A method for calculation of lateral displacements of buildings under distributed loads
Abstract
Lateral displacement is a vary important parameter that we need to calculate when structures are subjected to lateral loads like earthquake and wind loads. In this study, a method is proposed for lateral displacement calculation of structures with different structural systems in different planes. This method is based on the continuum system calculation model. The method suggested in the literature for only top displacement in the case of uniform loading, is developed in this study for the calculation of displacements at each storey level and also in both uniform and triangular loading conditions. At the end of the study, twenty-eight storey building with shear wall-frame bearing system, which was taken from the literature, was solved with the presented method and Finite Element Method. The shear walls were modelled with three different element types for the analysis with the Finite Element Method with structural engineering program used. The results, obtained from the Continuum Method and Finite Element Method were presented in tables and by figures. Thus, the compatibility of the proposed method with the classical Finite Element Method was investigated. From the compared results of the method and the literature or finite element models it was seen that the method used for the case of uniform or triangular distributed loading gives very close results.
Keywords
Lateral displacement, uniform distributed load, triangular distributed load, timoshenko beam model
References
- [1] Chitty L., “On the cantilever composed of a number of parallel beams interconnected by cross bars”, Philosophical Magazine, London, Series, 7 (38), (1947), 685–699.
- [2] Rosman R., “Approximate analysis of shear walls subject to lateral loads”, Proceedings of the American Concrete Institute, 61(6), (1964), 717–734.
- [3] Rutenberg, A., Heidebrecht A.C., “Approximate analysis of asymmetric wall-frame structures”, Building Science, 10(1), (1975), 731–745.
- [4] Murashev, V., Sigalov, E., Baikov, V.N., “Design of reinforced concrete structures”, Moscow, Mir Publishers, 1976.
- [5] Basu, A.K., Nagpal, A.K., & Kaul, S., “Charts for seismic design of frame-wall systems”, Journal of Structural Engineering ASCE ,110 (1), (1984), 31–46.
- [6] Stafford Smith B, Crowe E., “Estimating periods of vibration of tall building”, Journal of the Structural Division, ASCE 112(5), (1986), 1005–1019.
- [7] Smith B. S., Yoon Y. S., “Estimating seismic base shears of tall wall-frame buildings”, Journal of Structural Engineering ASCE, 117(10), (1991), 3026-3041.
- [8] Mancini, E., Savassi, W., “Tall building structures unified plane panels behavior”, Structural Design of Tall Buildings, 8, (1999), 155–170.
- [9] Ng, S.C., Kuang, J.S, “Triply coupled vibration of asymmetric wall–frame structures”, Journal of Structural Engineering ASCE, 126 (8), (2000), 982–987.
- [10] Wang, Y., Arnaouti, C., Guo S., “A simple approximate formulation for the first two frequencies of asymmetric wall–frame multi-storey building structures”, Journal of Sound and Vibration, 236 (1), (2000), 141–160.