The Staad Pro carries out the outcomes and describes the assessment of the M1, M2, and M3 models. To analyze the three modeled RC frames, M1, M2, and M3, by the time-history method, the following results have been obtained for the dynamic response of the structures modeled.
4.1 Time history Displacement Calculation
In all the models, the front frame has been considered an authentic replica of all the structures in its back, with bottom coordinates as x=0, y =0; x=12, y=0. The acceleration generated under zone-IV, which is responsible for displacement in the structure, has been tabulated in Table 4.
Table 4. Time history acceleration data for zone-IV
Sr. No.
|
Time (sec)
|
Acceleration(m/s2)
|
1
|
0
|
0.0063
|
2
|
0.02
|
0.00364
|
3
|
0.04
|
0.00099
|
4
|
0.06
|
0.00428
|
5
|
0.08
|
0.00758
|
6
|
0.1
|
0.01087
|
7
|
0.12
|
0.00682
|
8
|
0.14
|
0.00277
|
9
|
0.16
|
-0.00128
|
10
|
0.18
|
0.00368
|
Table 5.Time history displacement of Model M1(Geometrically less irregular structure)
Floors
|
X-Displacement (E-3 mm)
|
|
1
|
Node no.
|
6
|
7
|
8
|
9
|
10
|
|
Upper
|
11.6
|
11.6
|
11.6
|
11.6
|
11.6
|
|
lower
|
-12.6
|
-12.6
|
-12.6
|
-12.6
|
-12.6
|
2
|
Node no.
|
11
|
12
|
13
|
14
|
15
|
|
Upper
|
27.4
|
27.4
|
27.4
|
27.4
|
27.5
|
|
lower
|
-29.2
|
-29.3
|
-29.3
|
-29.3
|
-29.3
|
3
|
Node no.
|
16
|
17
|
18
|
19
|
20
|
|
upper
|
42.3
|
42.3
|
42.3
|
42.1
|
42
|
|
lower
|
-44.9
|
-44.9
|
-44.8
|
-44.7
|
-44.6
|
4
|
Node no.
|
21
|
22
|
23
|
24
|
|
|
upper
|
57.8
|
57.7
|
57.7
|
57.7
|
|
|
lower
|
-62.8
|
-62.8
|
-62.8
|
-62.7
|
|
5
|
Node no.
|
26
|
27
|
28
|
29
|
|
|
upper
|
72.4
|
72.4
|
72.4
|
72.4
|
|
|
lower
|
-81.8
|
-81.8
|
-81.8
|
-81.8
|
|
6
|
Node no.
|
31
|
32
|
33
|
34
|
|
|
upper
|
85.4
|
85.4
|
85.4
|
85.4
|
|
|
lower
|
-100
|
-100
|
-100
|
-100
|
|
7
|
Node no.
|
36
|
37
|
38
|
39
|
|
|
upper
|
96.2
|
96.2
|
96.2
|
96.2
|
|
|
lower
|
-116
|
-116
|
-116
|
-116
|
|
8
|
Node no.
|
41
|
42
|
43
|
44
|
|
|
upper
|
103
|
103
|
103
|
103
|
|
|
lower
|
-127
|
-127
|
-127
|
-127
|
|
The data generated from the model M1 have been tabulated in Table 5, which shows the upper values exhibit the displacement along the X-axis in the (+) direction. However, the lower displacement along the nodes indicates displacement in the (–) X-direction. Figure 4(a) shows that on the 1st floor, the displacement is 11.6 E-3 mm which further increases up to the 8th floor with the displacement of 103 E-3 mm in the upper direction. However, Figure 4(b) exhibits the displacement along the lower path, which is 12.6 E-3 mm at the 1st-floor level and increases up to 8th-floor displacement is 127 E-3 mm. The displacement increases with the order of increment up floors. This exhibits that the lateral force increases floor-wise in an upward direction. It has been observed that there is a change in displacement one story up and one level down on floor 3. Therefore floors 2 and 3 are affected by the geometric irregularity created on floor 3.
