Yarı Rijit Bağlı Betonarme Bacaların Serbest Titreşiminin Diferansiyel Transformasyon Metodu İle Analizi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2015Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2015Bu çalışmada; Timoshenko kiriş teorisi dikkate alınarak, yarı rijit bağlı betonarme bacaların serbest titreşim analizi incelenmiştir. Farklı zemin kayma modülleri için çökmeye ve dönmeye karşı elastik yaylar kullanılarak modellenen sabit enkesitli betonarme bacaların ilk üç modlarına ait doğal açısal frekansları, analitik metotla ve Diferansiyel Transformasyon Metodu (DTM) kullanılarak elde edilmiştir. Tüm analizlerde analitik yöntem ve DTM’nin yanında SAP2000 programı da kullanılmıştır. Sistemlerde kullanılan çökme ve dönme yayı rijitlikleri ASCE 4-98 yönetmeliği kapsamında zemine ait kayma modülüne, poisson oranına ve baca temelinin yarıçapına bağlı olarak hesaplanmıştır. DTM’den elde edilen sonuçların analitik yöntemle elde edilen sonuçlara oldukça başarılı bir şekilde yakınsadığı görülmüştür. Yarı rijit bağlı sistem için elde edilen açısal frekans değerleri, ankastre mesnetli sistem ile kıyaslanmıştır. Analizler sonucu elde edilen açısal frekans değerleri tablo halinde verilmiştir. İlk üç moda ait mod şekilleri ve normalize edilmiş eğilme momenti diyagramları sunulmuştur.In this study, the free vibration analysis of semi-rigid connected reinforced concrete chimneys is investigated. The first three natural circular frequencies of the chimneys which have uniform cross sections along their heights and modeled by using different translational and rotational springs due to different soil conditions, are obtained using analytical solution and Differential Transform Method (DTM). SAP2000 is used in addition to analytical solutions and DTM solutions in numerical analysis. The stiffnesses of elastic springs that are used in numerical analysis are calculated by means of shear modulus of the soil, poisson ratio of the soil and radius of the foundation in accordance with ASCE 4-98. The results obtained from DTM are compared with the results of the analytical solution and very good proximity is observed. The natural frequencies of semi-rigid systems are compared with the natural frequencies of clamped foundation system. The natural frequencies are tabulated. After all, the mod shapes and normalized bending moment diagrams are presented

Earthquake response of linear-elastic arch-frames using exact curved beam formulations

Purpose This study aims to obtain earthquake responses of linear-elastic multi-span arch-frames by using exact curved beam formulations. For this purpose, the dynamic stiffness method (DSM) which uses exact mode shapes is applied to a three-span arch-frame considering axial extensibility, shear deformation and rotational inertia for both columns and curved beams. Using exact free vibration properties obtained from the DSM approach, the arch-frame model is simplified into an equivalent single degree of freedom (SDOF) system to perform earthquake response analysis. Design/methodology/approach The dynamic stiffness formulations of curved beams for free vibrations are validated by using the experimental data in the literature. The free vibrations of the arch-frame model are investigated for various span lengths, opening angle and column dimensions to observe their effects on the dynamic behaviour. The calculated natural frequencies via the DSM are presented in comparison with the results of the finite element method (FEM). The mode shapes are presented. The earthquake responses are calculated from the modal equation by using Runge-Kutta algorithm. Findings The displacement, base shear, acceleration and internal force time-histories that are obtained from the proposed approach are compared to the results of the finite element approach where a very good agreement is observed. For various span length, opening angle and column dimension values, the displacement and base shear time-histories of the arch-frame are presented. The results show that the proposed approach can be used as an effective tool to calculate earthquake responses of frame structures having curved beam elements. Originality/value The earthquake response of arch-frames consisting of curved beams and straight columns using exact formulations is obtained for the first time according to the best of the author's knowledge. The DSM, which uses exact mode shapes and provides accurate free vibration analysis results considering each structural members as one element, is applied. The complicated structural system is simplified into an equivalent SDOF system using exact mode shapes obtained from the DSM and earthquake responses are calculated by solving the modal equation. The proposed approach is an important alternative to classical FEM for earthquake response analysis of frame structures having curved members

Seismic response of pile supported frames using the combination of dynamic stiffness approach and Galerkin's method

