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 = 30 kNABRA​RB​ = ?2 m3 m

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

L = 5 mP = 30 kN at 2 m
RB = kN
2.Easy
M₀ = 20 kN·mABRA​ = ?3 m1 m

The simply supported beam has a pin at A and a roller at B. It carries only a counter-clockwise couple of 20 kN·m applied at 3 m from A. Find the vertical reaction RA, taking upward as positive.

L = 4 mM₀ = 20 kN·m (counter-clockwise) at 3 m
RA = kN
3.Medium
P1​ = 30 kNP2​ = 15 kNABRA​ = ?RB​6 m1 m1 m

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

L = 8 mP1 = 30 kN at 6 mP2 = 15 kN at 7 m
RA = kN
4.Medium
P1​ = 40 kNP2​ = 75 kNABCRB​ = ?2 m6 m2 m

The beam has a pin at A and a roller at B, 8 m from A, and overhangs B to the free end C. Find the vertical reaction RB, taking upward as positive.

AB = 8 mAC = 10 mP1 = 40 kN at 2 mP2 = 75 kN at 10 m
RB = kN
5.Hard
w = 2 kN/mP = 65 kNABCRB​ = ?2 m1 m3 m4 m

The beam has a pin at A and a roller at B, 6 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 3 m to the free end at 10 m. Find the vertical reaction RB, taking upward as positive.

AB = 6 mAC = 10 mP = 65 kN at 2 mw = 2 kN/m from 3 to 10 m
RB = kN
6.Hard
w = 4 kN/mP = 80 kNADCRD​ = ?6 m3 m1 m

A compound beam is fixed to the wall at A, has an internal hinge at C (6 m from A) and rests on a roller at D (10 m from A). It carries a point load P at 9 m from A, a uniformly distributed load w on the whole part CD. Find the reaction RD at the roller.

AC = 6 mAD = 10 mP = 80 kN at 9 mw = 4 kN/m from 6 to 10 m
RD = kN

Answer key

  1. 1. RB = 12 kN
  2. 2. RA = 5 kN
  3. 3. RA = 9.375 kN
  4. 4. RB = 103.8 kN
  5. 5. RB = 36.83 kN
  6. 6. RD = 68 kN

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