Table 6. Time history displacement for model M2 (Geometrically more irregular structure)
Floors
|
X-Displacement (E-3 mm)
|
|
1
|
Node no.
|
6
|
7
|
8
|
9
|
10
|
|
Upper
|
17.5
|
17.5
|
17.5
|
17.5
|
17.5
|
|
lower
|
-20.7
|
-20.7
|
-20.8
|
-20.8
|
-20.8
|
2
|
Node no.
|
11
|
12
|
13
|
14
|
15
|
|
Upper
|
41.8
|
41.8
|
41.7
|
41.4
|
41.2
|
|
lower
|
-47.9
|
-47.9
|
-47.8
|
-47.6
|
-47.4
|
3
|
Node no.
|
16
|
17
|
18
|
19
|
|
|
upper
|
70.7
|
70.7
|
70.7
|
70.6
|
|
|
lower
|
-79.8
|
-79.8
|
-79.8
|
-79.8
|
|
4
|
Node no.
|
21
|
22
|
23
|
24
|
|
|
upper
|
101
|
101
|
101
|
101
|
|
|
lower
|
-114
|
-114
|
-114
|
-114
|
|
5
|
Node no.
|
26
|
27
|
28
|
29
|
|
|
upper
|
131
|
131
|
131
|
131
|
|
|
lower
|
-150
|
-150
|
-150
|
-150
|
|
6
|
Node no.
|
31
|
32
|
33
|
34
|
|
|
upper
|
158
|
158
|
158
|
158
|
|
|
lower
|
-185
|
-185
|
-185
|
-185
|
|
7
|
Node no.
|
36
|
37
|
38
|
39
|
|
|
upper
|
180
|
180
|
180
|
180
|
|
|
lower
|
-214
|
-214
|
-214
|
-214
|
|
8
|
Node no.
|
41
|
42
|
43
|
44
|
|
|
upper
|
195
|
195
|
195
|
195
|
|
|
lower
|
-233
|
-233
|
-233
|
-233
|
|
The displacement increases with the increase of floors. The dynamic response of the lateral force increases floor-wise in the upward direction of the structure. Figure 5(a) shows that the displacement in the upper path on the 1st floor is 17.5 E-3 mm, which further increases up to the 8th story to the extent of 195 E-3 mm, and Figure 5(b) exhibits the displacement in the lower direction on the 1st floor is 20.7 E-3 mm which increases up to 8th story to the extent 233 E-3 mm. The displacement increases with the increase in the height of the frame’s structure. It has been observed that the change in displacement is one story up and one level down on floor 2. Therefore floors 1 and 3 are affected by the geometrical irregularity created on floor 2.
Table 7. Time history displacement for model M3 (Geometrically regular structure)
Floor
|
X-Displacement (E-3 mm)
|
|
1
|
Node no.
|
6
|
7
|
8
|
9
|
10
|
|
Upper
|
16.8
|
16.8
|
16.8
|
16.9
|
16.8
|
|
lower
|
-19.6
|
-19.6
|
-19.6
|
-19.6
|
-19.6
|
2
|
Node no.
|
11
|
12
|
13
|
14
|
15
|
|
Upper
|
41
|
41
|
41
|
41
|
41
|
|
lower
|
-46.7
|
-46.8
|
-46.8
|
-46.8
|
-46.8
|
3
|
Node no.
|
16
|
17
|
18
|
19
|
20
|
|
upper
|
66.1
|
66.1
|
66.1
|
66.1
|
66.1
|
|
lower
|
-75.5
|
-75.5
|
-75.5
|
-75.5
|
-75.5
|
4
|
Node no.
|
21
|
22
|
23
|
24
|
25
|
|
upper
|
91
|
91
|
91
|
91
|
91
|
|
lower
|
-105
|
-105
|
-105
|
-105
|
-105
|
5
|
Node no.
|
26
|
27
|
28
|
29
|
30
|
|
upper
|
115
|
115
|
115
|
115
|
115
|
|
lower
|
-133
|
-133
|
-133
|
-133
|
-133
|
6
|
Node no.
|
31
|
32
|
33
|
34
|
35
|
|
upper
|
136
|
136
|
136
|
136
|
136
|
|
lower
|
-159
|
-159
|
-159
|
-159
|
-159
|
7
|
Node no.
|
36
|
37
|
38
|
39
|
40
|
|
upper
|
153
|
153
|
153
|
153
|
153
|
|
lower
|
-181
|
-181
|
-181
|
-181
|
-181
|
8
|
Node no.
|
41
|
42
|
43
|
44
|
45
|
|
upper
|
164
|
164
|
164
|
164
|
164
|
|
lower
|
-195
|
-195
|
-195
|
-195
|
-195
|
Figure 6(a) shows the ground surface floor-0 displacement is 0, which further increases up to the 8th story to the extent of 164 E-3 mm, and Figure 6(b) exhibits the displacement in the upper direction at 1st floor to the size of 19.6 E-3 mm which increases up to 8th Floor to the magnitude 195 E-3 mm. The displacement increases with the increase of subsequent base upwards, where each floor attains the height of 3.00 m.
