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 = 11 kNδL = 3 m

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

P = 11 kNL = 3 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
2.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 10 mm.

δ = 10 mmL = 1.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
P = kN
3.Medium
w = 5 kN/mABθ4 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θA of the beam at support A, in radians.

w = 5 kN/mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
θA = rad
4.Medium
w = 12 kN/mδL = 8 m

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

w = 12 kN/mL = 8 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 3 kN/mABδ4 m

A simply supported timber beam of rectangular section, 100 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/250. Find the smallest depth hreq of the section.

w = 3 kN/mL = 4 mE = 11 GPa (timber)b = 100 mm
hreq = mm
6.Hard
P = 5 kNABδ5 m3 m

A simply supported beam carries a point load P at b = 3 m from support B. Find the maximum deflection δmax of the beam.

P = 5 kNb = 3 mL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 3.094 mm
  2. 2. P = 40.89 kN
  3. 3. θA = 0.002268 rad
  4. 4. δmax = 76.19 mm
  5. 5. hreq = 189.6 mm
  6. 6. δmax = 1.533 mm

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