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 = 10 kNABRA​ = ?RB​3 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 = 10 kN at 3 m
RA = kN
2.Easy
M₀ = 50 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 50 kN·m applied at 1 m from A. Find the vertical reaction RB, taking upward as positive.

L = 8 mM₀ = 50 kN·m (clockwise) at 1 m
RB = kN
3.Medium
w0​ = 6 kN/mP = 65 kNABRB​ = ?2 m8 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 6 kN/m at A to zero at B. A point load P also acts at 2 m from A. Find the vertical support reaction RB.

L = 10 mw0 = 6 kN/mP = 65 kN at 2 m
RB = kN
4.Medium
P1​ = 60 kNP2​ = 35 kNABRA​RB​ = ?2 m1 m1 m

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

L = 4 mP1 = 60 kN at 2 mP2 = 35 kN at 3 m
RB = kN
5.Hard
w = 2 kN/mP = 30 kNABCRA​ = ?2 m1 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. It carries a point load P at 2 m from A and a uniformly distributed load w from 3 m to the free end at 10 m. Find the vertical reaction RA, taking upward as positive.

AB = 8 mAC = 10 mP = 30 kN at 2 mw = 2 kN/m from 3 to 10 m
RA = kN
6.Hard
P = 75 kN, 60°Q = 60 kNABα = ?2 m1.5 m0.5 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 3.5 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 = 4 mP = 75 kN at 3.5 m, θ = 60°Q = 60 kN at 2 m
α = °

Answer key

  1. 1. RA = 2.5 kN
  2. 2. RB = 6.25 kN
  3. 3. RB = 23 kN
  4. 4. RB = 56.25 kN
  5. 5. RA = 25.13 kN
  6. 6. α = 45.47 °

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