Natural Time Period Comparison
Table 9:1
Time Period of model for soft story in ground floor
Fixed end
|
Empirical formula
|
Modal Analysis
|
Without infill
|
With infill
|
Without infill
|
With infill
|
Tx (s)
|
0.46
|
0.28
|
0.65
|
0.49
|
Ty (s)
|
0.46
|
0.38
|
0.65
|
0.49
|
(Sa/g)x
|
2.50
|
2.50
|
2.11
|
2.50
|
(Sa/g)y
|
2.50
|
2.50
|
2.11
|
2.50
|
Table 9:2
Time period of model for soft story in first floor
Fixed end
|
Empirical formula
|
Modal Analysis
|
Without infill
|
With infill
|
Without infill
|
With infill
|
Tx (s)
|
0.46
|
0.28
|
0.65
|
0.47
|
Ty (s)
|
0.46
|
0.38
|
0.65
|
0.47
|
(Sa/g)x
|
2.50
|
2.50
|
2.11
|
2.50
|
(Sa/g)y
|
2.50
|
2.50
|
2.11
|
2.50
|
Table 9:3
Time period of model for soft story in second floor
Fixed end
|
Empirical formula
|
Modal Analysis
|
Without infill
|
With infill
|
Without infill
|
With infill
|
Tx (s)
|
0.46
|
0.28
|
0.65
|
0.29
|
Ty (s)
|
0.46
|
0.38
|
0.65
|
0.29
|
(Sa/g)x
|
2.50
|
2.50
|
2.11
|
2.50
|
(Sa/g)y
|
2.50
|
2.50
|
2.11
|
2.50
|
Table 9:1, 9:2, 9:3 shows that time period of bare frame model is high compared to other model which has effect of infill wall. Time period gradually decreases as soft story shifts at upper floors. The time period of model having soft story on ground floor is higher than model having soft story in first and second floor. It is because the lateral stiffness of second floor soft story model has high due to struts in ground as well and first floor but the lateral stiffness of ground floor soft story is low in base of the building. This shows that the lateral displacement is low for the model having high stiffness at base like soft story on second and first story whereas the displacement is high for bare frame model and soft story in ground floor.
Comparison of Displacement
Table 9:4
Maximum Joint Displacement along X-direction
Story No.
|
Bare Frame(mm)
|
Ground floor soft story(mm)
|
First floor soft story(mm)
|
Second floor soft story(mm)
|
4
|
19.8
|
8.9
|
9.8
|
7.0
|
3
|
17.0
|
6.6
|
7.5
|
4.2
|
2
|
12.2
|
5.9
|
6.6
|
0.4
|
1
|
5.4
|
4.7
|
1.2
|
0.2
|
0
|
0.0
|
0.0
|
0.0
|
0.0
|
Table 9:5
Maximum joint displacement along Y-direction
Story No.
|
Bare Frame(m)
|
Ground floor soft story(m)
|
First floor soft story(m)
|
Second floor soft story(m)
|
4
|
18.8
|
9.7
|
10.6
|
7.2
|
3
|
15.8
|
7.3
|
8.2
|
4.2
|
2
|
11.4
|
6.2
|
6.9
|
0.7
|
1
|
5.1
|
4.5
|
1.6
|
0.3
|
0
|
0.0
|
0.0
|
0.0
|
0.0
|
Referring to Figs. 2 and 3 shows that displacement of floor for bare frame model gradually increases from bottom and further rises up parabollically but model considering the infill wall and soft story, the floor having soft story have a significant displacement and other floor with infill wall has no tremendous displacement. The floor having soft story on ground floor has huge displacement in ground floor and other floors have less displacement, while first floor has remarkable displacement than other floors for model in first floor soft story. Similarly in model having soft story in second floor has significant displacement in second story can be seen and negligible displacement is noticed in ground floor and first floor. The displacement is high only in the story without infill walls because in other floors the lateral stiffness is high due to diagonal strut of masonry. This made a floor with soft story a flexible which caused a sway frame thus forming a huge displacement than other floors.
