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I have a very basic question regarding the topic of stress.While deriving the equations of equilibrium for a plane element,there is a concept called incremental stress.That is,if stress in the x direction for one face is σx the stress in the opposite face is σx + (δσx/δx)*dx. Where the partial derivative represents the rate of change of stress along the length of element and dx is the length of the element in x direction.

My question is, why is this considered in the first place ?

can anyone please explain this in the case where a bar is under uni axial tension ?

Does stress vary along the length of the bar at different cross sections?.I am having problems in understanding this topic and visualizing this.

I am learning this subject on my own.So I apologise if I have misstated something.

Thanks for going through the post.

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# Stress gradient

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