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 = 80 kNABRA​RB​ = ?3 m1 m

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

L = 4 mP = 80 kN at 3 m
RB = kN
2.Easy
P = 70 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 = 70 kN at 3 m
RA = kN
3.Medium
w = 5 kN/mP = 75 kNABRA​ = ?1.5 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 1.5 m from the wall. Find the vertical reaction RA at the wall.

L = 5 mP = 75 kN at 1.5 mw = 5 kN/m from 0 to 5 m
RA = kN
4.Medium
P1​ = 40 kNP2​ = 70 kNABCRB​ = ?1 m1.5 m1.5 m

The beam has a pin at A and a roller at B, 2.5 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 2.5 mAC = 4 mP1 = 40 kN at 1 mP2 = 70 kN at 4 m
RB = kN
5.Hard
P = 50 kNADCMA​ = ?3 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. Find the magnitude of the reaction moment MA at the wall.

AC = 3 mAD = 8 mP = 50 kN at 4 m
MA = kN·m
6.Hard
P = 80 kNADCMA​ = ?3 m5 m2 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 (10 m from A). It carries a point load P at 8 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3 mAD = 10 mP = 80 kN at 8 m
MA = kN·m

Answer key

  1. 1. RB = 60 kN
  2. 2. RA = 28 kN
  3. 3. RA = 100 kN
  4. 4. RB = 128 kN
  5. 5. MA = 120 kN·m
  6. 6. MA = 68.57 kN·m

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