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 = 13 kNδL = 2 m

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

P = 13 kNL = 2 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
w = 4 kN/mABθ2.5 m

A cantilever carries a uniformly distributed load w over its whole length. Find the slope θB of the beam at the free end B, in radians.

w = 4 kN/mL = 2.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
θB = rad
3.Medium
P = 13 kNABδ2 m1 m

A simply supported beam carries a point load P at a = 2 m from support A. Find the deflection δP under the load.

P = 13 kNa = 2 mL = 3 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δP = mm
4.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 = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 1.5 kN/mABδ3 m

A simply supported timber beam of rectangular section, 75 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 = 1.5 kN/mL = 3 mE = 11 GPa (timber)b = 75 mm
hreq = mm
6.Hard
P = 18 kNABδ3.5 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 = 18 kNb = 1.5 mL = 5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. δ = 37.52 mm
  2. 2. θB = 0.002264 rad
  3. 3. δP = 3.283 mm
  4. 4. δmax = 11.34 mm
  5. 5. hreq = 132 mm
  6. 6. δmid = 1.16 mm

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