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 = 8 kNδL = 2 m

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

P = 8 kNL = 2 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2.5 m2.5 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 10 mm.

δ = 10 mmL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
P = kN
3.Medium
w = 6 kN/mδL = 1.5 m

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

w = 6 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δ = mm
4.Medium
w = 5 kN/mABθ6 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θA of the beam at support A, in radians.

w = 5 kN/mL = 6 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
θA = rad
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 reaction RB at the prop.

L = 4 mw = 12 kN/m
RB = kN
6.Hard
w = 20 kN/mP = 18 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 = 18 kNw = 20 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 3.628 mm
  2. 2. P = 9.677 kN
  3. 3. δ = 1.507 mm
  4. 4. θA = 0.02647 rad
  5. 5. RB = 18 kN
  6. 6. δmax = 19.09 mm

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