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 = 65 kNABMA​ = ?4 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 = 4 mP = 65 kN at 4 m
MA = kN·m
2.Easy
P = 45 kNABRA​RB​ = ?2 m2 m

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

L = 4 mP = 45 kN at 2 m
RB = kN
3.Medium
P1​ = 20 kNP2​ = 30 kNABCRB​ = ?2.5 m1 m1.5 m

The beam has a pin at A and a roller at B, 3.5 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 3.5 mAC = 5 mP1 = 20 kN at 2.5 mP2 = 30 kN at 5 m
RB = kN
4.Medium
P1​ = 20 kNP2​ = 30 kNABCRB​ = ?6 m1 m3 m

The beam has a pin at A and a roller at B, 7 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 7 mAC = 10 mP1 = 20 kN at 6 mP2 = 30 kN at 10 m
RB = kN
5.Hard
w = 2 kN/mP = 25 kNABRA​ = ?RB​2 m1 m2 m3 m

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

L = 8 mP = 25 kN at 2 mw = 2 kN/m from 3 to 5 m
RA = kN
6.Hard
w0​ = 8 kN/mP = 40 kNABMA​ = ?7 m3 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 8 kN/m at the free end B, plus a point load P at 7 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mw0 = 8 kN/mP = 40 kN at 7 m
MA = kN·m

Answer key

  1. 1. MA = 260 kN·m
  2. 2. RB = 22.5 kN
  3. 3. RB = 57.14 kN
  4. 4. RB = 60 kN
  5. 5. RA = 20.75 kN
  6. 6. MA = 546.7 kN·m

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