Bending stress from 2 bending moments in different planes 1

[julian89]

Hi!

The problem is the same as this (though with a circular cross section):

Link

How to calculate this?

Do I take the resulting moment vector and calculate bending stress, or calculate both separately and add them together?

Thanks for any help!!

 

[rb1957]

taking the resultant moment (and then calc Mr/I) is the better approach.

if you use moment components and add you run the risk of being (unknowingly) conservative. Mx*r/I +My*r/I is conservative (why?).
the "proper" way is to maximise the function Mx*r*cos(theta)/I +My*r*sin(theta)/I ... using the reulstant M is much easier !

Quando Omni Flunkus Moritati

 

[julian89]

Thanks!!

 

[Tmoose]

By "adding" do you mean C = sqrt (A^2 + B^2) ?

if so, I think the answer would be the same either way (superposition).

 

[julian89]

by taking the resultant vector I mean C = sqrt (A^2 + B^2). Otherwise calculate the stress contribution from each moment individually and add them toghether

 

[rb1957]

i think Tmoose's point is that if you vector sum the two stresses (as opposed to simple addition) then you'll get the same result as if you apply the resultant moment.

this is correct, though i think apply the resultant moment is more intuitive. this is a special case, 'cause the round section has no "special" direction for the major/minor principal axes.

Quando Omni Flunkus Moritati

 

[fegenbush]

While taking the resultant moment would work well enough for circular members, it is not sufficient for members which are non-circular since the determination of the section modulus normal to the resultant moment would be cumbersome. Chapter H of AISC 360 (available in the Steel Construction Manual or as a free download from AISC) is a useful for non-circular sections.

 

[JStephen]

If you're designing to meet any kind of a standard, the standard may designate now that is to be done.