Page 238 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Steel Frame Building With Masonry Infill Walls Chapter 4 231

where:
V¼pseudo-lateral force based on Eq. (4.18); and
C vx ¼vertical distribution factor;
k¼2.0 for T 2.5s, 1.0 for T 0.5s, and 0.5 T+0.75 for 0.5<T<2.5s;
w i ¼portion of the effective seismic weight W located on or assigned to
level i;
w x ¼portion of the effective seismic weight W located on or assigned to
level x;
h i ¼height from the base to level i; and
h x ¼height from the base to level x.

Applicability of Linear Static Procedure
According to ASCE 41 [1], linear procedures are appropriate where the
expected level of nonlinearity is low. This is measured by component demand
capacity ratios (DCRs) of less than 2.0. As is shown in Section “The Results,”
most of the components’ DCRs in the example buildings are larger than 2.0.
However, in a case in which the DCR of even a single component is larger than
2.0, the LSP can still be utilized if at least two of the conditions below are met.

Irregularity
In-Plane Discontinuity. An in-plane discontinuity irregularity shall be con-
sideredtoexistinanyprimaryelementofthelateral-force-resistingsystem wher-
everalateral-force-resistingelementispresentinonestory,butdoesnotcontinue
or is offset within the plane of the element in the story immediately below.
Out-of-Plane Discontinuity. An out-of-plane discontinuity irregularity
shall be considered to exist in any primary element of the lateral-force-resisting
system where an element in one story is offset out-of-plane relative to that ele-
ment in an adjacent story.
Weak Story. A weak story irregularity shall be considered to exist in any
direction of the building if the ratio of the average shear DCRs of any story
to that of an adjacent story in the same direction exceeds 125%. The average
DCR of a story shall be calculated by Eq. (4.25):
n
X
DCR i V i
1
DCR ¼ n (4.25)
X
V i
1
where:
DCR ¼average DCR for the story;
DCR i ¼critical action DCR for element i of the story;
V i ¼total calculated lateral shear force in an element i due to earthquake
response, assuming that the structure remains elastic; and
n ¼total number of elements in the story.