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 = 55 kNABMA​ = ?6 m

The cantilever beam is fixed to the wall at A and carries a point load P at its free end B. Find the magnitude of the reaction moment MA at the wall.

L = 6 mP = 55 kN at 6 m
MA = kN·m
2.Easy
P = 55 kN, 50°ABAx​ = ?2 m6 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 50° to the horizontal. Find the magnitude of the horizontal reaction Ax at the pin A.

L = 8 mP = 55 kN at 2 mθ = 50°
Ax = kN
3.Medium
P1​ = 70 kNP2​ = 15 kNABCRA​ = ?1 m1.5 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 = 70 kN at 1 mP2 = 15 kN at 4 m
RA = kN
4.Medium
P1​ = 25 kNP2​ = 15 kNABRA​RB​ = ?1 m2 m3 m

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

L = 6 mP1 = 25 kN at 1 mP2 = 15 kN at 3 m
RB = kN
5.Hard
w = 2 kN/mP = 40 kNABRA​ = ?RB​4 m2 m2 m

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

L = 8 mP = 40 kN at 6 mw = 2 kN/m from 4 to 6 m
RA = kN
6.Hard
w = 4 kN/mP = 70 kNADCRD​ = ?4 m2 m4 m

A compound beam is fixed to the wall at A, has an internal hinge at C (4 m from A) and rests on a roller at D (10 m from A). It carries a point load P at 6 m from A, a uniformly distributed load w on the whole part CD. Find the reaction RD at the roller.

AC = 4 mAD = 10 mP = 70 kN at 6 mw = 4 kN/m from 4 to 10 m
RD = kN

Answer key

  1. 1. MA = 330 kN·m
  2. 2. Ax = 35.35 kN
  3. 3. RA = 33 kN
  4. 4. RB = 11.67 kN
  5. 5. RA = 11.5 kN
  6. 6. RD = 35.33 kN

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