A Study Of The Stability Of Bars In Steel Structure By Method Of Polynomial Deformation

In the study of the stability of members in steel structures,it’s necessary to consider that Initial defects of the member have adverse effects on the results of the calculation and Initial bending is one of the most important influence factors.So far,the initial bending expression of the steel pressure rod is relatively single,usually expressed as a half wave of a sinusoidalcurve,and its expression formula is y=v0sin πx/l,which is an idealized version of the simplest initial curved shape.y0 is the initial bending amplitude of the rod,v0 is the initial bending amplitude at the midpoint of the rod,and x is the distance from the endpoint of the rod to any point,x ∈[0,L].In fact,due to a variety of factors,the initial curved shapes of the members are various from production to use.Another form of of expression of initial bending is the polynomial of x.For instance,the formula of deflection curve that meets the articulation constraints at both ends is y=a1x(l-x)+a2x2(l-x)+....It is also straightforward and simple to express the initial bending and deformation of bars by polynomials.Currently,domestic scholars haven’t studied the influence of polynomial initial bending on the stable calculation of members of steel structure.Therefore,this paper makes some discussion about it.The initial bending of the sine half-wave curve has become the main form of studying the stability of the rod.So The paper takes it as a comparison in the study.The axial pressure stability bearing capacity is mainly calculated for members bar whose initial bending expression is sine half-wave curve and polynomial curve so as to better observe the difference between the calculation speed and the bearing capacity.Simultaneously,the deflection line after the instability of the rod is obtained,and observe whether the deflection line is consistent with the assumed initial bending curve in general form,and then to estimate that whether it is reasonable to study the stability of the steel structure of the polynomial as the initial bending of the member bars.The specific work of this paper is as follows:(1)In this paper,three cross-sectional steel pressure rods are selected for study,namely round steel pipe,square steel pipe and I-beam steel pipe.9 slenderness ratio are selected,whose slenderness ratio λ is 40,60,80,100,120,140,160,180,200 and constraints are hinged at both ends.Based on the basic principles of numerical integration,the Matlab program of three kinds of cross-section steel pressure rods was compiled,and the round steel pipe of φ200×8 was selected to calculate the stable ultimate bearing capacity.Compared it to several different calculations to verify the correctness of the program.(2)The validated Matlab program was used to calculate the stabilization limit bearing capacity and the deflection line after the instability of the three cross-sectional steel pressure rods at different slenderness ratios.Run the same program more than three times,record the operational time in the program,and calculate the average as the operational time.Introduce the formula in the design code of steel structure to calculate the ultimate bearing capacity of axial compression stability as a reference.The stable ultimate bearing capacity in two different initial bending is compared with the standard value,and the deviation is calculated.The deflection line after the instability of the rod is recorded.Find the curve closest to it and consistent with the general formula of the initial bending curve by the method with the smallest difference value.And calculate the deviation of the two curves at each node.(3)The stable ultimate bearing capacity calculated by considering the initial bending of the polynomial is compared with the test results of welded round steel pipes conducted by domestic scholars.Verify whether using polynomial curve as initial bending can correctly calculate the ultimate bearing capacity of axial compression bars.(4)Verify the validity of the polynomial curve as a numerical integration method for initial bending to calculate the stability of the axial compression bars by finite element modeling of square steel pipes and I-beam cross-section steel pressure rods and the calculation results of the stable ultimate bearing capacity and deflection curve were compared with the calculation results of the numerical integration method.