Distortional Buckling And Lateral-Torsional Buckling Of Purlin Under Wind Uplift Load

C-and Z-purlins are two popular types of purlins found in industry application,which have thin thickness but rather big bending stiffness.In the purlin-roof system,the top flange of the purlin is connected to the roof by self-drilling screw or standing seam.Under wind uplift load,the bottom flange is free without constraint and suffering compression stress,which is highly likely to have lateral-torsional buckling,local buckling,distortional buckling or combination of the three.Except local bucking,a lot of problems remain un-solved about the distortional buckling and the global buckling.This paper mainly focuses on the distortional and lateral-torsional buckling of C-and Z-purlins,especially under wind uplift load.Based on thin wall structure theory,the non-linear total potential energy of lateral buckling of open thin wall section is acquired.A unified model for the problem of distor-tional and lateral buckling of cold-formed C-and Z-purlins is proposed.Different from Hancock's classic model,the new model introduced one lateral restrain and one rotational restrain provided by the web to the compression flange-lip section,and also introduced an interactive spring between those two restraints.Part of the web is also considered in the new presented model.The total potential equation and the new model are used for solving the distortional and lateral buckling of C-and Z-purlins.A closed-form solution is acquired by using the Ritz method.For C-purlins,based on the non-linear total potential energy and the new model,the problems of distortional and lateral buckling of C-purlins bending about the horizontal axis X,vertical axis Y and bio-moment are solved.The biomoment is found to be unevenly distributed along the length of the purlin.An equivalent coefficient is introduced.The elastic buckling coefficients of twenty purlin sections predicted by the new method are compared with those from Finite Element Method,showing excellent agreement between them.Comparison is also pro-vided with Hancock's method.The effects of the width of the flange and the height of the lip on the buckling of C-purlins are studied.Widen the flange and the lip has a significant influence on the distortional buckling coefficient.Formulas for distortional buckling co-efficients of C-purlins are presented,which have been verified to have high accuracy as compared with the numerical results.The closed form solutions are also substituted into the Direct Strength Method to obtain nominal flexure strength of the purlins,and it is found that the proposed model predicted almost the same strength as the software CUFSM does and has great agreement with the test results.For Z-purlins,the unified model,composed of the compressive lipped flange and part of the web,are used to study both the distortional buckling and the global lateral buckling of cold-formed Z-purlins with vertical lips and sloping lips,bending about horizontal axis X and vertical axis Y.The distortional and lateral buckling capacities are obtained by Ritz method.Excellent agreement is observed between the results of the new model and the results of ANSYS.Comparison is also provided with Hancock's method.The inclination angle of the lip,the widths of the flange and of the lip,are varied in the parametric study.The results show that the inclination angle has a significant influence on the distortional buckling coefficient but a relatively less influence on lateral buckling.The distortional buckling coefficients increase as the flange and the lip widths become larger.The results are also used to predict the load-carrying capacity of available tests,and good agreement is achieved with the test results.Formulas for distortional buckling coefficients of Z-pur-lins with sloping lips are presented,which have been verified to have high accuracy as compared with the numerical resultsNine groups of purlin-roof specimens under wind uplift load are tested,includes dif-ferent kinds of sag rod,different numbers of sag rod,different types of purlin and different roofs and connecting systems.The results of four groups of C-purlins tests show that in-creasing the amount of the sag rod will increase the buckling load effectively.While,for the Z-purlins,adding more sag rods only changes the buckling mode without increasing the buckling moment.Using the rigid sag rod decreases the buckling moment.The Sag rod can decrease the horizontal displacement efficiently but not the vertical displacement.Before buckling,the rotation of the Z-purlin is relatively small compared with the rotation of the C-purlin.Increasing the sag rods or changing the self-drilling roof system to the standing seam roof system has positive effect on decreasing the rotation angle.C-purlins are found out to have higher buckling moment than Z-purlins when other parameters are the same.A simplified FEM model is build,and the simulation results are in good agree-ment with those obtained by experiment.