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 = ?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 8 mm.

δ = 8 mmL = 2.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
P = kN
2.Easy
P = 23 kNδL = 1.5 m

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

P = 23 kNL = 1.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δ = mm
3.Medium
w = 20 kN/mδL = 4 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 20 kN/mL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 20 kNABδ1 m5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1 m from A. Find the deflection δP under the load.

P = 20 kNa = 1 mL = 6 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δP = mm
5.Hard
w = 12 kN/mP = 20 kNδL = 3 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 = 20 kNw = 12 kN/mL = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 55 kNAB1.5 m1.5 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 reaction RB at the prop.

L = 3 mP = 55 kN at 1.5 m
RB = kN

Answer key

  1. 1. P = 7.066 kN
  2. 2. δ = 30.8 mm
  3. 3. δmax = 9.259 mm
  4. 4. δP = 5.051 mm
  5. 5. δmax = 9.961 mm
  6. 6. RB = 17.19 kN

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