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 = 14 kNABθ1.5 m

A cantilever carries a point load P at its free end. Find the slope θB of the beam at the free end B, in radians.

P = 14 kNL = 1.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
θB = rad
2.Easy
P = 23 kNABδ2.5 m2.5 m

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

P = 23 kNL = 5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 5 kN/mδL = 3 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 5 kN/mL = 3 mE = 11 GPa (timber)I = 57 × 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 = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
5.Hard
w = 5 kN/mAB3 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a uniformly distributed load w over its whole length. EI is constant. Find the reaction RB at the prop.

L = 3 mw = 5 kN/m
RB = kN
6.Hard
w = 15 kN/mδL = 1.5 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 = 15 kN/mL = 1.5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. θB = 0.01875 rad
  2. 2. δmax = 35.23 mm
  3. 3. δmax = 8.411 mm
  4. 4. δ = 2.325 mm
  5. 5. RB = 5.625 kN
  6. 6. Ireq = 1.187 × 10⁶ mm⁴

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