Wind Resistant Structural Optimization Design Of Long Span Portal-Rigid Steel Frame With Tapered Section

A wind-resistant structural optimization procedure for long-span portal rigidsteel frame with tapered section was proposed in this research project based on theOptimality Criteria (OC) method. First a finite element model was established for theportal steel frame by SAP2000software, the vertical displacement at the middle spanof the rafter and horizontal displacement atop of the steel column were selected as theconstrain variables for the structural optimization procedure, and they are obtainedthrough the virtual work by getting the results of internal forces of structural elementsvia SAP2000Application Programming Interface (API) and symbolic integrationfunction in MATLAB software. Meanwhile the strength and stability condition wereensured by setting the lower and upper bands of section sizes for optimized designvariables. The minimization of total weight of optimized structure was adopted to bethe objective function for the proposed structural optimization procedure. Based onthe above objective function, displacement constraints and optimized variables insome range, a special OC method and some key issues and research methodologieswere studied in this thesis for the optimization of long-span portal rigid steel framewith tapered section under dynamic wind actions.In order to simplify the structural optimization procedure, two categories ofequivalent static wind loads were first proposed: the Equivalent Static Wind Load(ESWL) based on Load Response Correlation (LRC) method, the static wind load bythe Gust Loading Factor (GLF) concept. On the other hand, structural optimization forthe same structure under the corresponding dynamic wind loads obtained from thewind tunnel test was also conducted for the comparison purposes. The effects ofinitialized optimized design variables, support stiffness at the column base and theconnection stiffness at the column-beam connection joint on the optimization resultswere analyzed and discussed, the different solutions for Lagrange multiplier were alsocompared. The optimization results for the same structure under dynamic wind loadsand its corresponding different categories ESWL are analyzed comprehensively andcompared in much detail in this thesis.For the structural optimization of portal rigid steel frame under the ESWLbased on LRC method, three types of loading cases were first studied: the ESWLsrelated for the horizontal displacement atop the steel column, the ESWLs related forthe vertical displacement at the mid-span of the steel rafter and the combined but non-synchronized acting ESWLs from the previous load cases. It was found that theoptimized total weights for the three static wind load cases are very close, theoptimized total weight was reduced to its initial values by about26%~28%.However the distributions of cross section size for optimized design section wereslightly different. The optimized weight for the same structure under static wind loadfrom GLF method was reduced by only23%, which indicated that it was morereasonable to conduct the structural optimization for the portal rigid frame byadopting the ESWLs from LRC method since it conformed to the wind loaddistribution on the structure more exactly. On the other hand, the optimized weightsgenerally reduced in the nonlinearity style with the increased support stiffness at thecolumn base and the connection stiffness at the beam-column connection joint.However the optimized weights of the structure remained at the almost the same valuewhen the support or connection stiffness reached above the some specified values.For the simplicity in the structural optimization for the long-span portal rigidframe under dynamic wind loads, the time instant when the largest displacements orthe equivalent displacements induced by the ESWL occurred were first recordedthrough the dynamic analysis of portal rigid frame. The instantaneous wind load andits corresponding internal force of structural elements at that time were then obtained,which was regarded as the different load cases for the optimized structure. Throughthis way, the structural optimization of the portal rigid steel frame under dynamicwind load was transformed to be the structural optimization procedure for the samestructure under a series of pseudo static wind load cases. It was showed that theoptimized weight of the structure under the dynamic wind load were almost same asthose for the corresponding EWSLs. Thus the validation of such treatment for thestructural optimization of the studied structure under time history dynamic wind loadswas testified. Although the optimized results of design variables fluctuated alongcertain values as the results of different time instants selected in different optimizationdesign cycles, the optimized total weight of the structure trended to be a more stableoptimized design value with the increase of optimization design cycle. Furthermorethe final optimized total weights of the structure were a little heavier than thosecorresponding optimized values from the ESWLs, indicating that the wind resistantoptimization design of such structure under time history dynamic wind loads arenecessary and can be used as the supplement for the optimized results from ESWLs.Compared with the vertical displacement at the mid-span of the rafter, the horizontal displacement atop of the column was mostly found to be the active constraints at thelatter design cycles during the optimization procedure under dynamic wind load cases.This would indicate that the horizontal displacement atop of the column would controlthe wind resistant optimization design for such long-span portal rigid steel frame withtapered section during wind actions.