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 = 5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴

δ = mm

2.Easy

A cantilever carries a point load P at its free end. Find the slope θ_B of the beam at the free end B, in radians.

P = 21 kNL = 2.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

θ_B = rad

3.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δ_P under the load.

P = 24 kNa = 1.5 mL = 2.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴

δ_P = 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 = 17 kNw = 6 kN/mL = 3 mE = 200 GPa (steel)I = 120 × 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 mE = 11 GPa (timber)b = 50 mm

h_req = mm

6.Hard

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area I_req that meets this limit.

w = 5 kN/mL = 5 mE = 200 GPa (steel)

I_req = × 10⁶ mm⁴

Answer key

1. δ = 41.77 mm
2. θ_B = 0.007813 rad
3. δ_P = 68.18 mm
4. δ = 8.906 mm
5. h_req = 132 mm
6. I_req = 14.65 × 10⁶ mm⁴

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