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 = 20 kNδL = 2 m

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

P = 20 kNL = 2 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
2.Easy
P = 21 kNABδ2.5 m2.5 m

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

P = 21 kNL = 5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 4 kN/mP = 14 kNABδ1.5 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 14 kNw = 4 kN/mL = 1.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
4.Medium
w = 15 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 = 15 kN/mL = 6 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 8 kN/mδL = 2 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 = 8 kN/mL = 2 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
P = 15 kNAB1.5 m1.5 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the reaction RB at the prop.

L = 3 mP = 15 kN at 1.5 m
RB = kN

Answer key

  1. 1. δ = 31.37 mm
  2. 2. δmax = 65.1 mm
  3. 3. δ = 10.75 mm
  4. 4. δmax = 22.2 mm
  5. 5. Ireq = 1.5 × 10⁶ mm⁴
  6. 6. RB = 4.688 kN

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