Stress Propotionality
Stress Propotionality
(OP)
I checking some FEM output and came across an elementary question since being out of school for such a while. In a linear elastic model, is there any time when stress is NOT proportional to external loading due to geometry, loading distribution, etc?
The person running the program needed to change all of the external loads by the same factor, and he wanted to open it up, change them, and re-run them all over again. I told him just to multiply the critical internal forces, stresses and displacements (from the original run) by the same factor so as not to waste time. He didn't agree and thus I am here. I tried to explain that it would be no different than noticing (WL^2)/8 is proportional to normal stresses in simple beam theory.
The person running the program needed to change all of the external loads by the same factor, and he wanted to open it up, change them, and re-run them all over again. I told him just to multiply the critical internal forces, stresses and displacements (from the original run) by the same factor so as not to waste time. He didn't agree and thus I am here. I tried to explain that it would be no different than noticing (WL^2)/8 is proportional to normal stresses in simple beam theory.
"Structural engineering is the art of modelling materials we do not wholly understand into shapes we cannot..."...ah...screw it, we don't know what the heck we are doing.





RE: Stress Propotionality
If your solver computed purely bending moments, ie My/I, I think you can get away with it. Just be careful I guess.
The linear elastic model is reserved for behaviors that are modeled by linear differential equations. Such models have deflections and slopes proportional to applied loads. In such cases you can apply the Method of Superposition, but doesn't necessarily you can apply to stresses.
RE: Stress Propotionality
"Structural engineering is the art of modelling materials we do not wholly understand into shapes we cannot..."...ah...screw it, we don't know what the heck we are doing.
RE: Stress Propotionality
RE: Stress Propotionality
Would you like to explain better why those square roots and other operators/functions do not change the proportionality between external loading and maximum stresses?
"Structural engineering is the art of modelling materials we do not wholly understand into shapes we cannot..."...ah...screw it, we don't know what the heck we are doing.
RE: Stress Propotionality
Given a body of linearly elastic, isotropic material, and a set of loads which can be characterized as proportional to some load factor, P.
A fundamental for linear elasticity (*) is that the components of the stress tensor vary linearly with the load vector, i.e. the principal stresses at any point in the body will vary linearly with P, i.e.
s1 = k1P
s2 = k2P
s3 = k3P
Von Mises' equation is
svm = sqrt[(k1P - k2P)^2 + (k2P-k3P)^2 + (k3P - k1P)2]
note we can factor out the P, giving
svm = P sqrt[(diff's of the k terms)]
Therefore von Mises stress magnitude is proportional to the load.
(*) I think it is, but couldn't find a reference. Others have made this statement above...if not a fundamental, then let's just make it an assumption for the discussion above, the math still holds.
RE: Stress Propotionality
"Structural engineering is the art of modelling materials we do not wholly understand into shapes we cannot..."...ah...screw it, we don't know what the heck we are doing.
RE: Stress Propotionality
assuming not, then the model is linear (which you can now verify looking at the rerun analysis). assuming not, i'd've done as your 1st thought, and factored the initial run.
RE: Stress Propotionality
"Structural engineering is the art of modelling materials we do not wholly understand into shapes we cannot..."...ah...screw it, we don't know what the heck we are doing.
RE: Stress Propotionality
RE: Stress Propotionality
"Structural engineering is the art of modelling materials we do not wholly understand into shapes we cannot..."...ah...screw it, we don't know what the heck we are doing.
RE: Stress Propotionality
Corus is correct if it is a true linear static analysis the ouput it proportional to input that is the whole premise of linear analysis.
there is such a thing as non linear elastic which includes geometric effects (gaps, stress stiffening, PD effects etc) but not linear material properties.
RE: Stress Propotionality
RE: Stress Propotionality
RE: Stress Propotionality
rb, I will check it out some more to see where the difference originated. I agree zero is incorrect solely based on the square roots, etc. argument. However, my problem is that he attacked zero instead of kindly adjusting his mistake. The tone of this forum should covey respect, correct? I will leave it at that. Thanks for your help, gents.
"Structural engineering is the art of modelling materials we do not wholly understand into shapes we cannot..."...ah...screw it, we don't know what the heck we are doing.
RE: Stress Propotionality
RE: Stress Propotionality
I repectfully disagree, the attack was prefaced with "no offence intended", and conveyed the tone that Zero should check his math, because he made a bonehead error. We all do it sometimes, no offense is intended.