Closed-Form Expressions for Lateral Deflection of Rigid Frames
Determining the magnitude of the lateral deflection of the building frame of low-rise rigidly framed structures, due to external loads, is needed in order to meet appropriate serviceability and design code requirements. In this chapter, a simplified ratio
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Closed-Form Expressions for Lateral Deflection of Rigid Frames
Abstract. Determining the magnitude of the lateral deflection of the building frame of low-rise rigidly framed structures, due to external loads, is needed in order to meet appropriate serviceability and design code requirements. In this chapter, a simplified rational closed form analytical expression is formulated for calculating the lateral deflection of low rise rigidly framed structures subjected to different lateral force distributions varying with the height of the frame.
3.1 Introduction Low-rise rigidly framed structures, such as small office buildings, apartment complexes, and parking garages are some of the most widely built structures in the world. Determining the magnitude of the lateral deflection of the building frame of these structures, due to external loads, is needed in order to meet appropriate serviceability and design code requirements. Classic methods of determining the deflection of a low-rise rigidly framed structure can be challenging and/or time consuming; especially when the building frame has many members. Therefore, the lateral deflection of such structures is typically obtained using the finite element method (FEM), which requires tedious data entry and is subject to human error. The availability of a simple method that can be used to determine the lateral deflections of rigidly framed structures would simplify the design process and provide an efficient means to verify computer aided calculations. In this chapter, a simplified rational closed form analytical expression is formulated for calculating the lateral deflection of low rise rigidly framed structures subjected to different lateral force distributions varying with the height of the frame, as shown in Fig. 3.1.
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Fig. 3.1 Pressure Distributions Used in this Study (a) Hydrostatic (Earth Pressure), (b) Triangular (Wind), (c) Uniform, and (d) Semi-Elliptical W. Aboumoussa and M. Iskander, Rigidly Framed Earth Retaining Structures, Springer Series in Geomechanics and Geoengineering, DOI: 10.1007/978-3-642-54643-3_3, © Springer-Verlag Berlin Heidelberg 2014
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3 Closed-Form Expressions for Lateral Deflection of Rigid Frames
3.2 Approximate Drift Analysis of Buildings A generalized method for estimating the drift of high-rise structures has been proposed by Heidebrecht and Smith (1973, 1974). The building was modeled as a combination of flexure and shear vertical cantilever beams interconnected by a number of rigid members that transmit horizontal forces between both cantilevers. The method was extended to asymmetric structures (Rutenberg and Heidebrecht 1975), and generalized to include the analysis of braced frames, rigid frames, and coupled shear walls (Smith et al. 1984). Although hand calculations can be used with this approach, the equations are tedious, so the finite strip method is sometimes used for decoupling frame elements to simplify the calculations (Swaddiwudhipong et al. 1988). In recent years there has been increasing interests
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