Question

a bar of solid circular cross section is loaded in tension by forces p. the bar has length l=16in and diameter 0.50in. the material is a magnessium alloy having modulus of elasticity E=6.4*10^6 psi. the allowable stress in tension is epsillon allow=17000psi and the elongation of the bar must not exceed 0.04 in. what is the allowable value of the forces p?

Answer 1

Answer:3142 Pound force

Step-by-step explanation:

Given

Length(L)=16 in.

diameter=0.5 in.

Modulus of elasticity (E)
`=6.4* 10^6 psi.`

Allowable stress
`\left ( \sigma _(allowable)\right )=17000 psi`

Max elongation of the bar =0.04 in.

Also we Know

Elongation is given

`\Delta L=(PL)/(AE)`

where

P=Force applied

L=length of bar

A=Cross-section

E=Modulus of Elasticity

`A=(\pi d^2)/(4)=(\pi)/(16) in.^2`

`0.04=(P* 16* 16)/(\pi * 6.4* 10^6)`

`P=3142 pound\ force\approx 13.976 kN`

corresponding stress is
`(3142)/((\pi )/(16))=16,000 psi`

Which is less than Allowable stress

thus allowable value of Force P is 3142 Pound force or 13.976 kN