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 = 26 kNδL = 2.5 m

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

P = 26 kNL = 2.5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
w = 8 kN/mABθ4 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 = 8 kN/mL = 4 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
θB = rad
3.Medium
w = 20 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 = 20 kN/mL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 8 kN/mδL = 2.5 m

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

w = 8 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
5.Hard
w = 2 kN/mδL = 5 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 = 2 kN/mL = 5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
P = 20 kNAB3 m3 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 = 6 mP = 20 kN at 3 m
RB = kN

Answer key

  1. 1. δ = 76.94 mm
  2. 2. θB = 0.007619 rad
  3. 3. δmax = 57.4 mm
  4. 4. δ = 3.488 mm
  5. 5. Ireq = 5.859 × 10⁶ mm⁴
  6. 6. RB = 6.25 kN

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