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 slope θ_B of the beam at the free end B, in radians.

P = 12 kNL = 2 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴

θ_B = rad

2.Easy

A cantilever carries a point load P at its free end. Find the deflection δ at the free end.

P = 16 kNL = 2 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴

δ = mm

3.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 3 m from A. Find the deflection δ_B at the free end B.

P = 27 kNa = 3 mL = 4 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴

δ_B = mm

4.Medium

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θ_A of the beam at support A, in radians.

w = 2 kN/mL = 2.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴

θ_A = rad

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 = 11 kNw = 2 kN/mL = 3 mE = 11 GPa (timber)I = 36 × 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 = 3 kN/mL = 4.5 mE = 11 GPa (timber)b = 75 mm

h_req = mm

Answer key

1. θ_B = 0.002143 rad
2. δ = 50.79 mm
3. δ_B = 11.39 mm
4. θ_A = 0.003288 rad
5. δ_max = 20.95 mm
6. h_req = 234.8 mm

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