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 = 60 kNABRA​ = ?RB​6 m4 m

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

L = 10 mP = 60 kN at 6 m
RA = kN
2.Easy
M₀ = 60 kN·mABRA​ = ?2.5 m1.5 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 60 kN·m applied at 2.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 4 mM₀ = 60 kN·m (clockwise) at 2.5 m
RA = kN
3.Medium
P1​ = 75 kNP2​ = 60 kNABCRB​ = ?1.5 m2.5 m1 m

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

AB = 4 mAC = 5 mP1 = 75 kN at 1.5 mP2 = 60 kN at 5 m
RB = kN
4.Medium
w0​ = 6 kN/mABRB​ = ?5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 6 kN/m at A to zero at B. Find the vertical support reaction RB.

L = 5 mw0 = 6 kN/m
RB = kN
5.Hard
w = 4 kN/mP = 20 kNQ = 80 kNADCRD​ = ?1.5 m0.5 m2.5 m1.5 m

A compound beam is fixed to the wall at A, has an internal hinge at C (2 m from A) and rests on a roller at D (6 m from A). It carries a point load P at 4.5 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 1.5 m from A. Find the reaction RD at the roller.

AC = 2 mAD = 6 mP = 20 kN at 4.5 mw = 4 kN/m from 2 to 6 mQ = 80 kN at 1.5 m
RD = kN
6.Hard
w0​ = 20 kN/mP = 75 kNABMA​ = ?2.5 m1.5 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 2.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mw0 = 20 kN/mP = 75 kN at 2.5 m
MA = kN·m

Answer key

  1. 1. RA = 24 kN
  2. 2. RA = −15 kN
  3. 3. RB = 103.1 kN
  4. 4. RB = 5 kN
  5. 5. RD = 20.5 kN
  6. 6. MA = 240.8 kN·m

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