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 = 80 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 = 80 kN at 7 m
RA = kN
2.Easy
P = 60 kNABRA​RB​ = ?7 m1 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 7 m
RB = kN
3.Medium
w = 8 kN/mP = 45 kNABMA​ = ?3 m2 m3 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 5 m and a point load P at 3 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mP = 45 kN at 3 mw = 8 kN/m from 0 to 5 m
MA = kN·m
4.Medium
P1​ = 80 kNP2​ = 80 kNABCRB​ = ?1.5 m2 m1.5 m

The beam has a pin at A and a roller at B, 3.5 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 3.5 mAC = 5 mP1 = 80 kN at 1.5 mP2 = 80 kN at 5 m
RB = kN
5.Hard
w = 5 kN/mP = 20 kNABCRA​ = ?2 m2.5 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. It carries a point load P at 2 m from A and a uniformly distributed load w from 4.5 m to the free end at 6 m. Find the vertical reaction RA, taking upward as positive.

AB = 4.5 mAC = 6 mP = 20 kN at 2 mw = 5 kN/m from 4.5 to 6 m
RA = kN
6.Hard
P = 15 kNQ = 10 kNADCMA​ = ?1 m1 m0.5 m3.5 m

A compound beam is fixed to the wall at A, has an internal hinge at C (2 m from A) and rests on a roller at D (6 m from A). It carries a point load P at 2.5 m from A and a point load Q at 1 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 2 mAD = 6 mP = 15 kN at 2.5 mQ = 10 kN at 1 m
MA = kN·m

Answer key

  1. 1. RA = 24 kN
  2. 2. RB = 52.5 kN
  3. 3. MA = 235 kN·m
  4. 4. RB = 148.6 kN
  5. 5. RA = 9.861 kN
  6. 6. MA = 36.25 kN·m

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