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 = 6 kN/mABMA​ = ?4 m4 m

The cantilever beam is fixed to the wall at A and carries a uniformly distributed load w from 4 m to 8 m (the free end). Find the magnitude of the reaction moment MA at the wall.

L = 8 mw = 6 kN/m from 4 to 8 m
MA = kN·m
2.Easy
P = 35 kNABRA​ = ?RB​2 m6 m

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

L = 8 mP = 35 kN at 2 m
RA = kN
3.Medium
P1​ = 40 kNP2​ = 15 kNABCRB​ = ?4 m2 m2 m

The beam has a pin at A and a roller at B, 6 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 6 mAC = 8 mP1 = 40 kN at 4 mP2 = 15 kN at 8 m
RB = kN
4.Medium
P1​ = 10 kNP2​ = 45 kNABRA​RB​ = ?1.5 m0.5 m3 m

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

L = 5 mP1 = 10 kN at 1.5 mP2 = 45 kN at 2 m
RB = kN
5.Hard
w = 5 kN/mP = 25 kNABCRA​ = ?1.5 m0.5 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. It carries a point load P at 2 m from A and a uniformly distributed load w from 1.5 m to the free end at 4 m. Find the vertical reaction RA, taking upward as positive.

AB = 2.5 mAC = 4 mP = 25 kN at 2 mw = 5 kN/m from 1.5 to 4 m
RA = kN
6.Hard
P = 60 kN, 30°Q = 80 kNABα = ?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 30° to the horizontal, and a vertical load Q acts at 3 m from A. Find the angle α between the total reaction force at the pin A and the horizontal.

L = 10 mP = 60 kN at 8 m, θ = 30°Q = 80 kN at 3 m
α = °

Answer key

  1. 1. MA = 144 kN·m
  2. 2. RA = 26.25 kN
  3. 3. RB = 46.67 kN
  4. 4. RB = 21 kN
  5. 5. RA = 3.75 kN
  6. 6. α = 50.03 °

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