Free vibration and harmonic response analyses of continuous parameter frames by using single variable shear deformation theory and dynamic stiffness method

Dynamic analysis plays an important role in the safe design of frame structures under dynamic excitations such as earthquake, wind and traffic loads. The accuracy of dynamic responses of structures is directly related to natural frequencies and mode shapes. Therefore, it is very important to perform free vibration analysis based on realistic mathematical models as much as possible in structural engineering applications. It is known that, theoretically exact dynamic analysis of frame structures can only be performed using continuous parameter models using various beam theories. Although the finite element method (SEM) that commonly used in dynamic analysis can provide close results to theoretically exact results when the finite element number is sufficiently increased, thousands of finite elements may be required for this convergence in multi-storey, multi-span or three-dimensional frames. For this reason, as computation times would be more than acceptable limits, the necessity of a dynamic analysis approach that quickly provides theoretically exact results for frame structures is arised. In this thesis, free vibration and harmonic response analyses of continuous parameter plane frames are performed using a single variable shear deformation theory (TDKDT) which considers a parabolic shear stress distribution along cross-sections of beam/column, Timoshenko beam theory (TKT) and dynamic stiffness method (DRM). The continuous parameter frames considered in the study are the fixed supported classical frame, infilled frame, frame with soil-structure interaction effects and arch-frames. For the continuous parameter frame models examined in the thesis, natural frequency values obtained from TDKDT and TKT using DRM are presented in comparison with SEM results obtained from the SAP2000 structural analysis software. The mode shapes of the frame models are plotted by equating a non-zero nodal displacement to the unit displacement. Also, harmonic responses of the frames are obtained for point harmonic loads and it is observed that logarithmic scaled harmonic response curves can be used as a very effective tool in the detection of natural frequencies. The results show that the combination of TDKDT with DRM can be used as an effective alternative in the dynamic analysis of frame structures.