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 = 15 kNδL = 5 m

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

P = 15 kNL = 5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = 24 kNABθ2.5 m

A cantilever carries a point load P at its free end. Find the slope θB of the beam at the free end B, in radians.

P = 24 kNL = 2.5 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
θB = rad
3.Medium
w = 15 kN/mδL = 2.5 m

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

w = 15 kN/mL = 2.5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
4.Medium
w = 12 kN/mδL = 8 m

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

w = 12 kN/mL = 8 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 4 kN/mAB5 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 reaction RB at the prop.

L = 5 mw = 4 kN/m
RB = kN
6.Hard
P = 2 kNABδ6 m2 m

A simply supported beam carries a point load P at b = 2 m from support B. Find the maximum deflection δmax of the beam.

P = 2 kNb = 2 mL = 8 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 19.53 mm
  2. 2. θB = 0.006579 rad
  3. 3. δ = 79.27 mm
  4. 4. δmax = 76.19 mm
  5. 5. RB = 7.5 kN
  6. 6. δmax = 3.241 mm

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