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 = 65 kNABRA​RB​ = ?1.5 m2.5 m

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

L = 4 mP = 65 kN at 1.5 m
RB = kN
2.Easy
P = 20 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 = 20 kN at 2.5 m
RA = kN
3.Medium
w = 2 kN/mP = 15 kNABMA​ = ?6 m4 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 6 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 10 mP = 15 kN at 6 mw = 2 kN/m from 0 to 10 m
MA = kN·m
4.Medium
P = 35 kNM = 50 kN·mABRA​ = ?2 m5 m1 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 2 m from A and a counter-clockwise couple M at 7 m from A. Find the vertical reaction RA, taking upward as positive.

L = 8 mP = 35 kN at 2 mM = 50 kN·m (counter-clockwise) at 7 m
RA = kN
5.Hard
w = 2 kN/mP = 50 kNABCRA​ = ?3 m2 m3 m

The beam has a pin at A and a roller at B, 5 m from A, and overhangs B to the free end C. It carries a point load P at 3 m from A and a uniformly distributed load w from 5 m to the free end at 8 m. Find the vertical reaction RA, taking upward as positive.

AB = 5 mAC = 8 mP = 50 kN at 3 mw = 2 kN/m from 5 to 8 m
RA = kN
6.Hard
w0​ = 10 kN/mP = 65 kNABMA​ = ?4 m4 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is zero at the wall and rises to 10 kN/m at the free end B, plus a point load P at 4 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mw0 = 10 kN/mP = 65 kN at 4 m
MA = kN·m

Answer key

  1. 1. RB = 24.38 kN
  2. 2. RA = 7.5 kN
  3. 3. MA = 190 kN·m
  4. 4. RA = 32.5 kN
  5. 5. RA = 18.2 kN
  6. 6. MA = 473.3 kN·m

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