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Cite five factors that lead to scatter in measured material properties. Upon what three criteria are factors of safety based? A large tower is to be supported by a series of steel wires. It is estimated the load on each wire will be 15,000 N. Determine the minimum required wire diameter, assuming a factor of safety = 2.0 and a yield strength of 800 MPa (125,000 psi) for the steel. Reflect by commenting on the meaning of your answer.

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Three questions there, let me try to organize them.

a) Cite five factors that lead to scatter in measured material properties.

  • Material inhomogeneities and/or compositional differences.
  • Variation in specimen fabrication procedure
  • Test method
  • Apparatus calibration
  • Operator bias

b) Upon what three criteria are factors of safety based?

  • Accuracy of measurement of mechanical forces and/or material properties
  • consequences of failure
  • Previous experience

A large tower is to be supported by a series of steel wires.  It is estimated the load on each wire will be 15,000 N.  Determine the minimum equired wire diameter, assuming a factor of safety = 2.0 and a yield strength of 800 MPa (125,000 psi) for the steel. Reflect by commenting on the meaning of your answer.

[tex]\sigma_w = \frac{\sigma_y}{N}[/tex]

Where,

[tex]\sigma_w=[/tex]Working stress

[tex]\sigma_y=[/tex]Allowable working unit stress

N= Factor of safety

Given the information we have,

[tex]\sigma_w=\frac{800}{2}=400Mpa[/tex]

Diameter and force are related by,

[tex]A_0=\frac{F}{\sigma_w} = \pi (\frac{d_0}{2})^2[/tex]

[tex]d_0 = \sqrt{\frac{4F}{\pi \sigma_w}} = \sqrt{\frac{4*15kN}{\pi(400*10^6)}}[/tex]

[tex]d_0=4.77mm = 0.185in[/tex]

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