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
P = 17 kNABδ2 m2 m

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

P = 17 kNL = 4 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 18 kNδL = 2 m

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

P = 18 kNL = 2 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δ = mm
3.Medium
w = 20 kN/mP = 24 kNABδ1.5 m

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 = 24 kNw = 20 kN/mL = 1.5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
4.Medium
w = 2 kN/mδL = 4 m

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

w = 2 kN/mL = 4 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
5.Hard
P = 30 kNAB1.5 m1.5 m

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 size of the bending moment MA at the fixed end.

L = 3 mP = 30 kN at 1.5 m
MA = kN·m
6.Hard
w = 15 kN/mP = 2 kNδL = 5 m

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

P = 2 kNw = 15 kN/mL = 5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δmax = 38.1 mm
  2. 2. δ = 19.05 mm
  3. 3. δ = 42.92 mm
  4. 4. δ = 69.26 mm
  5. 5. MA = 16.88 kN·m
  6. 6. δmax = 15.15 mm

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