Page 71 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Two-Story Unreinforced Masonry Building Chapter 2 63

Modification of Stiffness Relations for Piers in Multistory Buildings
Depending on the story, the piers in multistory masonry buildings have different
equations for their stiffness. This categorization is because of the effects of the
flexibility of the walls in lower stories which affects the stiffness of the wall in
the upper stories.
Piers in the Floor Story Similar to the definition of the “effective height” in
“Modification of the Stiffness Relations for Piers in Single-Story Buildings”
section, the “gross story height” is introduced in Eq. (2.14) to consider the effect
of OKB on the stiffness of piers in the floor story which is according to Eq.
(2.15). A comparison of stiffness of floor story piers in multistory masonry
buildings is made between the results of the proposed equation, the ASCE
41 equation, and the numerical simulation shown in Fig. 2.36. Again, the results
of the proposed equation are in close correlation with those of the numerical
simulation.

(2.14)
H s ¼ H w + H o
1
K ¼ (2.15)
H 3
s H s
+
12E m I g A v G m
Piers Above the Floor Story The effect of the flexibility of the piers in the
lower adjacent story is considered by two additional terms in the proposed equa-
tion in (2.16). One of these terms accounts for the flexural displacement of the

80
ASCE41
Proposed

60
K_Formula (MN/m) 40

20

0
0 20 40 60 80
K_numerical (MN/m)
FIG. 2.36 Comparison of stiffness of piers above the floor story in multistory masonry buildings.