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 = 40 kNABRA​ = ?RB​1.5 m4.5 m

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

L = 6 mP = 40 kN at 1.5 m
RA = kN
2.Easy
M₀ = 50 kN·mABRA​ = ?3 m5 m

The simply supported beam has a pin at A and a roller at B. It carries only a counter-clockwise couple of 50 kN·m applied at 3 m from A. Find the vertical reaction RA, taking upward as positive.

L = 8 mM₀ = 50 kN·m (counter-clockwise) at 3 m
RA = kN
3.Medium
P1​ = 15 kNP2​ = 80 kNABCRA​ = ?1.5 m1 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 RA, taking upward as positive.

AB = 2.5 mAC = 4 mP1 = 15 kN at 1.5 mP2 = 80 kN at 4 m
RA = kN
4.Medium
w0​ = 6 kN/mP = 15 kNABRB​ = ?0.5 m4.5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 6 kN/m at A to zero at B. A point load P also acts at 0.5 m from A. Find the vertical support reaction RB.

L = 5 mw0 = 6 kN/mP = 15 kN at 0.5 m
RB = kN
5.Hard
P = 70 kNADCRD​ = ?3 m1.5 m1.5 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 (6 m from A). It carries a point load P at 4.5 m from A. Find the reaction RD at the roller.

AC = 3 mAD = 6 mP = 70 kN at 4.5 m
RD = kN
6.Hard
w = 5 kN/mP = 65 kNQ = 65 kNADCRD​ = ?1 m2 m2 m3 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 5 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 1 m from A. Find the reaction RD at the roller.

AC = 3 mAD = 8 mP = 65 kN at 5 mw = 5 kN/m from 3 to 8 mQ = 65 kN at 1 m
RD = kN

Answer key

  1. 1. RA = 30 kN
  2. 2. RA = 6.25 kN
  3. 3. RA = −42 kN
  4. 4. RB = 6.5 kN
  5. 5. RD = 35 kN
  6. 6. RD = 38.5 kN

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