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 = 20 kNABRA​ = ?RB​5 m3 m

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

L = 8 mP = 20 kN at 5 m
RA = kN
2.Easy
P = 70 kNABMA​ = ?8 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 = 8 mP = 70 kN at 8 m
MA = kN·m
3.Medium
P = 20 kNM = 15 kN·mABRB​ = ?2 m3 m1 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 2 m from A and a clockwise couple M at 5 m from A. Find the vertical reaction RB, taking upward as positive.

L = 6 mP = 20 kN at 2 mM = 15 kN·m (clockwise) at 5 m
RB = kN
4.Medium
P1​ = 10 kNP2​ = 25 kNABCRA​ = ?3.5 m0.5 m1 m

The beam has a pin at A and a roller at B, 4 m from A, and overhangs B to the free end C. Find the vertical reaction RA, taking upward as positive.

AB = 4 mAC = 5 mP1 = 10 kN at 3.5 mP2 = 25 kN at 5 m
RA = kN
5.Hard
P = 45 kN, 60°Q = 75 kNABRA​ = ?2 m5 m1 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 7 m from A, inclined at 60° to the horizontal, and a vertical load Q acts at 2 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 8 mP = 45 kN at 7 m, θ = 60°Q = 75 kN at 2 m
RA = kN
6.Hard
w = 10 kN/mP = 30 kNABRA​RB​ = ?1 m2 m3 m

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

L = 6 mP = 30 kN at 3 mw = 10 kN/m from 0 to 1 m
RB = kN

Answer key

  1. 1. RA = 7.5 kN
  2. 2. MA = 560 kN·m
  3. 3. RB = 9.167 kN
  4. 4. RA = −5 kN
  5. 5. RA = 65.13 kN
  6. 6. RB = 15.83 kN

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