Beam support reactions worksheet with answers

Free printable Beam support reactions worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
P = 40 kNABMA​ = ?8 m

The cantilever beam is fixed to the wall at A and carries a point load P at its free end B. Find the magnitude of the reaction moment MA at the wall.

L = 8 mP = 40 kN at 8 m
MA = kN·m
2.Easy
P = 35 kNABRA​ = ?RB​2 m6 m

The simply supported beam has a pin at A and a roller at B. Find the vertical support reaction RA.

L = 8 mP = 35 kN at 2 m
RA = kN
3.Medium
w = 3 kN/mP = 50 kNABMA​ = ?2 m1 m1 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 2 m and a point load P at 3 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mP = 50 kN at 3 mw = 3 kN/m from 0 to 2 m
MA = kN·m
4.Medium
w = 12 kN/mP = 30 kNABMA​ = ?1.5 m2.5 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w along its whole length and a point load P at 1.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mP = 30 kN at 1.5 mw = 12 kN/m from 0 to 4 m
MA = kN·m
5.Hard
w0​ = 15 kN/mP = 40 kNABMA​ = ?2 m3 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 15 kN/m at the wall and falls to zero at the free end B, plus a point load P at 2 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 15 kN/mP = 40 kN at 2 m
MA = kN·m
6.Hard
w = 3 kN/mP = 70 kNABCRA​ = ?0.5 m2 m2 m1.5 m

The beam has a pin at A and a roller at B, 4.5 m from A, and overhangs B to the free end C. It carries a point load P at 0.5 m from A and a uniformly distributed load w from 2.5 m to the free end at 6 m. Find the vertical reaction RA, taking upward as positive.

AB = 4.5 mAC = 6 mP = 70 kN at 0.5 mw = 3 kN/m from 2.5 to 6 m
RA = kN

Answer key

  1. 1. MA = 320 kN·m
  2. 2. RA = 26.25 kN
  3. 3. MA = 156 kN·m
  4. 4. MA = 141 kN·m
  5. 5. MA = 142.5 kN·m
  6. 6. RA = 62.81 kN

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