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 = 27 kNδL = 3 m

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

P = 27 kNL = 3 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
2.Easy
P = 25 kNABθ5 m

A cantilever carries a point load P at its free end. Find the slope θB of the beam at the free end B, in radians.

P = 25 kNL = 5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
θB = rad
3.Medium
P = 22 kNABδ1 m2 m

A simply supported beam carries a point load P at a = 1 m from support A. Find the deflection δP under the load.

P = 22 kNa = 1 mL = 3 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δP = mm
4.Medium
w = 6 kN/mδL = 2 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 = 2 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δ = mm
5.Hard
w = 15 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 = 15 kN/mL = 1.5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
w = 1 kN/mABδ6 m

A simply supported timber beam of rectangular section, 150 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/360. Find the smallest depth hreq of the section.

w = 1 kN/mL = 6 mE = 11 GPa (timber)b = 150 mm
hreq = mm

Answer key

  1. 1. δ = 33.75 mm
  2. 2. θB = 0.01302 rad
  3. 3. δP = 24.69 mm
  4. 4. δ = 7.453 mm
  5. 5. Ireq = 1.187 × 10⁶ mm⁴
  6. 6. hreq = 194.5 mm

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