Which of the following is correct in respect of the influence line for the bending moment at ¼ of the span from left support of a prismatic beam simply supported at ends?
- AIt is composed of straight lines onlyCorrect
- BIt is composed of curved lines only
- CIt is composed of straight and curved lines
- DIt is parabolic.
Solution
Concept
For statically determinate structures, influence lines are made of straight lines only.
Formula
Max ordinate = a b / L
Step-by-step solution
1. A simply supported beam is statically determinate. 2. ILD for BM at a section is a triangle with its peak at the section. 3. With a = L/4 and b = 3L/4, peak ordinate = a b / L = 3L/16. 4. The ILD is two straight lines meeting at the section, so it has straight lines only.
Explanation
A simply supported beam is determinate, so all its influence lines are straight lines. The ILD for BM at L/4 is a triangle with maximum ordinate 3L/16 at the section. Curved ILDs come only in indeterminate structures.
Why the other options are wrong
B, C, D: Curved or parabolic ILDs occur only in indeterminate structures, not in a simply supported beam.
Shortcut
Determinate structure means straight-line ILD. Indeterminate structure means curved ILD.
Common mistake
Confusing the ILD with the BM diagram for UDL, which is parabolic.
Correct answer: A) It is composed of straight lines only