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 = 28 kNL = 2 mE = 200 GPa (steel)I = 84 × 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 = 7 kNL = 1.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴

θ_B = rad

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 = 8 kN/mL = 4 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴

δ_max = mm

4.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 = 15 kNw = 6 kN/mL = 2 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴

δ = 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 = 2 kNw = 2 kN/mL = 8 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

δ_max = mm

6.Hard

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a uniformly distributed load w over its whole length. EI is constant. Find the size of the bending moment M_A at the fixed end.

L = 4 mw = 4 kN/m

M_A = kN·m

Answer key

1. δ = 4.444 mm
2. θ_B = 0.01989 rad
3. δ_max = 15.15 mm
4. δ = 3.095 mm
5. δ_max = 15.24 mm
6. M_A = 8 kN·m

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