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 = 45 kNABMA​ = ?6 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 = 6 mP = 45 kN at 6 m
MA = kN·m
2.Easy
P = 35 kNABRA​RB​ = ?4.5 m1.5 m

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

L = 6 mP = 35 kN at 4.5 m
RB = kN
3.Medium
w0​ = 12 kN/mP = 75 kNABRA​ = ?2 m6 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 12 kN/m at A to zero at B. A point load P also acts at 2 m from A. Find the vertical support reaction RA.

L = 8 mw0 = 12 kN/mP = 75 kN at 2 m
RA = kN
4.Medium
P1​ = 55 kNP2​ = 15 kNABRA​ = ?RB​1 m1.5 m1.5 m

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

L = 4 mP1 = 55 kN at 1 mP2 = 15 kN at 2.5 m
RA = kN
5.Hard
w = 5 kN/mP = 55 kNABCRA​ = ?2 m1.5 m0.5 m1 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 2 m from A and a uniformly distributed load w from 3.5 m to the free end at 5 m. Find the vertical reaction RA, taking upward as positive.

AB = 4 mAC = 5 mP = 55 kN at 2 mw = 5 kN/m from 3.5 to 5 m
RA = kN
6.Hard
w = 12 kN/mP = 50 kNABCRB​ = ?1.5 m1 m1.5 m

The beam has a pin at A and a roller at B, 2.5 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 2.5 m to the free end at 4 m. Find the vertical reaction RB, taking upward as positive.

AB = 2.5 mAC = 4 mP = 50 kN at 1.5 mw = 12 kN/m from 2.5 to 4 m
RB = kN

Answer key

  1. 1. MA = 270 kN·m
  2. 2. RB = 26.25 kN
  3. 3. RA = 88.25 kN
  4. 4. RA = 46.88 kN
  5. 5. RA = 27.03 kN
  6. 6. RB = 53.4 kN

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