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
M₀ = 60 kN·mABRB​ = ?2 m8 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 60 kN·m applied at 2 m from A. Find the vertical reaction RB, taking upward as positive.

L = 10 mM₀ = 60 kN·m (clockwise) at 2 m
RB = kN
3.Medium
w = 2 kN/mP = 80 kNABRA​ = ?5 m2 m3 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 7 m and a point load P at 5 m from the wall. Find the vertical reaction RA at the wall.

L = 10 mP = 80 kN at 5 mw = 2 kN/m from 0 to 7 m
RA = kN
4.Medium
w0​ = 4 kN/mP = 25 kNABRB​ = ?3 m3 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 4 kN/m at A to zero at B. A point load P also acts at 3 m from A. Find the vertical support reaction RB.

L = 6 mw0 = 4 kN/mP = 25 kN at 3 m
RB = kN
5.Hard
w = 6 kN/mP = 35 kNABRA​ = ?RB​6 m2 m2 m

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

L = 10 mP = 35 kN at 8 mw = 6 kN/m from 6 to 10 m
RA = kN
6.Hard
w = 3 kN/mP = 25 kNABCRB​ = ?3 m1 m1 m3 m

The beam has a pin at A and a roller at B, 5 m from A, and overhangs B to the free end C. It carries a point load P at 4 m from A and a uniformly distributed load w from 3 m to the free end at 8 m. Find the vertical reaction RB, taking upward as positive.

AB = 5 mAC = 8 mP = 25 kN at 4 mw = 3 kN/m from 3 to 8 m
RB = kN

Answer key

  1. 1. MA = 32 kN·m
  2. 2. RB = 6 kN
  3. 3. RA = 94 kN
  4. 4. RB = 16.5 kN
  5. 5. RA = 11.8 kN
  6. 6. RB = 36.5 kN

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