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 = 25 kNABRA​ = ?RB​2 m6 m

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

L = 8 mP = 25 kN at 2 m
RA = kN
2.Easy
P = 70 kNABRA​RB​ = ?5 m1 m

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

L = 6 mP = 70 kN at 5 m
RB = kN
3.Medium
w = 5 kN/mP = 30 kNABRA​ = ?3.5 m2.5 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 3.5 m from the wall. Find the vertical reaction RA at the wall.

L = 6 mP = 30 kN at 3.5 mw = 5 kN/m from 0 to 6 m
RA = kN
4.Medium
P1​ = 55 kNP2​ = 25 kNABCRB​ = ?3 m3 m4 m

The beam has a pin at A and a roller at B, 6 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 6 mAC = 10 mP1 = 55 kN at 3 mP2 = 25 kN at 10 m
RB = kN
5.Hard
P = 35 kNQ = 15 kNADCRD​ = ?1 m3 m1 m5 m

A compound beam is fixed to the wall at A, has an internal hinge at C (4 m from A) and rests on a roller at D (10 m from A). It carries a point load P at 5 m from A and a point load Q at 1 m from A. Find the reaction RD at the roller.

AC = 4 mAD = 10 mP = 35 kN at 5 mQ = 15 kN at 1 m
RD = kN
6.Hard
P = 40 kNADCMA​ = ?5 m1 m4 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 6 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 5 mAD = 10 mP = 40 kN at 6 m
MA = kN·m

Answer key

  1. 1. RA = 18.75 kN
  2. 2. RB = 58.33 kN
  3. 3. RA = 60 kN
  4. 4. RB = 69.17 kN
  5. 5. RD = 5.833 kN
  6. 6. MA = 160 kN·m

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