The portal frame of post calculating length coefficient to questioned

You may have encountered such a situation, but think that do not understand the knowledge, so he let it go on precipitation, the longer the time, has become the more esoteric, slowly, it will idol.

In fact, I want to say is that some boring formula, in the design of steel portal frame, some calculation of the pillar stress is very low, but the slenderness ratio is greatly exceed the standard.For example, the following example.

This is a great cross (36m), side span is very small (6m) of the steel structure of light-weight portal frame, is not given in the section of members, also did not give a load, you can click the conventional numerical assumed, no matter what software do you use to calculate, on checking in accordance with the "door frame of technical specification for steel structure of light-weight CECS102:2002" (hereinafter uniformly referred to as "rules").

You can see from the results of internal force of the side column axial pressure is very small, and the calculation of members are from in side column slenderness ratio is very large.This a bit odd, and its cross section is very unbecoming, when we embrace the disturbed mood tracing the cause, you will find that this post calculating length coefficient of abnormal.The way for me, have been found "rules" on the column in frame calculation length calculation formula, that is, of which is calculated length coefficient, the calculation length coefficient, "rules" are given in three ways, respectively for the look-up table method, first order optimization method and two order analysis method.

Look up table method can cover the range was very limited, for example only for single span portal frame; only applies to the slope of the roof is not more than 1:5; multi-span frames considering only the intermediate column for swinging column and so on, let a person with no confidence.

And for the two order analysis, I'm afraid there is also much in some papers to roam.

So we can only hope to see the one order analysis formula is given, for "rules" in the formula and the formula of 6.1.3-7a 6.1.3-7b applies the scope is also limited, so a spotlight on the last dancer

(formula 6.1.3-8a)

(formula 6.1.3-8b)

For column hinged and rigid connection in two cases.Which is the Euler critical force, K columns under horizontal load lateral stiffness, the column vertical load and high ratio of column sum, this is worth thorough research, for the column vertical load, to question is when the column vertical load is small, the extreme situation in 0, according to the formula of calculating length coefficient of nature is infinite.

Then the formula of "vertical" in particular design should take what value?The [1] said "STS that will 'rules' for the I column subjected to vertical load into the I column in various working conditions of the greatest axial pressure", but the problem is you ask of a column in a certain working conditions stability stress, and the stability of stress the use of slenderness ratio should go to another condition combination calculation length.This is appropriate?But, even if we recognize this practice, still can find the maximum axial pressure close to the 0 column, we mentioned example is so.

So, it is necessary to trace the origin of the formula, "Regulations" provisions indicated in the description, the formula is in reference to American Standard AISC "steel structure housing the load and resistance factor design specification", consult the LRFD (1999) the relevant chapters, we make the following comb.

Involving the compression member is the most important is the stability problem, and in addition to load with constant in relation to the outside is "slenderness ratio" this parameter, calculate the slenderness ratio is to use "length" can be said to be the most mysterious of the basic parameters, and its associated reference is were for real hinge, the geometrical length is the length, in other cases the calculation length, through the geometric length by the last coefficient, the coefficient is called "calculation length coefficient", is mentioned above.The lateral displacement of frame column, taking into account the column on the lower end of the beam stiffness constraint, the actual calculation length should be less than the geometrical length, therefore, is less than 1 the number, and the lateral displacement of the frame column, value is greater than 1, are given in the reference [3] formula was deduced, and the "regulation for" in the formula is considered P-D effect method.The so-called P-D effect is belonged to the two order effect, is also the capital in order to analyze load under a horizontal displacement of D, whereas the role at the top of the column vertical force still exists, then there must be an additional P.D moment, the formula of lateral stiffness of P-D two order effect, and let us feel the formula in the denominator, the LRFD (1999) have the same representation.

(C-C2-5)

While the LRFD involved is described as follows: "the same floor additional moment and reassigned, bearing small column will bear the load of large column part".While the [3] of the formula is derived, which is the embodiment of a experience amplification coefficient.From here it is still very difficult to find some traces, but actually the arch-criminal is the derivation of this a series of formula one assumed, that is: "structural instability mode based on the same layer column at the same time according to the same pattern of symmetric or antisymmetric instability".You want to, in the same layer column, a column almost no axial pressure, if you want to make it with the other columns and buckling, not just let it calculated length of infinite growth.However, our other experts in office but the column slenderness as uniform very strict stipulation.

So the crux of the problem is the existing design methods for steel structure defect, norms is the structure of the components as the object of study, they are classified as a member in bending, axial compression, bending and so on, respectively, and define their under load condition, and for the structure as a whole bearing condition, also can only be embarrassed through the elastic analysis, the internal force in all member of each member's results, and overall structural instability mode, only through the same layer at the same time instability assumption, grudgingly reflected in the component calculation length coefficient, although we in the specific design activities, leisurely and used these huge simplified formula, but careful thought them behind the assumption conditions, and the derivation of these formulas for loading assumption, I almost forgot all the vertical load were assumed to act Yu Zhu top, they also seem to be irrelevant, so think about it or some horrendous.

So where is the outlet?A wise man said: "structure of higher analysis", wait and see them.