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 = ?ABδ1 m1 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 25 mm.

δ = 25 mmL = 2 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
P = kN
2.Easy
w = 15 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 = 15 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
θB = rad
3.Medium
P = 3 kNABδ3.5 m2.5 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 = 3 kNa = 3.5 mL = 6 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δP = mm
4.Medium
w = 12 kN/mδL = 5 m

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

w = 12 kN/mL = 5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
5.Hard
P = 12 kNABδ4 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 = 12 kNb = 2 mL = 6 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 4 kN/mP = 7 kNδL = 8 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 = 7 kNw = 4 kN/mL = 8 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. P = 59.4 kN
  2. 2. θB = 0.02426 rad
  3. 3. δP = 7.25 mm
  4. 4. δ = 29.3 mm
  5. 5. δmax = 55.3 mm
  6. 6. δmax = 25.71 mm

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