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 = 65 kNABRA​ = ?RB​5 m1 m

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

L = 6 mP = 65 kN at 5 m
RA = kN
2.Easy
P = 30 kNABRA​RB​ = ?3 m1 m

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

L = 4 mP = 30 kN at 3 m
RB = kN
3.Medium
w = 2 kN/mP = 30 kNABMA​ = ?3.5 m0.5 m1 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 3.5 m and a point load P at 4 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mP = 30 kN at 4 mw = 2 kN/m from 0 to 3.5 m
MA = kN·m
4.Medium
w0​ = 12 kN/mABRB​ = ?5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 12 kN/m at A to zero at B. Find the vertical support reaction RB.

L = 5 mw0 = 12 kN/m
RB = kN
5.Hard
w0​ = 10 kN/mP = 30 kNABMA​ = ?7 m1 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 10 kN/m at the wall and falls to zero at the free end B, plus a point load P at 7 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mw0 = 10 kN/mP = 30 kN at 7 m
MA = kN·m
6.Hard
w = 3 kN/mP = 30 kNABCRB​ = ?3 m2 m1 m2 m

The beam has a pin at A and a roller at B, 6 m from A, and overhangs B to the free end C. It carries a point load P at 3 m from A and a uniformly distributed load w from 5 m to the free end at 8 m. Find the vertical reaction RB, taking upward as positive.

AB = 6 mAC = 8 mP = 30 kN at 3 mw = 3 kN/m from 5 to 8 m
RB = kN

Answer key

  1. 1. RA = 10.83 kN
  2. 2. RB = 22.5 kN
  3. 3. MA = 132.3 kN·m
  4. 4. RB = 10 kN
  5. 5. MA = 316.7 kN·m
  6. 6. RB = 24.75 kN

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