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 = 10 kNδL = 4 m

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

P = 10 kNL = 4 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = 8 kNABθ1.5 m

A cantilever carries a point load P at its free end. Find the slope θB of the beam at the free end B, in radians.

P = 8 kNL = 1.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
θB = rad
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 = 160 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 8 kN/mδL = 5 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 = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
5.Hard
w = 3 kN/mABδ4 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/300. Find the smallest depth hreq of the section.

w = 3 kN/mL = 4 mE = 11 GPa (timber)b = 100 mm
hreq = mm
6.Hard
w = 15 kN/mP = 15 kNδL = 2.5 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 = 15 kNw = 15 kN/mL = 2.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 6.667 mm
  2. 2. θB = 0.00375 rad
  3. 3. δmax = 2.083 mm
  4. 4. δ = 37.2 mm
  5. 5. hreq = 201.5 mm
  6. 6. δmax = 31.6 mm

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