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 kNABδ2 m2 m

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

P = 30 kNL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 15 kNδL = 1.5 m

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

P = 15 kNL = 1.5 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δ = mm
3.Medium
P = 11 kNABδ3.5 m1.5 m

A simply supported beam carries a point load P at a = 3.5 m from support A. Find the deflection δP under the load.

P = 11 kNa = 3.5 mL = 5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δP = mm
4.Medium
w = 20 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 = 20 kN/mL = 2 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 4 kN/mP = 30 kNδL = 2.5 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 = 30 kNw = 4 kN/mL = 2.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δmax = mm
6.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 reaction RB at the prop.

L = 3 mP = 30 kN at 1.5 m
RB = kN

Answer key

  1. 1. δmax = 1.667 mm
  2. 2. δ = 1.48 mm
  3. 3. δP = 1.805 mm
  4. 4. δmax = 1.044 mm
  5. 5. δmax = 29.8 mm
  6. 6. RB = 9.375 kN

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