4.2 Time-frequency calculation
Figure 7(a) shows the time frequencies mode shape for model M1. However, in Figure 7 (b), there are variations in the frequencies in each mode. In the first Mode, the time frequency is 1.024 Hz, and it is 4.941 Hz in the 8th mode. The frequency increases with the extent to standard mode M3 subsequently. The increase in the frequency concerning the first to the last mode is 382.51% which means the modal frequency in the previous mode is 4.83 times that first mode. The functional relationship of increment in frequency ratio w.r.t 1st-floor for model 1 is shown in Figure 8 (a). However, in Figure 7 (c), there is a variation in the frequencies from the first node to 8 nodes. The frequency varies from 1.013 HZ to 4.921 HZ. The frequency increases with every mode, which means the higher mode has a higher frequency than its lower one. The increase in the frequency from the first to the highest is 385.78 percent. That means the highest modal frequency is 4.86 times the first mode frequency. The functional relationship of increment in frequency ratio w.r.t 1st-floor in model 2 is shown in Figure 8(b). However, In Figure 7(d), there is variation in the frequencies on each floor, which varies from 0.969 HZ to 4.909 HZ from the 1st floor to the top floor. The frequency increases with the increase in the modes. That means the higher method has a higher frequency than its lower one. The increase in the frequency from the first to the highest is 406.60 percent. That means the highest modal frequency is 5.07 times the first mode frequency. The functional relationship of increment in frequency ratio w.r.t 1st-floor in model 3 is shown in Figure 8(c).
4.3 Relationship of frequency ratio
Figure 8 shows the relationship of frequencies ratio concerning the fundamental frequency for models M1, M2, and M3 w.r.t the ground floor.
4.4 Time acceleration calculation
Figure 9(a) describes that time acceleration on the 1st floor is 3.9 E-3 m/s2, further increasing on the up bases and reaching 13.4 E-3 m/s2 on the 8th floor in the upper direction. Figure 9(b) observed acceleration in the lower order of 2.6 E-3 m/s2 to the magnitude of (1st floor), which further increases upto10.8 E-3 m/s2 on the 8th floor. The time acceleration increases with the increase in height, which means that the higher floor will have higher acceleration than the lower ones.
Figure 9 (c) exhibits the time acceleration at a 1st-floor level to the magnitude of 5.84 E-3 m/s2, which further increases on the up floors and reaches 23 E-3 m/s2 on the 8th floor in the upper direction, and Figure 9 (d) exhibits time acceleration to the extent of 4.84 E-3 m/s2 at (1-floor), which increase to 17.5 E-3 m/s2 at 8th floor in the lower direction. The time acceleration increases with the increase in height, which means that the higher floor will have higher acceleration than the lower ones. Figure 9(e) displays the acceleration at the first-floor level (1st floor) to the extent of 5.58 E-3 m/s2, which further increases on the up bases and reaches 17.9 E-3 m/s2 on the 8th floor in the upper direction, and Figure 9(f) show lower direction time acceleration, i.e., 3.94 E-3 m/s2 at (1st floor), which increase 16.2 E-3 m/s2 at 8th floor in the more downward direction. The time acceleration increases with the increase in height, which means that the higher floor will have higher acceleration than the lower ones.
4.5 Time velocity calculation
Figure 10(a) displays the velocity in the upper direction on the 1st floor to the extent of 162 E-3 mm/s and on the 8th floor is 895 E-3 mm/s velocity, and Figure 10(b) shows the velocity in the lower direction on the 1st floor to the extent of 140 E-3 mm/s. On the 8th floor, it is 811 E-3 mm/s. In Figure 10(c), the velocity (upper) on the 1st-floor magnitude of 282 E-3 mm/s, and at the last base (8th), it is 1480 E-3 mm/s, and Figure 10(d) shows the lower direction velocity at 1st floor, i.e., 208 E-3 mm/s and at 8th floor, velocity is 1450 E-3 mm/s. The time velocity has different behavior on floors 2 to 4. As discussed, the geometric irregularity has affected a change in velocity one foot up, and one is floor down.
