Analysis Of The Overall Stability Of Tapered Cantilevered Castellated Steel Beams

Tapered castellated beam has advantages of both tapered beam and castellatedbeam, which is reasonable force, strong flexural rigidity, light dead-weight, easy forrough-in pipelines, economical for floor height, beautiful, inexpensive, etc. With thedevelopment of economy, tapered castellated beam is widely used in structures ofcanopy, balcony, workshop, bridge, huge and complex floor structure and so on.However, there is no computational formula concerning the overall stability oftapered castellated beam. Therefore, this thesis, based on such backgrounds, carrieson correlation studies on the overall stability of tapered cantilevered castellated steelbeam.On the basis of energy method principle and considering non-linear strain energy,the thesis establishes the total potential energy formula of elastic flexural-torsionalbucking when tapered cantilevered castellated beam which is under the influence offree end pure bending load, free end top flange concentrated load or top flangeuniformly distributed load. In addition, the thesis, substituting Rayleigh-Ritz’sdisplace function that is supposed in accordance with the geometric boundarycondition into each total potential energy formula, calculates out the theoreticalcomputational formula of elastic flexural-torsional bucking critical load of taperedcantilevered castellated beam.The thesis, separating the flange and web of tapered castellated beam in that thecomputational method of flange is the same as that of solid web girder, employs theprinciple of equal volume to compute the equivalent stiffness of web. By changing thethickness of castellated beam’s web through the principle of equal volume, the thesiscalculates out the equivalent stiffness reduction factor, and thus employing thisreduction factor, calculates out the lateral flexural rigidity, free torsion rigidity andwarping torsion rigidity of castellated beam.The thesis, establishing276different finite-element models of tapered cantilevercastellated beam by means of ANSYS software, calculates out the finite-elementsolution of flexural-torsional elastic bucking critical load of tapered cantileveredcastellated beam. In addition, through the comparison between the ANSYSfinite-element solution and theoretical formula solution deduced in this thesis, theauthor analyzes reasons that leads to the errors and proves their reliability. The thesis, through comparative analysis of finite-element results, finds theinfluence of factors such as forms of load, pitch of holes, taper, depth-span ratio, holetype of webs, top flange level, etc. on the elastic flexural-torsional bucking criticalload of tapered cantilevered castellated beam, and analyzes the reasons. The authoralso puts forward some detailing requirements of tapered cantilevered castellatedbeam.Finally, considering the influence of elastic-plastic instability, the thesis, inaccordance with formulas in codes and related documents, calculates out the overallstability factor of tapered cantilevered castellated beam by using inverse analysis. Inaddition, the thesis also calculates out the overall stability formula of taperedcantilevered castellated beam that can be directly used in engineering practice.