Page 89 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Two-Story Unreinforced Masonry Building Chapter 2 81

Q CE ¼expected strength of component deformation-controlled action of an
element at the deformation level under consideration which is determined
according to Section 2.7.5.1; and
κ ¼knowledge factor defined in according to Table 2.12 which is assumed
to be 1.0 because usual level of knowledge exists about the example buildings
including material properties, as-built sketches, etc. This factor is used to
account for uncertainty in the collection of as-built data, a knowledge factor,
κ, shall be selected considering the selected performance objective, analysis
procedure, and data collection process.
It is noteworthy that only Code 360 considers the effects if confining ties in
capacity calculation for URM walls, whereas the previous version of this code,
that is, Code 360-2006, does not take this effect into account. ASCE 41 is also
silent about confined masonry walls.

2.7.6.2 Force-Controlled Actions
Acceptance criteria for force-controlled actions in components shall satisfy
Eq. (2.39):
κQ CL > Q UF (2.39)

where Q CL ¼lower-bound strength of a force-controlled action of an element at
the deformation level under consideration which is determined according to
Section 2.7.5.2.
Code 360 allows increasing the lower-bound strength of a force-controlled
action for unreinforced confined masonry walls by 20% [10].

2.7.7 Final Results and Conclusions
The values of Q CE and Q CL , together with their vulnerability, failure mode, and
their DCR for the walls in the example building, are presented in Appendix
Tables A-C-2-11, A-C-2-12, and A-C-2-13, for the example building with a
rigid diaphragm, with a flexible diaphragm having horizontal ties, and with a
flexible diaphragm without horizontal ties, respectively. As an example, the
related calculations of Wall#1 on the first row of these tables are as follows.
The vulnerability of the walls of the example building in the two stories
under various diaphragm conditions are shown in Figs. 2.40–2.42. In these
figures, the vulnerable walls are shown in blue. Also, the failure mode and their
DCR are also shown besides each wall, with “B” and “R” indicating bed-joint
sliding and rocking failure modes, respectively. As can be seen, the example
building is vulnerable in all the considered cases. As an example, calculations
of DCR for different failure modes of Wall#1 are presented here.