Figure 10(e) shows the velocity in the upper direction on the 1st floor to 255 E-3 mm/s. At the last base (8th), it is 1130 E-3 mm/s, and Figure 10(f) shows the lower direction the velocity on the 1st floor is 213 E-3 mm/s, and on the 8th floor, velocity is 1160 E-3 mm/s in the more downward movement. There is variation in time acceleration at floors/stories. This is probably due to a change in acceleration from ground to first floor/story. The results reveal a lot of variation in the dynamic response of the structure due to changes in geometrical shape in RC frame models M1, M2, and M3. Each frame has eight floors (8 stories). Each frame has four outputs for each bed in terms of displacement, frequency, acceleration, and velocity. The fundamental frequency contributes to mass participation of 71.26% in M1, 78.15% in M2, and 83.17% in M3. Consequently, results focus more on floor level one for M1, M2, and M3 RC frames models. A comparison has been described between standard model M3 and the other two models, M1 and M2. The input data has created 3-D models in STAAD Pro. Software along with the formation of the nodes and elements. The effect of the geometrical shape of the structures has been reflected in the irregularity shape factor ISF. The geometrical moment of inertia has been correlated by the square root of the sum of square (SRSS) method taking into consideration the effect of both geometrical moments of inertia about xx and yy axes in the analysis. The geometrical moment of inactivity has been assigned because this is not the actual moment of inertia of the structure. Instead, it is related to the structure’s geometry, so is the name geometry assigned.
4.6 Time history displacement
It has been observed from the results that the displacement increases with the increment in the height of the structural frame, and the removal of the floor situated at a higher level has higher displacements, as can be seen in the models M1, M2, and M3. The highest floor (8th floor) has the highest displacement. However, the ground level has zero displacements.
Time history displacement has been considered zero on the ground floor as the base is fixed concerning other floors. In model M1, the displacement increases in an upper direction from 11.6 E-3 mm on the first floor to 103 E-3 mm on the 8th floor. It varies from 17.5 E-3 mm to 195 E-3 mm in model M2 and 16.8 E-3 mm to 164 E-3 mm in the case of model M3. In general, it has been observed that the displacement in model M1 is higher than in model M2. Model M2 has a higher displacement in comparison to model M3. The increase in displacement in model M1 is 30.95% (11.6 E-3mm) and 4.1 % (17.5 E-3mm) in M2 concerning M3 (16.8 E-3 mm) at the first-floor level, and the model M2 has the higher displacement in comparison to model M3. The increase in displacement in model M1 is 37.19% (103 E-3mm) and 18.90% (195 E-3 mm) in M2 concerning M3 (164 E-3 mm) on the 8th floor. There is an increase in the horizontal displacement concerning the rise in height, i.e., as the height of the structure increases, removal at a higher level also increases. The displacement at the level of geometric irregularity, there is a change in the displacement in the node where abnormality (cut) has been generated. It also has been observed that there is a change in displacement one story down and one story up in the adjacent stories (M1). This can be observed that the geometric irregularity starts at level 3 in M1, and floor disturbance in displacement has been observed on floors 2 and 4. That indicates one floor up and one down adjoining the affected floor needs to be paid attention to special structural treatment. This disturbance is due to geometric irregularity. The displacement has also affected the entire length of 5 modes on floor three. Therefore, a complete story/floor must be paid attention to. It can be restricted that floors 2, 3, 4 need special attention for structural treatment. Similarly, in the case of M2, the variation in the upper displacement in the outer node varied from 41.2 E-3 mm to 41.8 E-3 mm in story second, where irregularity is present in M2. However, the changes in one floor up and one floor down displacement has been noticed. It also has been observed that the geometric irregularity changes the displacement behavior affecting the entire floor as in the case of M1 on floors 2, 3, 4 in the case of M2 and, affected feet are 1, 2, 3. The displacement in the adjoining floor up and down needs special attention under such circumstances. Appropriate reinforcement treatment may have to be required to treat the concentration of stresses. Figure 10(a-f) exhibit that the behavior of the function of displacement is almost similar except from floor 2 to 4, which is the area where irregularity in the geometry has been created in M1; however, the function of displacement does change from floor 1 to 3 in case of M2. That means irregularity plays a vital role in the response behavior of the structures.
4.6 Time history frequency
It has been observed that the frequency increases with the irregularity generated in the frame structure, which means the models M1 and M2, which have disturbed regularity, have a higher frequency than the regular model M1. The comparison has been drawn in Table 8.
