# Stress and strain compound bar question

1. Dec 15, 2013

### anthonyk2013

A compound bar is made using stainless steel tube with an aluminium alloy bar positioned concentrically inside it, and rigidly fixed at each end. The cross sectional area of the tube is 400mm^2 and the cross sectional area of the bar is 300mm^2. The combination is in tension and limiting stress in the aluminium alloy is 60MN/m^2.
Calculate the maximum (1) Stress
σ alumimium =60MN/m^2
E of (s)stainless=180GN/m^2
E of (a)aluminium=120GN/m^2

Area of the tube is 400mm^2
Area of aluminium bar is 300mm^2
Area of stainless tube is 300-400=100mm^2

σa/Ea=σs/Es→σa=σs*Ea/Es

σa=σs*120/180→σa=σs*.666

60=σs*.666→σs=60/.666=90

F=Fs+Fa
F=σs*As+σa*Aa
F=60*100+90*300
F=6000+27000
F=33000 or 33KN

Past paper question Is the answers right or wrong?

Last edited: Dec 15, 2013
2. Dec 15, 2013

### haruspex

, then calculate

3. Dec 15, 2013

### anthonyk2013

so its wrong.

4. Dec 15, 2013

### anthonyk2013

I have amended the original solution

5. Dec 15, 2013

### haruspex

You still haven't defined your symbols, so I have to guess what they mean.
It looks like σs should mean, by analogy with σa, the limiting stress of the steel. Why should that satisfy the equation σa/Ea=σs/Es? What is the reasoning behind that equation?

The steel tube is extended by some amount, resulting in a certain tension.
The aluminium core is extended by some amount, resulting in a certain tension.
What value is common to those two equations?

6. Dec 16, 2013

### anthonyk2013

I dont understand what you mean by defining symbols, σs=stress of steel, σa=stress of aluminium. Is this what you mean.

As for the equation it comes from total force=force of steel+force of aluminium. F=Fs+Fa

Not sure if this is what you want.

7. Dec 16, 2013

### haruspex

Sorry, I wasn't thinking straight. Yes, I agree with your revised solution until here:
To recap:
σa = 60MN/m2
σs = 90MN/m2
Aa = 300mm2
As = 100mm2

8. Dec 16, 2013

### anthonyk2013

Ya trying to remember what I was thinking last night, yes your right I need to revise that total force equation did it wrong. Cheers

Last edited: Dec 16, 2013
9. Dec 16, 2013

### anthonyk2013

F=σs*Asa*Aa

F=90*100+60*300

F=9000+18000

F=27000 or 27KN/m2

10. Dec 16, 2013

### haruspex

Looks good, except that I don't understand where the /m2 comes from. This is a force.