Matrix analysis of framed structures

[Xclusiveee]

I have a question related to the stiffness method of structural analysis.
As we use EI for the purpose of analysis in the stiffness method, will change of material change the results of member end forces and support reactions ?
My current understanding was that it wont effect the member forces and support reactions no matter whatever material was being used but GT Strudl gave me varying answers for different material properties having same structural configuration and same loading.

Can anyone please answer this question and if the member end forces and reaction do change, is there an explanation for it?


Thank You

Regards

 

[logicway]

Almost all softwares use different values of EI for different materials. e.g. u can find defining material in stadd pro, etabs, sap2000, etc. if you define the material as concrete, steel, timber etc you will find different values of EI as default values. And also we can modify the values manually.

Regarding your above question, it is the matter of stresses and overstressing. Let suppose you introduce steel as material in a structure, the use concrete for same structure same loading, then timber for same loading same structure. You can visualize that at peak stresses points, a member may (or may not) fail aur go plastic as a certain stress level. suppose concrete member overstressed and redistributes the stresses, and steel member remains elastic, without redistributing the force. In both cases, the end member forces and support reactions will be different.

 

[logicway]

another point is, that for each material, moment transfer is different. for steel, we can assume a fixed joint for a complete transfer of moment. but still we dont introduce fixed joints. in rcc we assume rigid connections transferring full moment at joints. due to complete or partiall transfer of moments, the end reactions and support reactions will be different. I didnt use GT Studdal software but I expect that there might be default settings of partial or complete moment transfers, or moment release at certain points which are changing the end results.

 

[TERIO]

Some questions for you to think about:

- Is your problem statically determinate?
- Are the loads forces/moments, displacements (e.g., settlements) or both?
- Did you change the stiffness of all members or just a portion of them?

 

[Xclusiveee]

I get all your points.
But the confusion which surrounds me is if my structure is determinate for example a simply supported beam or frame. I would go ahead and use the equilibrium equations to get my member forces and support reactions. Now these answers would be independent of the material used for the beam or the frame. No mater if the beam is concrete, steel or timber, reactions and member forces stay the same.

So my question is, why isn't this concept valid if the structures becomes indeterminate and we have to use methods like stiffness analysis? Shouldn't the forces and reactions be same?
Stiffness methods uses the equation P=KD. So doesn't it mean lesser stiffness more deflection and more stiffness lesser deflection, which in turn keeps the forces same ?

I am not sure if i was able to clarify my question. Would be glad if you guyz could help me understand this.

 

[TERIO]

The sum of all reactions still have to be the same to satisfy equilibrium, but the the loads on each member and the individual support reactions will vary based on stiffness of the members.

Start with something simple like two springs in parallel. Vary the stiffness of one of the springs and see how it changes how the force is distributed between the two springs.

 

[IDS]

In an indeterminate structure the distribution of forces is affected by their relative stiffness. In a linear analysis the results won't change if the relative stiffness values are kept the same (K is factored by a constant), but if the relative stiffness values are changed K will change and you will get different results.

If you think of changing the stiffness of the central support of a 2 span beam it should be obvious that this will change the reactions at the supports, and also bending moments and shear forces.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[logicway]

your question is very much clear and i will try to explain my opinion.

There is a difference in determinate and indeterminate structures, i.e. the statically determinate structure will only resist in couple action, but indeterminate structure has a number of alternate ways to resist the applied moments, in addition to couple action.

Let me explain me this first, and then I hope you will get the point exactly. I recommend you to read this post twice.

For statically indeterminate structures, a simple rule governs, "The stiffer portion will attract more load" .. i.e. If at a certain region, the stiffness is increased, then that stiffer part will ultimately tend to become the support for the less stiffer part, and it will absorb more Moment and will resist greater Load in axial and shear. This simple rules implies that as much you change the stiffness in the indeterminate structure, every time you will observe change in support reactions and analysis. you can try this in a model, make two or three similar models with similar loadings, only change the depth of beams and size of columns, soas to change the stiffness. You will find different results in allcases.

For a determinate structure, there is no need of stiffness. simple equilibrium equations are enough. Determinate structure nevertheless usually consists of two supports only, so from moment equation and parallel axis equation, we can find the forces. Stiffness is never involved in such analysis. Thats why it will always end in a similar result, no matter the material is wood, concrete, steel, because the member is pinned at supports. For pinned support, NO MOMENT TRANSFER, so support reaction will resist the applied moments only in couple action. (For a determinate cantilever structure you can visualize the only ONE support definitely will not require stiffness for analysis)

This is not the case with indeterminate structures. In indeterminate structures, almost all members are fixed or partially fixed with their supports, so that they can respond to the applied forces in a number of ways. The basic point which governs is the stiffness. So every time you change the stiffness of any location, you will find a different solution. Stiffness is changed when you change the sections, when you change the material, etc.

I hope you got the point this time. If you need further elaboration, I will.