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 = 80 kNABRA​RB​ = ?2.5 m3.5 m

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

L = 6 mP = 80 kN at 2.5 m
RB = kN
2.Easy
P = 10 kNABMA​ = ?4 m4 m

The cantilever beam is fixed to the wall at A and carries a point load P at 4 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 8 mP = 10 kN at 4 m
MA = kN·m
3.Medium
P1​ = 55 kNP2​ = 75 kNABCRA​ = ?2 m0.5 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 = 55 kN at 2 mP2 = 75 kN at 4 m
RA = kN
4.Medium
P = 50 kNM = 60 kN·mABRA​ = ?4 m2 m2 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 6 m from A. Find the vertical reaction RA, taking upward as positive.

L = 8 mP = 50 kN at 4 mM = 60 kN·m (counter-clockwise) at 6 m
RA = kN
5.Hard
w = 3 kN/mP = 80 kNQ = 50 kNADCMA​ = ?2 m1 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 2 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3 mAD = 8 mP = 80 kN at 5 mw = 3 kN/m from 3 to 8 mQ = 50 kN at 2 m
MA = kN·m
6.Hard
w = 10 kN/mP = 50 kNABRA​ = ?RB​2 m3 m2 m1 m

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

L = 8 mP = 50 kN at 5 mw = 10 kN/m from 2 to 7 m
RA = kN

Answer key

  1. 1. RB = 33.33 kN
  2. 2. MA = 40 kN·m
  3. 3. RA = −34 kN
  4. 4. RA = 32.5 kN
  5. 5. MA = 266.5 kN·m
  6. 6. RA = 40.63 kN

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