Question

A structural design requires that a brass cable does not elongate more than 0.1 cm. What is the minimum diameter of the wire required if the anticipated load will be 6,000 pounds and the length of the cable is 20 feet?( Young’s Modulus for brass is 15 X 10⁶ psi.)

Answer 1

Answer: The Young's Modulus,

$E=\frac{F\times l}{A\times \delta l}$      

where Area $A=\pi r^2$ , $F=mg=6000\times0.453\times9.8=26636.4~N$ and $E=15\times10^{6}psi=15\times10^{6}\times6894.76~Pa=103421.4\times10^6Pa$

Therefore,

$r^2=\frac{mgl}{\pi E\delta l}=\frac{26636.4\times20\times0.3048}{3.14\times103421.4\times10^6\times0.1\times10^{-2}}=5\times10^{-4}$

$r=2.24\times10^{-2}m=2.24cm$

diameter $D=2r=4.48cm$