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 kNABδ1 m1 m

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

P = 28 kNL = 2 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 7 kNABθ3 m

A cantilever carries a point load P at its free end. Find the slope θB of the beam at the free end B, in radians.

P = 7 kNL = 3 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
θB = rad
3.Medium
w = 4 kN/mδL = 8 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 4 kN/mL = 8 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 15 kN/mδL = 3 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 = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δ = mm
5.Hard
w = 6 kN/mP = 3 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 = 3 kNw = 6 kN/mL = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 20 kN/mδL = 2.5 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 = 20 kN/mL = 2.5 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δmax = 2.899 mm
  2. 2. θB = 0.007895 rad
  3. 3. δmax = 8.889 mm
  4. 4. δ = 63.28 mm
  5. 5. δmax = 3.34 mm
  6. 6. Ireq = 20.93 × 10⁶ mm⁴

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