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 kNABRA​ = ?RB​3 m2 m

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

L = 5 mP = 30 kN at 3 m
RA = kN
2.Easy
P = 20 kNABRA​RB​ = ?3 m1 m

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

L = 4 mP = 20 kN at 3 m
RB = kN
3.Medium
P = 45 kNM = 40 kN·mABRA​ = ?2 m5 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 7 m from A. Find the vertical reaction RA, taking upward as positive.

L = 8 mP = 45 kN at 2 mM = 40 kN·m (clockwise) at 7 m
RA = kN
4.Medium
w = 10 kN/mP = 65 kNABMA​ = ?2 m1.5 m1.5 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 3.5 m and a point load P at 2 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mP = 65 kN at 2 mw = 10 kN/m from 0 to 3.5 m
MA = kN·m
5.Hard
w0​ = 4 kN/mP = 25 kNABMA​ = ?4 m2 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is zero at the wall and rises to 4 kN/m at the free end B, plus a point load P at 4 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 6 mw0 = 4 kN/mP = 25 kN at 4 m
MA = kN·m
6.Hard
P = 10 kN, 45°Q = 65 kNABRA​ = ?2 m2.5 m1.5 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 4.5 m from A, inclined at 45° 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 = 6 mP = 10 kN at 4.5 m, θ = 45°Q = 65 kN at 2 m
RA = kN

Answer key

  1. 1. RA = 12 kN
  2. 2. RB = 15 kN
  3. 3. RA = 28.75 kN
  4. 4. MA = 191.3 kN·m
  5. 5. MA = 148 kN·m
  6. 6. RA = 45.65 kN

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