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 = 45 kNABRA​RB​ = ?3 m2 m

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

L = 5 mP = 45 kN at 3 m
RB = kN
2.Easy
w = 8 kN/mABMA​ = ?4 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 = 4 mw = 8 kN/m from 0 to 4 m
MA = kN·m
3.Medium
P1​ = 10 kNP2​ = 55 kNABRA​ = ?RB​1.5 m0.5 m2 m

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

L = 4 mP1 = 10 kN at 1.5 mP2 = 55 kN at 2 m
RA = kN
4.Medium
w = 2 kN/mP = 10 kNABMA​ = ?3 m1 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 3 m and a point load P at 4 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mP = 10 kN at 4 mw = 2 kN/m from 0 to 3 m
MA = kN·m
5.Hard
w0​ = 10 kN/mP = 75 kNABMA​ = ?9 m1 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 9 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mw0 = 10 kN/mP = 75 kN at 9 m
MA = kN·m
6.Hard
w = 3 kN/mP = 30 kNQ = 60 kNADCRD​ = ?3 m1 m3 m1 m

A compound beam is fixed to the wall at A, has an internal hinge at C (4 m from A) and rests on a roller at D (8 m from A). It carries a point load P at 7 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 3 m from A. Find the reaction RD at the roller.

AC = 4 mAD = 8 mP = 30 kN at 7 mw = 3 kN/m from 4 to 8 mQ = 60 kN at 3 m
RD = kN

Answer key

  1. 1. RB = 27 kN
  2. 2. MA = 64 kN·m
  3. 3. RA = 33.75 kN
  4. 4. MA = 49 kN·m
  5. 5. MA = 841.7 kN·m
  6. 6. RD = 28.5 kN

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