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 slope θ_B of the beam at the free end B, in radians.

P = 29 kNL = 4 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴

θ_B = rad

2.Easy

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

P = 15 kNL = 1.5 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴

δ = mm

3.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 = 10 kN/mL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴

θ_A = rad

4.Medium

A simply supported beam carries a point load P at a = 5.5 m from support A. Find the deflection δ_P under the load.

P = 6 kNa = 5.5 mL = 8 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴

δ_P = mm

5.Hard

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δ_max.

P = 24 kNw = 4 kN/mL = 3 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴

δ_max = 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/300. Find the smallest depth h_req of the section.

w = 1.5 kN/mL = 3 mE = 11 GPa (timber)b = 100 mm

h_req = mm

Answer key

1. θ_B = 0.01381 rad
2. δ = 2.87 mm
3. θ_A = 0.02067 rad
4. δ_P = 75.38 mm
5. δ_max = 7.031 mm
6. h_req = 120 mm

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