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 = 2.5 m

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

P = 3 kNL = 2.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
2.Easy
w = 6 kN/mABθ2.5 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 = 6 kN/mL = 2.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
θB = rad
3.Medium
w = 5 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 = 5 kN/mL = 4 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 25 kNABδ3 m1 m

A simply supported beam carries a point load P at a = 3 m from support A. Find the deflection δP under the load.

P = 25 kNa = 3 mL = 4 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δP = mm
5.Hard
w = 12 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 = 12 kN/mL = 1.5 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
P = 65 kNAB1.5 m1.5 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 = 3 mP = 65 kN at 1.5 m
RB = kN

Answer key

  1. 1. δ = 3.397 mm
  2. 2. θB = 0.01184 rad
  3. 3. δmax = 65.88 mm
  4. 4. δP = 31.51 mm
  5. 5. Ireq = 17.26 × 10⁶ mm⁴
  6. 6. RB = 20.31 kN

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