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 = 17 kNδL = 1.5 m

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

P = 17 kNL = 1.5 mE = 11 GPa (timber)I = 160 × 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 10 mm.

δ = 10 mmL = 2.5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
P = kN
3.Medium
w = 10 kN/mABθ6 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 = 10 kN/mL = 6 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
θA = rad
4.Medium
P = 8 kNABδ1.5 m1 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δP under the load.

P = 8 kNa = 1.5 mL = 2.5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δP = mm
5.Hard
w = 15 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 = 15 kN/m
MA = kN·m
6.Hard
P = 30 kNP = 30 kNABδ1.667 m1.666 m1.667 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 30 kNL = 5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 10.87 mm
  2. 2. P = 21.5 kN
  3. 3. θA = 0.005357 rad
  4. 4. δP = 2.256 mm
  5. 5. MA = 46.88 kN·m
  6. 6. δmax = 15.85 mm

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