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 = 20 kNABMA​ = ?10 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 = 10 mP = 20 kN at 10 m
MA = kN·m
2.Easy
M₀ = 10 kN·mABRB​ = ?1 m7 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 10 kN·m applied at 1 m from A. Find the vertical reaction RB, taking upward as positive.

L = 8 mM₀ = 10 kN·m (clockwise) at 1 m
RB = kN
3.Medium
w0​ = 15 kN/mABRA​ = ?4 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. Find the vertical support reaction RA.

L = 4 mw0 = 15 kN/m
RA = kN
4.Medium
P = 35 kNM = 40 kN·mABRB​ = ?0.5 m1.5 m2 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 2 m from A and a clockwise couple M at 0.5 m from A. Find the vertical reaction RB, taking upward as positive.

L = 4 mP = 35 kN at 2 mM = 40 kN·m (clockwise) at 0.5 m
RB = kN
5.Hard
w = 6 kN/mP = 60 kNABRA​ = ?RB​1 m2 m2 m

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

L = 5 mP = 60 kN at 3 mw = 6 kN/m from 0 to 1 m
RA = kN
6.Hard
w = 12 kN/mP = 60 kNABRA​RB​ = ?4 m0.5 m0.5 m1 m

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

L = 6 mP = 60 kN at 4.5 mw = 12 kN/m from 4 to 5 m
RB = kN

Answer key

  1. 1. MA = 200 kN·m
  2. 2. RB = 1.25 kN
  3. 3. RA = 10 kN
  4. 4. RB = 27.5 kN
  5. 5. RA = 29.4 kN
  6. 6. RB = 54 kN

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