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 = ?ABδ6 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 25 mm.

δ = 25 mmL = 6 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
P = kN
2.Easy
P = ?ABδ1 m1 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 12 mm.

δ = 12 mmL = 2 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
P = kN
3.Medium
P = 7 kNABδ2 m1 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 δP under the load.

P = 7 kNa = 2 mL = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δP = mm
4.Medium
w = 10 kN/mδL = 6 m

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

w = 10 kN/mL = 6 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 12 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 = 12 kN/mL = 3 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
P = 6 kNP = 6 kNABδ1.667 m1.666 m1.667 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 6 kNL = 5 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. P = 2.5 kN
  2. 2. P = 66.53 kN
  3. 3. δP = 7.778 mm
  4. 4. δmax = 10.04 mm
  5. 5. Ireq = 138.1 × 10⁶ mm⁴
  6. 6. δmax = 2.335 mm

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