Page 64 - Advanced Design Examples of Seismic Retrofit of Structures

56 Advanced Design Examples of Seismic Retrofit of Structures

W i h k i Q E
F UFi ¼ X n k (2.9)
W j h C 1 C 2 J
j¼1 j
where J ¼force-delivery reduction factor, greater than or equal to 1.0, taken as
the smallest DCR of the components in the load path delivering force to the
component in question. Alternatively, values of J equal to 2.0 for a high level
of seismicity, 1.5 for a moderate level of seismicity, and 1.0 for a low level of
seismicity shall be permitted where not based on calculated DCRs. In any case
where the forces contributing to Q UF are delivered by components of the
seismic-force-resisting system that remain elastic, J shall be taken as 1.0 [2].
In this example, this factor is conservatively assumed to be 2.0, based on the
fact the considered building is located in Tehran, which has a high level of
seismicity.
Other parameters in the equation above have already been defined in Eqs.
(2.8) and (2.1).
For the floor and the first stories, we have:
1,012,585 3 2,156,407
F UF1 ¼ ¼ 278Ton
1,012,585 3 + 843,386 6:3 1:41 1 2
843,386 6:3 2,156,407
F UF2 ¼ ¼ 487Ton
1,012,585 3 + 843,386 6:3 1:41 1 2

2.7.3 Horizontal Distribution of Demand Forces
Once the vertical distribution of the total demand force has been determined,
the story demand forces should be distributed between the structural compo-
nents in that particular story. The diaphragm’s rigidity directly influences the
distribution of the story demand, that is, the story shear force is distributed
stiffness-proportionally when the diaphragm is rigid. For flexible diaphragms,
each structural component (load-bearing wall in this example) receives a seis-
mic force based on its seismic mass. When calculating the horizontal distri-
bution of demand forces for rigid diaphragms, story torsion caused by
eccentricity of the center of rigidity with respect to the center of mass should
be considered. For that purpose, the coordinates of these two centers have to
be determined.

2.7.3.1 Rigid Diaphragms
Determination of Center of Mass
The position in which the resultant of the total seismic demands in each story
acting on all the structural components in that particular story can be substituted
is called center of mass. The mass of the diaphragm and half of walls’ height