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 worksheet Practise 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

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 = 5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴

P = kN

2.Easy

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 20 mm.

δ = 20 mmL = 6 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

P = kN

3.Medium

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

w = 12 kN/mL = 1.5 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴

δ_max = mm

4.Medium

A simply supported beam carries a point load P at a = 4 m from support A. Find the deflection δ_P under the load.

P = 27 kNa = 4 mL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴

δ_P = mm

5.Hard

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δ_max.

P = 4 kNw = 15 kN/mL = 3 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴

δ_max = mm

6.Hard

A simply supported timber beam of rectangular section, 75 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/250. Find the smallest depth h_req of the section.

w = 4 kN/mL = 4 mE = 11 GPa (timber)b = 75 mm

h_req = mm

Answer key

1. P = 11.06 kN
2. P = 2.333 kN
3. δ_max = 8.46 mm
4. δ_P = 1.714 mm
5. δ_max = 7.171 mm
6. h_req = 229.7 mm

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