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
w = 4 kN/mABMA​ = ?4 m

The cantilever beam is fixed to the wall at A and carries a uniformly distributed load w along its whole length. Find the magnitude of the reaction moment MA at the wall.

L = 4 mw = 4 kN/m from 0 to 4 m
MA = kN·m
2.Easy
P = 75 kNABRA​RB​ = ?3 m1 m

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

L = 4 mP = 75 kN at 3 m
RB = kN
3.Medium
P1​ = 40 kNP2​ = 75 kNABCRA​ = ?1 m5 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 = 40 kN at 1 mP2 = 75 kN at 8 m
RA = kN
4.Medium
P1​ = 25 kNP2​ = 10 kNABRA​ = ?RB​1.5 m0.5 m3 m

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

L = 5 mP1 = 25 kN at 1.5 mP2 = 10 kN at 2 m
RA = kN
5.Hard
w0​ = 4 kN/mP = 70 kNABMA​ = ?2 m2 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is zero at the wall and rises to 4 kN/m at the free end B, plus a point load P at 2 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mw0 = 4 kN/mP = 70 kN at 2 m
MA = kN·m
6.Hard
w = 5 kN/mP = 65 kNABCRB​ = ?2.5 m1.5 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 2.5 m from A and a uniformly distributed load w from 2.5 m to the free end at 6 m. Find the vertical reaction RB, taking upward as positive.

AB = 4 mAC = 6 mP = 65 kN at 2.5 mw = 5 kN/m from 2.5 to 6 m
RB = kN

Answer key

  1. 1. MA = 32 kN·m
  2. 2. RB = 56.25 kN
  3. 3. RA = 8.333 kN
  4. 4. RA = 23.5 kN
  5. 5. MA = 161.3 kN·m
  6. 6. RB = 59.22 kN

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