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 20 mm.

δ = 20 mmL = 6 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴

P = kN

2.Easy

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 15 mm.

δ = 15 mmL = 1.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴

P = kN

3.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δ_P under the load.

P = 12 kNa = 2 mL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴

δ_P = mm

4.Medium

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δ_max, at midspan.

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

δ_max = mm

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 = 1 kN/mL = 4.5 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/360. Find the smallest depth h_req of the section.

w = 1 kN/mL = 4.5 mE = 11 GPa (timber)b = 100 mm

h_req = mm

Answer key

1. P = 20.44 kN
2. P = 22.67 kN
3. δ_P = 1.333 mm
4. δ_max = 15.07 mm
5. h_req = 183.8 mm
6. h_req = 167 mm

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