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 = 6 mE = 200 GPa (steel)I = 36 × 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 15 mm.

δ = 15 mmL = 3 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

P = kN

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 = 12 kN/mL = 1.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴

δ_max = mm

4.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 0.5 m from A. Find the deflection δ_B at the free end B.

P = 24 kNa = 0.5 mL = 3 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

δ_B = mm

5.Hard

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δ_max.

P = 10 kNw = 2 kN/mL = 2 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴

δ_max = mm

6.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/250. Find the smallest depth h_req of the section.

w = 1.5 kN/mL = 3 mE = 11 GPa (timber)b = 50 mm

h_req = mm

Answer key

1. δ = 50 mm
2. P = 14 kN
3. δ_max = 1.998 mm
4. δ_B = 1.012 mm
5. δ_max = 3.501 mm
6. h_req = 142.2 mm

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