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 = 6 kNABδ1.5 m1.5 m

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

P = 6 kNL = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
2.Easy
P = ?ABδ2 m2 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 5 mm.

δ = 5 mmL = 4 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
P = kN
3.Medium
P = 27 kNABδ2 m1 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 = 27 kNa = 2 mL = 3 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δP = mm
4.Medium
w = 5 kN/mP = 27 kNABδ1.5 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 27 kNw = 5 kN/mL = 1.5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
5.Hard
w = 6 kN/mδL = 2.5 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 = 6 kN/mL = 2.5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
w = 5 kN/mAB8 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 = 8 mw = 5 kN/m
RB = kN

Answer key

  1. 1. δmax = 1.406 mm
  2. 2. P = 9.45 kN
  3. 3. δP = 9.091 mm
  4. 4. δ = 1.397 mm
  5. 5. Ireq = 2.197 × 10⁶ mm⁴
  6. 6. RB = 15 kN

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