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 = 50 kNABRA​RB​ = ?2 m2 m

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

L = 4 mP = 50 kN at 2 m
RB = kN
2.Easy
M₀ = 30 kN·mABRA​ = ?5.5 m0.5 m

The simply supported beam has a pin at A and a roller at B. It carries only a counter-clockwise couple of 30 kN·m applied at 5.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 6 mM₀ = 30 kN·m (counter-clockwise) at 5.5 m
RA = kN
3.Medium
P1​ = 35 kNP2​ = 50 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 RA.

L = 4 mP1 = 35 kN at 2 mP2 = 50 kN at 3 m
RA = kN
4.Medium
w = 12 kN/mP = 20 kNABRA​ = ?4.5 m0.5 m1 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 4.5 m and a point load P at 5 m from the wall. Find the vertical reaction RA at the wall.

L = 6 mP = 20 kN at 5 mw = 12 kN/m from 0 to 4.5 m
RA = kN
5.Hard
w = 2 kN/mP = 35 kNABCRA​ = ?2 m1 m3 m4 m

The beam has a pin at A and a roller at B, 6 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 = 6 mAC = 10 mP = 35 kN at 2 mw = 2 kN/m from 3 to 10 m
RA = kN
6.Hard
w = 8 kN/mP = 50 kNABCRB​ = ?3 m2 m2 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 5 m to the free end at 10 m. Find the vertical reaction RB, taking upward as positive.

AB = 7 mAC = 10 mP = 50 kN at 3 mw = 8 kN/m from 5 to 10 m
RB = kN

Answer key

  1. 1. RB = 25 kN
  2. 2. RA = 5 kN
  3. 3. RA = 30 kN
  4. 4. RA = 74 kN
  5. 5. RA = 22.17 kN
  6. 6. RB = 64.29 kN

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