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 = 50 kNABRA​RB​ = ?4 m1 m

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

L = 5 mP = 50 kN at 4 m
RB = kN
2.Easy
P = 75 kNABRA​ = ?RB​5 m5 m

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

L = 10 mP = 75 kN at 5 m
RA = kN
3.Medium
P = 40 kNM = 50 kN·mABRB​ = ?3 m2 m3 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 5 m from A and a clockwise couple M at 3 m from A. Find the vertical reaction RB, taking upward as positive.

L = 8 mP = 40 kN at 5 mM = 50 kN·m (clockwise) at 3 m
RB = kN
4.Medium
w0​ = 6 kN/mP = 20 kNABRA​ = ?1.5 m3.5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 6 kN/m at A to zero at B. A point load P also acts at 1.5 m from A. Find the vertical support reaction RA.

L = 5 mw0 = 6 kN/mP = 20 kN at 1.5 m
RA = kN
5.Hard
w0​ = 20 kN/mP = 30 kNABMA​ = ?3.5 m1.5 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 20 kN/m at the wall and falls to zero at the free end B, plus a point load P at 3.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 20 kN/mP = 30 kN at 3.5 m
MA = kN·m
6.Hard
w = 5 kN/mP = 60 kNABCRB​ = ?1.5 m0.5 m1 m2 m

The beam has a pin at A and a roller at B, 3 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 1.5 m to the free end at 5 m. Find the vertical reaction RB, taking upward as positive.

AB = 3 mAC = 5 mP = 60 kN at 2 mw = 5 kN/m from 1.5 to 5 m
RB = kN

Answer key

  1. 1. RB = 40 kN
  2. 2. RA = 37.5 kN
  3. 3. RB = 31.25 kN
  4. 4. RA = 24 kN
  5. 5. MA = 188.3 kN·m
  6. 6. RB = 58.96 kN

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