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 = 4 kNδL = 2.5 m

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

P = 4 kNL = 2.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2 m2 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 20 mm.

δ = 20 mmL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
P = kN
3.Medium
w = 10 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 = 10 kN/mL = 8 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 8 kN/mδL = 1.5 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 8 kN/mL = 1.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
5.Hard
w = 4 kN/mδL = 4 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 = 4 kN/mL = 4 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
w = 8 kN/mAB4 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 = 4 mw = 8 kN/m
RB = kN

Answer key

  1. 1. δ = 24.8 mm
  2. 2. P = 69 kN
  3. 3. δmax = 74.07 mm
  4. 4. δ = 1.101 mm
  5. 5. Ireq = 17.14 × 10⁶ mm⁴
  6. 6. RB = 12 kN

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