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 = 15 kN, 30°ABRA​ = ?1.5 m2.5 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 1.5 m from A, inclined at 30° to the horizontal. Find the vertical support reaction RA.

L = 4 mP = 15 kN at 1.5 mθ = 30°
RA = kN
2.Easy
P = 15 kNABRA​ = ?RB​9 m1 m

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

L = 10 mP = 15 kN at 9 m
RA = kN
3.Medium
P1​ = 20 kNP2​ = 60 kNABCRA​ = ?0.5 m3.5 m2 m

The beam has a pin at A and a roller at B, 4 m from A, and overhangs B to the free end C. Find the vertical reaction RA, taking upward as positive.

AB = 4 mAC = 6 mP1 = 20 kN at 0.5 mP2 = 60 kN at 6 m
RA = kN
4.Medium
P1​ = 15 kNP2​ = 45 kNABRA​RB​ = ?2 m5 m3 m

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

L = 10 mP1 = 15 kN at 2 mP2 = 45 kN at 7 m
RB = kN
5.Hard
w = 3 kN/mP = 15 kNABCRB​ = ?3 m4 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. It carries a point load P at 3 m from A and a uniformly distributed load w from 3 m to the free end at 10 m. Find the vertical reaction RB, taking upward as positive.

AB = 7 mAC = 10 mP = 15 kN at 3 mw = 3 kN/m from 3 to 10 m
RB = kN
6.Hard
P = 35 kN, 40°Q = 20 kNABα = ?5 m3 m2 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 5 m from A, inclined at 40° to the horizontal, and a vertical load Q acts at 8 m from A. Find the angle α between the total reaction force at the pin A and the horizontal.

L = 10 mP = 35 kN at 5 m, θ = 40°Q = 20 kN at 8 m
α = °

Answer key

  1. 1. RA = 4.688 kN
  2. 2. RA = 1.5 kN
  3. 3. RA = −12.5 kN
  4. 4. RB = 34.5 kN
  5. 5. RB = 25.93 kN
  6. 6. α = 29.63 °

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