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 uniformly distributed load w over its whole length. Find the slope θ_B of the beam at the free end B, in radians.

w = 10 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 23 × 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 = 17 kNL = 2 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴

δ = mm

3.Medium

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 5 kN/mL = 3 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴

δ = 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 = 10 kN/mL = 5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴

θ_A = rad

5.Hard

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area I_req that meets this limit.

w = 12 kN/mL = 3 mE = 200 GPa (steel)

I_req = × 10⁶ mm⁴

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

w = 2 kN/mL = 6 mE = 11 GPa (timber)b = 125 mm

h_req = mm

Answer key

1. θ_B = 0.003494 rad
2. δ = 28.16 mm
3. δ = 4.52 mm
4. θ_A = 0.01132 rad
5. I_req = 7.594 × 10⁶ mm⁴
6. h_req = 245.1 mm

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