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 = 80 kN, 50°ABAx​ = ?6 m4 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 6 m from A, inclined at 50° to the horizontal. Find the magnitude of the horizontal reaction Ax at the pin A.

L = 10 mP = 80 kN at 6 mθ = 50°
Ax = kN
2.Easy
P = 30 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 = 30 kN at 2 m
RB = kN
3.Medium
w = 3 kN/mP = 80 kNABRA​ = ?3.5 m0.5 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w along its whole length and a point load P at 3.5 m from the wall. Find the vertical reaction RA at the wall.

L = 4 mP = 80 kN at 3.5 mw = 3 kN/m from 0 to 4 m
RA = kN
4.Medium
P = 65 kNM = 30 kN·mABRA​ = ?4 m0.5 m1.5 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 4.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 6 mP = 65 kN at 4 mM = 30 kN·m (counter-clockwise) at 4.5 m
RA = kN
5.Hard
w = 8 kN/mP = 20 kNABRA​ = ?RB​1 m1 m2 m

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

L = 4 mP = 20 kN at 2 mw = 8 kN/m from 1 to 2 m
RA = kN
6.Hard
P = 15 kN, 60°Q = 65 kNABα = ?0.5 m1.5 m4 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 0.5 m from A, inclined at 60° to the horizontal, and a vertical load Q acts at 2 m from A. Find the angle α between the total reaction force at the pin A and the horizontal.

L = 6 mP = 15 kN at 0.5 m, θ = 60°Q = 65 kN at 2 m
α = °

Answer key

  1. 1. Ax = 51.42 kN
  2. 2. RB = 12 kN
  3. 3. RA = 92 kN
  4. 4. RA = 26.67 kN
  5. 5. RA = 15 kN
  6. 6. α = 82.27 °

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