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 = ?ABδ8 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 8 mm.

δ = 8 mmL = 8 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
P = kN
2.Easy
P = 15 kNδL = 2 m

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

P = 15 kNL = 2 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
3.Medium
P = 25 kNABδ1 m5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1 m from A. Find the deflection δB at the free end B.

P = 25 kNa = 1 mL = 6 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δB = mm
4.Medium
P = 8 kNABδ2.5 m3.5 m

A simply supported beam carries a point load P at a = 2.5 m from support A. Find the deflection δP under the load.

P = 8 kNa = 2.5 mL = 6 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δP = mm
5.Hard
w = 1 kN/mABδ5 m

A simply supported timber beam of rectangular section, 100 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/360. Find the smallest depth hreq of the section.

w = 1 kN/mL = 5 mE = 11 GPa (timber)b = 100 mm
hreq = mm
6.Hard
P = 30 kNABδ3 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 = 30 kNb = 1 mL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. P = 1.125 kN
  2. 2. δ = 5.556 mm
  3. 3. δB = 41.67 mm
  4. 4. δP = 7.397 mm
  5. 5. hreq = 185.6 mm
  6. 6. δmid = 5.978 mm

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