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 = ?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 5 mm.

δ = 5 mmL = 1.5 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
P = kN
2.Easy
P = 11 kNδL = 2.5 m

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

P = 11 kNL = 2.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δ = mm
3.Medium
P = 15 kNABδ1 m1 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1 m from A. Find the deflection δP under the load.

P = 15 kNa = 1 mL = 2 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δP = mm
4.Medium
w = 12 kN/mδL = 3 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 12 kN/mL = 3 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
5.Hard
w = 5 kN/mAB5 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 reaction RB at the prop.

L = 5 mw = 5 kN/m
RB = kN
6.Hard
w = 4 kN/mABδ3 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/360. Find the smallest depth hreq of the section.

w = 4 kN/mL = 3 mE = 11 GPa (timber)b = 100 mm
hreq = mm

Answer key

  1. 1. P = 1.124 kN
  2. 2. δ = 22.73 mm
  3. 3. δP = 3.788 mm
  4. 4. δ = 16.88 mm
  5. 5. RB = 9.375 kN
  6. 6. hreq = 176.8 mm

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