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 = 29 kNδL = 1.5 m

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

P = 29 kNL = 1.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
2.Easy
P = 13 kNABδ1 m1 m

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

P = 13 kNL = 2 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 21 kNABδ2 m4 m

A simply supported beam carries a point load P at a = 2 m from support A. Find the deflection δP under the load.

P = 21 kNa = 2 mL = 6 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δP = mm
4.Medium
w = 10 kN/mABθ8 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 = 10 kN/mL = 8 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
θA = rad
5.Hard
P = 9 kNABδ4 m2 m

A simply supported beam carries a point load P at b = 2 m from support B. Find the deflection δmid at midspan.

P = 9 kNb = 2 mL = 6 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmid = mm
6.Hard
P = 9 kNABδ5.5 m2.5 m

A simply supported beam carries a point load P at b = 2.5 m from support B. Find the deflection δmid at midspan.

P = 9 kNb = 2.5 mL = 8 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. δ = 19.19 mm
  2. 2. δmax = 1.275 mm
  3. 3. δP = 8.889 mm
  4. 4. θA = 0.01871 rad
  5. 5. δmid = 41.07 mm
  6. 6. δmid = 10.87 mm

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