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 = 60 kNABRA​RB​ = ?5 m3 m

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

L = 8 mP = 60 kN at 5 m
RB = kN
2.Easy
w = 6 kN/mABMA​ = ?3 m7 m

The cantilever beam is fixed to the wall at A and carries a uniformly distributed load w from 3 m to 10 m (the free end). Find the magnitude of the reaction moment MA at the wall.

L = 10 mw = 6 kN/m from 3 to 10 m
MA = kN·m
3.Medium
P1​ = 65 kNP2​ = 60 kNABCRB​ = ?2.5 m2 m1.5 m

The beam has a pin at A and a roller at B, 4.5 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 4.5 mAC = 6 mP1 = 65 kN at 2.5 mP2 = 60 kN at 6 m
RB = kN
4.Medium
w0​ = 20 kN/mP = 35 kNABRB​ = ?3.5 m1.5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 20 kN/m at B. A point load P also acts at 3.5 m from A. Find the vertical support reaction RB.

L = 5 mw0 = 20 kN/mP = 35 kN at 3.5 m
RB = kN
5.Hard
w0​ = 15 kN/mP = 65 kNABMA​ = ?10 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 15 kN/m at the wall and falls to zero at the free end B, plus a point load P at 10 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mw0 = 15 kN/mP = 65 kN at 10 m
MA = kN·m
6.Hard
w = 3 kN/mP = 70 kNQ = 40 kNADCRD​ = ?2.5 m1 m2 m0.5 m

A compound beam is fixed to the wall at A, has an internal hinge at C (3.5 m from A) and rests on a roller at D (6 m from A). It carries a point load P at 5.5 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 2.5 m from A. Find the reaction RD at the roller.

AC = 3.5 mAD = 6 mP = 70 kN at 5.5 mw = 3 kN/m from 3.5 to 6 mQ = 40 kN at 2.5 m
RD = kN

Answer key

  1. 1. RB = 37.5 kN
  2. 2. MA = 273 kN·m
  3. 3. RB = 116.1 kN
  4. 4. RB = 57.83 kN
  5. 5. MA = 900 kN·m
  6. 6. RD = 59.75 kN

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