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
M₀ = 15 kN·mABRA​ = ?6 m2 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 15 kN·m applied at 6 m from A. Find the vertical reaction RA, taking upward as positive.

L = 8 mM₀ = 15 kN·m (clockwise) at 6 m
RA = kN
2.Easy
P = 70 kNABRA​ = ?RB​7 m1 m

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

L = 8 mP = 70 kN at 7 m
RA = kN
3.Medium
P1​ = 20 kNP2​ = 60 kNABRA​RB​ = ?1 m5 m4 m

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

L = 10 mP1 = 20 kN at 1 mP2 = 60 kN at 6 m
RB = kN
4.Medium
w = 5 kN/mP = 65 kNABMA​ = ?4 m2 m4 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 4 m and a point load P at 6 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mP = 65 kN at 6 mw = 5 kN/m from 0 to 4 m
MA = kN·m
5.Hard
w0​ = 8 kN/mP = 70 kNABMA​ = ?6 m4 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 6 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mw0 = 8 kN/mP = 70 kN at 6 m
MA = kN·m
6.Hard
P = 15 kN, 50°Q = 80 kNABRA​ = ?3 m2 m3 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 3 m from A, inclined at 50° to the horizontal, and a vertical load Q acts at 5 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 8 mP = 15 kN at 3 m, θ = 50°Q = 80 kN at 5 m
RA = kN

Answer key

  1. 1. RA = −1.875 kN
  2. 2. RA = 8.75 kN
  3. 3. RB = 38 kN
  4. 4. MA = 430 kN·m
  5. 5. MA = 553.3 kN·m
  6. 6. RA = 38.41 kN

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