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
M₀ = 60 kN·mABRB​ = ?1 m9 m

The simply supported beam has a pin at A and a roller at B. It carries only a counter-clockwise couple of 60 kN·m applied at 1 m from A. Find the vertical reaction RB, taking upward as positive.

L = 10 mM₀ = 60 kN·m (counter-clockwise) at 1 m
RB = kN
2.Easy
M₀ = 10 kN·mABRA​ = ?4 m1 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 10 kN·m applied at 4 m from A. Find the vertical reaction RA, taking upward as positive.

L = 5 mM₀ = 10 kN·m (clockwise) at 4 m
RA = kN
3.Medium
P = 75 kNM = 15 kN·mABRB​ = ?0.5 m0.5 m3 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 0.5 m from A. Find the vertical reaction RB, taking upward as positive.

L = 4 mP = 75 kN at 1 mM = 15 kN·m (counter-clockwise) at 0.5 m
RB = kN
4.Medium
w = 10 kN/mP = 70 kNABMA​ = ?1.5 m2.5 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 1.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mP = 70 kN at 1.5 mw = 10 kN/m from 0 to 4 m
MA = kN·m
5.Hard
w = 2 kN/mP = 55 kNABRA​ = ?RB​2 m1 m2 m

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

L = 5 mP = 55 kN at 2 mw = 2 kN/m from 3 to 5 m
RA = kN
6.Hard
w = 6 kN/mP = 35 kNABRA​RB​ = ?1 m1.5 m1.5 m

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

L = 4 mP = 35 kN at 2.5 mw = 6 kN/m from 1 to 4 m
RB = kN

Answer key

  1. 1. RB = −6 kN
  2. 2. RA = −2 kN
  3. 3. RB = 15 kN
  4. 4. MA = 185 kN·m
  5. 5. RA = 33.8 kN
  6. 6. RB = 33.13 kN

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