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 = 2 kNL = 2 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴

δ = mm

2.Easy

A simply supported beam carries a point load P at midspan. Find the midspan deflection δ_max.

P = 27 kNL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴

δ_max = mm

3.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δ_B at the free end B.

P = 27 kNa = 2 mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴

δ_B = 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 = 11 kNw = 4 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

δ = mm

5.Hard

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the reaction R_B at the prop.

L = 5 mP = 30 kN at 2.5 m

R_B = kN

6.Hard

A simply supported timber beam of rectangular section, 150 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 = 2 kN/mL = 4.5 mE = 11 GPa (timber)b = 150 mm

h_req = mm

Answer key

1. δ = 1.159 mm
2. δ_max = 20.66 mm
3. δ_B = 30.61 mm
4. δ = 9.146 mm
5. R_B = 9.375 kN
6. h_req = 162.8 mm

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