Frequency Analysis of Thin-Walled Shear Walls

The coupled equations of motion for a thin-walled shear wall of monosymmetric cross section are presented based on thin-walled beam theory. An exact coupled solution is obtained by simultaneously solving a coupled polynomial and set of homogeneous linear algebraic equations, in order to obtain the natural frequencies and mode shapes. An approximate solution is obtained by using the uncoupled flexural and torsional mode shapes in applying the virtual work principle in order to obtain the appropriate eigenvalues. A comparison of the exact and approximate solutions for a single shear wall of E-shaped cross section indicates extremely close agreement for both frequencies and mode shapes. The approximate solution requires considerably less computer time than the exact solution and consequently provides a valuable alternative.