Geology Reference
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Table 2. The worst-out-best-in method
Table 3. The exhaustive-single-point substitution
search method
Step by Step Procedure
Step 1: Select I 0 (a r vector containing initial configuration
of damper locations obtained by either the sequential search
method or any given pre-design method), stiffness k d and
damping coefficients c d.
Step 2: Assemble A , B , E, E 0 matrices.
Step 3: Assemble the damper matrix G.
Step 4: Evaluate the objective function f 0 , corresponding to the
initial damper configuration I 0.
Step 5: Remove one damper from I 0 and calculate the
objective function f for each of the r configurations of (r-1).
Step 6: Select the worst damper and remove it in order to
produce a configuration I 1 of (r-1) dampers.
Step 7: Try the removed damper at the remaining (n-r) story
units and evaluate the corresponding objective function.
Step 8: The configuration which corresponds to the optimal
objective function, namely f 2 , is denoted by I 2.
Step 9: If f 2 is better than f 0 , the next iteration is started by
I 0 = I 2 and go to step 3.
Instead, if f 0 is better than f 2 , the iteration ends.
Step by Step Procedure
Step 1: Select I 0 (a r vector containing initial configuration
of damper locations obtained by either the sequential search
method or any given pre-design method), stiffness k d and
damping coefficients c d .
Step 2: Assemble A , B , E, E 0 matrices.
Step 3: Assemble the damper matrix G .
Step 4: Evaluate the objective function f 0 , corresponding to the
initial damper configuration I 0 .
Step 5: Remove one damper from I 0 and place it at each of
(n-r) unused locations (not included in I 0 ).
Step 6: Evaluate the objective function f for each of the (n-r)
r configurations.
Step 7: Label the objective function with best f as f 1 and the
corresponding configuration as I 1 .
Step 8: If f 1 is better than f 0 , the next iteration is started by
I 0 = I 1 and go to step 3.
Instead, if f 0 is better than f 1 , the iteration ends.
considering the additional stiffness of the
equivalent braces. For preliminary design
it is assumed to have one damper for story;
4. 4.Modal analysis of the building is obtained
using the stiffness matrix obtained from
point 3 and a new value of the fundamental
period T 1f,trial is obtained;
5. The new stiffness values of the braced
structures are evaluated with the following
expression:
PRELIMINARY DESIGN
The preliminary design of viscous dampers of
the framed structure can be done starting from
the dynamic characteristics of the unbraced
building and in particular from the fundamental
period T 1U . The approximate method is based on
the following steps:
1. The damping ratio ξ 1 related to the first mode
T 1u of the unbraced structures is selected.
k
0
,
trial
k
=
(23)
1
,
trial
2
2
T
T
2. The fundamental period of the braced struc-
ture with fictitious springs is obtained using
the following expression:
1
f
1
f trial
,
1
2
2
T
T
1
f
1
u
6. Repeat step 4 and 5 iteratively until the i th
iteration satisfies the condition
k
T
T
=
1
u
(22)
1
f
ξ
+
2
1
1 . A single
iteration is sufficient, because the stiffness
variation is linearly proportional to the square
of the period of the building;
1
k
e T
T
1
i trial
,
i
,
trial
i f trial
,
i
f trial
,
3. An initial stiffness value k o_trial of the fictitious
springs equivalent t oe the viscous dampers is
assumed. A new stiffness matrix is obtained
 
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