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 = 30 kNABMA​ = ?4 m

The cantilever beam is fixed to the wall at A and carries a point load P at its free end B. Find the magnitude of the reaction moment MA at the wall.

L = 4 mP = 30 kN at 4 m
MA = kN·m
2.Easy
P = 50 kNABRA​ = ?RB​3.5 m2.5 m

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

L = 6 mP = 50 kN at 3.5 m
RA = kN
3.Medium
P = 55 kNM = 15 kN·mABRA​ = ?2 m2 m4 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 4 m from A and a clockwise couple M at 2 m from A. Find the vertical reaction RA, taking upward as positive.

L = 8 mP = 55 kN at 4 mM = 15 kN·m (clockwise) at 2 m
RA = kN
4.Medium
P1​ = 55 kNP2​ = 25 kNABRA​RB​ = ?1.5 m0.5 m2 m

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

L = 4 mP1 = 55 kN at 1.5 mP2 = 25 kN at 2 m
RB = kN
5.Hard
P = 40 kN, 45°Q = 65 kNABRA​ = ?1 m3 m2 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 4 m from A, inclined at 45° to the horizontal, and a vertical load Q acts at 1 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 6 mP = 40 kN at 4 m, θ = 45°Q = 65 kN at 1 m
RA = kN
6.Hard
P = 80 kN, 50°Q = 30 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 1.5 m from A, inclined at 50° to the horizontal, and a vertical load Q acts at 3 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 5 mP = 80 kN at 1.5 m, θ = 50°Q = 30 kN at 3 m
RA = kN

Answer key

  1. 1. MA = 120 kN·m
  2. 2. RA = 20.83 kN
  3. 3. RA = 25.63 kN
  4. 4. RB = 33.13 kN
  5. 5. RA = 69.6 kN
  6. 6. RA = 75.22 kN

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