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Displacement by Maxwell Reciprocity

Easyreciprocitymaxwell-betti
A stable, linearly elastic structure is initially unloaded. A 10 kN force at point A in direction a causes a displacement of 3 mm at point B in direction b. In a separate load case, only a 15 kN force acts at B in direction b. The supports and members are the same. Find the displacement at A in direction a for the second case.
  1. A4.50 mm
  2. B3.00 mm
  3. C2.00 mm
  4. D0.300 mm
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Answer: A. 4.50 mm

Flexibility coefficient fBA = 3 mm / 10 kN = 0.300 mm/kN. Maxwell–Betti reciprocity: fAB = fBA = 0.300 mm/kN. For 15 kN at B: δA = 0.300(15) = 4.50 mm. Check by reciprocal work: 10(4.5) = 15(3) = 45 kN·mm. Wrong: 3.00 mm equates displacements even though the forces differ; 2.00 mm scales in the wrong direction (3 × 10/15); 0.300 mm is the flexibility coefficient, never multiplied by the 15 kN.
mm
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