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 cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 12 mm.

δ = 12 mmL = 4 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴

P = kN

2.Easy

A cantilever carries a uniformly distributed load w over its whole length. Find the slope θ_B of the beam at the free end B, in radians.

w = 2 kN/mL = 3 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴

θ_B = rad

3.Medium

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 = 27 kNw = 12 kN/mL = 2 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

δ = mm

4.Medium

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

w = 2 kN/mL = 5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴

δ_max = mm

5.Hard

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area I_req that meets this limit.

w = 2 kN/mL = 3 mE = 11 GPa (timber)

I_req = × 10⁶ mm⁴

6.Hard

A simply supported beam carries a point load P at b = 1.5 m from support B. Find the maximum deflection δ_max of the beam.

P = 16 kNb = 1.5 mL = 4 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴

δ_max = mm

Answer key

1. P = 6.3 kN
2. θ_B = 0.003571 rad
3. δ = 11.43 mm
4. δ_max = 9.248 mm
5. I_req = 23.01 × 10⁶ mm⁴
6. δ_max = 12.19 mm

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