Page 69 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Two-Story Unreinforced Masonry Building Chapter 2 61

FIG. 2.33 Geometrical parameters of piers.

Modification of the Stiffness Relations for Piers in Single-Story Buildings
In order to consider the flexibility of OKB which is frequently found in masonry
buildings, the effective height of the pier is defined as Eq. (2.12). This param-
eter is used for determination of stiffness of piers in single-story masonry build-
ings according to Eq. (2.13):
H o
H e ¼ H w + (2.12)
2
1
K ¼ 3 (2.13)
H
e H e
+
3E m I g A v G m
where:
H w ¼pier height; and
H o ¼OKB height.
In order to verify the accuracy of the proposed equation, several cases with
various pier lengths (L w in Fig. 2.34), OKB’s length (L o ) and OKB’s height (H o )
are considered. These cases are modeled in general purpose finite element soft-
ware Abaqus [13], and the resulted set of stiffness is compared with that of the
proposed Eq. (2.13), which is shown in Fig. 2.35. As can be seen, using ASCE
41 results in considerable overestimation of the pier’s stiffness because this
equation cannot take the effects of the OKB’s flexibility into account. However,
the proposed equation can accurately predict the stiffness of such piers under
different conditions.