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 = 5 mE = 70 GPa (aluminium)I = 160 × 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 = 12 kN/mL = 2.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴

θ_B = rad

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 = 6 kN/mL = 4 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴

δ_max = 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 = 4 kN/mL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴

θ_A = rad

5.Hard

A simply supported timber beam of rectangular section, 125 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 = 4 kN/mL = 6 mE = 11 GPa (timber)b = 125 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 = 6 kN/mL = 4 mE = 200 GPa (steel)

I_req = × 10⁶ mm⁴

Answer key

1. δ = 44.64 mm
2. θ_B = 0.02367 rad
3. δ_max = 15.15 mm
4. θ_A = 0.002319 rad
5. h_req = 290.6 mm
6. I_req = 9 × 10⁶ mm⁴

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