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
w = 4 kN/mABMA​ = ?10 m

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

L = 10 mw = 4 kN/m from 0 to 10 m
MA = kN·m
2.Easy
M₀ = 10 kN·mABRA​ = ?1 m7 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 10 kN·m applied at 1 m from A. Find the vertical reaction RA, taking upward as positive.

L = 8 mM₀ = 10 kN·m (clockwise) at 1 m
RA = kN
3.Medium
P1​ = 15 kNP2​ = 50 kNABRA​ = ?RB​2 m2 m4 m

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

L = 8 mP1 = 15 kN at 2 mP2 = 50 kN at 4 m
RA = kN
4.Medium
w0​ = 4 kN/mP = 20 kNABRB​ = ?2 m4 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 4 kN/m at B. A point load P also acts at 2 m from A. Find the vertical support reaction RB.

L = 6 mw0 = 4 kN/mP = 20 kN at 2 m
RB = kN
5.Hard
w0​ = 8 kN/mP = 10 kNABMA​ = ?5 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 5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 8 kN/mP = 10 kN at 5 m
MA = kN·m
6.Hard
P = 70 kN, 40°Q = 70 kNABRA​ = ?1.5 m1.5 m2 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 3 m from A, inclined at 40° to the horizontal, and a vertical load Q acts at 1.5 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 5 mP = 70 kN at 3 m, θ = 40°Q = 70 kN at 1.5 m
RA = kN

Answer key

  1. 1. MA = 200 kN·m
  2. 2. RA = −1.25 kN
  3. 3. RA = 36.25 kN
  4. 4. RB = 14.67 kN
  5. 5. MA = 83.33 kN·m
  6. 6. RA = 85.81 kN

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