Table 8. Time history Frequency for models M1, M2, and M3
Mode
|
Frequency of model M1
m sec
|
Frequency of model M2
m sec
|
Frequency of model M3
m sec
|
Percentage change in frequency of M1 concerning M3
(%)
|
Percentage change in frequency of M2 concerning M3
(%)
|
1
|
1.024
|
1.013
|
0.969
|
-5.67
|
-4.54
|
2
|
1.295
|
1.264
|
1.204
|
-7.55
|
-4.983
|
3
|
1.433
|
1.388
|
1.253
|
-14.3655
|
-10.77
|
4
|
2.91
|
2.99
|
2.911
|
0.03
|
-2.71
|
5
|
3.574
|
3.692
|
3.662
|
2.40
|
-0.81
|
6
|
3.659
|
3.922
|
3.705
|
1.241
|
-5.85
|
7
|
4.758
|
4.835
|
4.205
|
-13.151
|
-14.98
|
8
|
4.941
|
4.921
|
4.909
|
-0.132
|
-0.04
|
Time-frequency increases from 1.024 Hz to 4.941Hz in model M1, from 1.013 Hz to 4.921Hz in model M2, and from 9.69 Hz to 4.909 Hz in the case of model M3. In general, it has been observed that the frequency in models M1 and M2 is higher than in model M3 except at floor levels 4,5,6, where the frequency is lower in M1 than M2. Model M2 has a higher frequency in comparison to model M3. The increase in frequency in model M1 is 5.67% (1.024HZ) and 4.54% (1.013HZ) in M2 concerning M3 (0.969HZ) at the first-floor level, and the decrease in frequency in model M1 is 0.132 % (4.941HZ) and -0.04% (4.941HZ) in M2 concerning M3 (4.909HZ) at 8th floor. Percentage increase in frequency M1 concerning M3 from mode -1to mode-3 is 5.67% to 14.36%, and then it decreases from mode 4 to 6, and again, it increases in mode-7 to mode-8. The percentage change in frequency M2 concerning M3 from mode-1 to mode-8 is 4.54% to 0.04%. Since mode-3 has shown significant change, it may have some relationship in 3-floor level geometrically M1 and M2 at floor-2. Table 8 exhibits the function’s behavior of frequency changes at level 3 and level 7 in M1. Therefore, there appears to be some relation between the point of geometric irregularity and frequency modes as on floor 3; mode 3 has a significant change in its frequency increased to M3. Frequency has another considerable change at mode seven which means a band formation in frequency has happened. Therefore, irregularity plays a vital role in the response behavior of the structures. The model M2, which is more irregular, shows more frequency than M1 and has a higher frequency than M3 (regular).
4.7 Time history acceleration
Table 9. Time acceleration in seismic zone IV for models M1, M2, and M3
Mode
|
X- Acceleration of model M1
(E-3 m/s2)
|
X-Acceleration of model M2
(E-3 m/s2)
|
X- Acceleration of model M3
(E-3 m/s2)
|
% Change in the acceleration of M1 concerning M3 (%)
|
% Change in the acceleration of M2 concerning M3 (%)
|
1
|
3.904
|
5.84
|
5.58
|
30.03
|
-4.65
|
2
|
7.994
|
11.8
|
11.3
|
29.25
|
-4.42
|
3
|
9.68
|
14.5
|
13.3
|
27.21
|
-9.022
|
4
|
8.59
|
14.5
|
11.7
|
26.58
|
-23.93
|
5
|
7.28
|
13
|
9.68
|
24.79
|
-34.29
|
6
|
7.49
|
12.7
|
10.1
|
25.841
|
-25.74
|
7
|
10.3
|
18.3
|
13.9
|
25.899
|
-31.65
|
8
|
13.4
|
23.2
|
17.9
|
25.1396
|
-29.60
|
Table 10. Time acceleration ratio of models M1, M2, and M3
Time
acceleration
(M1)
(E-3 m/s2)
|
Time
acceleration
(M2)
(E-3 m/s2)
|
Time
acceleration
(M3)
(E-3 m/s2)
|
Time acceleration ratio concerning the lower floor
(M1)
|
Time acceleration ratio concerning the lower floor
(M2)
|
Time acceleration ratio concerning the lower floor
(M3)
|
3.904
|
5.84
|
5.58
|
1
|
1
|
1
|
7.994
|
11.8
|
11.3
|
1.047643
|
1.020548
|
1.02509
|
9.68
|
14.5
|
13.3
|
0.210908
|
0.228814
|
0.176991
|
8.59
|
14.5
|
11.7
|
-0.1126
|
0
|
-0.1203
|
7.28
|
13
|
9.68
|
-0.1525
