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 = 30 kNδL = 2 m

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

P = 30 kNL = 2 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = 29 kNABδ1 m1 m

A simply supported beam carries a point load P at midspan. Find the midspan deflection δmax.

P = 29 kNL = 2 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 4 kN/mP = 5 kNABδ2.5 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 5 kNw = 4 kN/mL = 2.5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
4.Medium
w = 2 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 = 2 kN/mL = 4 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 20 kN/mδL = 1.5 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 = 1.5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
w = 4 kN/mAB4 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a uniformly distributed load w over its whole length. EI is constant. Find the size of the bending moment MA at the fixed end.

L = 4 mw = 4 kN/m
MA = kN·m

Answer key

  1. 1. δ = 4.762 mm
  2. 2. δmax = 8.123 mm
  3. 3. δ = 49.32 mm
  4. 4. δmax = 3.788 mm
  5. 5. Ireq = 1.582 × 10⁶ mm⁴
  6. 6. MA = 8 kN·m

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