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 = 40 kNABRA​RB​ = ?5 m1 m

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

L = 6 mP = 40 kN at 5 m
RB = kN
2.Easy
M₀ = 10 kN·mABRB​ = ?6 m4 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 6 m from A. Find the vertical reaction RB, taking upward as positive.

L = 10 mM₀ = 10 kN·m (clockwise) at 6 m
RB = kN
3.Medium
w = 4 kN/mP = 40 kNABMA​ = ?3 m3 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 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 6 mP = 40 kN at 3 mw = 4 kN/m from 0 to 6 m
MA = kN·m
4.Medium
P1​ = 10 kNP2​ = 55 kNABRA​ = ?RB​1 m2 m1 m

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

L = 4 mP1 = 10 kN at 1 mP2 = 55 kN at 3 m
RA = kN
5.Hard
P = 30 kN, 50°Q = 75 kNABRA​ = ?5 m2 m1 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 5 m from A, inclined at 50° to the horizontal, and a vertical load Q acts at 7 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 8 mP = 30 kN at 5 m, θ = 50°Q = 75 kN at 7 m
RA = kN
6.Hard
w = 3 kN/mP = 15 kNABCRA​ = ?1 m4 m3 m

The beam has a pin at A and a roller at B, 5 m from A, and overhangs B to the free end C. It carries a point load P at 1 m from A and a uniformly distributed load w from 5 m to the free end at 8 m. Find the vertical reaction RA, taking upward as positive.

AB = 5 mAC = 8 mP = 15 kN at 1 mw = 3 kN/m from 5 to 8 m
RA = kN

Answer key

  1. 1. RB = 33.33 kN
  2. 2. RB = 1 kN
  3. 3. MA = 192 kN·m
  4. 4. RA = 21.25 kN
  5. 5. RA = 26.37 kN
  6. 6. RA = 9.3 kN

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