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 = ?ABδ1.5 m1.5 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 = 3 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
P = kN
2.Easy
P = 14 kNδL = 2 m

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

P = 14 kNL = 2 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
3.Medium
w = 6 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 = 6 kN/mL = 4 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 2 kNABδ1 m4 m

A simply supported beam carries a point load P at a = 1 m from support A. Find the deflection δP under the load.

P = 2 kNa = 1 mL = 5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δP = mm
5.Hard
P = 55 kNAB2.5 m2.5 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 = 5 mP = 55 kN at 2.5 m
RB = kN
6.Hard
w = 5 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 = 5 kN/mL = 2.5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. P = 149.3 kN
  2. 2. δ = 3.333 mm
  3. 3. δmax = 23.81 mm
  4. 4. δP = 1.616 mm
  5. 5. RB = 17.19 kN
  6. 6. Ireq = 1.831 × 10⁶ mm⁴

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