Wind-induced motion of tall buildings A. Tallin Department of Civil Engineering, Polytechnic Institute of New York, 333 Jay Street, NY 11201, USA B. Ellingwood Center for Building Technology, National Engineering Laboratory, National Bureau of Standards, Gaithersburg, MD 20899, USA (Received January 1985; revised April 1985) Modern buildings designed such that their lateral drifts under statically applied wind loads are less than some fraction of building height, may vibrate excessively during winds and cause occupant discomfort. Methods are presented for evaluating the vibration characteristics of buildings using random vibration theory to relate the fluctuating wind forces to structural response. These methods can be used to evaluate serviceability or to plan wind tunnel tests of buildings. Key words: building specifications, deflections, random vibration, stiffness, structural engineering, wind Building serviceability is often checked by imposing a limit on the allowable lateral frame deflection (drift), calculated on the basis of a uniform statically applied wind load. Drift limits ranging from/-//400 to H/600, in which H is the overall height of the building, are commonly used) Such limits control the stiffness and curvature of the structural frame, thereby preventing damage to non- structural components and the development of second- order forces that could lead to member or frame instability. Although these traditional drift limits have usually led to satisfactory building performance, fluctuating wind forces may cause modern flexible buildings to vibrate excessively from the point of view of their occupants. Designers of wind-sensitive structures deal with this problem by specifying boundary layer wind tunnel tests to assist in the design of the structural frame and cladding. 2 Many buildings in the range 300-600 ft (91-183 m) in height border on being wind-sensitive, however, and may or may not be subjected to wind tunnel testing in the course of their design. As an alternative, potential motions of such buildings can be evaluated using random vibration theory 3 to relate the fluctuating wind forces to structural deflections and accelerations. This approach can be used to evaluate serviceability of some buildings or to establish the need for and to plan wind tunnel tests. The random vibra- tion analysis requires realistic descriptions of fluctuating along-wind, across-wind and torsional wind forces. More- over, correlations between components of response may be introduced by the presence of statistical correlations between forces or mechanical coupling caused by eccen- tricities of mass and rigidity. These effects may amplify the overall dynamic response considerably and the analysis should take them into account. Analysis of structural response At service load levels, the building may be expected to behave elastically. It will be assumed that it can be modelled as a lightly damped system .with three degrees-of- freedom: two perpendicular translational motions and one rotational motion. The fluctuating components of wind forces are modelled as zero-mean stationary random processes, and it is assumed that they have acted on the structure for a sufficient time for the responses to be stationary. The equations of motion are written in matrix form as: MX + C?~ + KX = F(t) (1) in which X is a vector of generalized displacements, M, C and K are mass, damping and stiffness matrices; F(t) is the vector of generalized wind forces acting on the building; and dots indicate differentiation with respect to time. The matrix of power spectral densities of structural response (e.g. acceleration) can be written as: 4 Syi(n) = CH(n) dpTSr(n) CH*(n) ¢7 (2) 0141-0296/85/04245-08/$03.00 © 1985 Butterworth & Co. (Publishers) Ltd Engng Struct., 1985, Vol. 7, October 245