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 = 4 kNL = 4 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴

δ = mm

2.Easy

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

P = 16 kNL = 6 mE = 70 GPa (aluminium)I = 36 × 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 = 8 kN/mL = 2 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴

δ_max = mm

4.Medium

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 2 kN/mL = 3 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴

δ = mm

5.Hard

A simply supported timber beam of rectangular section, 50 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/300. Find the smallest depth h_req of the section.

w = 1 kN/mL = 3.5 mE = 11 GPa (timber)b = 50 mm

h_req = mm

6.Hard

A simply supported timber beam of rectangular section, 150 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/300. Find the smallest depth h_req of the section.

w = 2 kN/mL = 5 mE = 11 GPa (timber)b = 150 mm

h_req = mm

Answer key

1. δ = 35.56 mm
2. δ_max = 28.57 mm
3. δ_max = 6.588 mm
4. δ = 5.075 mm
5. h_req = 154 mm
6. h_req = 192.2 mm

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