Buddy, I replied to your metal fraction already. Twice. Even though it is obviously a meaningless question. Had a question back to you, that would lead you to understand why your question is meaningless.
Can you justify less than 98.5-99% steel?
http://911research.wtc7.net/mirrors/CSEC/Salvarinas_1986.pdf
So what, exactly, did the firefighters see Oystein?
Cool. What were your assumptions when you filled that Langrangian with number? What was your solution? Show some work!
First, what is screaming at you in this Lagrange method energy equation?
Second, let me tell you some problems involved when trying to handle indeterminate systems, which is one reason why I've been harping the same questions (1659, how are we coming on these?). The stability issue needs to be worked out, and is far easier than hanlding the collapse. But assuming that the initiation happened (and NIST does not establish this well), we have to use the most appropriate method.
Coordinate functions involving hand calculations with geometrically complex, discontinuous loads, discontinuous material or geometric properties can turn into a lifetime chore. Even in cases where the coordinate functions are available, the computation of associated coefficient matrices can't be automated for a fixed class of problems (W shape columns, bars, plates) because coordinate functions are not always algebraic polynomials and they depend on the boundary condition of the specific problem. Each time the essential boundary condition or conditions are changed for the same differential equation, the approximation functions are changed and the coefficient matrices have to be recalculated. Even state space numerical integration and similar methods are not readily adaptable to ever changing coordinate functions.
FEA (Finite element analysis) uses the philosophy of traditional variation methods to derive the equations relating undetermined coefficients. FEA is an energy method. FEA differs in two ways from the traditional variation methods in generating the equations of the problem. First, the approximation functions are often algebraic polynomials that are developed using ideas from the interpolation theory. Second, the approximation functions are developed for sub domains into which a given domain is divided. The sub domains, called finite elements, are geometrically simple shapes that permit a systematic construction of the approximation functions over the element. The division of the whole domain into finite elements not only simplifies the task of generating the approximation functions, but allows representation of the solution over individual elements. Therefore, geometric and/or material discontinuities can be naturally included and since the approximation functions are algebraic polynomials, the computation of the coefficient matrices of the approximation can be automated by the software. The construction of the approximation solutions with FEA is systematic, and the process is independent of the boundary conditions of the data of the problem. In short, FEA is a piecewise application of classical variation methods. The undetermined parameters often, but not always, represent the values of the dependent variables at a finite number of preselected points, whose number and location dictate the degree and form of the approximation functions used. FEA is modular and therefore suited for our use as applied to problems such as this. This is the appropriate choice for the initiation and collapse. I agree with NIST 100% for selecting this energy method. It’s their roughshod application and refusal to show the details of what went into the model that I have issues with.
No matter which energy theory you draw from, there are going to be characteristic polynomials that involve transient (time-dependent) functions and damping. This "damping" term is very explicit in Lagrangian mechanics, as well as Hamiltonian mechanics and even in classical plate theory. The friction involved in the buckling of the 81 (built up and non built up) heavily defies NIST's "stage 2". Simply, it is impossible without manipulation or at least more information. Tranparancy?
With that stated, the Lagrange energy method equation I am presenting you points out some obvious things without the need for exhaustive FEA, what are they?
No. Not from me. I am not an engineer. I just wonder why you use that buzz-word Lagrangian all the time, without putting numbers to it?
There is no such thing as a "Lagrangian energy theory", and certainly none that makes any sense without putting numbers to it, this much I know.
http://www.efunda.com/formulae/solid_mechanics/columns/calc_column_structural_steel.cfm
Yes, definitely from you. You don't have to be an engineer. Don't be lazy. You want to figure this out or not? There is such a thing as Lagrange mechanics or Lagrange energy method, which is simply one of many energy methods. The friction is more explicitly defined than it is in classical plate theory, which makes it more suitable for discussion when your dealing with a system that is one minute very stable and somehow became very unstable. The stable to unstable condition of WTC 7 on 9-11-2001 has not been well established by NIST, and their refusal to release the critical data of how they arrived at answers is begging for deeper study and 3rd party investigations.
For right now, let's establish the structural stability in terms of the column load carrying capacities (critical and allowable) vs gravity loads, let's see if we can get a fire-breathing "twoofie-crushing" JREFer to work through the column analysis. TFK told me there were plenty here "more than able" to answer my questions. Is this really true?
TFK also made this statement in response to my prodding for him to do a quick column buckling analysis check:
"I'll leave the "brainlessly plug into on-line calculators" to you. One thing that you might do first is to produce a sketch of the constraint & loading conditions at the moment of buckling of any particular column that you (not me) might be interested in. C'mon, kid. You can do this. Come to think of it, you probably can not do this. Either way, it's a virtual certainty that you won't do it, of course. That takes effort..."
This is not a statement any engineer would make. There are strict guidelines when performing column analysis and software is common for such analysis. The equations are ultimately derived from Euler's buckling theory, but with many refinements since his time. Column buckling equations, graphs and so forth are ubiquitous to solid mechanics and structural design textbooks at the present. Telling me to sketch "constraint & loading conditions at the moment of buckling of any particular column that you..." is like telling me to breathe. I’ve worked out some of the Stability Council’s numerical equations and methods in C++ as an exercise. Pencil and paper is fine the extent of understanding algorithms, but TFK’s comment is revealing. There is only "brainless" activity if the origin of the solving mechanism, equations, graphs etc is not understood with respect to the Stability Research Council.
The question TFK, (if he really is an engineer) should have asked is, what is the basis of the algorithm of the calculator, software or program? Are they derived in accordance with the Stability Research Council?
TFK appears to be posing as an engineer. If he really is, he has hitherto made a litany of statements that defies engineering practice, thought, knowledge, culture, methodology, testing and analysis.
