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 = 5 kNδL = 5 m

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

P = 5 kNL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
2.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 15 mm.

δ = 15 mmL = 2.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
P = kN
3.Medium
w = 8 kN/mδL = 3 m

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

w = 8 kN/mL = 3 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
4.Medium
w = 2 kN/mABθ6 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θA of the beam at support A, in radians.

w = 2 kN/mL = 6 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
θA = rad
5.Hard
w = 2 kN/mABδ6 m

A simply supported timber beam of rectangular section, 100 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 = 6 mE = 11 GPa (timber)b = 100 mm
hreq = mm
6.Hard
w = 2 kN/mδL = 6 m

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area Ireq that meets this limit.

w = 2 kN/mL = 6 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 12.4 mm
  2. 2. P = 3.802 kN
  3. 3. δ = 2.531 mm
  4. 4. θA = 0.04545 rad
  5. 5. hreq = 280.6 mm
  6. 6. Ireq = 10.13 × 10⁶ mm⁴

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