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​ = ?4 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 = 4 mw = 4 kN/m from 0 to 4 m
MA = kN·m
2.Easy
P = 55 kNABRA​RB​ = ?2 m8 m

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

L = 10 mP = 55 kN at 2 m
RB = kN
3.Medium
w = 2 kN/mP = 65 kNABMA​ = ?5 m1 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 5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 6 mP = 65 kN at 5 mw = 2 kN/m from 0 to 6 m
MA = kN·m
4.Medium
P1​ = 15 kNP2​ = 30 kNABCRB​ = ?2 m0.5 m1.5 m

The beam has a pin at A and a roller at B, 2.5 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 2.5 mAC = 4 mP1 = 15 kN at 2 mP2 = 30 kN at 4 m
RB = kN
5.Hard
P = 35 kN, 30°Q = 15 kNABRA​ = ?0.5 m3 m1.5 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 3.5 m from A, inclined at 30° to the horizontal, and a vertical load Q acts at 0.5 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 5 mP = 35 kN at 3.5 m, θ = 30°Q = 15 kN at 0.5 m
RA = kN
6.Hard
P = 50 kNADCMA​ = ?4 m3 m1 m

A compound beam is fixed to the wall at A, has an internal hinge at C (4 m from A) and rests on a roller at D (8 m from A). It carries a point load P at 7 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 4 mAD = 8 mP = 50 kN at 7 m
MA = kN·m

Answer key

  1. 1. MA = 32 kN·m
  2. 2. RB = 11 kN
  3. 3. MA = 361 kN·m
  4. 4. RB = 60 kN
  5. 5. RA = 35.64 kN
  6. 6. MA = 50 kN·m

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