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 = 11 kNδL = 2.5 m

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

P = 11 kNL = 2.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = 14 kNABθ3 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 = 3 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
θB = rad
3.Medium
w = 12 kN/mABθ3 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 = 12 kN/mL = 3 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
θA = rad
4.Medium
w = 8 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 = 8 kN/mL = 3 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 70 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 = 70 kN at 4 m
RB = kN
6.Hard
w = 6 kN/mδL = 4 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 = 6 kN/mL = 4 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 6.82 mm
  2. 2. θB = 0.00375 rad
  3. 3. θA = 0.002935 rad
  4. 4. δmax = 1.435 mm
  5. 5. RB = 21.88 kN
  6. 6. Ireq = 9 × 10⁶ mm⁴

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