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 = 3 kNδL = 1.5 m

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

P = 3 kNL = 1.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
2.Easy
P = 26 kNABδ4 m4 m

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

P = 26 kNL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 12 kN/mδL = 4 m

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

w = 12 kN/mL = 4 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 20 kN/mABθ4 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 = 20 kN/mL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
θA = rad
5.Hard
w = 4 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 = 4 kN/mL = 8 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
P = 50 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 reaction RB at the prop.

L = 4 mP = 50 kN at 2 m
RB = kN

Answer key

  1. 1. δ = 1.985 mm
  2. 2. δmax = 8.667 mm
  3. 3. δmax = 43.29 mm
  4. 4. θA = 0.01159 rad
  5. 5. Ireq = 48 × 10⁶ mm⁴
  6. 6. RB = 15.63 kN

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