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 = 10 kNABRA​RB​ = ?1.5 m2.5 m

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

L = 4 mP = 10 kN at 1.5 m
RB = kN
2.Easy
M₀ = 30 kN·mABRB​ = ?3.5 m0.5 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 30 kN·m applied at 3.5 m from A. Find the vertical reaction RB, taking upward as positive.

L = 4 mM₀ = 30 kN·m (clockwise) at 3.5 m
RB = kN
3.Medium
w = 2 kN/mP = 80 kNABRA​ = ?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 vertical reaction RA at the wall.

L = 10 mP = 80 kN at 6 mw = 2 kN/m from 0 to 10 m
RA = kN
4.Medium
P1​ = 55 kNP2​ = 15 kNABRA​ = ?RB​2.5 m0.5 m2 m

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

L = 5 mP1 = 55 kN at 2.5 mP2 = 15 kN at 3 m
RA = kN
5.Hard
w0​ = 8 kN/mP = 15 kNABMA​ = ?6 m2 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 8 kN/m at the wall and falls to zero at the free end B, plus a point load P at 6 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mw0 = 8 kN/mP = 15 kN at 6 m
MA = kN·m
6.Hard
P = 45 kN, 60°Q = 60 kNABRA​ = ?1 m7 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 60° to the horizontal, and a vertical load Q acts at 1 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 = 60°Q = 60 kN at 1 m
RA = kN

Answer key

  1. 1. RB = 3.75 kN
  2. 2. RB = 7.5 kN
  3. 3. RA = 100 kN
  4. 4. RA = 33.5 kN
  5. 5. MA = 175.3 kN·m
  6. 6. RA = 65.76 kN

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