Answer: Factor of Safety for Bolt Shear & Tensile Stress

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SUMMARY

The discussion focuses on calculating the factor of safety for a bolt subjected to shear and tensile stresses. The bolt has an ultimate tensile strength of 500 MPa and a shear strength of 300 MPa, with a diameter of 8 mm. The calculated shear stress is 54.7 MPa, resulting in a shear factor of safety of 5.48, while the tensile stress is 94.7 MPa, yielding a tensile factor of safety of 5.27. It is emphasized that tension and shear should be considered together, and the relationship between shear and tensile strengths is not linear but rather parabolic or elliptical, as per Eurocode standards.

PREREQUISITES
  • Understanding of shear and tensile stress calculations
  • Familiarity with ultimate tensile strength and shear strength concepts
  • Knowledge of Eurocode design principles
  • Basic proficiency in mechanical engineering principles
NEXT STEPS
  • Research the Eurocode EC3 for shear and tensile strength relationships
  • Study the implications of combined loading on factor of safety
  • Learn about the parabolic relationship between shear and tensile strengths
  • Explore advanced bolt design techniques and failure modes
USEFUL FOR

Mechanical engineers, structural engineers, and students studying materials science or mechanical design will benefit from this discussion, particularly those involved in bolt design and analysis under combined loading conditions.

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Homework Statement



The material for the bolt shown in the angled joint above has an ultimate tensile strength of 500 MPa and a shear strength of 300 MPa. The diameter of the bolt is 8 mm. Determine the factor of safety in operation.


Homework Equations





The Attempt at a Solution



Shear stress= 5,5 . cos 60 (pi . 8 . 2/4)

= 0.0547kn

= 54.70 mPA



Shear Fs= 300/ 54.7 = 5.48



b) Tensile Stress = 5,5 . sin 60 (pi . 8. 2.4) = 94. 7 Mpa


Tensile Fs = 500/94.7 5.27



Is this correct?
 

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You have considered tension and shear independently, but actually they are acting together. To solve, you need to know the shear/tension strength characteristic. The graph of shear stress/ ult shear stress versus tensile stress/ ult tensile stress is sometimes assumed linear, but that is a 'safe' assumption. The experimental results were used to determine at least the relationship for the eurocode and is approximately parabolic or elliptical (I can't remember which without looking it up in ec3)
 

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