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 = 55 kNABRA​ = ?RB​1 m9 m

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

L = 10 mP = 55 kN at 1 m
RA = kN
2.Easy
P = 70 kNABRA​RB​ = ?1 m3 m

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

L = 4 mP = 70 kN at 1 m
RB = kN
3.Medium
w0​ = 4 kN/mABRB​ = ?5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 4 kN/m at B. Find the vertical support reaction RB.

L = 5 mw0 = 4 kN/m
RB = kN
4.Medium
P1​ = 35 kNP2​ = 10 kNABCRB​ = ?0.5 m2.5 m2 m

The beam has a pin at A and a roller at B, 3 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 3 mAC = 5 mP1 = 35 kN at 0.5 mP2 = 10 kN at 5 m
RB = kN
5.Hard
P = 10 kNQ = 20 kNADCRD​ = ?1 m1 m0.5 m3.5 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 2.5 m from A and a point load Q at 1 m from A. Find the reaction RD at the roller.

AC = 2 mAD = 6 mP = 10 kN at 2.5 mQ = 20 kN at 1 m
RD = kN
6.Hard
w = 8 kN/mP = 80 kNABCRB​ = ?3 m3 m1 m3 m

The beam has a pin at A and a roller at B, 7 m from A, and overhangs B to the free end C. It carries a point load P at 6 m from A and a uniformly distributed load w from 3 m to the free end at 10 m. Find the vertical reaction RB, taking upward as positive.

AB = 7 mAC = 10 mP = 80 kN at 6 mw = 8 kN/m from 3 to 10 m
RB = kN

Answer key

  1. 1. RA = 49.5 kN
  2. 2. RB = 17.5 kN
  3. 3. RB = 6.667 kN
  4. 4. RB = 22.5 kN
  5. 5. RD = 1.25 kN
  6. 6. RB = 120.6 kN

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