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 = 40 kNABRA​ = ?RB​4 m1 m

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

L = 5 mP = 40 kN at 4 m
RA = kN
2.Easy
P = 10 kNABRA​RB​ = ?2 m3 m

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

L = 5 mP = 10 kN at 2 m
RB = kN
3.Medium
w0​ = 15 kN/mP = 75 kNABRA​ = ?2.5 m3.5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 15 kN/m at A to zero at B. A point load P also acts at 2.5 m from A. Find the vertical support reaction RA.

L = 6 mw0 = 15 kN/mP = 75 kN at 2.5 m
RA = kN
4.Medium
P = 50 kNM = 30 kN·mABRB​ = ?3.5 m1.5 m1 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 3.5 m from A. Find the vertical reaction RB, taking upward as positive.

L = 6 mP = 50 kN at 5 mM = 30 kN·m (clockwise) at 3.5 m
RB = kN
5.Hard
w0​ = 4 kN/mP = 35 kNABMA​ = ?5 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 4 kN/m at the wall and falls to zero at the free end B, plus a point load P at 5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 4 kN/mP = 35 kN at 5 m
MA = kN·m
6.Hard
w0​ = 8 kN/mP = 25 kNABMA​ = ?4.5 m0.5 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 8 kN/m at the wall and falls to zero at the free end B, plus a point load P at 4.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 8 kN/mP = 25 kN at 4.5 m
MA = kN·m

Answer key

  1. 1. RA = 8 kN
  2. 2. RB = 4 kN
  3. 3. RA = 73.75 kN
  4. 4. RB = 46.67 kN
  5. 5. MA = 191.7 kN·m
  6. 6. MA = 145.8 kN·m

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