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 = 15 kNABRA​ = ?RB​3.5 m1.5 m

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

L = 5 mP = 15 kN at 3.5 m
RA = kN
2.Easy
P = 20 kNABRA​RB​ = ?5 m1 m

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

L = 6 mP = 20 kN at 5 m
RB = kN
3.Medium
w = 5 kN/mP = 10 kNABMA​ = ?4 m6 m

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

L = 10 mP = 10 kN at 4 mw = 5 kN/m from 0 to 4 m
MA = kN·m
4.Medium
w = 8 kN/mP = 15 kNABRA​ = ?2 m0.5 m1.5 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 2.5 m and a point load P at 2 m from the wall. Find the vertical reaction RA at the wall.

L = 4 mP = 15 kN at 2 mw = 8 kN/m from 0 to 2.5 m
RA = kN
5.Hard
w = 3 kN/mP = 10 kNABCRB​ = ?2 m1 m1.5 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 3 m to the free end at 6 m. Find the vertical reaction RB, taking upward as positive.

AB = 4.5 mAC = 6 mP = 10 kN at 2 mw = 3 kN/m from 3 to 6 m
RB = kN
6.Hard
P = 40 kNQ = 30 kNADCMA​ = ?0.5 m3 m1.5 m1 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 m from A and a point load Q at 0.5 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3.5 mAD = 6 mP = 40 kN at 5 mQ = 30 kN at 0.5 m
MA = kN·m

Answer key

  1. 1. RA = 4.5 kN
  2. 2. RB = 16.67 kN
  3. 3. MA = 80 kN·m
  4. 4. RA = 35 kN
  5. 5. RB = 13.44 kN
  6. 6. MA = 71 kN·m

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