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​ = ?4 m1 m

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

L = 5 mP = 55 kN at 4 m
RB = kN
2.Easy
P = 55 kNABRA​ = ?RB​2.5 m1.5 m

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

L = 4 mP = 55 kN at 2.5 m
RA = kN
3.Medium
w = 2 kN/mP = 50 kNABMA​ = ?3 m3 m2 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 6 m and a point load P at 3 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mP = 50 kN at 3 mw = 2 kN/m from 0 to 6 m
MA = kN·m
4.Medium
P = 65 kNM = 50 kN·mABRA​ = ?1 m1.5 m1.5 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 1 m from A and a counter-clockwise couple M at 2.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 4 mP = 65 kN at 1 mM = 50 kN·m (counter-clockwise) at 2.5 m
RA = kN
5.Hard
w = 5 kN/mP = 45 kNABCRA​ = ?2 m0.5 m1 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 2.5 m to the free end at 5 m. Find the vertical reaction RA, taking upward as positive.

AB = 3.5 mAC = 5 mP = 45 kN at 2 mw = 5 kN/m from 2.5 to 5 m
RA = kN
6.Hard
w = 6 kN/mP = 45 kNABCRA​ = ?1.5 m1.5 m1 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. It carries a point load P at 1.5 m from A and a uniformly distributed load w from 3 m to the free end at 4 m. Find the vertical reaction RA, taking upward as positive.

AB = 3 mAC = 4 mP = 45 kN at 1.5 mw = 6 kN/m from 3 to 4 m
RA = kN

Answer key

  1. 1. RB = 44 kN
  2. 2. RA = 20.63 kN
  3. 3. MA = 186 kN·m
  4. 4. RA = 61.25 kN
  5. 5. RA = 18.39 kN
  6. 6. RA = 21.5 kN

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