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 = 45 kNABRA​ = ?RB​3 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 = 45 kN at 3 m
RA = kN
2.Easy
P = 20 kNABRA​RB​ = ?1 m7 m

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

L = 8 mP = 20 kN at 1 m
RB = kN
3.Medium
w = 5 kN/mP = 55 kNABRA​ = ?2.5 m3.5 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 2.5 m from the wall. Find the vertical reaction RA at the wall.

L = 6 mP = 55 kN at 2.5 mw = 5 kN/m from 0 to 6 m
RA = kN
4.Medium
P = 25 kNM = 30 kN·mABRA​ = ?6 m1 m1 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 6 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 = 25 kN at 6 mM = 30 kN·m (counter-clockwise) at 7 m
RA = kN
5.Hard
P = 30 kN, 30°Q = 10 kNABRA​ = ?0.5 m3 m0.5 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 3.5 m from A, inclined at 30° to the horizontal, and a vertical load Q acts at 0.5 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 4 mP = 30 kN at 3.5 m, θ = 30°Q = 10 kN at 0.5 m
RA = kN
6.Hard
P = 65 kNADCMA​ = ?3.5 m0.5 m2 m

A compound beam is fixed to the wall at A, has an internal hinge at C (3.5 m from A) and rests on a roller at D (6 m from A). It carries a point load P at 4 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3.5 mAD = 6 mP = 65 kN at 4 m
MA = kN·m

Answer key

  1. 1. RA = 18 kN
  2. 2. RB = 2.5 kN
  3. 3. RA = 85 kN
  4. 4. RA = 10 kN
  5. 5. RA = 28.07 kN
  6. 6. MA = 182 kN·m

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