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 = 8 kNδL = 5 m

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

P = 8 kNL = 5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ3 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 15 mm.

δ = 15 mmL = 3 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
P = kN
3.Medium
w = 6 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 = 6 kN/mL = 2.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
4.Medium
w = 2 kN/mδL = 6 m

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

w = 2 kN/mL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 25 kNAB3 m3 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 = 6 mP = 25 kN at 3 m
RB = kN
6.Hard
w = 1.5 kN/mABδ5 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/250. Find the smallest depth hreq of the section.

w = 1.5 kN/mL = 5 mE = 11 GPa (timber)b = 125 mm
hreq = mm

Answer key

  1. 1. δ = 46.3 mm
  2. 2. P = 12 kN
  3. 3. δ = 17.23 mm
  4. 4. δmax = 5.74 mm
  5. 5. RB = 7.813 kN
  6. 6. hreq = 174.6 mm

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