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 = 28 kNδL = 1.5 m

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

P = 28 kNL = 1.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
w = 10 kN/mABθ2 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 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
θB = rad
3.Medium
w = 12 kN/mABθ3 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 = 12 kN/mL = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
θA = rad
4.Medium
P = 21 kNABδ3 m2 m

A simply supported beam carries a point load P at a = 3 m from support A. Find the deflection δP under the load.

P = 21 kNa = 3 mL = 5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δP = mm
5.Hard
w = 12 kN/mP = 7 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 = 7 kNw = 12 kN/mL = 2.5 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 18 kNP = 18 kNABδ1.333 m1.334 m1.333 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 18 kNL = 4 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 13.13 mm
  2. 2. θB = 0.002899 rad
  3. 3. θA = 0.005625 rad
  4. 4. δP = 31.3 mm
  5. 5. δmax = 33.13 mm
  6. 6. δmax = 48.68 mm

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