2sin
5.3.3 Modal Analysis of Numerical Models
Modal analyses of all the SAP models with different case of wall openings described in subsection 5.3.3 have been carried out and the frequencies along the direction of excitation have been presented in Table 5.10. It may be mentioned that the computed modal
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frequencies for all the cases of wall openings of all the three test models are in good agreement with identified frequencies of their respective test models.
Table 5.10 Natural frequencies corresponding to mode shapes of different numerical models with different cases of wall openings
Test Models
Cases of Wall Opening
Frequency (rad/sec) Error in Frequency ( in %) for First
Mode
Second Mode
First Mode Second Mode
Model W-I
Case-1 49.15 209.69 6.96 2.49
Case-2 48.55 191.97 7.25 2.77
Case-3 47.83 177.57 6.86 2.92
Case-4 46.64 158.94 5.88 3.30
Case-5 45.69 148.14 4.75 2.71
Case-6 45.00 142.08 5.34 3.90
Case-7 43.74 133.00 4.22 2.90
Case-8 40.14 117.85 2.27 3.87
Model W-II
Case-1 67.55 218.26 3.29 4.01
Case-2 65.82 200.11 0.11 2.81
Case-3 64.05 186.38 1.03 1.02
Case-4 60.87 169.19 1.20 0.14
Case-5 58.38 159.69 2.06 2.17
Case-6 56.67 154.41 1.32 1.56
Case-7 53.49 146.63 2.45 1.68
Case-8 47.17 135.96 1.77 1.19
Model W- III
Case-1 67.16 221.13 2.00 2.52
Case-2 65.31 202.69 1.23 2.06
Case-3 63.48 188.87 1.20 1.23
Case-4 60.21 171.73 1.43 0.19
Case-5 57.68 162.31 0.63 0.55
Case-6 55.95 157.10 0.94 0.17
Case-7 52.77 149.42 0.63 0.68
Case-8 46.55 138.91 2.39 4.82
The computed modal frequencies for all the cases of wall openings of Model W-I as shown in Table 5.10 are comparable with the corresponding identified frequencies of Model W-I as furnished in Table 5.3. Similar observations have also been drawn for test Models W-II and W-III.
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5.3.4 Comparison of Dynamic Responses of Numerical Models with Laboratory Model based results
Time history analyses of the numerical models with infill walls have been carried out with recorded table acceleration histories acquired during shake table test as input. Floor acceleration responses have been acquired from each test models and are as shown in Fig.
5.20.
(a) At first floor of Model W-I (b) At roof of Model W-I
(a) At first floor of Model W-II (b) At roof of Model W-II
(a) At first floor of Model W-III (b) At roof of Model W-III
Fig. 5.20 Computed floor acceleration time histories under El Centro (1940): Comp - 180 earthquake component
0 5 10 15
-0.04 -0.02 0 0.02
Time in Sec Acceleration in g RMS = 0.010
0 5 10 15
-0.05 0 0.05
Time in Sec
Acceleration in g
RMS = 0.012
0 5 10 15
-0.05 0 0.05
Time in Sec
Acceleration in g RMS = 0.013
0 5 10 15
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
Time in Sec
Acceleration in g RMS = 0.016
0 5 10 15
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
Time in Sec
Acceleration in g RMS = 0.013
0 5 10 15
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
Time in Sec
Acceleration in g RMS = 0.017
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The root-mean-square (RMS) values of acceleration amplitudes of dynamic responses at first and roof floor levels of the numerical models subjected table acceleration due to scaled El Centro (1940): Comp - 180 earthquake motion as input excitation have also been estimated and are shown in Fig.5.21.
Comparison of Fig. 5.21 and 5.5, established a good agreement in the RMS values of acceleration histories obtained from scaled test models and the numerical models. Further, the peak values of floor accelerations are also presented in the Table 5.11 for comparison of the same with peak floor accelerations of the corresponding numerical models.
