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 = 15 kNABRA​ = ?RB​6 m2 m

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

L = 8 mP = 15 kN at 6 m
RA = kN
2.Easy
P = 60 kNABMA​ = ?10 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 = 10 mP = 60 kN at 10 m
MA = kN·m
3.Medium
P1​ = 35 kNP2​ = 25 kNABRA​RB​ = ?2.5 m1.5 m2 m

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

L = 6 mP1 = 35 kN at 2.5 mP2 = 25 kN at 4 m
RB = kN
4.Medium
w = 2 kN/mP = 50 kNABMA​ = ?4 m3 m3 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 4 m and a point load P at 7 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mP = 50 kN at 7 mw = 2 kN/m from 0 to 4 m
MA = kN·m
5.Hard
P = 50 kN, 30°Q = 15 kNABα = ?2 m1.5 m1.5 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 2 m from A, inclined at 30° to the horizontal, and a vertical load Q acts at 3.5 m from A. Find the angle α between the total reaction force at the pin A and the horizontal.

L = 5 mP = 50 kN at 2 m, θ = 30°Q = 15 kN at 3.5 m
α = °
6.Hard
w = 6 kN/mP = 40 kNABCRB​ = ?1.5 m1.5 m0.5 m1.5 m

The beam has a pin at A and a roller at B, 3.5 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 1.5 m to the free end at 5 m. Find the vertical reaction RB, taking upward as positive.

AB = 3.5 mAC = 5 mP = 40 kN at 3 mw = 6 kN/m from 1.5 to 5 m
RB = kN

Answer key

  1. 1. RA = 3.75 kN
  2. 2. MA = 600 kN·m
  3. 3. RB = 31.25 kN
  4. 4. MA = 366 kN·m
  5. 5. α = 24.24 °
  6. 6. RB = 53.79 kN

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