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.

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1.Easy

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

P = 18 kNL = 1.5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴

δ = mm

2.Easy

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

P = 21 kNL = 4 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴

δ_max = mm

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 = 20 kN/mL = 6 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴

δ_max = mm

4.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 = 23 kNw = 12 kN/mL = 2.5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴

δ = mm

5.Hard

A simply supported timber beam of rectangular section, 125 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/360. Find the smallest depth h_req of the section.

w = 3 kN/mL = 4 mE = 11 GPa (timber)b = 125 mm

h_req = mm

6.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 = 4 kN/mL = 8 mE = 70 GPa (aluminium)

I_req = × 10⁶ mm⁴

Answer key

1. δ = 34.03 mm
2. δ_max = 21.21 mm
3. δ_max = 29.61 mm
4. δ = 5.575 mm
5. h_req = 198.8 mm
6. I_req = 137.1 × 10⁶ mm⁴

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