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 = 75 kNABMA​ = ?2 m2 m

The cantilever beam is fixed to the wall at A and carries a point load P at 2 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mP = 75 kN at 2 m
MA = kN·m
2.Easy
P = 65 kNABRA​RB​ = ?4 m6 m

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

L = 10 mP = 65 kN at 4 m
RB = kN
3.Medium
P = 70 kNM = 50 kN·mABRB​ = ?2 m2 m4 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 4 m from A and a counter-clockwise couple M at 2 m from A. Find the vertical reaction RB, taking upward as positive.

L = 8 mP = 70 kN at 4 mM = 50 kN·m (counter-clockwise) at 2 m
RB = kN
4.Medium
w0​ = 10 kN/mABRA​ = ?10 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 10 kN/m at B. Find the vertical support reaction RA.

L = 10 mw0 = 10 kN/m
RA = kN
5.Hard
w = 10 kN/mP = 40 kNABRA​ = ?RB​1 m0.5 m1.5 m1 m

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

L = 4 mP = 40 kN at 1.5 mw = 10 kN/m from 1 to 3 m
RA = kN
6.Hard
P = 10 kN, 50°Q = 35 kNABα = ?1 m4.5 m0.5 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 1 m from A, inclined at 50° to the horizontal, and a vertical load Q acts at 5.5 m from A. Find the angle α between the total reaction force at the pin A and the horizontal.

L = 6 mP = 10 kN at 1 m, θ = 50°Q = 35 kN at 5.5 m
α = °

Answer key

  1. 1. MA = 150 kN·m
  2. 2. RB = 26 kN
  3. 3. RB = 28.75 kN
  4. 4. RA = 16.67 kN
  5. 5. RA = 35 kN
  6. 6. α = 55.35 °

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