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​ = ?1 m9 m

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

L = 10 mP = 60 kN at 1 m
RB = kN
2.Easy
P = 70 kNABRA​ = ?RB​1 m4 m

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

L = 5 mP = 70 kN at 1 m
RA = kN
3.Medium
P1​ = 50 kNP2​ = 45 kNABCRB​ = ?3 m4 m3 m

The beam has a pin at A and a roller at B, 7 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 7 mAC = 10 mP1 = 50 kN at 3 mP2 = 45 kN at 10 m
RB = kN
4.Medium
w = 4 kN/mP = 60 kNABMA​ = ?1.5 m1.5 m1 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 3 m and a point load P at 1.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mP = 60 kN at 1.5 mw = 4 kN/m from 0 to 3 m
MA = kN·m
5.Hard
w = 2 kN/mP = 35 kNABCRB​ = ?3.5 m0.5 m2 m

The beam has a pin at A and a roller at B, 4 m from A, and overhangs B to the free end C. It carries a point load P at 3.5 m from A and a uniformly distributed load w from 4 m to the free end at 6 m. Find the vertical reaction RB, taking upward as positive.

AB = 4 mAC = 6 mP = 35 kN at 3.5 mw = 2 kN/m from 4 to 6 m
RB = kN
6.Hard
w = 10 kN/mP = 70 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. It carries a point load P at 5 m from A and a uniformly distributed load w from 5 m to the free end at 8 m. Find the vertical reaction RA, taking upward as positive.

AB = 6 mAC = 8 mP = 70 kN at 5 mw = 10 kN/m from 5 to 8 m
RA = kN

Answer key

  1. 1. RB = 6 kN
  2. 2. RA = 56 kN
  3. 3. RB = 85.71 kN
  4. 4. MA = 108 kN·m
  5. 5. RB = 35.63 kN
  6. 6. RA = 9.167 kN

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