Lumped mass model

1
Lumped mass model
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
2
Natural Frequencies
EIGEN VALUES
MODAL ANALSYS
EIGEN VECTORS
Mode Shapes
3
Mode 1 Freq. 1.44119 Hz Period
0.69387 sec Mode shape 0 0.1513 0.368
7 0.5796 0.7631 0.9059 1
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
4
Mode 2 Freq. 4.51039 Hz Period
0.22171 sec Mode shape 0 -0.5293 -1
-0.9604 -0.4110 0.36629 0.98395
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
5
Mode 3 Freq. 8.09847 Hz Period
0.12348 sec Mode shape 0 0.82371 0.86
138 -0.23909 -1 -0.38232 0.8038
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
6
Mode 4 Freq. 11.78133 Hz Period
0.08488 sec Mode shape 0 -1 -0.04656
0.99903 -0.2653 -0.90232 0.60635
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
7
Mode 5 Freq. 15.30924 Hz Period
0.06532 sec Mode shape 0 1 -0.8364
0.02677 0.8128 -0.98924 0.41538
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
8
Modes I II III IV V
Levels Mode Shapes
1 0 0 0 0 0
2 0.151 -0.53 0.824 -1 1
3 0.369 -1 0.861 -0.047 -0.836
4 0.58 -0.96 -0.24 0.999 0.027
5 0.763 -0.41 -1 -0.265 0.813
6 0.906 0.366 -0.38 -0.902 -0.989
7 1 0.984 0.804 0.606 0.415

Period (sec) 0.694 0.222 0.123 0.085 0.065
Freq(Hz) 1.441 4.51 8.098 11.78 15.31
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
9
Check Mass Participation (7.8.4.5(a),
IS1893(Part 1)-2002)
For kth mode,
Where, n no. of levels m no. of modes
Mode I II III IV V
Mk(kN) 115.5 16.31 5.424 2.686 1.237
Participating mass 115.516.315.4242.6861.237
141.183kN Total mass 23.57 x 6 141.42
kN Mass participation 100x141.183/141.42
99.8326
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
10
Calculate Mode Participation factors (7.8.4.5(b),
IS1893(Part 1)-2002)
For kth mode,
Where, n no. of levels
Mode I II III IV V
Pk 1.30049 -0.44635 0.26529 -0.18718 0.12223
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
11
Calculate Mode Participation factors




x 0.12223

x -0.18718
x 0.26529
x -0.44635
x 1.30049
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
12
Calculate Mode Participation factors

(Had all the mode shapes been utilized)
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
13
Modes I II III IV V
Fs
1 0 0 0 0 0
2 0.1513 -0.5293 0.8237 -1 1
3 0.3688 -1 0.8614 -0.0466 -0.8364
4 0.5796 -0.9604 -0.239 0.999 0.0268
5 0.7631 -0.4111 -1 -0.2653 0.8128
6 0.906 0.3663 -0.382 -0.9023 -0.9892
7 1 0.984 0.8038 0.6064 0.4154

W
0
23.57
23.57
23.57
23.57
23.57
23.57
WF
0 0 0 0 0
3.566 -12.48 19.415 -23.57 23.57
8.692 -23.57 20.303 -1.097 -19.71
13.66 -22.64 -5.6354 23.547 0.631
17.99 -9.689 -23.57 -6.253 19.16
21.35 8.6335 -9.0113 -21.27 -23.32
23.57 23.192 18.946 14.292 9.791
88.83 -36.55 20.447 -14.35 10.12
WF2
0 0 0 0 0
0.54 6.6043 15.992 23.57 23.57
3.206 23.57 17.488 0.0511 16.49
7.919 21.74 1.3474 23.524 0.017
13.73 3.9826 23.57 1.659 15.57
19.34 3.1623 3.4452 19.19 23.07
23.57 22.819 15.228 8.6658 4.067
68.3 81.879 77.072 76.66 82.78
Mk 115.5 16.313 5.4243 2.6859 1.2369
Pk 1.300 -0.4464 0.2653 -0.1872 0.1222
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
14
Period 0.693 0.221 0.123 0.084 0.065
Sa/g 1.4411 2.5 2.5 1.1273 1.0979
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
15
Calculate Design horizontal seismic coefficient
Z Zone factor 0.16 I Importance factor
1 R Response reduction coefficient 3
Period 0.693 0.221 0.123 0.084 0.065
Sa/g 1.441 2.5 2.5 1.1273 1.0979
Ah 0.0384 0.0667 0.0667 0.0300 0.0292
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
16
Calculate horizontal force due to each mode
0
0.178
0.434
0.683
0.899
1.067
1.178
0
0.151
0.369
0.58
0.763
0.906
1
0
23.57
23.57
23.57
23.57
23.57
23.57
Eg - for mode 1

kN
0.0384 x 1.30049 x

Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building
17
Calculate horizontal force due to each mode and
combined
Mode I II III IV V
Levels Qik (kN)
1 0 0 0 0 0
2 0.178 0.371 0.343 0.133 0.084
3 0.434 0.701 0.359 0.006 -0.071
4 0.683 0.674 -0.1 -0.133 0.002
5 0.899 0.288 -0.42 0.035 0.069
6 1.067 -0.26 -0.16 0.12 -0.083
7 1.178 -0.69 0.335 -0.08 0.035
SRSS
0
0.559
0.903
0.973
1.035
1.119
1.409
Eg - for level 7
SRSS v(1.178)2 (-0.69)2 (0.335)2
(-0.08)2 (0.035)2 1.409
Presented by Rahul Leslie
Seismic Analysis of Multi-storied RC Building