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 = 15 kNABRA​ = ?RB​2 m3 m

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

L = 5 mP = 15 kN at 2 m
RA = kN
2.Easy
P = 35 kNABRA​RB​ = ?1.5 m2.5 m

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

L = 4 mP = 35 kN at 1.5 m
RB = kN
3.Medium
w0​ = 4 kN/mP = 45 kNABRA​ = ?4 m1 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 4 m from A. Find the vertical support reaction RA.

L = 5 mw0 = 4 kN/mP = 45 kN at 4 m
RA = kN
4.Medium
P = 50 kNM = 25 kN·mABRB​ = ?4 m1 m5 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 4 m from A and a counter-clockwise couple M at 5 m from A. Find the vertical reaction RB, taking upward as positive.

L = 10 mP = 50 kN at 4 mM = 25 kN·m (counter-clockwise) at 5 m
RB = kN
5.Hard
w0​ = 10 kN/mP = 10 kNABMA​ = ?3.5 m0.5 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is zero at the wall and rises to 10 kN/m at the free end B, plus a point load P at 3.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mw0 = 10 kN/mP = 10 kN at 3.5 m
MA = kN·m
6.Hard
w = 5 kN/mP = 75 kNABCRA​ = ?4 m3 m1 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. It carries a point load P at 4 m from A and a uniformly distributed load w from 7 m to the free end at 10 m. Find the vertical reaction RA, taking upward as positive.

AB = 8 mAC = 10 mP = 75 kN at 4 mw = 5 kN/m from 7 to 10 m
RA = kN

Answer key

  1. 1. RA = 9 kN
  2. 2. RB = 13.13 kN
  3. 3. RA = 15.67 kN
  4. 4. RB = 17.5 kN
  5. 5. MA = 88.33 kN·m
  6. 6. RA = 36.56 kN

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