Civil Engineering Reference
In-Depth Information
3.2 Approximate Drift Analysis of Buildings
A generalized method for estimating the drift of high-rise structures has been pro-
posed 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 some-
times used for decoupling frame elements to simplify the calculations
(Swaddiwudhipong et al. 1988).
In recent years there has been increasing interests in approximate methods to
predict the lateral drift under seismic loading. For example, Miranda (1999) pre-
sented an approximate method similar to Heidebrecht and Smith (1973) to com-
pute the drift of buildings responding to earthquakes in the building's fundamental
mode and expanded the method to buildings with non-uniform stiffness (Miranda
and Reyes (2002).
Alternatively, Bang and Lee (2004) proposed an energy based analytical ap-
proach for tall rigidly framed structures. The effect of the shear deformation of
the wall and the flexure deformation of the frame were shown to be important for
tall or slender buildings. Although Bang and Lee's approach yield good results,
the equations cannot be easily solved manually.
When a rigidly framed structure is subject to lateral loading, it deflects in a
flexure mode near the top and in a shear mode near the bottom. For tall buildings,
the deflection mode is a hybrid of both mechanisms. The available approximate
methods are geared towards taller buildings, and account for both mechanisms us-
ing a variety of approaches. For shorter structures an approximation based on
shear deflections only may yield simpler equations. These expressions would be
particularly beneficial for analysis of rigidly framed earth retaining structures
(RFERS), which are commonly used in urban and suburban locations to maximize
land use in hilly sites. The expressions would also be useful for analysis of short
structures under any loading condition.
3.3 Simplified Expression for Lateral Deflection of Rigidly
Framed Structures
In a rigid frame, the lateral deflection of one floor relative to the floor below (sto-
ry drift) due to lateral pressure results from a combination of shear and bending
deformation of the beams and columns, as shown in Fig. 3.2. Bending moment
causes the greatest deflection in a long beam (length > depth). Shear forces cause
the greatest deflection in short beams (depth > length). A beam is considered
short when the span-to-depth ratio is less than 8, depending on the material
(Young and Budynas, 2004).
