Aerospace Fitting Section Analysis and Failure Theory 1

[stressebookllc]

Dear Friends, one of my subscribers had an interesting question.

There are 5 failure theories for metals:
1) Maximum Principal Stress
2) Maximum Principal Strain
3) Maximum shear stress
4) Total strain energy
5) Shear Strain Energy or Distortion Energy (Von Mises)

We know Aluminum is classified under ductile materials and Von Mises theory is suitable.

But when we perform a typical static section analysis in aerospace on a fitting for example, we are looking at normal (bending + axial)and shear stresses on a critical section at ultimate loading.
Once we have those, then we simply use one of the interactive margin calculation equations in Bruhn or Niu and we are done.

But Von Mises theory is generally used for designing to yield as failure point, not ultimate.

So the question is which failure theory are we really using if any for the above fitting analysis case?

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Stressing Stresslessly!

 

[rb1957]

where you're calculating P/A and My/I i'd say you're using a "bastard" form of principal stress (cause you're saying shear = 0); really you're using failure mode 0) normal stress ('cause it's simpler and more basic than principal stress).

if you're looking at a 3D FEM, then you'll probably use max principal stress or von Mises ?

another day in paradise, or is paradise one day closer ?

 

[stressebookllc]

Since the general procedure is:
1) Get loads, get the FBD worked out and then pick a section.
2) Work out the combined stresses and write the margin.

The margin will include shear stress. But it is in the form of the interaction equation:
MS = 1/ [1.15 * sqrt(Rt^2+Rs^2)] - 1

Rt = Total calculated tensile normal stress / ultimate tensile
Rs = Total calculated shear stress / ultimate shear

FEM only typically comes into picture for LCF or HCF margins or F&DT type models. But mostly its loads models, no detail stress models are acceptable.

Actually, I need to read up on Section C1.1 in Bruhn first.. let me see what I can dig up.

http://www.stressebook.com

Stressing Stresslessly!

 

[rb1957]

that looks like a fastener calc, with tension and shear loads. your previous example combined bending and axial stresses ... normal stresses. if your hand calc includes normal and shear stresses, then combining them as sum of squares is essentially a principal stress (with zero transverse normal stress).

i feel your pain, brother; not using detail FEMs is IMHO "stupid".

another day in paradise, or is paradise one day closer ?

 

[stressebookllc]

Principal stress state is for zero shear stress though, unless I am missing something.

RB can you please explain what you mean by zero transverse normal stress bud?

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Stressing Stresslessly!

 

[rb1957]

principal stress combines normal and shear stresses together; on principal directions there is no shear.

principal stresses combine all three stress elements together, both normal stresses (-x and -y directions) and shear stress ... Mohr's circle. if you calc a normal stress and "vector sum" with the shear stress (sum of squares) to create a principal stress, you are implying that the 2nd normal stress (-y, or transverse on the element, yes?) is zero.

another day in paradise, or is paradise one day closer ?

 

[stressebookllc]

Correct, I should have said "Max Principal" stress state which acts on the principal planes after rotating by angle 'Phi' and thus shear stress is zero.

I see your point now, there could be some minor stresses due to poisson's effect though and we would be ignoring that in this margin calculation. So it is not really any of the standard failure theories...

Did I get it right?

http://www.stressebook.com

Stressing Stresslessly!

 

[rb1957]

before principal stress, your theory 1), there was max normal stress (< Ftu) what I've called theory 0). The most basic MS calc is Ftu/stress - 1.

another day in paradise, or is paradise one day closer ?

 

[mscarey]

Great information. I'll check this out!