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​ = ?5 m5 m

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

L = 10 mP = 25 kN at 5 m
RB = kN
2.Easy
P = 60 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 = 60 kN at 3 m
RA = kN
3.Medium
P1​ = 65 kNP2​ = 70 kNABCRB​ = ?2 m6 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 RB, taking upward as positive.

AB = 8 mAC = 10 mP1 = 65 kN at 2 mP2 = 70 kN at 10 m
RB = kN
4.Medium
P = 20 kNM = 60 kN·mABRB​ = ?0.5 m3 m1.5 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 3.5 m from A and a counter-clockwise couple M at 0.5 m from A. Find the vertical reaction RB, taking upward as positive.

L = 5 mP = 20 kN at 3.5 mM = 60 kN·m (counter-clockwise) at 0.5 m
RB = kN
5.Hard
w0​ = 12 kN/mP = 25 kNABMA​ = ?7 m3 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is zero at the wall and rises to 12 kN/m 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 = 10 mw0 = 12 kN/mP = 25 kN at 7 m
MA = kN·m
6.Hard
P = 45 kN, 45°Q = 50 kNABα = ?2 m1 m1 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 45° to the horizontal, and a vertical load Q acts at 3 m from A. Find the angle α between the total reaction force at the pin A and the horizontal.

L = 4 mP = 45 kN at 2 m, θ = 45°Q = 50 kN at 3 m
α = °

Answer key

  1. 1. RB = 12.5 kN
  2. 2. RA = 15 kN
  3. 3. RB = 103.8 kN
  4. 4. RB = 2 kN
  5. 5. MA = 575 kN·m
  6. 6. α = 41.76 °

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