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 = 12 kNL = 1.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴

δ = mm

2.Easy

A cantilever carries a uniformly distributed load w over its whole length. Find the slope θ_B of the beam at the free end B, in radians.

w = 10 kN/mL = 6 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

θ_B = rad

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 = 6 kNw = 2 kN/mL = 5 mE = 70 GPa (aluminium)I = 160 × 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 = 5 kN/mL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴

δ_max = 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 = 20 kNw = 5 kN/mL = 2 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴

δ_max = mm

6.Hard

A simply supported timber beam of rectangular section, 75 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 = 2 kN/mL = 3 mE = 11 GPa (timber)b = 75 mm

h_req = mm

Answer key

1. δ = 21.53 mm
2. θ_B = 0.04286 rad
3. δ = 36.27 mm
4. δ_max = 2.422 mm
5. δ_max = 5.208 mm
6. h_req = 136.7 mm

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