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 kN, 45°ABRA​ = ?2 m3 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 2 m from A, inclined at 45° to the horizontal. Find the vertical support reaction RA.

L = 5 mP = 40 kN at 2 mθ = 45°
RA = kN
2.Easy
M₀ = 60 kN·mABRA​ = ?0.5 m5.5 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 0.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 6 mM₀ = 60 kN·m (counter-clockwise) at 0.5 m
RA = kN
3.Medium
P = 50 kNM = 50 kN·mABRA​ = ?2 m4 m2 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 2 m from A. Find the vertical reaction RA, taking upward as positive.

L = 8 mP = 50 kN at 6 mM = 50 kN·m (counter-clockwise) at 2 m
RA = kN
4.Medium
w0​ = 4 kN/mP = 75 kNABRA​ = ?1.5 m2.5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 4 kN/m at A to zero at B. A point load P also acts at 1.5 m from A. Find the vertical support reaction RA.

L = 4 mw0 = 4 kN/mP = 75 kN at 1.5 m
RA = kN
5.Hard
w = 10 kN/mP = 60 kNABCRB​ = ?1 m2 m2 m

The beam has a pin at A and a roller at B, 3 m from A, and overhangs B to the free end C. It carries a point load P at 1 m from A and a uniformly distributed load w from 3 m to the free end at 5 m. Find the vertical reaction RB, taking upward as positive.

AB = 3 mAC = 5 mP = 60 kN at 1 mw = 10 kN/m from 3 to 5 m
RB = kN
6.Hard
w = 8 kN/mP = 20 kNABRA​RB​ = ?2 m0.5 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 = 20 kN at 2.5 mw = 8 kN/m from 2 to 4 m
RB = kN

Answer key

  1. 1. RA = 16.97 kN
  2. 2. RA = 10 kN
  3. 3. RA = 18.75 kN
  4. 4. RA = 52.21 kN
  5. 5. RB = 46.67 kN
  6. 6. RB = 24.5 kN

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