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 = 13 kNABδ4 m4 m

A simply supported beam carries a point load P at midspan. Find the midspan deflection δmax.

P = 13 kNL = 8 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 29 kNδL = 1.5 m

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

P = 29 kNL = 1.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δ = mm
3.Medium
w = 6 kN/mP = 29 kNABδ1.5 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 29 kNw = 6 kN/mL = 1.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δ = mm
4.Medium
P = 10 kNABδ0.5 m5.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 0.5 m from A. Find the deflection δB at the free end B.

P = 10 kNa = 0.5 mL = 6 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δB = mm
5.Hard
w = 10 kN/mAB8 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 = 8 mw = 10 kN/m
MA = kN·m
6.Hard
P = 24 kNABδ5 m1 m

A simply supported beam carries a point load P at b = 1 m from support B. Find the deflection δmid at midspan.

P = 24 kNb = 1 mL = 6 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. δmax = 30.14 mm
  2. 2. δ = 52.03 mm
  3. 3. δ = 15.18 mm
  4. 4. δB = 28.82 mm
  5. 5. MA = 80 kN·m
  6. 6. δmid = 11.3 mm

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