|
-0.10345
|
-0.17265
|
7.49
|
12.7
|
10.1
|
0.028846
|
-0.02308
|
0.043388
|
10.3
|
18.3
|
13.9
|
0.375167
|
0.440945
|
0.376238
|
13.4
|
23.2
|
17.9
|
0.300971
|
0.26776
|
0.28777
|
The acceleration increases along with the floors. It varies from 3.90% to 13.40% in case of M1; 5.84 % to 23.2% in M2 and 5.58% to 17.9% in M3 from floor -1 to floor 8. The acceleration change is almost the same in M1 and M2 concerning M3 after floor -3, an area of geometric irregularity interference. However, From Figure 11(a-b), acceleration in model M1 is less s in all floors than in model M2 and model M3. Last floor which is 8th floor in each models has the highest time acceleration i.e., 13.4 E-3 m/s2, 23.2 E-3 m/s2, and 17.9 E-3 m/s2 for M1, M2, M3 respectively. The decrease in Time Acceleration in frame model M1 is 30.03 % (3.904 E- m/s2), and an increase of 4.65 % (5.84 E-3 m/s2) in M2 concerning M3 (5.58 E-3) m/s2 at the first-floor level is the most critical level for such studies as most of the mass participation comes from this floor. The decrease in Time Acceleration in frame model M1 is 25.13% (13.4 E -3 m/s2) and increase of 29.60 % (23.2 E-3 m/s2) in model M2 with reference to model M3 (17.9 E-3 m/s2) at 8-floor level. Figure 11(c-d) exhibits that time acceleration has tangible effects at level 2, the area of geometric irregularity for M2. Due to geometric irregularity, the time acceleration behavior differs from floors 2 to 4.
4.8 ComparisonTime history velocity
Table 11. Time velocity of models M1, M2, and M3
Mode
|
X- Velocity of model M1
(E-3 m/s2)
|
X- Velocity of model M2
(E-3 m/s2)
|
X- Velocity of model M3
(E-3 m/s2)
|
Percentage change in velocity of M1 concerning M3 (%)
|
Percentage change in the rate of M2 concerning M3 (%)
|
1
|
165
|
282
|
255.5
|
35
|
-10.37
|
2
|
361
|
629
|
571
|
36
|
-10.15
|
3
|
507
|
931
|
807
|
37.17
|
-15.36
|
4
|
604
|
1140
|
951
|
36.48
|
99.47
|
5
|
676
|
1260
|
1030
|
34.36
|
-22.33
|
6
|
752
|
1330
|
1070
|
29.71
|
-24.29
|
7
|
825
|
1400
|
1100
|
25
|
-27.27
|
8
|
895
|
1480
|
1130
|
20.79
|
-30.97
|
Figure 12 of time history velocity is zero at the ground because the base is fixed. For the 2nd floor in the model, M1 velocity is 165 E-3 m/s on the 1st floor and 895 E-3 mm/s on the 8th floor. Model M2 velocity is 282 E-3 mm/s on the 1st floor and 1480 E-3 mm/s on the 8th floor. In model M3 velocity varies with height i.e., 255.5 E-3 m/s to 1130 E-3 m/s. The velocities in all the M1, M2, and M3 models are different. It can be observed that the M2 has the highest velocity, which is a most irregular model. The time velocity is lower in M1 than in M2, which has less geometric irregularity. Therefore, it can be concluded that geometric irregularity affects the time velocity in the structure, and it is different in some of the interference of geometric irregularity.
4.9 Irregularty shape factor
An attempt has been made to define an irregularity shape factor (ISF) for a rectangular geometrical structure. The use of the moment of inertia has been made a basis for such a factor. The effect of the geometry of the designs has been reflected in terms of irregularity shape factor ISF. A comparison has been made concerning the regular geometrical shaped model M3. The variation in the response behavior has been attributed to the irregularity in geometry created in the structure. The Regularity Ratio (RR) has been defined as the ratio of Igxy (M1 or M2) / Igxy for (M3) as per the model studies in consideration.