Effects of stiffness ratio and rotational degree of freedom on natural frequencies and mode shapes in dynamic analysis of a planar frame

In practice a dynamic analysis is usually preceded by static analysis for dead and live loads. The structural idealization for the static analysis is dictated by the complexity of the structure, and several hundred to a few thousand degree of freedoms may be necessary for accurate evaluation of the internal element forces and stresses in a complex structure. The same refined idealization may be used for dynamic analysis of the structure, but this may be unnecessarüy refined and drastically fewer DOFs could suffice. Such is the case because the dynamic response of many structures can be represented well by the first few natural modes, and these modes can be determined accurately from a structural idealization with drastically fewer DOFs than required for static analysis. One of the aim of this study is to reduce the the number of DOFs as much as resonably possible before proceeding with computation of natural frequncies and modes, which is perhaps the most demanding phase of dynamic analysis. Rotational degrees of freedoms are the ones which are used for the reduction of the system stiflhess matrix's order. For the reduction procedure Static Condensation method is used. In Static Condensation method, one uses, for dynamic analysis, only degree of freedoms which masses are assigned. These DOFs are called dynamic degree of freedoms. Horizontal degree of freedoms are chosen as dynamic DOFs which can be interpreted as mass lumped degree of freedoms. The effect of the rotational degree of freedoms to dynamic behaviour of frame system has been studied in doing so. While studying the effects of joint rotation, moment of inertia ratios have been changed continously for fiirther understanding of the effects of rotational degree of freedoms.Also some other assumptions about joint rotations have been made for studying the subject in a dualistic manner. The assumptions are as follows: Case A: No joint rotation lakes place. Case B: All joints within a floor undergo an equal rotation. Case C: No restriction is placed on joint rotation. By doing these assumptions the study is enhanced for understanding the effects of joint rotations on natural frequencies and mode shapes of frame systems. All the assumptions which have been made proved that rotational degree of freedoms effect drastically both the natural frequencies and the mode shapes of frame systems. The results obtained for Case B and Case C are almost the same; but in Case B one deals with much smaller matrix orders than Case C. Then it can be concluded that Case B can be used for taking the effects of joint rotations in place of Case C with Static Condensation method. By doing so obtained results are much more reliable than not considering the joint rotations and cancelling them out in system stifmess matrix. TC YÜKSEKÖ?RETİM KURUU, ifcîKÜMArfTASYON MERKEZÎ