Multi-axial bending and Superposition

[evilspeeder]

I have beam (no this is not a homework problem!) that's loaded in two axis, both x-x and y-y. Is it valid in any way to calculate each stress and deflection of each separately and then combine them to get the overall case? If this approach isn't valid, what should I look at next?

Thanks!

John

 

[corus]

Yes, superposition is the way to calculate the overall stresses when stresses are within yield.

corus

 

[kelowna]

... and if ignoring second order effects.

 

[rb1957]

it's probably more accurate to resolve the applied moment (the two components make one vector) into the principal axes of the section and superimpose from there.

 

[evilspeeder]

If I resolve the applied moment into one vector, how do I calculate the moment of inertia?

Thanks,

John

 

[rb1957]

principal axes ... Ixx, Iyy, Ixy ...
the principal axes will be at some angle to the resultant moment vector ...
components into the principal axes directions ...
superimpose the stresses at key points on the section from both moment components.
it's a bunch of work (but then that's what we're paid for, right ?)

 

[Lion06]

There's no point in calc'ing a single moment and changing up I's. Just use superposition for stresses (adding algebraically), and combine the deflections vectorially.
If you have no P, then you have no second order effects (read P-delta) effects - no P means no P-delta.

 

[JAE]

I agree with StructuralEIT - perform calculations about each principle axis separately and then you can combine them to get a resultant deflection (square root of the sum of squares). For bending, it depends on the method you use (ASD or LRFD perhaps). Working with stresses you can add the two together to check against a limit state.

Working with factored loads (LRFD) you'd find Mx and My and then check them with an interaction equation such as what AISC provides in their spec.