Answer:
the factor of safety was used in the design of the cable is 2.6146
Explanation:
Given the data in the question;
Load on the main capable [tex]P_{initial[/tex] = 2600000 lb
number of parallel wires n = 1470
Diameter d = 0.16 in
average ultimate strength [tex]S_{ultimate[/tex] = 230000 psi
First we calculate the Load acting on each cable;
[tex]P_{initial[/tex] = P × n
P = [tex]P_{initial[/tex] / n
we substitute
P = 2600000 lb / 1470
P = 1768.70748 lb
Next we determine the working stress acting in a member;
[tex]S_{working[/tex] = P/A
{ Area A = [tex]\frac{\pi }{4}[/tex]d² }
[tex]S_{working[/tex] = P / [tex]\frac{\pi }{4}[/tex]d²
we substitute
[tex]S_{working[/tex] = 1768.70748 / [tex]\frac{\pi }{4}[/tex](0.16)²
[tex]S_{working[/tex] = 1768.70748 / 0.02010619298
[tex]S_{working[/tex] = 87968.29 psi
Now we calculate the factor of safety F.S
F.S = [tex]S_{ultimate[/tex] / [tex]S_{working[/tex]
we substitute
F.S = 230000 psi / 87968.29 psi
F.S = 2.6145785 ≈ 2.6146
Therefore, the factor of safety was used in the design of the cable is 2.6146
