According to IS 456:2000, equivalent moment in rectangular RCC beam under torsion can be calculated as
- AMe = Mu + (1 + b/D) / 1.7
- BMe = Mu + (1 – b/D) / 1.7
- CMe = Mu + (1 + D/b) / 1.7Correct
- DMe = Mu + (1 – D/b) / 1.7
Solution
Concept
Equivalent Bending Moment under Torsion
Formula
Mel = Mu + (Tu / 1.7) × (1 + D/b)
Step-by-step solution
Calculate the torsional bending moment Mt using Mt = (Tu / 1.7) × (1 + D/b), then add Mt to the ultimate bending moment Mu to obtain the equivalent bending moment Mel = Mu + Mt.
Explanation
According to IS 456:2000, when a beam experiences torsion along with bending, the torsional moment Tu is converted into an additional equivalent bending moment Mt, given by Mt = (Tu / 1.7) × (1 + D/b). Adding this extra moment to the actual bending moment Mu gives the total equivalent bending moment Mel = Mu + Mt.
Shortcut
Remember the formula using the ratio of overall depth to width (D/b) added to 1, divided by 1.7: Mel = Mu + (1 + D/b) / 1.7 Key trick: The section dimension ratio always puts the larger dimension Depth (D) on top over Width (b) as (1 + D/b), and the sign is always positive (+).
Common mistake
A common mistake is confusing the ratio of section dimensions by using width over depth (b/D) instead of depth over width (D/b), leading students to incorrectly choose Option A. Another frequent error is confusing the sign in the formula and using a minus sign instead of a plus sign.
Correct answer: C) Me = Mu + (1 + D/b) / 1.7