgetting to check the 1.5 × (DL + EL) combination which yields the maximum critical value of 37.5 kNm.
Correct answer: C) 37.5 kNm