Question

A large tower is to be supported by a series of steel wires. It is estimated that the load on each wire will be 11,100 N. Determine the minimum required wire diameter assuming a factor of safety of 2 and a yield strength of 1030 MPa.

Answer 1

Step-by-step explanation:

The given data is as follows.

Load on each wire = 11,100 N

Factor of safety (N) = 2

`\sigma_(yield)` = 1030 MPa (150,000 Psi)

Now,

`\sigma_(working) = (\sigma_(yield))/(2)`

=
`(1030 MPa)/(2)`

= 515 MPa (75,000 Psi)

So, we will calculate the diameter as follows.

`\sigma_(w) = (F)/(A_(o))`

or,
`A_(o) = (F)/(\sigma_(w))`

`(\pi)/(4) * d^(2) = (11,100)/(515) * 10^(6) N/m^(2)}`

`d^(2)` = 27.45

d = 5.24 mm

Thus, we can conclude that the minimum required wire diameter is 5.24 mm.