Understanding a stress equation

[EGill]

I really need help understanding how the book created the equation from the book. I would really appreciate help understanding it. The attachment shows an image and the equation.

 

[Mapes]

They've divided by dz and canceled out some terms; that might be why it's a little confusing. The force (pressure times area) on the top surface is

$$\left[\sigma_y+\left(\frac{\partial \sigma_y}{\partial y}\right)dy\right]dx\,dz$$

and the distance (lever arm length) is $dx/2$. But the force on the bottom surface is

$$\sigma_y\,dx\,dz$$

which creates a moment in the opposite direction that cancels out part of the moment from the force on the top surface. Starting to make sense now?

 

[EGill]

Wow, thanks so much. The cancelling of dz was part of what was confusing me. Also, I was just looking at the diagram incorrectly for no particular reason, but since I saw it wrong initially I could not get it out of my head.

Also, how do you type formulas into this forum?

 

[Mapes]

Just click on the formula to see the markup language.

 

[redune]

I really need help understanding how the book created the equation from the book. I would really appreciate help understanding it. The attachment shows an image and the equation.

tanks