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 = 9 kNL = 6 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴

δ = mm

2.Easy

A cantilever carries a point load P at its free end. Find the slope θ_B of the beam at the free end B, in radians.

P = 13 kNL = 3 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴

θ_B = rad

3.Medium

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 22 kNw = 6 kN/mL = 4 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴

δ = 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 = 20 kN/mL = 1.5 mE = 11 GPa (timber)I = 57 × 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/250. Find the smallest depth h_req of the section.

w = 4 kN/mL = 4.5 mE = 11 GPa (timber)b = 75 mm

h_req = mm

6.Hard

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δ_max.

P = 26 kNL = 5 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴

δ_max = mm

Answer key

1. δ = 56.84 mm
2. θ_B = 0.01466 rad
3. δ = 20.67 mm
4. δ_max = 2.103 mm
5. h_req = 258.4 mm
6. δ_max = 19.62 mm

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