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 = 14 kNL = 4 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴

δ = mm

2.Easy

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 5 mm.

δ = 5 mmL = 5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴

P = kN

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 = 8 kN/mL = 4 mE = 70 GPa (aluminium)I = 160 × 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 = 15 kN/mL = 3 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴

θ_A = rad

5.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/360. Find the smallest depth h_req of the section.

w = 4 kN/mL = 3.5 mE = 11 GPa (timber)b = 75 mm

h_req = mm

6.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/250. Find the smallest depth h_req of the section.

w = 2 kN/mL = 3 mE = 11 GPa (timber)b = 100 mm

h_req = mm

Answer key

1. δ = 26.2 mm
2. P = 2.534 kN
3. δ_max = 2.381 mm
4. θ_A = 0.01048 rad
5. h_req = 227 mm
6. h_req = 124.2 mm

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