The aim of this study is to obtain seismic response of pile supported frames using exact mode shapes. The dynamic stiffness method (DSM) is applied to obtain natural frequencies and mode shapes of frame model which has Timoshenko element beams, columns, piles and flexible pile cap. Free vibration analysis is performed for various soil conditions, pile dimensions and column dimensions. The calculated natural frequencies using DSM are tabulated with the natural frequency values obtained from finite element method (FEM). The FEM convergence for the first three natural frequencies are presented. The mode shapes are plotted. The agreement between the mode shapes obtained from the DSM and FEM is observed by means of modal assurance criterion (MAC). Using the Galerkin's method, the generalized displacement function of the frame model is obtained by a linear combination of mode shapes and generalized coordinates. The generalized mass, stiffness and force for the equivalent model are obtained and earthquake response analysis is performed. At first, the FEM convergence for the roof displacement and base shear is presented. Then, effects of soil conditions, pile diameter and column dimensions on the seismic response of the frame model are revealed using the proposed approach. The timehistories for the roof displacement and base shear are calculated using the Runge-Kutta method. As the accuracy of the seismic response is strictly related to free vibration characteristics of the system, the natural frequencies of a single-storey frame model obtained using the DSM are presented in comparison with the experimental data in literature. Moreover, an additonal validation is presented for the natural frequencies of a beam on elastic foundation using the dynamic stiffness formulation and experimental data for various boundary conditions. The results show that the proposed approach for seismic response analysis of pile supported frames is very effective and straightforward

Dynamic response of damaged rigid-frame bridges subjected to moving loads using analytical based formulations

PurposeThis study aims to perform dynamic response analysis of damaged rigid-frame bridges under multiple moving loads using analytical based transfer matrix method (TMM). The effects of crack depth, moving load velocity and damping on the dynamic response of the model are discussed. The dynamic amplifications are investigated for various damage scenarios in addition to displacement time-histories.Design/methodology/approachTimoshenko beam theory (TBT) and Rayleigh-Love bar theory (RLBT) are used for bending and axial vibrations, respectively. The cracks are modeled using rotational and extensional springs. The structure is simplified into an equivalent single degree of freedom (SDOF) system using exact mode shapes to perform forced vibration analysis according to moving load convoy.FindingsThe results are compared to experimental data from literature for different damaged beam under moving load scenarios where a good agreement is observed. The proposed approach is also verified using the results from previous studies for free vibration analysis of cracked frames as well as dynamic response of cracked beams subjected to moving load. The importance of using TBT and RLBT instead of Euler-Bernoulli beam theory (EBT) and classical bar theory (CBT) is revealed. The results show that peak dynamic response at mid-span of the beam is more sensitive to crack length when compared to moving load velocity and damping properties.Originality/valueThe combination of TMM and modal superposition is presented for dynamic response analysis of damaged rigid-frame bridges subjected to moving convoy loading. The effectiveness of transfer matrix formulations for the free vibration analysis of this model shows that proposed approach may be extended to free and forced vibration analysis of more complicated structures such as rigid-frame bridges supported by piles and having multiple cracks

EFFECTS OF INFILL WALLS ON FREE VIBRATION CHARACTERISTICS OF MULTI-STOREY FRAMES USING DYNAMIC STIFFNESS METHOD

This study aims to obtain exact natural frequencies and mode shapes of infilled multi-storey frames using single variable shear deformation theory (SVSDT) which considers parabolic transverse shear stress distribution across the cross-section. The effects of infill walls on free vibration characteristics are investigated for different frame models such as one storey infilled, soft storey and fully infilled. The infill walls are modeled using equivalent diagonal strut approach. Natural frequencies are calculated via dynamic stiffness formulations for different wall thickness values. The results of SVSDT are tabulated with Euler-Bernoulli beam theory (EBT) and Timoshenko beam theory (TBT) results. Additionally, finite element solutions are presented to verify the natural frequencies that obtained from dynamic stiffness formulations. The results show that SVSDT can be used effectively for free vibration analysis of infilled frame structures by using dynamic stiffness formulations. The numerical analyses show that the effects of shear deformation and rotation inertia become observable for higher modes of infilled frame structures. It is seen from the results that ignoring effects of infill walls may cause significant errors on calculation of natural frequencies of frames