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 = 2 kN/mL = 3 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴

θ_B = rad

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 = 6 kNL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴

θ_B = rad

3.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1 m from A. Find the deflection δ_B at the free end B.

P = 2 kNa = 1 mL = 2 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴

δ_B = mm

4.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δ_B at the free end B.

P = 20 kNa = 1.5 mL = 2.5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴

δ_B = 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 = 9 kNw = 5 kN/mL = 4 mE = 11 GPa (timber)I = 36 × 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 reaction R_B at the prop.

L = 6 mw = 5 kN/m

R_B = kN

Answer key

1. θ_B = 0.02273 rad
2. θ_B = 0.004464 rad
3. δ_B = 1.263 mm
4. δ_B = 4.018 mm
5. δ_max = 72.39 mm
6. R_B = 11.25 kN

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