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 = 70 kNABRA​RB​ = ?6 m2 m

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

L = 8 mP = 70 kN at 6 m
RB = kN
2.Easy
M₀ = 40 kN·mABRB​ = ?4 m1 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 40 kN·m applied at 4 m from A. Find the vertical reaction RB, taking upward as positive.

L = 5 mM₀ = 40 kN·m (clockwise) at 4 m
RB = kN
3.Medium
w = 4 kN/mP = 35 kNABMA​ = ?7 m3 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w along its whole length 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 = 35 kN at 7 mw = 4 kN/m from 0 to 10 m
MA = kN·m
4.Medium
P1​ = 15 kNP2​ = 35 kNABRA​ = ?RB​2 m6 m2 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 = 35 kN at 8 m
RA = kN
5.Hard
w = 3 kN/mP = 25 kNQ = 30 kNADCRD​ = ?4 m1 m4 m1 m

A compound beam is fixed to the wall at A, has an internal hinge at C (5 m from A) and rests on a roller at D (10 m from A). It carries a point load P at 9 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 4 m from A. Find the reaction RD at the roller.

AC = 5 mAD = 10 mP = 25 kN at 9 mw = 3 kN/m from 5 to 10 mQ = 30 kN at 4 m
RD = kN
6.Hard
w = 5 kN/mP = 10 kNABCRA​ = ?5 m1 m2 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. It carries a point load P at 5 m from A and a uniformly distributed load w from 6 m to the free end at 10 m. Find the vertical reaction RA, taking upward as positive.

AB = 8 mAC = 10 mP = 10 kN at 5 mw = 5 kN/m from 6 to 10 m
RA = kN

Answer key

  1. 1. RB = 52.5 kN
  2. 2. RB = 8 kN
  3. 3. MA = 445 kN·m
  4. 4. RA = 19 kN
  5. 5. RD = 27.5 kN
  6. 6. RA = 3.75 kN

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