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 = 55 kNABMA​ = ?5 m

The cantilever beam is fixed to the wall at A and carries a point load P at its free end B. Find the magnitude of the reaction moment MA at the wall.

L = 5 mP = 55 kN at 5 m
MA = kN·m
2.Easy
P = 10 kN, 45°ABAx​ = ?5 m5 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 5 m from A, inclined at 45° to the horizontal. Find the magnitude of the horizontal reaction Ax at the pin A.

L = 10 mP = 10 kN at 5 mθ = 45°
Ax = kN
3.Medium
w0​ = 15 kN/mP = 50 kNABRB​ = ?4.5 m1.5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 15 kN/m at B. A point load P also acts at 4.5 m from A. Find the vertical support reaction RB.

L = 6 mw0 = 15 kN/mP = 50 kN at 4.5 m
RB = kN
4.Medium
P1​ = 60 kNP2​ = 60 kNABCRA​ = ?3 m5 m2 m

The beam has a pin at A and a roller at B, 8 m from A, and overhangs B to the free end C. Find the vertical reaction RA, taking upward as positive.

AB = 8 mAC = 10 mP1 = 60 kN at 3 mP2 = 60 kN at 10 m
RA = kN
5.Hard
w = 12 kN/mP = 20 kNABCRA​ = ?0.5 m2.5 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 0.5 m from A and a uniformly distributed load w from 3 m to the free end at 5 m. Find the vertical reaction RA, taking upward as positive.

AB = 3 mAC = 5 mP = 20 kN at 0.5 mw = 12 kN/m from 3 to 5 m
RA = kN
6.Hard
w = 6 kN/mP = 80 kNABCRA​ = ?0.5 m3.5 m0.5 m1.5 m

The beam has a pin at A and a roller at B, 4.5 m from A, and overhangs B to the free end C. It carries a point load P at 0.5 m from A and a uniformly distributed load w from 4 m to the free end at 6 m. Find the vertical reaction RA, taking upward as positive.

AB = 4.5 mAC = 6 mP = 80 kN at 0.5 mw = 6 kN/m from 4 to 6 m
RA = kN

Answer key

  1. 1. MA = 275 kN·m
  2. 2. Ax = 7.071 kN
  3. 3. RB = 67.5 kN
  4. 4. RA = 22.5 kN
  5. 5. RA = 8.667 kN
  6. 6. RA = 69.78 kN

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