Issue 59
J. W. S. Brito et alii, Frattura ed Integrità Strutturale, 59 (2022) 326-343; DOI: 10.3221/IGF-ESIS.59.22
stFloor
1
m N
TMD
k 1,1 d
1 k k
k
k
k
k
0
0
0
0
0
di
d
dm
2
,1
2
2,1
,1
i
1
stFloor
2
m N
TMD
k 1,2 d
k
k k
k
k
k
0
0
0
0
0
di
d
dm
2
2
3
,2
2,2
,2
i
1
stFloor n TMD
m N
k
k
k
0
0
0
0
0
0
0
0
n
, di n
, dm n
i
1
k k
k
0 0
0 0
0
0 0
0 0
0 0
0 0
0 0
K
d
d
1,1
1,1
k
0
d
d
2
,1
2,1
k
k
0
0 0 0
0 0 0
0 0 0
0
0 0
0 0 0
0 0 0
dm
dm
,1
,1
k k
k
0 0
0 0
d
d
1,2
1,2
k
0
d
d
2,2
2,2
k
k
0 0
0
0 0
0 0
0 0
0 0
0 0
0
dm
dm
,2
,2
(4)
k
k
0
0
, dm n
, dm n
P ROPOSED METHODOLOGY
Analyzed Structure he structural model is a 42-story reinforced concrete buildong, ν = 0.2, p = 2500 kg/m³, and modulus of elasticity calculated in accordance with [20]. The total height of the structure is 105.38 meters, with 324 bars, modeled in Octave using the 2D frame element with 2 nodes and 3 degrees of freedom (DOFs) for each node. There are 185 nodes and therefore 555 DOFs. The sections of the bars are rectangular, with dimensions as explained in Tab. 1. T
Bars
Dimensions (cm)
Areas (m²)
Inertia Moment (m 4 )
1 to 36 / 145 to 180
100x25
0.25
1.30e-4
37 to 72 / 109 to 144
25x120
0.30
0.036
73 to 108
40x157
0.628
0.129
181 to 324
12x65
0.078
2.75e-3
Table 1: Geometrical properties of the structure
The structure is shown in Fig. 3. The dimensions are in meters (m). The Rayleigh Damping Matrix is used, where the critical damping ratio ( ζ ) was specified as 1% for the first two modes of vibration. The mass matrix of the structure is consistent where for each element, the mass and stiffness matrix in the local system, is represented by M L and K L
0 0 156 22 0 54 13 0 22 4 0 13 3 70 0 0 140 0 0 0 54 13 0 156 22 0 13 3 0 22 4 L L L L L L L L L L L L 2 2 140 0 0 70 0
AL
L m
(5)
420
330
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