The present paper considers the dynamic behavior of beams with open thin-walled cross-sections along their length with bracings (connecting beams and truss). The effect of the constrained torsion warping, rotary inertia, and flexural-torsion coupling due to nonsymmetric cross-sections is included. In the case of simply supported beams, closed-form solutions for determining coupled natural frequencies and corresponding mode shapes are newly derived. The frequency equation, given in a determinantal form, is expanded in an explicit analytical form and then solved using the Mathcad 2001 Professional symbolic computing package. Some illustrative examples on the application of the present theory are given for coupled bending-torsion vibrations of braced thin-walled beams. As compared with FEM, numerical results demonstrate the accuracy and effectiveness of the proposed method Introduction. Thin-walled beams with open cross-section are basic structural elements extensively used in various fields of engineering applications due to their outstanding properties: they offer high performance in terms of the minimum weight for a given strength. However, the behavior of such constructions is very complex and, therefore, the accurate prediction of their dynamic characteristics is of fundamental importance in the design of thin-walled structures. Most of thin-walled beams with open sections have good bending resistance but low torsional resistance. One of the ways how the torsional rigidity and, consequently, the load-carrying capacity of open thin-walled members can be significantly increased is to use intermediate connecting beams and trusses that reduce cross-sectional warping (Fig. 1). The shape, size, and position of the bracings provoke significant changes in the dynamic behavior of thin-walled structures. The purpose of this paper is to investigate the magnitude of such changes by using an exact numerical solution.Because of the practical importance of thin-walled beams, a number of studies dealing with coupled bending-torsional vibrations of beams and shells were conducted [1][2][3][4][5][6][7][8][9][10][11]. However, these studies cover only unbraced thin-walled members. A large amount of research work has been done to analyze open-section core structures in tall buildings, incorporating the effects of the interconnecting lintel beams, but only a static analysis was presented [12][13][14][15][16][17][18]. According to the authors' knowledge, there is no work in the literature studying coupled vibrations of thin-walled beams with bracings. This problem is presented in this paper. A general closed-form solution to the equations of motion, irrespective of the kind, stiffness, and number of bracings along the length, is obtained. The solution is limited to simply supported ends.The proposed method is simple, rapid, and accurate enough to be used in a preliminary design stage and also for verifying numerical results of complex and time-consuming computer procedures. It is expected that this investigation will be useful for b...
UVODRealna procena dinami ki indukovanih prese nih sila u tunelskoj konstrukciji predstavlja veoma važan aspekt aseizmi kog projektovanja tunelskih objekata. U analizi odgovora tunelskih konstrukcija na seizmi ke uticaje, koriste se dva postupka: metoda slobodnih deformacija tla i metoda interakcije konstrukcije i tla [6,23].Najjednostavniji pristup u analizi seizmi kog odgovora tunelskih konstrukcija jeste metoda slobodnih deformacija tla. Termin slobodna deformacija tla opisuje deformaciju usled prostiranja seizmi kih talasa u tlu bez tunelske konstrukcije ili iskopa. Ideja ovog pojednostavljenog postupka jeste sra unavanje seizmi ki indukovanih deformacija tla u odsustvu tunelskog objekta, nanošenje tako sra unatih deformacija tla na tunelsku konstrukciju u stati kim uslovima, i projektovanje tunelske konstrukcije za tako definisano optere enje. Samim tim, ovim postupkom krutost tunelske konstrukcije nije uzeta u obzir, ime je interakcija konstrukcije i okolnog tla zanemarena. Ipak, ovom metodom je mogu a veoma jednostavna i brza procena reakcije konstrukcije na seizmi ka dejstva. Veli ine deformacija tunelske konstrukcije Asistent Elefterija Zlatanovi , dipl.inž.gra . Univerzitet u Nišu, Gra evinsko-arhitektonski fakultet,
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