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 kNABδ1.5 m1.5 m

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

P = 7 kNL = 3 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 10 kNδL = 2.5 m

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

P = 10 kNL = 2.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
3.Medium
w = 4 kN/mδL = 3 m

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

w = 4 kN/mL = 3 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δ = mm
4.Medium
w = 15 kN/mδL = 1.5 m

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

w = 15 kN/mL = 1.5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 4 kNABδ4.5 m3.5 m

A simply supported beam carries a point load P at b = 3.5 m from support B. Find the deflection δmid at midspan.

P = 4 kNb = 3.5 mL = 8 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmid = mm
6.Hard
P = 45 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 = 45 kN at 2 m
RB = kN

Answer key

  1. 1. δmax = 6.618 mm
  2. 2. δ = 6.2 mm
  3. 3. δ = 48.21 mm
  4. 4. δmax = 1.07 mm
  5. 5. δmid = 49.65 mm
  6. 6. RB = 14.06 kN

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