Question

The 10-mm-diameter steel bolt is surrounded by a bronze sleeve. The outer diameter of this sleeve is 20 mm, and its inner diameter is 10 mm. If the yield stress for the steel is

(σγ)st=640MPa,(σ_γ)_{st} = 640 MPa,

and for the bronze

(σγ)br=520MPa,(σ_γ)_{br} = 520 MPa,

determine the magnitude of the largest elastic load P that can be applied to the assembly.

Est=200GPa,Ebr=100GPa.E_{st} = 200 GPa, E_{br} = 100 GPa.

Solutions

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Given:

  • Diameter of steel bolt: dst=10 mmd_\text{st} = 10 \text{ mm};
  • Outer diameter of bronze sleeve: Dbr=20 mmD_\text{br} = 20 \text{ mm};
  • Inner diameter of bronze sleeve: dbr=10 mmd_\text{br} = 10 \text{ mm};
  • Yield stress for the steel: (σY)st=640 MPa(\sigma_Y)_\text{st} = 640 \text{ MPa};
  • Yield stress for the bronze: (σY)br=520 MPa(\sigma_Y)_\text{br} = 520 \text{ MPa};
  • Modulus of elasticity of the steel: Est=200 GPaE_\text{st} = 200 \text{ GPa};
  • Modulus of elasticity of the bronze: Ebr=100 GPaE_\text{br} = 100 \text{ GPa}

Required:

  • Maximum value of force PP ;

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