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​ = ?3 m5 m

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

L = 8 mP = 40 kN at 3 m
MA = kN·m
2.Easy
P = 60 kNABRA​ = ?RB​5 m3 m

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

L = 8 mP = 60 kN at 5 m
RA = kN
3.Medium
w = 2 kN/mP = 25 kNABMA​ = ?6 m4 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 6 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mP = 25 kN at 6 mw = 2 kN/m from 0 to 10 m
MA = kN·m
4.Medium
P1​ = 70 kNP2​ = 55 kNABCRA​ = ?0.5 m3.5 m2 m

The beam has a pin at A and a roller at B, 4 m from A, and overhangs B to the free end C. Find the vertical reaction RA, taking upward as positive.

AB = 4 mAC = 6 mP1 = 70 kN at 0.5 mP2 = 55 kN at 6 m
RA = kN
5.Hard
P = 45 kN, 50°Q = 45 kNABRA​ = ?3 m5 m2 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 8 m from A, inclined at 50° to the horizontal, and a vertical load Q acts at 3 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 10 mP = 45 kN at 8 m, θ = 50°Q = 45 kN at 3 m
RA = kN
6.Hard
w = 6 kN/mP = 45 kNABRA​RB​ = ?2 m1 m1 m1 m

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

L = 5 mP = 45 kN at 4 mw = 6 kN/m from 2 to 3 m
RB = kN

Answer key

  1. 1. MA = 120 kN·m
  2. 2. RA = 22.5 kN
  3. 3. MA = 250 kN·m
  4. 4. RA = 33.75 kN
  5. 5. RA = 48.07 kN
  6. 6. RB = 39 kN

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