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 = 30 kNABRA​RB​ = ?2 m6 m

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

L = 8 mP = 30 kN at 2 m
RB = kN
2.Easy
P = 50 kNABMA​ = ?3 m1 m

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

L = 4 mP = 50 kN at 3 m
MA = kN·m
3.Medium
w0​ = 6 kN/mP = 35 kNABRA​ = ?3.5 m0.5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 6 kN/m at B. A point load P also acts at 3.5 m from A. Find the vertical support reaction RA.

L = 4 mw0 = 6 kN/mP = 35 kN at 3.5 m
RA = kN
4.Medium
P = 45 kNM = 60 kN·mABRA​ = ?2 m2.5 m0.5 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 4.5 m from A and a clockwise couple M at 2 m from A. Find the vertical reaction RA, taking upward as positive.

L = 5 mP = 45 kN at 4.5 mM = 60 kN·m (clockwise) at 2 m
RA = kN
5.Hard
w0​ = 12 kN/mP = 30 kNABMA​ = ?8 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 12 kN/m at the free end B, plus a point load P at 8 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mw0 = 12 kN/mP = 30 kN at 8 m
MA = kN·m
6.Hard
w = 4 kN/mP = 55 kNABRA​ = ?RB​5 m1 m2 m

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

L = 8 mP = 55 kN at 5 mw = 4 kN/m from 6 to 8 m
RA = kN

Answer key

  1. 1. RB = 7.5 kN
  2. 2. MA = 150 kN·m
  3. 3. RA = 8.375 kN
  4. 4. RA = −7.5 kN
  5. 5. MA = 496 kN·m
  6. 6. RA = 21.63 kN

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