# Finding elongation of bar and maximum tensile stress

• Blugga
In summary, the maximum tensile stress in the bar is 3P/A, and it cannot exceed 5000 psi. The maximum tension occurs at AB, and the other sections will be less prone to failure.
Blugga

L=52 in
A=2.76 in^2
E=10.4*10^6 psi

σ=F/A
ε=σ/E
δ=εL

## The Attempt at a Solution

4) σAB = (3P)/A
ε=(3P)/(AE)
δAB=(3PL)/(6AE) → δAB=(PL)/(2AE)
solving for P
P=[0.17*2*2.76*(10.4*106)]/52 → P=187680 lb → P=187.7 kip

5) Because AB and CD are in tension i did this...
σmaxABCD
σmax=[(-2P)/A]+[P/A]
solving for P and using 5000psi for σmax i get
P=-5000*2.76 → P=13800 lb → P=13.8kip

I tried looking for an example in the book to follow, but they were completely different. I hope i didn't mess up too bad.

Last edited:

afreiden said:

So i should only do one of them? σmaxAB
or do the entire bar?
Can I get a better hint than that?

I confirmed that I did part 4 right. I still need help with part 5. Anyone?

I made a mistake on part 5. I plugged in the value of σBC (-2P/A) in place for σAB (3P/A) in σmaxABCD

Now i get σmax=3450 lb or 3.45 kip. But still don't know if it's right.

Part 5:

You correctly determined the stresses in the 3 sections of the bar.

AB = 3P/A
BC = -2P/A
CD = P/A

So, you already know that the maximum tensile stress in the bar is 3P/A. This cannot exceed 5000 psi = 5 ksi

chet

So what I'm getting from this is that the maximum tension occurs at AB so I only set σmax=σAB and don't add them with the other member in tension.

Thanks :)

Blugga said:
So what I'm getting from this is that the maximum tension occurs at AB so I only set σmax=σAB and don't add them with the other member in tension.

Thanks :)

Yes. That's right. The other sections will be less prone to failure.

## 1. What is elongation of a bar?

Elongation of a bar refers to the increase in length of a bar under tensile stress. It is a measure of how much a bar deforms or stretches when subjected to a pulling force.

## 2. How do you calculate the elongation of a bar?

The elongation of a bar can be calculated using the formula: elongation (δ) = (F * L) / (A * E), where F is the applied force, L is the original length of the bar, A is the cross-sectional area of the bar, and E is the modulus of elasticity of the material.

## 3. What is the maximum tensile stress?

The maximum tensile stress, also known as ultimate tensile stress, is the maximum amount of stress that a material can withstand before breaking or fracturing. It is a measure of the strength of a material under tension.

## 4. How is the maximum tensile stress calculated?

The maximum tensile stress can be calculated by dividing the maximum load that can be applied to the bar before it breaks by the original cross-sectional area of the bar. It is expressed in units of force per unit area, such as pounds per square inch (psi) or megapascals (MPa).

## 5. What factors affect the elongation and maximum tensile stress of a bar?

The elongation and maximum tensile stress of a bar are influenced by various factors such as the material properties (e.g. modulus of elasticity, yield strength), the dimensions of the bar (e.g. length, cross-sectional area), and the applied load (e.g. magnitude, direction). Other factors like temperature, strain rate, and the presence of defects or imperfections can also affect these values.

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