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 = 30 kNδL = 3 m

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

P = 30 kNL = 3 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ3 m3 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 12 mm.

δ = 12 mmL = 6 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
P = kN
3.Medium
P = 24 kNABδ1 m1.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1 m from A. Find the deflection δB at the free end B.

P = 24 kNa = 1 mL = 2.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δB = mm
4.Medium
w = 5 kN/mABθ2 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 = 5 kN/mL = 2 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
θA = rad
5.Hard
w = 10 kN/mδL = 8 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 = 10 kN/mL = 8 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
P = 30 kNAB2 m2 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 size of the bending moment MA at the fixed end.

L = 4 mP = 30 kN at 2 m
MA = kN·m

Answer key

  1. 1. δ = 8.438 mm
  2. 2. P = 44.8 kN
  3. 3. δB = 10.32 mm
  4. 4. θA = 0.006588 rad
  5. 5. Ireq = 120 × 10⁶ mm⁴
  6. 6. MA = 22.5 kN·m

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