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 = 25 kNABRA​RB​ = ?1 m4 m

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

L = 5 mP = 25 kN at 1 m
RB = kN
2.Easy
M₀ = 50 kN·mABRB​ = ?1.5 m2.5 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 50 kN·m applied at 1.5 m from A. Find the vertical reaction RB, taking upward as positive.

L = 4 mM₀ = 50 kN·m (clockwise) at 1.5 m
RB = kN
3.Medium
w0​ = 15 kN/mP = 35 kNABRB​ = ?0.5 m3.5 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 15 kN/m at B. A point load P also acts at 0.5 m from A. Find the vertical support reaction RB.

L = 4 mw0 = 15 kN/mP = 35 kN at 0.5 m
RB = kN
4.Medium
P = 15 kNM = 15 kN·mABRB​ = ?3 m6 m1 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 3 m from A and a clockwise couple M at 9 m from A. Find the vertical reaction RB, taking upward as positive.

L = 10 mP = 15 kN at 3 mM = 15 kN·m (clockwise) at 9 m
RB = kN
5.Hard
w = 4 kN/mP = 20 kNABCRA​ = ?0.5 m2 m1.5 m2 m

The beam has a pin at A and a roller at B, 4 m from A, and overhangs B to the free end C. It carries a point load P at 0.5 m from A and a uniformly distributed load w from 2.5 m to the free end at 6 m. Find the vertical reaction RA, taking upward as positive.

AB = 4 mAC = 6 mP = 20 kN at 0.5 mw = 4 kN/m from 2.5 to 6 m
RA = kN
6.Hard
P = 75 kNADCMA​ = ?3 m1 m6 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 4 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3 mAD = 10 mP = 75 kN at 4 m
MA = kN·m

Answer key

  1. 1. RB = 5 kN
  2. 2. RB = 12.5 kN
  3. 3. RB = 24.38 kN
  4. 4. RB = 6 kN
  5. 5. RA = 16.63 kN
  6. 6. MA = 192.9 kN·m

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