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 kNABδ2.5 m2.5 m

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

P = 3 kNL = 5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
2.Easy
P = ?ABδ0.75 m0.75 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 8 mm.

δ = 8 mmL = 1.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
P = kN
3.Medium
P = 13 kNABδ2 m3 m

A simply supported beam carries a point load P at a = 2 m from support A. Find the deflection δP under the load.

P = 13 kNa = 2 mL = 5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δP = mm
4.Medium
w = 6 kN/mδL = 2.5 m

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

w = 6 kN/mL = 2.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 10 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 = 10 kN at 3 m
RB = kN
6.Hard
w = 6 kN/mP = 13 kNδL = 8 m

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δmax.

P = 13 kNw = 6 kN/mL = 8 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δmax = 4.439 mm
  2. 2. P = 273.1 kN
  3. 3. δP = 1.3 mm
  4. 4. δmax = 7.706 mm
  5. 5. RB = 3.125 kN
  6. 6. δmax = 19.11 mm

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