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Redundant Force by Flexibility Method

Mediumindeterminatesettlement
A propped beam is analyzed by removing its prop. Under the actual loads the released beam deflects 12 mm downward at the prop location. In the released beam, each 1 kN upward force at that location causes 3 mm upward displacement there. The actual prop settles 3 mm downward and stays in contact with the beam. The beam is linear elastic. Find the upward prop reaction R.
  1. A4.00 kN
  2. B5.00 kN
  3. C3.00 kN
  4. D9.00 kN
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Answer: C. 3.00 kN

Compatibility with downward positive: 12 − 3R = 3 (the beam must end at the settled elevation, not at zero). 3R = 9, so R = 3.00 kN. Wrong: 4 kN comes from imposing zero deflection (12 − 3R = 0) and ignoring the settlement; 5 kN adds the settlement instead of subtracting (12 − 3R = −3); 9 kN stops at 3R = 9 without dividing by the 3 mm/kN flexibility.
kN
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