whats the general way of deriving an equation of the area or force when there is a nonuniform AXIAL deformation?

the cross sectional area is is varying at a distance x and the internal force is also varying at a distance x.
i know i have to integrate but how should i approach it

This post was edited by FamilyGuyViewer on Jan 14 2014 02:19pm

guess noone knows?

post actual problem

dont have an actual problem on hand, but do u knwo what im talkin about?

After rereading like 5 time,rofl

I assume you actually want elongation given you have internal force?

axial elongation = stress* Length / E

E is modulus
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differential elongation = (force(x) / area(x) ) dx /E

you know your force and area functions
,just integrate 0 to Length
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i think you meant to say stress instead of internal force; your force will most likely be a constant

This post was edited by saber_x3 on Jan 17 2014 01:02am

So, the "general way" is nothing more than using the basic equation given to you and model it for a small piece +integrate. Have all parts of the equation in 1 variable

"the cross sectional area is is varying at a distance x and the internal force is also varying at a distance x."

already given, so no work there

This post was edited by saber_x3 on Jan 17 2014 01:06am

internal force =stress no?

axial elongation is PL/EA , where P is the stress, L length, E modulus, A Area


yea i know the general elongation equation but the tougher questions are when the force and area functions are not given and ur suppose to derive it somehow, tahts what im tryna ask for.

like a trapezoidal shape with applied loads at varrying from top or bottom.

this is the hardest chapter, AKA chapter 2 in this course

This post was edited by FamilyGuyViewer on Jan 17 2014 01:31am

u got an example?

a typical problem would usually provide the area/force equations?

This post was edited by FamilyGuyViewer on Jan 17 2014 01:24am

o, that depends on the geometries. simplest i can think is a circular rod tapering. the radius is modeled by a simple line. that part is more mathematics than mom. like in calculus, get one variable into another for simple optimization etc. it should be simple as long as the start and end point is a line. no, i dont have or know any problems.


usually you have external force, constant . you use it to get stress by force/ area equation

This post was edited by saber_x3 on Jan 17 2014 01:43am

how do yu know when the strain/elongation applied in this section is the same as the strain applied in another?

This post was edited by FamilyGuyViewer on Jan 17 2014 01:47am