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 = 30 kNABδ1 m1 m

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

P = 30 kNL = 2 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 26 kNδL = 2 m

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

P = 26 kNL = 2 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
3.Medium
w = 2 kN/mδL = 4 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 2 kN/mL = 4 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 22 kNABδ3 m2 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 3 m from A. Find the deflection δB at the free end B.

P = 22 kNa = 3 mL = 5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δB = mm
5.Hard
w = 6 kN/mAB3 m

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 MA at the fixed end.

L = 3 mw = 6 kN/m
MA = kN·m
6.Hard
w = 15 kN/mP = 29 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 = 29 kNw = 15 kN/mL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δmax = 3.788 mm
  2. 2. δ = 15.07 mm
  3. 3. δmax = 16.84 mm
  4. 4. δB = 47.14 mm
  5. 5. MA = 6.75 kN·m
  6. 6. δmax = 11.76 mm

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