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​ = ?7 m1 m

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

L = 8 mP = 50 kN at 7 m
RB = kN
2.Easy
M₀ = 15 kN·mABRA​ = ?4 m2 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 15 kN·m applied at 4 m from A. Find the vertical reaction RA, taking upward as positive.

L = 6 mM₀ = 15 kN·m (clockwise) at 4 m
RA = kN
3.Medium
P1​ = 15 kNP2​ = 30 kNABRA​ = ?RB​2 m4 m4 m

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

L = 10 mP1 = 15 kN at 2 mP2 = 30 kN at 6 m
RA = kN
4.Medium
P = 45 kNM = 60 kN·mABRB​ = ?5 m1 m4 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 5 m from A and a counter-clockwise couple M at 6 m from A. Find the vertical reaction RB, taking upward as positive.

L = 10 mP = 45 kN at 5 mM = 60 kN·m (counter-clockwise) at 6 m
RB = kN
5.Hard
w = 5 kN/mP = 15 kNABCRB​ = ?2 m1 m1 m

The beam has a pin at A and a roller at B, 3 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 2 m to the free end at 4 m. Find the vertical reaction RB, taking upward as positive.

AB = 3 mAC = 4 mP = 15 kN at 2 mw = 5 kN/m from 2 to 4 m
RB = kN
6.Hard
w0​ = 10 kN/mP = 25 kNABMA​ = ?4 m6 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 10 kN/m at the wall and falls to zero at the free end B, plus a point load P at 4 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mw0 = 10 kN/mP = 25 kN at 4 m
MA = kN·m

Answer key

  1. 1. RB = 43.75 kN
  2. 2. RA = −2.5 kN
  3. 3. RA = 24 kN
  4. 4. RB = 16.5 kN
  5. 5. RB = 20 kN
  6. 6. MA = 266.7 kN·m

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