Strength of materials- simple truss problem

[Jeff231]

Homework Statement

The bars in the truss each have a cross sectional area of 1.2in^2. If the maximum axial stress in any bar is not to exceed 25ksi, determine the maximum magnitude of P of the loads that can be applied to the truss. Determine the elongation of each member.

E=29,000 ksi

Homework Equations

$$\sigma$$ = E* $$\epsilon$$

$$\sigma$$ = P/A


$$\epsilon$$ = $$\delta$$ / L

Having trouble with Latex, but the top equation should read:
sigma=E*epsilon

the other two equations are stress=force/area and strain=elongation/lenth.

The Attempt at a Solution

I got an answer, but I'm not sure if it's correct and if I'm solving this correctly.

Since I know $$\sigma$$=25ksi, and E=29,000 ksi I used $$\sigma$$=P/A solving for P, P= $$\sigma$$A=(25ksi)(1.2in^2)=30 kip.

I assumed this to be Pmax.

Using $$\sigma$$=E*epsilon I solved for epsilon. epsilon= $$\sigma$$/E=25ksi/29000ksi = 8.62E-4.

Then used epsilon=delta/L. Solved for elongation, delta. delta=epsilon*L.

Then I just used plugged in my solved value of epsilon, and then the length of each bar.

Here's an example for AC: delta=epsilon*L=(8.62E-4)(4ft)(12in/1ft)=0.0414in.


I'm not sure if this correct since it would mean every bar that is the same length would have the same elongation. Is this correct? Or do I need to solve the system for the forces and then do something? I'm confused. Thank you for the help.

 

[john.phillip]

Axial stress is generated by a force perpendicular to the cross section, what is the direction of P in the diagram ?

 

[pongo38]

Can you determine the force in each member of the truss, as a function of P?