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 = 11 kNL = 2 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴

δ = mm

2.Easy

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 25 mm.

δ = 25 mmL = 6 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴

P = kN

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 = 8 kNw = 12 kN/mL = 1.5 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 = 12 kN/mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴

δ_max = mm

5.Hard

A simply supported timber beam of rectangular section, 100 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 = 3 kN/mL = 5 mE = 11 GPa (timber)b = 100 mm

h_req = mm

6.Hard

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

P = 24 kNb = 1.5 mL = 4 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴

δ_mid = mm

Answer key

1. δ = 31.75 mm
2. P = 11.11 kN
3. δ = 1.975 mm
4. δ_max = 6.803 mm
5. h_req = 251.9 mm
6. δ_mid = 18.17 mm

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