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 = 70 kNABRA​ = ?RB​1.5 m3.5 m

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

L = 5 mP = 70 kN at 1.5 m
RA = kN
2.Easy
P = 40 kNABRA​RB​ = ?1 m4 m

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

L = 5 mP = 40 kN at 1 m
RB = kN
3.Medium
w = 6 kN/mP = 40 kNABRA​ = ?3.5 m1.5 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 3.5 m from the wall. Find the vertical reaction RA at the wall.

L = 5 mP = 40 kN at 3.5 mw = 6 kN/m from 0 to 5 m
RA = kN
4.Medium
w = 10 kN/mP = 30 kNABRA​ = ?4 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 4 m from the wall. Find the vertical reaction RA at the wall.

L = 4 mP = 30 kN at 4 mw = 10 kN/m from 0 to 4 m
RA = kN
5.Hard
w0​ = 8 kN/mP = 40 kNABMA​ = ?4.5 m0.5 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 4.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 8 kN/mP = 40 kN at 4.5 m
MA = kN·m
6.Hard
P = 55 kN, 50°Q = 70 kNABα = ?2 m1.5 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 50° to the horizontal, and a vertical load Q acts at 2 m from A. Find the angle α between the total reaction force at the pin A and the horizontal.

L = 5 mP = 55 kN at 3.5 m, θ = 50°Q = 70 kN at 2 m
α = °

Answer key

  1. 1. RA = 49 kN
  2. 2. RB = 8 kN
  3. 3. RA = 70 kN
  4. 4. RA = 70 kN
  5. 5. MA = 213.3 kN·m
  6. 6. α = 57.1 °

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