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 = 9 kNδL = 4 m

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

P = 9 kNL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
2.Easy
P = 16 kNABδ2 m2 m

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

P = 16 kNL = 4 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 4 kN/mδL = 2.5 m

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

w = 4 kN/mL = 2.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
4.Medium
w = 6 kN/mP = 10 kNABδ5 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 = 10 kNw = 6 kN/mL = 5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
5.Hard
P = 80 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 reaction RB at the prop.

L = 4 mP = 80 kN at 2 m
RB = kN
6.Hard
w = 2 kN/mABδ3 m

A simply supported timber beam of rectangular section, 125 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/360. Find the smallest depth hreq of the section.

w = 2 kN/mL = 3 mE = 11 GPa (timber)b = 125 mm
hreq = mm

Answer key

  1. 1. δ = 41.74 mm
  2. 2. δmax = 35.85 mm
  3. 3. δ = 11.49 mm
  4. 4. δ = 27.67 mm
  5. 5. RB = 25 kN
  6. 6. hreq = 130.2 mm

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