Table 5.11 Peak values of floor accelerations of different models
Models Peak floor accelerations (g)
First floor Roof floor
Experimental Numerical Experimental Numerical
Model W-I 0.040 0.040 0.048 0.049
Model W-II 0.048 0.048 0.059 0.059
Model W-III 0.051 0.051 0.061 0.061
Peak values acceleration histories established a good agreement between scale test models and corresponding numerical models. Thus, the numerically simulated models are appropriate representations of their respective laboratory models.
5.3.5 Comparison of Modal Parameters from Numerical Models with Equivalent Diagonal Strut Based on Different Recommendations
The stiffness of the infill wall have been observed to be different for different analogies of diagonal strut recommended by different investigators as observed from the Table 5.9. The infill walls in the first storey of the test Model W-I have been modeled separately by GAP element using recommendations mentioned in Table 5.9 and proposed expression. The numerical models with GAP element representing different diagonal strut have been
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analyzed for evaluating modal frequencies considering 5% proportional damping. The modal frequencies corresponding to the mode shapes in the shorter direction of the model have been extracted and are furnished in Table 5.12. Modal frequencies in Table 5.12 indicate that modal frequencies corresponding to different diagonal strut analogies adopted for modeling GAP element are different from method to method. The modal frequencies of models corresponding to approach FEMA 306 and proposed correlation are close to each other.
Table 5.12 Modal frequencies of the numerical model of test Model W-I for different recommendations of diagonal strut
Diagonal Strut Analogies Modal Frequencies (rad/sec) First Mode Second Mode
Paulay and Priestly (P&P) 46.69 248.40
Stafford-Smith (S-S) 47.12 282.36
Original Stafford-Smith & Carter (OSSC) 46.34 227.20
IITK-GSDMA 46.91 264.63
FEMA 306 45.54 193.81
Proposed 45.82 203.87
5.4 VALIDATION OF PROPOSED CORRELATIONS FOR WALL
CONTRIBUTION
The study related to the contribution of infill wall to the lateral stiffness of scaled building models has been carried out in the previous section. Numerical modeling of diagonal strut in a full size building that corresponds to 1/5 scale laboratory test Model I has been carried out to examine whether the proposed expressions represented by Eq. 5.2 - 5.4 will be appropriate for full size building. Similar material properties as those for the laboratory test Model I have been considered to model full size building and infill walls on first storey in the shorter direction of the building. Different cases of wall openings have also been considered and natural frequencies have been evaluated through modal analysis
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considering 5% proportional damping. Evaluated modal frequencies corresponding to the mode shape in the shorter direction of the building have been scaled as per similitude requirement. The scaled modal frequencies of the full size building with different sizes of opening have been compared with the corresponding modal frequencies of the model of the test Model I. These are furnished in Table 5.13.
Table 5.13 Modal analysis results of prototype building and corresponding scaled building model
Wall Opening
Frequency (rad/sec)
First Mode Second Mode
Test Model W-I
Prototype Model
Prototype Model x
S
Test Model W-I
Prototype Model
Prototype Model x
S
Case-1 49.15 22.03 49.26 209.69 93.85 209.85
Case-2 48.55 21.73 48.60 191.97 85.89 192.05
Case-3 47.83 21.42 47.89 177.57 79.43 177.60
Case-4 46.64 20.92 46.78 158.94 71.12 159.03
Case-5 45.69 20.45 45.72 148.14 66.29 148.23
Case-6 45.00 20.14 45.03 142.08 63.56 142.13
Case-7 43.74 19.57 43.76 133.00 59.52 133.10
Case-8 39.14 17.52 39.17 117.85 52.73 117.90
A very good agreement may be observed between scaled natural frequencies of the full size building model with the corresponding modal frequencies of numerical model of the scaled test model. Thus, it may be inferred that though the correlations related to contribution of infill wall have been developed based on scaled laboratory models, these expressions are applicable to full size buildings without any further correction to address size effect related issues.