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​ = ?1.5 m2.5 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 1.5 m
RB = kN
2.Easy
w = 5 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 = 5 kN/m from 0 to 8 m
MA = kN·m
3.Medium
w = 6 kN/mP = 30 kNABRA​ = ?4 m3 m3 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 7 m from the wall. Find the vertical reaction RA at the wall.

L = 10 mP = 30 kN at 7 mw = 6 kN/m from 0 to 4 m
RA = kN
4.Medium
P = 60 kNM = 10 kN·mABRB​ = ?1 m1 m6 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 1 m from A and a clockwise couple M at 2 m from A. Find the vertical reaction RB, taking upward as positive.

L = 8 mP = 60 kN at 1 mM = 10 kN·m (clockwise) at 2 m
RB = kN
5.Hard
w0​ = 10 kN/mP = 70 kNABMA​ = ?5 m5 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 10 kN/m at the wall and falls to zero at the free end B, plus a point load P at 5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mw0 = 10 kN/mP = 70 kN at 5 m
MA = kN·m
6.Hard
w0​ = 4 kN/mP = 15 kNABMA​ = ?5 m1 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 5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 6 mw0 = 4 kN/mP = 15 kN at 5 m
MA = kN·m

Answer key

  1. 1. RB = 7.5 kN
  2. 2. MA = 160 kN·m
  3. 3. RA = 54 kN
  4. 4. RB = 8.75 kN
  5. 5. MA = 516.7 kN·m
  6. 6. MA = 123 kN·m

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