Difficulty: Medium
Correct Answer: under the load
Explanation:
Introduction / Context:
Moving load analysis is essential for bridges and cranes. Two classic results exist: (1) the absolute maximum bending moment for a single point load occurs at midspan; (2) the maximum bending moment at a given section occurs when the load is directly over that section. The question asks the general location where the maximum occurs for the moving load itself.
Given Data / Assumptions:
Concept / Approach:
For a given position x of the load, the bending moment at that same section is M = R_left * x, and the influence line for bending moment at a section peaks when the load is at the section. Therefore, as the load travels, the bending moment is most intense directly under the load. The absolute maximum over the entire span occurs when the load is at midspan, which still satisfies “under the load.”
Step-by-Step Solution:
Write bending moment at a section z: M_z = IL_M(z) * W.Influence line IL_M(z) attains its peak when the load is at section z.Hence, for the moving load, the maximum at any location is under the load; the global maximum is at midspan when the load is there.
Verification / Alternative check:
Setting derivative dM/dx = 0 for a single point load yields x = L/2 as the position for absolute maximum; this still coincides spatially with the load location.
Why Other Options Are Wrong:
At the supports bending moment is zero for simple supports. At the mid span is true for the absolute maximum location but misses the general “under the load” principle. Anywhere on the beam is vague and incorrect.
Common Pitfalls:
Confusing “absolute maximum over the span” with “location of maximum at any instant.” The correct unifying statement is that the maximum occurs under the load.
Final Answer:
under the load
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