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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
M₀ = 15 kN·mABRB​ = ?3.5 m0.5 m

The simply supported beam has a pin at A and a roller at B. It carries only a counter-clockwise couple of 15 kN·m applied at 3.5 m from A. Find the vertical reaction RB, taking upward as positive.

L = 4 mM₀ = 15 kN·m (counter-clockwise) at 3.5 m
RB = kN
2.Easy
P = 70 kN, 40°ABAx​ = ?2 m2 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 40° to the horizontal. Find the magnitude of the horizontal reaction Ax at the pin A.

L = 4 mP = 70 kN at 2 mθ = 40°
Ax = kN
3.Medium
w = 6 kN/mP = 10 kNABRA​ = ?4 m6 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w along its whole length and a point load P at 4 m from the wall. Find the vertical reaction RA at the wall.

L = 10 mP = 10 kN at 4 mw = 6 kN/m from 0 to 10 m
RA = kN
4.Medium
P1​ = 25 kNP2​ = 15 kNABRA​ = ?RB​2 m2.5 m1.5 m

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

L = 6 mP1 = 25 kN at 2 mP2 = 15 kN at 4.5 m
RA = kN
5.Hard
P = 50 kN, 30°Q = 15 kNABRA​ = ?1 m3 m6 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 4 m from A, inclined at 30° to the horizontal, and a vertical load Q acts at 1 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 10 mP = 50 kN at 4 m, θ = 30°Q = 15 kN at 1 m
RA = kN
6.Hard
w0​ = 12 kN/mP = 30 kNABMA​ = ?4.5 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 12 kN/m at the free end B, plus a point load P at 4.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 12 kN/mP = 30 kN at 4.5 m
MA = kN·m

Answer key

  1. 1. RB = −3.75 kN
  2. 2. Ax = 53.62 kN
  3. 3. RA = 70 kN
  4. 4. RA = 20.42 kN
  5. 5. RA = 51.84 kN
  6. 6. MA = 235 kN·m

Full step-by-step solutions: practise this topic on examproblems.com.