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Maximum Moment at a Section, Moving Load

Mediuminfluence-linesmoving-load
A single 30 kN downward point load can be placed anywhere on a 10 m simply supported beam. There are no other loads. Consider the fixed section 4 m from the left support, with sagging moment positive. Find the greatest bending moment at that section and where the load must be to cause it.
  1. A75.0 kN·m, load at x = 5 m
  2. B72.0 kN·m, load at x = 4 m
  3. C72.0 kN·m, load at x = 5 m
  4. D120 kN·m, load at x = 4 m
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Answer: B. 72.0 kN·m, load at x = 4 m

The moment influence line for the section peaks at the section itself, with ordinate ab/L = 4(6)/10 = 2.4 m. Place the load there: M = 30(2.4) = 72.0 kN·m. Wrong: 75 kN·m = PL/4 is the absolute maximum anywhere on the beam (load at midspan), not at this section; 72 at x = 5 has the right value but the wrong position (with the load at x = 5 the section moment is only 30(2.0) = 60 kN·m); 120 = P·a omits the factor b/L.
kN·m
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