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 = 4 kNδL = 3 m

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

P = 4 kNL = 3 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2.5 m2.5 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 25 mm.

δ = 25 mmL = 5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
P = kN
3.Medium
P = 14 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 = 14 kNa = 1 mL = 5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δP = mm
4.Medium
w = 10 kN/mδL = 3 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 10 kN/mL = 3 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
5.Hard
w = 4 kN/mδL = 6 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 = 6 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
P = 70 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 = 70 kN at 2 m
RB = kN

Answer key

  1. 1. δ = 6.122 mm
  2. 2. P = 15.46 kN
  3. 3. δP = 9.275 mm
  4. 4. δ = 3.164 mm
  5. 5. Ireq = 57.86 × 10⁶ mm⁴
  6. 6. RB = 21.88 kN

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