## 2

From Equation 22.55

Assuming a peak factor of 4, the peak acceleration in the cross wind direction is

22.5.6 Torsional Response

A building will be subjected to torsional motion when the instantaneous point of application of resultant aerodynamic load does not coincide with the center of mass and the elastic center. The major source for dynamic torque is the flow-induced asymmetries in the lift force and the pressure fluctuation on the leeward side caused by the vortex shedding. Any eccentricities between the center of mass and center of stiffness present in asymmetrical buildings can amplify the torsional effects.

Balendra et al. (1989) have presented a time domain approach to estimate the coupled lateral-torsional motion of buildings due to along wind turbulence and across wind forces and torque due to wake excitation. The experimentally measured power spectra of across wind force and torsional moment (Reinhold 1977) were used in this analysis. This method is useful at the final stages of design as specific details that are unique for a particular building can be easily incorporated in the analytical model. A useful method to assess the torsional effects at the preliminary design stage is given by the following empirical relation (Simiu and Scanlan 1986), which yields the peak base torque induced by wind speed U(H) at the top of the building as

where C is a reduction coefficient, gT is the torsional peak factor equal to 3.8, and T and Trms are the mean and root mean square base torques that are given by

V cT

where p is the density, H is the height of the building, nT and CT are the frequency and damping ratio in the fundamental torsional mode of vibration, | r| is the distance between the elastic center and the normal to an element ds on the boundary of the building, and A is the cross-sectional area of the building. The expressions for T and Trms are obtained for the most unfavorable directions for the mean and root mean square values of the base torque. In general, these directions do not coincide and furthermore will not be along the direction of the extreme winds expected to occur at the site. As such, a reduction coefficient C (0.75 < C < 1) is incorporated in Equation 22.56.

For a linear fundamental mode shape, the peak torsional induced horizontal accelerations at the top of the building at a distance ''a" from the elastic center is given by (Greig 1980)

where 6 is the peak angular acceleration, pb is the mass density of the building, B and D are the breadth and depth of the building, and rm is the radius of gyration. For a rectangular building with uniform mass density rm = 13 (B2 + D2) (22.62)

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