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 = 80 kNABRA​RB​ = ?4 m2 m

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

L = 6 mP = 80 kN at 4 m
RB = kN
2.Easy
P = 80 kNABRA​ = ?RB​4 m4 m

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

L = 8 mP = 80 kN at 4 m
RA = kN
3.Medium
P1​ = 80 kNP2​ = 45 kNABCRB​ = ?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. Find the vertical reaction RB, taking upward as positive.

AB = 4 mAC = 6 mP1 = 80 kN at 1.5 mP2 = 45 kN at 6 m
RB = kN
4.Medium
w0​ = 6 kN/mABRA​ = ?6 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 6 kN/m at A to zero at B. Find the vertical support reaction RA.

L = 6 mw0 = 6 kN/m
RA = kN
5.Hard
w0​ = 15 kN/mP = 65 kNABMA​ = ?2.5 m2.5 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 15 kN/m at the wall and falls to zero at the free end B, plus a point load P at 2.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 15 kN/mP = 65 kN at 2.5 m
MA = kN·m
6.Hard
P = 50 kNQ = 45 kNADCRD​ = ?5 m1 m2 m2 m

A compound beam is fixed to the wall at A, has an internal hinge at C (6 m from A) and rests on a roller at D (10 m from A). It carries a point load P at 8 m from A and a point load Q at 5 m from A. Find the reaction RD at the roller.

AC = 6 mAD = 10 mP = 50 kN at 8 mQ = 45 kN at 5 m
RD = kN

Answer key

  1. 1. RB = 53.33 kN
  2. 2. RA = 40 kN
  3. 3. RB = 97.5 kN
  4. 4. RA = 12 kN
  5. 5. MA = 225 kN·m
  6. 6. RD = 25 kN

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