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 = 29 kNδL = 1.5 m

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

P = 29 kNL = 1.5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2.5 m2.5 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 = 5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
P = kN
3.Medium
P = 9 kNABδ1.5 m2.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δB at the free end B.

P = 9 kNa = 1.5 mL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δB = mm
4.Medium
w = 5 kN/mδL = 2 m

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

w = 5 kN/mL = 2 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δ = mm
5.Hard
P = 20 kNAB4 m4 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the reaction RB at the prop.

L = 8 mP = 20 kN at 4 m
RB = kN
6.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/360. Find the smallest depth hreq of the section.

w = 1.5 kN/mL = 3 mE = 11 GPa (timber)b = 75 mm
hreq = mm

Answer key

  1. 1. δ = 35.31 mm
  2. 2. P = 1.142 kN
  3. 3. δB = 4.922 mm
  4. 4. δ = 16.81 mm
  5. 5. RB = 6.25 kN
  6. 6. hreq = 140.3 mm

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