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 kN, 45°ABAx​ = ?4.5 m0.5 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 4.5 m from A, inclined at 45° to the horizontal. Find the magnitude of the horizontal reaction Ax at the pin A.

L = 5 mP = 70 kN at 4.5 mθ = 45°
Ax = kN
2.Easy
P = 65 kNABMA​ = ?3 m2 m

The cantilever beam is fixed to the wall at A and carries a point load P at 3 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mP = 65 kN at 3 m
MA = kN·m
3.Medium
w = 3 kN/mP = 50 kNABMA​ = ?5 m3 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 5 m and a point load P at 8 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mP = 50 kN at 8 mw = 3 kN/m from 0 to 5 m
MA = kN·m
4.Medium
P1​ = 45 kNP2​ = 35 kNABRA​RB​ = ?3 m1 m4 m

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

L = 8 mP1 = 45 kN at 3 mP2 = 35 kN at 4 m
RB = kN
5.Hard
w = 8 kN/mP = 80 kNQ = 65 kNADCRD​ = ?2 m1 m1 m4 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 (8 m from A). It carries a point load P at 4 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 2 m from A. Find the reaction RD at the roller.

AC = 3 mAD = 8 mP = 80 kN at 4 mw = 8 kN/m from 3 to 8 mQ = 65 kN at 2 m
RD = kN
6.Hard
w = 10 kN/mP = 80 kNABCRA​ = ?1.5 m0.5 m1.5 m1.5 m

The beam has a pin at A and a roller at B, 3.5 m from A, and overhangs B to the free end C. It carries a point load P at 2 m from A and a uniformly distributed load w from 1.5 m to the free end at 5 m. Find the vertical reaction RA, taking upward as positive.

AB = 3.5 mAC = 5 mP = 80 kN at 2 mw = 10 kN/m from 1.5 to 5 m
RA = kN

Answer key

  1. 1. Ax = 49.5 kN
  2. 2. MA = 195 kN·m
  3. 3. MA = 437.5 kN·m
  4. 4. RB = 34.38 kN
  5. 5. RD = 36 kN
  6. 6. RA = 36.79 kN

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