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 = 18 kNδL = 2 m

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

P = 18 kNL = 2 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
w = 20 kN/mABθ5 m

A cantilever carries a uniformly distributed load w over its whole length. Find the slope θB of the beam at the free end B, in radians.

w = 20 kN/mL = 5 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
θB = rad
3.Medium
P = 23 kNABδ2 m0.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δB at the free end B.

P = 23 kNa = 2 mL = 2.5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δB = mm
4.Medium
P = 16 kNABδ3.5 m1.5 m

A simply supported beam carries a point load P at a = 3.5 m from support A. Find the deflection δP under the load.

P = 16 kNa = 3.5 mL = 5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δP = mm
5.Hard
w = 4 kN/mP = 16 kNδL = 6 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 = 16 kNw = 4 kN/mL = 6 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 25 kNAB2 m2 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the size of the bending moment MA at the fixed end.

L = 4 mP = 25 kN at 2 m
MA = kN·m

Answer key

  1. 1. δ = 4.286 mm
  2. 2. θB = 0.03655 rad
  3. 3. δB = 2.635 mm
  4. 4. δP = 18.26 mm
  5. 5. δmax = 12.46 mm
  6. 6. MA = 18.75 kN·m

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