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6.D1 A large tower is to be supported by a series of steel wires. It is estimated that the load on each wire will be 13,300 N (3000 lbf). Determine the minimum required wire diameter assuming a factor of safety of 2 and a yield strength of 860 MPa (125,000 psi).

Sagot :

raphealnwobi

Answer:

6.33 mm

Explanation:

Stress is an internally resistive force produced by the molecules of the object to resist the deformation when an amount of load acts on the object. The SI unit of stress is measured in Pascal.

Given that force (F) = 13300 N, factor of safety (λ) = 2, yield strength (σy) = 860 MPa

The working stress [tex](\sigma_w)=\frac{\sigma_y}{\lambda}=\frac{860\ MPa}{2}=430\ MPa[/tex]

Let d be the minimum diameter, hence it is calculated using:

[tex]\sigma_w=\frac{F}{A}\\\\430 *10^6=\frac{13300}{A}\\\\A=30.93*10^{-6}\ m^2\\\\A=area=\frac{\pi d^2}{4} \\\\30.93*10^{-6}\ m^2=\frac{\pi d^2}{4} \\\\d=\sqrt{\frac{4*30.93*10^{-6}}{\pi } } \\\\d=0.0063\ m=6.3\ mm[/tex]

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