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 = 75 kNABMA​ = ?3.5 m0.5 m

The cantilever beam is fixed to the wall at A and carries a point load P at 3.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mP = 75 kN at 3.5 m
MA = kN·m
2.Easy
P = 35 kNABRA​ = ?RB​1.5 m4.5 m

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

L = 6 mP = 35 kN at 1.5 m
RA = kN
3.Medium
P1​ = 40 kNP2​ = 75 kNABCRB​ = ?7 m1 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 = 40 kN at 7 mP2 = 75 kN at 10 m
RB = kN
4.Medium
P1​ = 55 kNP2​ = 15 kNABRA​RB​ = ?4 m3 m1 m

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

L = 8 mP1 = 55 kN at 4 mP2 = 15 kN at 7 m
RB = kN
5.Hard
w0​ = 4 kN/mP = 30 kNABMA​ = ?10 m

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

L = 10 mw0 = 4 kN/mP = 30 kN at 10 m
MA = kN·m
6.Hard
w = 10 kN/mP = 15 kNQ = 10 kNADCMA​ = ?1 m2 m1 m2 m

A compound beam is fixed to the wall at A, has an internal hinge at C (3 m from A) and rests on a roller at D (6 m from A). It carries a point load P at 4 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 1 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3 mAD = 6 mP = 15 kN at 4 mw = 10 kN/m from 3 to 6 mQ = 10 kN at 1 m
MA = kN·m

Answer key

  1. 1. MA = 262.5 kN·m
  2. 2. RA = 26.25 kN
  3. 3. RB = 128.8 kN
  4. 4. RB = 40.63 kN
  5. 5. MA = 366.7 kN·m
  6. 6. MA = 85 kN·m

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