Combined Loading Vs. Principle Stress Analysis 1

[ForeverConfused]

Hello All,
I'm working on a beam bending analysis and I have simultaneous bending and shear throughout the cross-section. I've determined the separate margins of Safety for Tension (in the upper flange), crippling/buckling (in the lower flange), and shear at the center. I've also determined the Margin of safety for the combined shear and normal stresses using the interaction curve (Rn^2+Rs^2=1). Lastly, I've also computed the principle normal and shear stresses. I've compared the maximum principle normal stress to the tensile allowable for the material for the Margin of Safety, however, what do I compare the minimum principle normal stress to? (for the margin of safety). I assume it would be the crippling stress? Or am I overdoing it by using combined load theory (i.e. Rn^2+Rs^2=1)AND Principle stresses since they are both "simultaneous stress" theories?
Thanks

 

[rb1957]

1) its principal
2) why combine normal stress from bending (at the extreme fiber) with shear stress (near the NA) ?
3) compare compression bending stress with crippling allowable. compare shear stress to Fsu.

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

 

[ForeverConfused]

Thanks for the quick response!

1. what do you mean by "its principle"? Should I not be using the interaction curves (They are defined in most literature as accurate)?
2. The section is an I-beam. I'm evaluating my Margins at the lower edge of the upper flange where the normal stress is ALMOST maximum and there is also SOME shear.
3. Glad to hear that! I assumed it was crippling but needed clarity

3a. Am I correct in saying that the compression side of a beam in bending should never directly be compared to Fcy for a margin of safety(since yielding of the ENTIRE section would only occur after the tensile fibers would fail. Therefore Ftu is limiting)? The only compression failures to consider are local buckling/crippling?​

 

[SWComposites]

1. Spelling.

 

[ForeverConfused]

Ahhh. gotcha!

 

[rb1957]

2 an I section has a small shear at the extreme fiber, so you can combine stresses, but it's not IMO common practice 'cause it leads to the next question "do I combine compression bending and shear ?". I don't think I've ever seen that done (unless as a super-conservatism with a +ve MS).

3a … no, I don't think you are. A stable section (with a high crippling stress) could use Fcy. Of course you could say that doing a crippling check and using the cut-offs would say crippling stress = fcy so you'd still be using the crippling stress.

3a ii … no there are other compression failures to consider. You need to establish if your problem is short column or long column, and take it from there.

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

 

[ForeverConfused]

Thanks rb1957
Following up...

2. I understand the conservatism of combining these loads at the extreme fibers and I've removed it from the report as per your suggestion. All that being said, when there is a member subjected to bending and torsion, I'm still not sure on whether to use the principal stresses to derive M.S. (resulting in an M.S. for shear, tension, and compression) or use the interaction curve to derive M.S. (resulting in a single M.S.)? two sides of the same coin? Or calculate both and take lowest?

3a. When determining the breaking strength (ultimate strength) M.S. of beams (assume rectangular for simplicity), I've typically always used the maximum tensile stress (at the upper extreme fiber) and compared it to the Ftu of the material and not considered the maximum compressive stress (at the lower extreme fiber) and compared it to the Fcy which would typically always have a lower M.S. (with a symmetric section and Fcy<Ftu). I have never received any criticism on not considering this compressive side (unless there is a crippling or local buckling failure consideration in which case the maximum compressive stress is compared to Fcr)?
Is this because I'm evaluating for fracture (which allows plastic deformation)and not yield? i.e. If my M.S. were for yield strength (or against a working load and not an ultimate load) and not breaking strength then I would consider Fcy?

3a ii. Understood thanks

Appreciate the help!

 

[rb1957]

2 if I was combining Bending and Torsion, I might use an interaction approach. For each load (in isolation) determine the allowable load and then the faction of applied/allowable (Rb and Rt). Then combine these as either …
RF*Rb + RF*Rt = 1 … simply RF (= MS +1) = 1/(Rb+Rt) or
(RF*Rb) + (RF*Rt)^2 = 1 … not so simple … RF = (sqrt(Rb^2+4Rt^2)-Rb)/(2Rt^2) or
(RF*Rb)^2 +(RF*Rt)^2 = 1 … simply RF = 1/sqrt(Rb^2+Rt^2)

3a yes, plastic bending of prismatic (stable) shapes. Yes, the typical assumption is to assume the compression stress/strain curve is equal to the tension stress/strain curve. This is probably conservative considering that tensile strains (and tensile yielding) will have more impact on the plastic hinge than compression yielding. I haven't heard about compression yielding and compression ductile strains as we hear about them in regards to tension loading.


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

 

[ForeverConfused]

Great! Thanks rb1957
I've gone through the equations for the interaction curve Margins and the principal stress Margins and it seems that the Interaction curve Approach are slightly more conservative than the Principal Stress approach (if my arithmetic is correct?) however they do align fairly well! So I think I will proceed with the Interaction approach as suggested.
Thanks again for the assistance.