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 = 5 kNL = 6 mE = 200 GPa (steel)I = 84 × 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 12 mm.

δ = 12 mmL = 2 mE = 70 GPa (aluminium)I = 23 × 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 = 20 kN/mL = 5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

δ_max = mm

4.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 5 m from A. Find the deflection δ_B at the free end B.

P = 21 kNa = 5 mL = 6 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴

δ_B = mm

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 = 1.5 kN/mL = 4.5 mE = 11 GPa (timber)b = 125 mm

h_req = mm

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

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

h_req = mm

Answer key

1. δ = 21.43 mm
2. P = 115.9 kN
3. δ_max = 19.38 mm
4. δ_B = 67.71 mm
5. h_req = 157.2 mm
6. h_req = 229.7 mm

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