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
M₀ = 15 kN·mABRA​ = ?1 m9 m

The simply supported beam has a pin at A and a roller at B. It carries only a counter-clockwise couple of 15 kN·m applied at 1 m from A. Find the vertical reaction RA, taking upward as positive.

L = 10 mM₀ = 15 kN·m (counter-clockwise) at 1 m
RA = kN
2.Easy
P = 60 kNABRA​RB​ = ?3 m3 m

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

L = 6 mP = 60 kN at 3 m
RB = kN
3.Medium
P1​ = 60 kNP2​ = 30 kNABRA​ = ?RB​2.5 m0.5 m3 m

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

L = 6 mP1 = 60 kN at 2.5 mP2 = 30 kN at 3 m
RA = kN
4.Medium
w = 10 kN/mP = 80 kNABMA​ = ?6 m1 m3 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 6 m and a point load P at 7 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mP = 80 kN at 7 mw = 10 kN/m from 0 to 6 m
MA = kN·m
5.Hard
P = 75 kNQ = 75 kNADCMA​ = ?1.5 m1.5 m2 m1 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 5 m from A and a point load Q at 1.5 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3 mAD = 6 mP = 75 kN at 5 mQ = 75 kN at 1.5 m
MA = kN·m
6.Hard
w = 4 kN/mP = 70 kNABCRA​ = ?1.5 m2.5 m2 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. It carries a point load P at 1.5 m from A and a uniformly distributed load w from 4 m to the free end at 6 m. Find the vertical reaction RA, taking upward as positive.

AB = 4 mAC = 6 mP = 70 kN at 1.5 mw = 4 kN/m from 4 to 6 m
RA = kN

Answer key

  1. 1. RA = 1.5 kN
  2. 2. RB = 30 kN
  3. 3. RA = 50 kN
  4. 4. MA = 740 kN·m
  5. 5. MA = 187.5 kN·m
  6. 6. RA = 41.75 kN

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