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 = 3 kNABδ3 m3 m

A simply supported beam carries a point load P at midspan. Find the midspan deflection δmax.

P = 3 kNL = 6 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
2.Easy
P = ?ABδ1.5 m1.5 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 5 mm.

δ = 5 mmL = 3 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
P = kN
3.Medium
P = 24 kNABδ4 m1 m

A simply supported beam carries a point load P at a = 4 m from support A. Find the deflection δP under the load.

P = 24 kNa = 4 mL = 5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δP = mm
4.Medium
w = 4 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 = 4 kN/mL = 6 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 2 kN/mABδ4.5 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/250. Find the smallest depth hreq of the section.

w = 2 kN/mL = 4.5 mE = 11 GPa (timber)b = 100 mm
hreq = mm
6.Hard
w = 20 kN/mδL = 2 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 = 20 kN/mL = 2 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δmax = 21.53 mm
  2. 2. P = 40.89 kN
  3. 3. δP = 5.565 mm
  4. 4. δmax = 2.813 mm
  5. 5. hreq = 186.4 mm
  6. 6. Ireq = 68.18 × 10⁶ mm⁴

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