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 = 28 kNδL = 1.5 m

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

P = 28 kNL = 1.5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2 m2 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 15 mm.

δ = 15 mmL = 4 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
P = kN
3.Medium
w = 6 kN/mδL = 4 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 6 kN/mL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
4.Medium
w = 6 kN/mδL = 4 m

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

w = 6 kN/mL = 4 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 20 kN/mP = 18 kNδL = 6 m

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δmax.

P = 18 kNw = 20 kN/mL = 6 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 20 kN/mδL = 5 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 = 20 kN/mL = 5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 1.875 mm
  2. 2. P = 28.35 kN
  3. 3. δ = 8 mm
  4. 4. δmax = 79.05 mm
  5. 5. δmax = 36.71 mm
  6. 6. Ireq = 58.59 × 10⁶ mm⁴

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