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 = 70 kN, 40°ABAx​ = ?2.5 m3.5 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 2.5 m from A, inclined at 40° to the horizontal. Find the magnitude of the horizontal reaction Ax at the pin A.

L = 6 mP = 70 kN at 2.5 mθ = 40°
Ax = kN
2.Easy
P = 15 kNABRA​RB​ = ?2.5 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 = 15 kN at 2.5 m
RB = kN
3.Medium
P1​ = 70 kNP2​ = 35 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. Find the vertical reaction RB, taking upward as positive.

AB = 3 mAC = 5 mP1 = 70 kN at 1 mP2 = 35 kN at 5 m
RB = kN
4.Medium
P1​ = 80 kNP2​ = 25 kNABCRA​ = ?4 m2 m2 m

The beam has a pin at A and a roller at B, 6 m from A, and overhangs B to the free end C. Find the vertical reaction RA, taking upward as positive.

AB = 6 mAC = 8 mP1 = 80 kN at 4 mP2 = 25 kN at 8 m
RA = kN
5.Hard
P = 55 kN, 50°Q = 40 kNABRA​ = ?1.5 m1 m1.5 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 2.5 m from A, inclined at 50° to the horizontal, and a vertical load Q acts at 1.5 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 4 mP = 55 kN at 2.5 m, θ = 50°Q = 40 kN at 1.5 m
RA = kN
6.Hard
P = 55 kNADCMA​ = ?4 m3 m1 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 (8 m from A). It carries a point load P at 7 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 4 mAD = 8 mP = 55 kN at 7 m
MA = kN·m

Answer key

  1. 1. Ax = 53.62 kN
  2. 2. RB = 9.375 kN
  3. 3. RB = 81.67 kN
  4. 4. RA = 18.33 kN
  5. 5. RA = 53.99 kN
  6. 6. MA = 55 kN·m

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