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 = ?ABδ1.5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 20 mm.

δ = 20 mmL = 1.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
P = kN
2.Easy
P = 3 kNδL = 2.5 m

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

P = 3 kNL = 2.5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δ = mm
3.Medium
w = 2 kN/mδL = 2.5 m

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

w = 2 kN/mL = 2.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 8 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 = 8 kN/mL = 3 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
θA = rad
5.Hard
w = 2 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 = 2 kN/mL = 2.5 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
P = 5 kNABδ5 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 = 5 kNb = 1 mL = 6 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. P = 14.93 kN
  2. 2. δ = 3.916 mm
  3. 3. δmax = 2.569 mm
  4. 4. θA = 0.00559 rad
  5. 5. Ireq = 13.32 × 10⁶ mm⁴
  6. 6. δmid = 12.9 mm

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