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 kNABRA​RB​ = ?2.5 m2.5 m

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

L = 5 mP = 15 kN at 2.5 m
RB = kN
2.Easy
M₀ = 20 kN·mABRB​ = ?4 m1 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 20 kN·m applied at 4 m from A. Find the vertical reaction RB, taking upward as positive.

L = 5 mM₀ = 20 kN·m (clockwise) at 4 m
RB = kN
3.Medium
P1​ = 80 kNP2​ = 35 kNABCRA​ = ?3 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. Find the vertical reaction RA, taking upward as positive.

AB = 8 mAC = 10 mP1 = 80 kN at 3 mP2 = 35 kN at 10 m
RA = kN
4.Medium
P1​ = 55 kNP2​ = 60 kNABRA​ = ?RB​1 m3 m6 m

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

L = 10 mP1 = 55 kN at 1 mP2 = 60 kN at 4 m
RA = kN
5.Hard
P = 20 kNADCRD​ = ?4 m1 m3 m

A compound beam is fixed to the wall at A, has an internal hinge at C (4 m from A) and rests on a roller at D (8 m from A). It carries a point load P at 5 m from A. Find the reaction RD at the roller.

AC = 4 mAD = 8 mP = 20 kN at 5 m
RD = kN
6.Hard
P = 20 kN, 60°Q = 25 kNABα = ?2 m5 m3 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 2 m from A, inclined at 60° to the horizontal, and a vertical load Q acts at 7 m from A. Find the angle α between the total reaction force at the pin A and the horizontal.

L = 10 mP = 20 kN at 2 m, θ = 60°Q = 25 kN at 7 m
α = °

Answer key

  1. 1. RB = 7.5 kN
  2. 2. RB = 4 kN
  3. 3. RA = 41.25 kN
  4. 4. RA = 85.5 kN
  5. 5. RD = 5 kN
  6. 6. α = 64.91 °

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