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 = 24 kNδL = 3 m

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

P = 24 kNL = 3 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2.5 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 = 2.5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
P = kN
3.Medium
w = 20 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 = 20 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
4.Medium
w = 20 kN/mABθ2.5 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 = 20 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
θA = rad
5.Hard
w = 2 kN/mδL = 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 = 5 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
w = 12 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 size of the bending moment MA at the fixed end.

L = 5 mw = 12 kN/m
MA = kN·m

Answer key

  1. 1. δ = 25.71 mm
  2. 2. P = 92.16 kN
  3. 3. δ = 2.152 mm
  4. 4. θA = 0.003263 rad
  5. 5. Ireq = 16.74 × 10⁶ mm⁴
  6. 6. MA = 37.5 kN·m

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