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Bending Moment from an Influence Line

Mediuminfluence-linesmoment
A simply supported beam has a pin at A and a roller at B, span 10 m, with x measured from A. Two downward point loads act: 20 kN at x = 2 m and 30 kN at x = 8 m. Neglect self-weight. Using the influence line for bending moment, find the sagging bending moment at the section x = 4 m.
  1. A24.0 kN·m
  2. B88.0 kN·m
  3. C52.0 kN·m
  4. D48.0 kN·m
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Answer: D. 48.0 kN·m

Moment influence ordinates for a section a = 4, b = 6, L = 10: for a load left of the section y = xb/L, right of it y = a(L−x)/L. 20 kN at x = 2: y = 2(6)/10 = 1.2 m. 30 kN at x = 8: y = 4(2)/10 = 0.8 m. M = 20(1.2) + 30(0.8) = 24 + 24 = 48 kN·m. Check: RA = 22 kN, M = 22(4) − 20(2) = 48. Wrong: 24 counts only one load; 88 is RA·4 without subtracting the 20 kN load's moment; 52 swaps the two ordinates (20 × 0.8 + 30 × 1.2).
kN·m
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