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 = 22 kNABδ1.5 m1.5 m

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

P = 22 kNL = 3 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δmax = mm
2.Easy
P = ?ABδ2.5 m2.5 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 5 mm.

δ = 5 mmL = 5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
P = kN
3.Medium
P = 26 kNABδ2.5 m2.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2.5 m from A. Find the deflection δB at the free end B.

P = 26 kNa = 2.5 mL = 5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δB = mm
4.Medium
w = 6 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 = 6 kN/mL = 3 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
5.Hard
w = 10 kN/mAB5 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a uniformly distributed load w over its whole length. EI is constant. Find the reaction RB at the prop.

L = 5 mw = 10 kN/m
RB = kN
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 = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δmax = 1.473 mm
  2. 2. P = 3.379 kN
  3. 3. δB = 73.6 mm
  4. 4. δ = 35.74 mm
  5. 5. RB = 18.75 kN
  6. 6. Ireq = 289.3 × 10⁶ mm⁴

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