Beam deflection worksheet with answers

Free printable Beam deflection 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
P = ?ABδ1.5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 8 mm.

δ = 8 mmL = 1.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
P = kN
2.Easy
P = 4 kNδL = 5 m

A cantilever carries a point load P at its free end. Find the deflection δ at the free end.

P = 4 kNL = 5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
3.Medium
P = 12 kNABδ2 m2 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δB at the free end B.

P = 12 kNa = 2 mL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δB = mm
4.Medium
w = 4 kN/mδL = 5 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 4 kN/mL = 5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 25 kNABδ3.5 m1.5 m

A simply supported beam carries a point load P at b = 1.5 m from support B. Find the maximum deflection δmax of the beam.

P = 25 kNb = 1.5 mL = 5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 8 kN/mδL = 3 m

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area Ireq that meets this limit.

w = 8 kN/mL = 3 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. P = 12.09 kN
  2. 2. δ = 5.208 mm
  3. 3. δB = 17.39 mm
  4. 4. δmax = 51.92 mm
  5. 5. δmax = 1.631 mm
  6. 6. Ireq = 5.063 × 10⁶ mm⁴

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