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 = 2 kN/mABθ5 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 = 2 kN/mL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
θB = rad
2.Easy
P = 30 kNδL = 3 m

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

P = 30 kNL = 3 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
3.Medium
w = 6 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 = 6 kN/mL = 4 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 9 kNABδ2.5 m1.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2.5 m from A. Find the deflection δB at the free end B.

P = 9 kNa = 2.5 mL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δB = mm
5.Hard
w = 5 kN/mP = 21 kNδL = 3 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 = 21 kNw = 5 kN/mL = 3 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 60 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 = 60 kN at 2 m
RB = kN

Answer key

  1. 1. θB = 0.00248 rad
  2. 2. δ = 45.92 mm
  3. 3. δmax = 8.333 mm
  4. 4. δB = 22.32 mm
  5. 5. δmax = 1.499 mm
  6. 6. RB = 18.75 kN

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