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/mABθ6 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 = 6 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
θB = rad
2.Easy
P = 25 kNABδ3 m3 m

A simply supported beam carries a point load P at midspan. Find the midspan deflection δmax.

P = 25 kNL = 6 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 15 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 = 15 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
4.Medium
P = 8 kNABδ2 m6 m

A simply supported beam carries a point load P at a = 2 m from support A. Find the deflection δP under the load.

P = 8 kNa = 2 mL = 8 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δP = mm
5.Hard
w = 6 kN/mδL = 8 m

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area Ireq that meets this limit.

w = 6 kN/mL = 8 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
w = 10 kN/mP = 9 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 = 9 kNw = 10 kN/mL = 3 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. θB = 0.03214 rad
  2. 2. δmax = 3.516 mm
  3. 3. δ = 1.13 mm
  4. 4. δP = 29.81 mm
  5. 5. Ireq = 1309 × 10⁶ mm⁴
  6. 6. δmax = 9.695 mm

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