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 = ?ABδ4 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 10 mm.

δ = 10 mmL = 4 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
P = kN
2.Easy
P = 13 kNδL = 2 m

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

P = 13 kNL = 2 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δ = mm
3.Medium
w = 12 kN/mδL = 4 m

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

w = 12 kN/mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
4.Medium
w = 20 kN/mABθ8 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 = 8 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
θA = rad
5.Hard
w = 2 kN/mP = 24 kNδL = 2 m

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δmax.

P = 24 kNw = 2 kN/mL = 2 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 12 kN/mAB6 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 = 6 mw = 12 kN/m
MA = kN·m

Answer key

  1. 1. P = 15 kN
  2. 2. δ = 21.53 mm
  3. 3. δ = 65.31 mm
  4. 4. θA = 0.03743 rad
  5. 5. δmax = 1.753 mm
  6. 6. MA = 54 kN·m

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