Analysis Method And Its Applications Of Thin-Walled Steel Beam Considering The Effects Of Shear Deformation

Thin-walled steel beams are widely used in the fields of civil, mechanical, and navalconstructions. In order to guarantee the security and applicability of these steel members, it isvery important to build reasonable and reliable physical model and analysis method. Theclassical Euler-Bernoulli beam theory and Timoshenko beam theory as well as thecorresponding beam element are used extensively in engineering analysis. Euler-Bernoullibeam theory does not consider the effect of shear deformation on the behavior of beams.Timoshenko beam theory includes the effect of shear deformation, but is limited to flexuralanalysis of solid beam as well as Euler-Bernoulli beam theory and cannot be used to flexuraland torsional analysis of thin-walled beam. Vlasov developed an integrated theory which cananalyze the flexural and torsional behavior of thin-walled beam. However, due to theignorance of shear deformation in middle surface, Vlasov theory is only applicable forthin-walled beams with span-height-ratio greater than10.With the growth of national economy and city construction, steel members are widelyused in heavy structures, such as high-rise, super high-rise and heavy industrial buildings. Inthese buildings, the span-height-ratio of steel beam is small and the effect of sheardeformation becomes obvious. In order to include the effect of shear deformation due toflexure and torsion, in this thesis, a first-order thin-walled beam theory is developed based onVlasov theory. This theory can analyze the flexural and torsional problems of thin-walledbeam. Due to the shear center of thin-walled cross section, the flexural and torsional problems of thin-walled beams can be analyzed respectively. Accordingly, the governing differentialequations are obtained for flexure and torsion of thin-walled beam respectively. Asecond-order elasto-plastic beam element based on the first-order thin-walled beam theory isobtained, and the corresponding code is written. The specific contents are given as follows.Firstly the first-order thin-walled beam theory is developed for flexural and torsionalproblems of open thin-walled beam. The expressions of flexural stress, deformation andtransverse shear coefficient are given. The relationships between transverse deflection androtation are obtained. When analyzing the restrained torsion of open thin-walled beam, thetotal rotation of section is divided into free warping rotation and restrained shear rotation. Theexpression of warping deformation, the warping normal stress and warping shear stress arederived based on this assumption. And the torsion shear coefficient is then obtained on thebasis of energy principle. Torsion shear coefficient could account for the true shear stressdistribution in the cross section. Program is compiled to calculate the geometric properties ofopen thin-walled section.The new governing differential equations of the restrained torsion are derived and thecorresponding initial method is given to solve the equations. The relationship between totalrotation and free warping rotation is obtained. A parameter λ, which is associated with thestiffness property of a cross section and the beam length, is introduced to determine thecondition, under which the St. Venant constant is negligible. Consequently a simplifiedmethod of restrained torsion is derived. The simple method has the same style withTimoshenko beam theory. Numerical examples are illustrated to validate the current approachand the results of the current theory are compared with those of some other available methods.The results of comparison show that the current theory predicts the torsion behavior ofthin-walled beam more accurately.The restrained torsion of closed thin-walled beam is analyzed. The first-order torsiontheory of closed thin-walled beam is proposed. The various stresses in closed cross section are analyzed and divided into categories, and the expressions of these stresses are given. Thetorsion shear coefficient is then obtained on the basis of energy principle. The governingdifferential equations of the restrained torsion of closed thin-walled beam are derived and thecorresponding initial method is given to solve the equation. These equations can be used asunified theory for restrained torsion of arbitrary cross section. The effect of restrained shearrotation on torsional behavior of closed thin-walled beam is investigated through numericalanalysis.The thin-walled beam element is derived. The displacement mode of thin-walled beamelement is obtained through the relationship between deflection and rotation and that betweentotal rotation and free warping rotation. Only two nodes are needed in this displacement mode,which avoid the deriving process of beam element with internal node. The new beam elementis obtained through the updated Lagrange (UL) method on the basis of finite deformationtheory in continuum mechanics. This new beam element avoids the phenomenon of shearlocking and includes the effects of warping deformation and the coupling of flexure andtorsion.An incremental method is proposed based on UL method in order to include the P-δeffect more accurately. This method makes up the defect of the cubic interpolation function intangential stiffness matrix and avoids the problem of variation of stiffness matrix derivedfrom stable interpolation function with the direction of axial force.It is assumed that the Von Mises yield criterion, associated flow rules and isotropichardening model are applied to the material that used in this paper. Plastic-zone method isused and the thin-walled section is divided into a number of finite parts along the s directionand three Guass integral points are placed along the length of thin-walled beam in order totrace the plasticity development in the beam. And the plasticity development can be judged bythe stress condition in finite parts.Finally, on the basis of derivation of new thin-walled beam element, nonlinear analysis program is compiled by using the object oriented program language C++. And numericalexamples are illustrated to validate the current approach. The results of the current theory arecompared with those of some other available methods. The results of comparison show thatthe current theory provides more accurate results and avoids the phenomenon of shearlocking.