A series of equal point loads moves across a simply supported beam. To obtain the maximum bending moment at any given section, the loads should be positioned such that
- AAll loads are placed over the longer segment of the span.
- BAll loads are placed over the shorter segment of the span.
- CThe load configuration is symmetric about the section.Correct
- DThe leading load is exactly at the section.
Solution
Concept
Maximum bending moment from moving point loads
Formula
Wleft / a = Wright / b
Step-by-step solution
1. The influence line diagram for bending moment at a given section is triangular, with its apex at the section. 2. For a series of concentrated loads, maximum moment at the section occurs when a load is at the apex and the average load on the left equals the average load on the right. 3. For equal concentrated loads with uniform spacing, this criterion is satisfied when the load group is placed symmetrically about the section. 4. Thus, the load configuration should be symmetric about the section. Answer: C
Explanation
Under a moving series of equal concentrated loads crossing a simply supported beam, the maximum bending moment at a designated cross section occurs when the load system is positioned symmetrically about that section, ensuring equal average load intensity on both sides.
Why the other options are wrong
A) Placing all loads on the longer segment leaves the section with low influence line ordinates. B) Concentrating loads on the shorter segment does not engage peak ILD ordinates. D) Positioning the leading load at the section is the condition for maximum shear force, not bending moment.
Shortcut
Max BM at section = Load system balanced/symmetric about the section (equal average load left and right).
Common mistake
Believing the leading load must be at the section, which maximizes shear force rather than bending moment.
Correct answer: C) The load configuration is symmetric about the section.