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 = 17 kNL = 6 mE = 200 GPa (steel)I = 84 × 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 = 15 kN/mL = 2 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴

θ_B = rad

3.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 = 12 kN/mL = 8 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴

θ_A = rad

4.Medium

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 10 kN/mL = 3 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴

δ = 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 = 1 kN/mL = 4 mE = 11 GPa (timber)b = 100 mm

h_req = mm

6.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 = 6 kNw = 2 kN/mL = 6 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴

δ_max = mm

Answer key

1. δ = 72.86 mm
2. θ_B = 0.02381 rad
3. θ_A = 0.04354 rad
4. δ = 6.027 mm
5. h_req = 139.7 mm
6. δ_max = 8.438 mm

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