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 simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 15 mm.

δ = 15 mmL = 2.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴

P = kN

2.Easy

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

P = 9 kNL = 1.5 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴

δ = mm

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 = 5 kN/mL = 3 mE = 70 GPa (aluminium)I = 36 × 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 = 5 kN/mL = 8 mE = 70 GPa (aluminium)I = 84 × 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/300. Find the smallest depth h_req of the section.

w = 4 kN/mL = 5 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 = 5 kN/mL = 6 mE = 200 GPa (steel)

I_req = × 10⁶ mm⁴

Answer key

1. P = 116.1 kN
2. δ = 76.7 mm
3. δ_max = 2.093 mm
4. θ_A = 0.01814 rad
5. h_req = 257.4 mm
6. I_req = 25.31 × 10⁶ mm⁴

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