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 = 5 kNL = 2 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴

δ = mm

2.Easy

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

P = 30 kNL = 6 mE = 70 GPa (aluminium)I = 57 × 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 = 5 kN/mL = 6 mE = 70 GPa (aluminium)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 = 2 kNw = 12 kN/mL = 4 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴

δ = mm

5.Hard

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δ_max.

P = 12 kNL = 8 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴

δ_max = mm

6.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 = 1 kN/mL = 6 mE = 11 GPa (timber)b = 125 mm

h_req = mm

Answer key

1. δ = 7.576 mm
2. δ_max = 33.83 mm
3. δ_max = 21.15 mm
4. δ = 38.1 mm
5. δ_max = 9.086 mm
6. h_req = 206.7 mm

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