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 = 20 kNABδ2.5 m2.5 m

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

P = 20 kNL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm
2.Easy
P = ?ABδ5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 25 mm.

δ = 25 mmL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
P = kN
3.Medium
w = 12 kN/mδL = 2 m

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

w = 12 kN/mL = 2 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 10 kN/mABθ4 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 = 10 kN/mL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
θA = rad
5.Hard
P = 18 kNABδ4 m1 m

A simply supported beam carries a point load P at b = 1 m from support B. Find the deflection δmid at midspan.

P = 18 kNb = 1 mL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmid = mm
6.Hard
w = 20 kN/mδL = 6 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 = 6 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δmax = 3.1 mm
  2. 2. P = 10.08 kN
  3. 3. δmax = 18.94 mm
  4. 4. θA = 0.006683 rad
  5. 5. δmid = 1.585 mm
  6. 6. Ireq = 101.3 × 10⁶ mm⁴

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