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 = 27 kNδL = 1.5 m

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

P = 27 kNL = 1.5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ4 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 8 mm.

δ = 8 mmL = 4 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
P = kN
3.Medium
w = 12 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 = 12 kN/mL = 6 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
θA = rad
4.Medium
w = 5 kN/mδL = 3 m

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

w = 5 kN/mL = 3 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 11 kNABδ6.5 m1.5 m

A simply supported beam carries a point load P at b = 1.5 m from support B. Find the deflection δmid at midspan.

P = 11 kNb = 1.5 mL = 8 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmid = mm
6.Hard
w = 4 kN/mABδ4 m

A simply supported timber beam of rectangular section, 150 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 = 4 kN/mL = 4 mE = 11 GPa (timber)b = 150 mm
hreq = mm

Answer key

  1. 1. δ = 17.26 mm
  2. 2. P = 4.275 kN
  3. 3. θA = 0.015 rad
  4. 4. δmax = 8.411 mm
  5. 5. δmid = 26.21 mm
  6. 6. hreq = 193.7 mm

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