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 = 25 kNABRA​RB​ = ?2 m6 m

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

L = 8 mP = 25 kN at 2 m
RB = kN
2.Easy
P = 40 kNABRA​ = ?RB​4 m2 m

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

L = 6 mP = 40 kN at 4 m
RA = kN
3.Medium
P = 50 kNM = 60 kN·mABRA​ = ?0.5 m4 m0.5 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 0.5 m from A and a clockwise couple M at 4.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 5 mP = 50 kN at 0.5 mM = 60 kN·m (clockwise) at 4.5 m
RA = kN
4.Medium
w = 12 kN/mP = 75 kNABMA​ = ?1.5 m1 m2.5 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 2.5 m and a point load P at 1.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mP = 75 kN at 1.5 mw = 12 kN/m from 0 to 2.5 m
MA = kN·m
5.Hard
w0​ = 20 kN/mP = 20 kNABMA​ = ?7 m1 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 20 kN/m at the wall and falls to zero at the free end B, plus a point load P at 7 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mw0 = 20 kN/mP = 20 kN at 7 m
MA = kN·m
6.Hard
P = 40 kN, 50°Q = 45 kNABα = ?1.5 m2 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 50° to the horizontal, and a vertical load Q acts at 1.5 m from A. Find the angle α between the total reaction force at the pin A and the horizontal.

L = 4 mP = 40 kN at 3.5 m, θ = 50°Q = 45 kN at 1.5 m
α = °

Answer key

  1. 1. RB = 6.25 kN
  2. 2. RA = 13.33 kN
  3. 3. RA = 33 kN
  4. 4. MA = 150 kN·m
  5. 5. MA = 353.3 kN·m
  6. 6. α = 51.18 °

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