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 = 7 kNABδ4 m4 m

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

P = 7 kNL = 8 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 5 kNδL = 2 m

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

P = 5 kNL = 2 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δ = mm
3.Medium
P = 17 kNABδ1.5 m1.5 m

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 δP under the load.

P = 17 kNa = 1.5 mL = 3 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δP = mm
4.Medium
w = 8 kN/mδL = 2 m

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

w = 8 kN/mL = 2 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 10 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 = 10 kN/mL = 5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 60 kNAB2.5 m2.5 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 = 5 mP = 60 kN at 2.5 m
MA = kN·m

Answer key

  1. 1. δmax = 6.55 mm
  2. 2. δ = 1.17 mm
  3. 3. δP = 48.3 mm
  4. 4. δmax = 12.63 mm
  5. 5. δmax = 39.32 mm
  6. 6. MA = 56.25 kN·m

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