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$(σ_γ)_{st} = 640 MPa,$and for the bronze$(σ_γ)_{br} = 520 MPa,$determine the magnitude of the largest elastic load P that can be applied to the assembly.$E_{st} = 200 GPa, E_{br} = 100 GPa.$

Solutions

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Given:

• Diameter of steel bolt: $d_\text{st} = 10 \text{ mm}$;
• Outer diameter of bronze sleeve: $D_\text{br} = 20 \text{ mm}$;
• Inner diameter of bronze sleeve: $d_\text{br} = 10 \text{ mm}$;
• Yield stress for the steel: $(\sigma_Y)_\text{st} = 640 \text{ MPa}$;
• Yield stress for the bronze: $(\sigma_Y)_\text{br} = 520 \text{ MPa}$;
• Modulus of elasticity of the steel: $E_\text{st} = 200 \text{ GPa}$;
• Modulus of elasticity of the bronze: $E_\text{br} = 100 \text{ GPa}$

Required:

• Maximum value of force $P$ ;

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