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 = 50 kNABRA​ = ?RB​7 m3 m

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

L = 10 mP = 50 kN at 7 m
RA = kN
2.Easy
w = 10 kN/mABMA​ = ?2 m2 m

The cantilever beam is fixed to the wall at A and carries a uniformly distributed load w from 2 m to 4 m (the free end). Find the magnitude of the reaction moment MA at the wall.

L = 4 mw = 10 kN/m from 2 to 4 m
MA = kN·m
3.Medium
P1​ = 50 kNP2​ = 35 kNABRA​RB​ = ?1.5 m1 m2.5 m

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

L = 5 mP1 = 50 kN at 1.5 mP2 = 35 kN at 2.5 m
RB = kN
4.Medium
P1​ = 35 kNP2​ = 10 kNABCRA​ = ?5 m1 m2 m

The beam has a pin at A and a roller at B, 6 m from A, and overhangs B to the free end C. Find the vertical reaction RA, taking upward as positive.

AB = 6 mAC = 8 mP1 = 35 kN at 5 mP2 = 10 kN at 8 m
RA = kN
5.Hard
w = 10 kN/mP = 70 kNABCRA​ = ?1 m3 m1 m3 m

The beam has a pin at A and a roller at B, 5 m from A, and overhangs B to the free end C. It carries a point load P at 1 m from A and a uniformly distributed load w from 4 m to the free end at 8 m. Find the vertical reaction RA, taking upward as positive.

AB = 5 mAC = 8 mP = 70 kN at 1 mw = 10 kN/m from 4 to 8 m
RA = kN
6.Hard
w = 10 kN/mP = 15 kNABCRA​ = ?1.5 m1.5 m1 m

The beam has a pin at A and a roller at B, 3 m from A, and overhangs B to the free end C. It carries a point load P at 1.5 m from A and a uniformly distributed load w from 3 m to the free end at 4 m. Find the vertical reaction RA, taking upward as positive.

AB = 3 mAC = 4 mP = 15 kN at 1.5 mw = 10 kN/m from 3 to 4 m
RA = kN

Answer key

  1. 1. RA = 15 kN
  2. 2. MA = 60 kN·m
  3. 3. RB = 32.5 kN
  4. 4. RA = 2.5 kN
  5. 5. RA = 48 kN
  6. 6. RA = 5.833 kN

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