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
M₀ = 25 kN·mABRA​ = ?2.5 m1.5 m

The simply supported beam has a pin at A and a roller at B. It carries only a counter-clockwise couple of 25 kN·m applied at 2.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 4 mM₀ = 25 kN·m (counter-clockwise) at 2.5 m
RA = kN
2.Easy
P = 15 kN, 40°ABAx​ = ?8 m2 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 8 m from A, inclined at 40° to the horizontal. Find the magnitude of the horizontal reaction Ax at the pin A.

L = 10 mP = 15 kN at 8 mθ = 40°
Ax = kN
3.Medium
P1​ = 40 kNP2​ = 20 kNABRA​ = ?RB​1.5 m1.5 m1 m

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

L = 4 mP1 = 40 kN at 1.5 mP2 = 20 kN at 3 m
RA = kN
4.Medium
P1​ = 45 kNP2​ = 35 kNABCRA​ = ?2 m5 m3 m

The beam has a pin at A and a roller at B, 7 m from A, and overhangs B to the free end C. Find the vertical reaction RA, taking upward as positive.

AB = 7 mAC = 10 mP1 = 45 kN at 2 mP2 = 35 kN at 10 m
RA = kN
5.Hard
w = 10 kN/mP = 30 kNQ = 15 kNADCMA​ = ?1.5 m0.5 m2.5 m1.5 m

A compound beam is fixed to the wall at A, has an internal hinge at C (2 m from A) and rests on a roller at D (6 m from A). It carries a point load P at 4.5 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 1.5 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 2 mAD = 6 mP = 30 kN at 4.5 mw = 10 kN/m from 2 to 6 mQ = 15 kN at 1.5 m
MA = kN·m
6.Hard
P = 45 kN, 30°Q = 75 kNABRA​ = ?3 m4 m3 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 3 m from A, inclined at 30° to the horizontal, and a vertical load Q acts at 7 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 10 mP = 45 kN at 3 m, θ = 30°Q = 75 kN at 7 m
RA = kN

Answer key

  1. 1. RA = 6.25 kN
  2. 2. Ax = 11.49 kN
  3. 3. RA = 30 kN
  4. 4. RA = 17.14 kN
  5. 5. MA = 85 kN·m
  6. 6. RA = 54.61 kN

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