Optimal Performance- Based Seismic Design - Structural Seismic Design Optimization and Earthquake Engineering - page 179

The Vertical Distribution of Lateral Load usually more accurate than those predicted by the

linear static analysis; accordingly compared to the
first method, there are fewer limitations on use
of linear dynamic analysis. Whenever applicable,
either of the response spectrum method or time
history method may be used for linear dynamic
analysis.
When the linear type of analysis is used for
demand evaluation, the structure is loaded to the
extent that reaches the target displacement. At
this stage, every structural component experi-
ences a deformation and corresponding internal
force. All structural components have to be
checked against acceptance criteria pertaining
to the desired performance level. Discussion
on “how the acceptance criteria are obtained”
is out of the scope of this chapter, but it worth
knowing that these criteria are specified using
actual laboratory test results, supplemented by
the engineering judgment of various development
teams of FEMA 1 . Acceptance criteria are different
for deformation-controlled (ductile) and force-
controlled (inductile) members. They also vary
depending on the type of structural component,
(i.e., beam, column etc.), its material, physical
properties, and performance level. Acceptance
criteria are given differently for the results of lin-
ear and nonlinear type of structural analyses. For
forced controlled members, depending on the type
of structural element and the performance level
in question, if a linear type of analysis is used,
the internal force of member due to lateral load is
multiplied by a reduction factor, to rationalize it
for the given performance level. Alternatively for
deformation controlled components, the strength
of structural component is multiplied by an m-
factor and checked against design forces due
to the gravity and earthquake loads. FEMA356
(2000) recommends the following formula for
deformation-controlled components:

To perform a linear or nonlinear static analysis,
the distribution of base shear or pseudo-lateral
force over the storys in the vertical direction of a
building, has to be such applied that it simulates
the earthquake effect accounting for dynamic
characteristics. According to ASCE41, the base
shear should be vertically distributed according
to the following equations.

F = C V (1)

x vx

k

w h

C =

x x

V (2)

vx n

∑ 1

k

w h

i i

i

=

where

C vx = vertical distribution factor;

k = 2.0 for T ≥ 2.5 sec; k = 1.0 for T≤ 0.5 sec
and linear interpolation shall be used to calcu-
late values of k for intermediate values of T.

V = Base shear or pseudo-lateral force;

w i = portion of the effective seismic weight W
located on or assigned to floor level i;

w x = portion of the effective seismic weight W
located on or assigned to floor level x;

h i = height from the base to floor level i; and h x
= height from the base to floor level x.

Linear Analyses

Among the above four methods, the first one is the
most accessible method for engineers. However,
there are some limitations on its use for irregular
structures. The distribution of demands predicted
by a linear dynamic analysis (the 2 nd method), is

mkQ ≥ Q (3)

CE UD