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 = 13 kNδL = 1.5 m

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

P = 13 kNL = 1.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = 6 kNABδ1.25 m1.25 m

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

P = 6 kNL = 2.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = 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 = 120 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 12 kN/mP = 10 kNABδ4 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 = 10 kNw = 12 kN/mL = 4 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
5.Hard
P = 50 kNAB2 m2 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 reaction RB at the prop.

L = 4 mP = 50 kN at 2 m
RB = kN
6.Hard
P = 8 kNABδ3.5 m1.5 m

A simply supported beam carries a point load P at b = 1.5 m from support B. Find the deflection δmid at midspan.

P = 8 kNb = 1.5 mL = 5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. δ = 11.08 mm
  2. 2. δmax = 2.325 mm
  3. 3. δmax = 5.051 mm
  4. 4. δ = 35.56 mm
  5. 5. RB = 15.63 kN
  6. 6. δmid = 4.135 mm

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