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
w = 2 kN/mABMA​ = ?8 m

The cantilever beam is fixed to the wall at A and carries a uniformly distributed load w along its whole length. Find the magnitude of the reaction moment MA at the wall.

L = 8 mw = 2 kN/m from 0 to 8 m
MA = kN·m
2.Easy
M₀ = 25 kN·mABRA​ = ?5.5 m0.5 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 25 kN·m applied at 5.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 6 mM₀ = 25 kN·m (clockwise) at 5.5 m
RA = kN
3.Medium
P1​ = 40 kNP2​ = 60 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 RA.

L = 6 mP1 = 40 kN at 1 mP2 = 60 kN at 3 m
RA = kN
4.Medium
P1​ = 55 kNP2​ = 20 kNABRA​RB​ = ?1.5 m1.5 m2 m

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

L = 5 mP1 = 55 kN at 1.5 mP2 = 20 kN at 3 m
RB = kN
5.Hard
w0​ = 8 kN/mP = 50 kNABMA​ = ?3 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 8 kN/m at the free end B, plus a point load P at 3 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 8 kN/mP = 50 kN at 3 m
MA = kN·m
6.Hard
w0​ = 10 kN/mP = 60 kNABMA​ = ?3 m5 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 10 kN/m at the free end B, plus a point load P at 3 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mw0 = 10 kN/mP = 60 kN at 3 m
MA = kN·m

Answer key

  1. 1. MA = 64 kN·m
  2. 2. RA = −4.167 kN
  3. 3. RA = 63.33 kN
  4. 4. RB = 28.5 kN
  5. 5. MA = 216.7 kN·m
  6. 6. MA = 393.3 kN·m

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