The strain of a dog-bone specimen

[10hi-f9s]

Homework Statement

A dog-bone specimen made by aluminum alloy is used for tensile testing by a force of 4000N via two steel pins. The dimension of the specimen is shown in the following picture; the thickness of specimen and the length of pins are 4mm and 8mm, respectively. The mechanical properties of aluminum alloy and steel are: EAl = 70GPa, νAl = 0.3, ESteel = 200GPa, νSteel = 0.3. The measured values via the testing are “average” strain of reduced section and maximum Von-Mises stress of the aluminum specimen.
1. Calculate the strain of the aluminum specimen by the theoretical solution.

I have attached a picture of the specimen

Homework Equations

The Attempt at a Solution

I am unsure of how to calculate the strain with such an advanced geometry. I would solve this as a bar in tension with the dimensions 100x20x4mm with a force of 4000N in each end. This way the applied stress can be calculated:
$$\sigma=\frac{F}{A}$$
With F being the force applied and A the section area.
From this the strain can be found by:
$$\sigma=E\varepsilon$$

I am sure there must be another more correct way, but this is only thing I've come up with so far..

I hope you guys can help

 

[Chestermiller]

It looks like your approach is perfect. The rest of the dogbone geometry is designed to guarantee that the 100 mm section in the middle can be treated the way that you are treating it.

Chet

 

[10hi-f9s]

Hi Cheat
Thank you so much for your answer. It really helped me!