The problems of calculating the load-bearing structures made of light steel thin-walled profiles

The article presents the results of a study of bearing capacity of thin-walled cold-formed steel beam of the guide profile. Such profiles have a small thickness and complex cross-sectional shape. Bending deformation develops in the cross-sectional plane under the influence of loads in beam. In addition, deformation of constrained torsion and warping arise. These deformations influence the stress distribution at the points of the crosssection of the beam and thereby determine its load-bearing capacity.


Introduction
Today in Russia buildings with load-bearing frame of thin-walled cold-formed sections are widely used [1].They have a number of technological and operational advantages (lightness, high speed of erection, etc.) [2].
As practice shows, often due to errors in the design of buildings of light steel thinwalled structures (LSTS), frequent cases of emergency [3].Sustaining the work of such structures is a major problem to the widespread introduction of LSTS in massive construction.Obviously, the thin-walled structures at the design stage requires a thorough analysis of their bearing capacity.Not paying attention to the growing popularity of such structures and a large amount of research on all LSTS stage of development, today in Russia there are significant deficiencies in the prescriptive, methodological and computational databases of design of LSTS which does not make it easy and clear to make their calculation.
Theory of calculation based on the hypothesis of plane sections, are not applicable to the thin-walled bars, due to their small thickness and mismatch the centers of gravity and bending.To solve engineering problems of calculation of elements of thin-walled structures can distinguish two groups of ways to calculate: based on the modeling of shells and rods.The first group of methods is associated with the representation of a thin-walled rod in the form of a shell and further numerical calculation, as a rule, using the finite element method, in the program complexes SCAD, Lira, SOFiSTiK etc.Such methods of calculation are accurate enough, but very time-consuming in the engineering design activities especially in terms of the complex structure analysis.In the second group of methods can be distinguished analytical and numerical methods for calculation of thin rods associated with the introduction of additional "seventh" degree of freedom and the corresponding power factor -bimoment [2,4,5].

Statement of the research problem
Let us analyze the degree of influence of component of warping on the stress-strain state of the thin-walled bar.
We will lead the calculation for cantilever balcony beam with cross section GP 254-1.5 [22] like for beam having strain of warping.[22].

Fig. 2. Cross section
Geometric characteristics in calculation are taken the lower of two: by assortment [22] and by calculation in the program TONUS (PC SCAD Office) -table 1. Flexural-torsional characteristics (it is a physical constant of cross section and mathematically representing a characteristic number of differential equation of equilibrium 4th order) [23] amount to: Upon application of a uniformly distributed load and bringing it up to the maximum (destructive) value due to a sufficiently high ductility of the top shelf, which will be significantly deformed, the profile loses its original geometric shape.Load, in most cases being a "stamping" that is more rigid than the section by its nature, will not have tightly fit to the shelf.To indirect accounting for this geometric nonlinearity we will apply the load is not uniform along the shelf, but on the law of the triangle, which is a fairly common method.Then, the resultant load vector will pass through the center of gravity of the load diagram, lying in the intersection of the medians of the triangle, that is, at a distance (b/3) from the wall edge [4].
As can be seen from Fig. 3 full eccentricity of load application will consist of the eccentricity, due to the mismatch between the center of gravity and the center of the  Diagram of sectoral coordinates of section is shown in Fig. 4. The maximum sectoral coordinates are necessary for detecting the stress from bimoment; they comprise: where x and y -the distance from the main axis to the point of the section under consideration; while the action in the wall of the beam moment and shear forces.
The bending moment in the reference section: M = P 1 t 1 P 2 t 2 P 3 t 3 (6) M = 1.48 + 600 0.93 + 342.2 0.43) = = 480.3+ 558.0 + 147.4 = 118540 kg cm 2 (7) where t -the distance from the end of beam to the point of load application, P -applied load Assuming that the bending occurs only in one plane, taking M y = 0 The formula for the bimoment in the case of a cantilever beam, according to the technical literature [2]: B 1 = 162077.9kg cm 2 The maximum normal stress σ 1 , σ 2 , σ 3 , σ 4 occurring in the most tense cross-section, located in the middle of the span, will be different in the four characteristic points (1, 2, 3 and 4, respectively) of the cross-section will be:

The calculation using the finite element method (analysis of stress-strain state)
According to p. 8.2.1.SR 16.13330-2011 [24], values of stress in the wall of the beam must be checked according to the following formula in the two principal planes of bending:  For this, we use the finite element method in a static statement and solve the problem in the software package SCAD Office.For this, we use the finite element method in a static statement and solve the problem in the software package SCAD Office.!cm kg (23)

Fig. 3 .
Fig. 3. Scheme of axes and load application, points numbering of σ y .

4 )
According to p. 8.2.1.SR 16.13330-2011[24], calculation of the strength of the beams should be carried out under the action of moments in the two principal planes (and bimoment available) according to the formula

20 )
σ x -normal stress in the median plane of the wall, parallel to the longitudinal axis of the beam; σ y -same, perpendicular to the longitudinal axis of the beam; τ xy -shear stress in the wall.
σ x and σ y , taken in formula(20) with their signs and τ xy , should be determined in the same point of the beam wall.