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 = 30 kNABRA​ = ?RB​1 m3 m

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

L = 4 mP = 30 kN at 1 m
RA = kN
2.Easy
P = 30 kNABMA​ = ?4 m

The cantilever beam is fixed to the wall at A and carries a point load P at its free end B. Find the magnitude of the reaction moment MA at the wall.

L = 4 mP = 30 kN at 4 m
MA = kN·m
3.Medium
w0​ = 8 kN/mABRA​ = ?10 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 8 kN/m at B. Find the vertical support reaction RA.

L = 10 mw0 = 8 kN/m
RA = kN
4.Medium
P1​ = 20 kNP2​ = 60 kNABRA​RB​ = ?3.5 m0.5 m1 m

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

L = 5 mP1 = 20 kN at 3.5 mP2 = 60 kN at 4 m
RB = kN
5.Hard
P = 20 kNADCMA​ = ?2.5 m3 m0.5 m

A compound beam is fixed to the wall at A, has an internal hinge at C (2.5 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. Find the magnitude of the reaction moment MA at the wall.

AC = 2.5 mAD = 6 mP = 20 kN at 5.5 m
MA = kN·m
6.Hard
w = 10 kN/mP = 20 kNQ = 80 kNADCRD​ = ?1 m2 m1 m4 m

A compound beam is fixed to the wall at A, has an internal hinge at C (3 m from A) and rests on a roller at D (8 m from A). It carries a point load P at 4 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 1 m from A. Find the reaction RD at the roller.

AC = 3 mAD = 8 mP = 20 kN at 4 mw = 10 kN/m from 3 to 8 mQ = 80 kN at 1 m
RD = kN

Answer key

  1. 1. RA = 22.5 kN
  2. 2. MA = 120 kN·m
  3. 3. RA = 13.33 kN
  4. 4. RB = 62 kN
  5. 5. MA = 7.143 kN·m
  6. 6. RD = 29 kN

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