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
w = 10 kN/mABθ2.5 m

A cantilever carries a uniformly distributed load w over its whole length. Find the slope θB of the beam at the free end B, in radians.

w = 10 kN/mL = 2.5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
θB = rad
2.Easy
P = 11 kNδL = 1.5 m

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

P = 11 kNL = 1.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δ = mm
3.Medium
P = 5 kNABδ1.5 m0.5 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 δB at the free end B.

P = 5 kNa = 1.5 mL = 2 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δB = mm
4.Medium
w = 12 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 = 12 kN/mL = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 12 kN/mAB4 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 size of the bending moment MA at the fixed end.

L = 4 mw = 12 kN/m
MA = kN·m
6.Hard
P = 7 kNABδ4.5 m1.5 m

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

P = 7 kNb = 1.5 mL = 6 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. θB = 0.0148 rad
  2. 2. δ = 9.375 mm
  3. 3. δB = 5.241 mm
  4. 4. δmax = 4.762 mm
  5. 5. MA = 24 kN·m
  6. 6. δmax = 23.82 mm

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