Question

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.

Answer 1

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.

$\sigma_w = \frac{\sigma_y}{N}$

Where,

$\sigma_w=$Working stress

$\sigma_y=$Allowable working unit stress

N= Factor of safety

Given the information we have,

$\sigma_w=\frac{800}{2}=400Mpa$

Diameter and force are related by,

$A_0=\frac{F}{\sigma_w} = \pi (\frac{d_0}{2})^2$

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

$d_0=4.77mm = 0.185in$