---

For calculating the natural frequency of structures such as buildings, chimneys, bridges and silos appropriate analytical

formulas exist. However, in the case of retaining walls undergoing the soil pressure at one side, calculating the natural frequency

is not a straightforward task and requires the effects of soil-structure interactions to be considered. By modeling the soil as series

of linear springs, a new formulation is presented in this article, to calculate the natural frequency of retaining walls. This formula

considers the vertical cross sectional width change, and hence, enables us to calculating the natural frequency of retaining walls

with different types of backfill. The geometrical properties of the retaining walls and its bending rigidity together with the soil’s

modulus of elasticity and its Poisson’s ratio are the most important parameters to calculate. A comparison of the results for

retaining walls with constant cross section obtained from the suggested method with those of the software analyses was carried

out and good agreement was detected. A second comparison of the results with those of other researchers revealed that the natural

frequency of flexible retaining wall is an upper bound for natural frequency of rigid walls. The Selected shape function is also

very close to the real shape mode.

---

In this paper, an approximate method is proposed for determining sway of multistory RC buildings subjected to various types of lateral loads. The calculation of both fundamental period and stability index in RC building requires the sway term at each story level. Using approximate method design engineers can estimate sway terms at each story level. The developed analytical expressions are inserted into fundamental period and stability index equations to replace the sway terms, which yields modified equations for fundamental period and stability index without any sway terms. It is fairly easier to employ these equations developed by eliminating all sway terms. Results obtained from the equations are remarkably close to those generated by the related computer program. Consequently, design engineers can reliably use the simple equations to calculate stability index and fundamental period, which enables the determination of these parameters without referring to the complex sway terms. The capability and accuracy of the proposed equations are demonstrated by a numerical example in which computer program results are compared with the proposed methodology.