Comparison of Story Drift
Table 9:6
Drift ratio along X and Y direction
Story No
|
Bare frame
|
Ground floor soft story
|
First floor soft story
|
Second floor soft story
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
4
|
0.101
|
0.105
|
0.082
|
0.085
|
0.082
|
0.085
|
0.102
|
0.106
|
3
|
0.170
|
0.157
|
0.026
|
0.039
|
0.033
|
0.046
|
0.134
|
0.125
|
2
|
0.243
|
0.227
|
0.043
|
0.061
|
0.193
|
0.189
|
0.008
|
0.015
|
1
|
0.193
|
0.181
|
0.168
|
0.162
|
0.043
|
0.058
|
0.007
|
0.011
|
0
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
Table 9:7
Variation of drift of bare frame and ground floor soft story
Story No
|
Bare frame
|
|
Ground floor soft story
|
|
Varitation
|
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
4
|
0.101
|
0.105
|
0.082
|
0.085
|
19%
|
19%
|
3
|
0.170
|
0.157
|
0.026
|
0.039
|
85%
|
75%
|
2
|
0.243
|
0.227
|
0.043
|
0.061
|
82%
|
73%
|
1
|
0.193
|
0.181
|
0.168
|
0.162
|
13%
|
11%
|
0
|
0.000
|
0.000
|
0.000
|
0.000
|
0%
|
0%
|
Table 9:8
Variation of drift of bare frame and first floor soft story
Story No
|
Bare frame
|
|
First floor soft story
|
|
Varitation
|
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
4
|
0.101
|
0.105
|
0.082
|
0.085
|
19%
|
19%
|
3
|
0.170
|
0.157
|
0.033
|
0.046
|
81%
|
71%
|
2
|
0.243
|
0.227
|
0.193
|
0.189
|
20%
|
17%
|
1
|
0.193
|
0.181
|
0.043
|
0.058
|
78%
|
68%
|
0
|
0.000
|
0.000
|
0.000
|
0.000
|
0%
|
0%
|
Table 9:9
Variation of drift of bare frame and second floor soft story
Story No
|
Bare frame
|
|
Second floor soft story
|
|
Varitation
|
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
4
|
0.101
|
0.105
|
0.102
|
0.106
|
-2%
|
-1%
|
3
|
0.170
|
0.157
|
0.134
|
0.125
|
21%
|
20%
|
2
|
0.243
|
0.227
|
0.008
|
0.015
|
97%
|
94%
|
1
|
0.193
|
0.181
|
0.007
|
0.011
|
97%
|
94%
|
0
|
0.000
|
0.000
|
0.000
|
0.000
|
0%
|
0%
|
Drift is difference between displacements two consecutive floor normalized with height of the story. Generally it is seen that drift ratio is minimum at lower floor and rises maximum at middle floor and again lowers at top story but it can be observed that considering the effect of infill wall, the drift ratio is not remarkable whereas at the location of soft story, drift ratio increases significantly. As seen in Figs. 4 and 5, the drift for bare frame is 0 at the base and it parabolically varies from first story and up to roof. The drift is maximum at story 2 rising from base and reduces on story 3 and roof. In Fig. 5 (i),(ii),(iii), drift ratio for model which is soft story on ground floor, first floor and second floor is shown. In Fig. 5 (i), the drift of model having soft story on ground floor is shown where the drift isn maximum for ground floor only and no tremendous drifts in other floor. Table 9 − 7 shows that the drift ratio of ground floor of bare frame model and model with soft story on ground floor has nearly similar type of drift having only variation to be 13%. But on other floor there is huge variation of drift about 82–85% which means there is no huge drift due to infill walls. In Fig. 5 (ii) the drift of model having soft story on first floor is shown where the drift is maximum for first floor only and no tremendous drifts in other floor. Table 9-8shows that the drift ratio of first floor of bare frame model and model with soft story on first floor has nearly similar type of drift having only variation to be 20%. But on other floor there is huge variation of drift about 78–81%. In Fig. 5 (iii) the drift of model having soft story on second floor is shown where the drift is maximum for second floor only and no tremendous drifts in other floor. Table <link rid="tb16">9</link>–9 shows that the drift ratio of second floor of bare frame model and model with soft story on second floor has nearly similar type of drift having only variation to be 21%. But on other floor there is huge variation of drift about 97%.
Multiplication factor
Table 9:10
Calculation of Multiplication factor for different forms
MULTIPLICATION FACTOR
|
Ground floor soft story
|
Column shear
|
1.016
|
59%<2.5
|
|
Column moment
|
1.1
|
56%<2.5
|
First floor soft story
|
Column shear
|
1
|
60%<2.5
|
|
Column moment
|
1.16
|
54%<2.5
|
Second floor soft story
|
Column shear
|
1
|
60%<2.5
|
|
Column moment
|
1
|
60%<2.5
|
According to IS 1893:2002, the members of soft story have to be designed for 2.5 times the story shear and moments obtained without considering the effects of masonry infill in any story. This value of 2.5 is specified to incorporate the extent of irregularities. It is quite conservative and empirical method and have to be modified for different scopes of improvement.
$$\mathbf{M}.\mathbf{F}=\frac{\mathbf{M}\mathbf{e}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r} \mathbf{f}\mathbf{o}\mathbf{r}\mathbf{c}\mathbf{e}\mathbf{s} \mathbf{o}\mathbf{f} \mathbf{i}\mathbf{n}\mathbf{f}\mathbf{i}\mathbf{l}\mathbf{l}\mathbf{e}\mathbf{d} \mathbf{f}\mathbf{r}\mathbf{a}\mathbf{m}\mathbf{e}\mathbf{s}}{\mathbf{M}\mathbf{e}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r} \mathbf{f}\mathbf{o}\mathbf{r}\mathbf{c}\mathbf{e}\mathbf{s} \mathbf{o}\mathbf{f}\mathbf{b}\mathbf{a}\mathbf{r}\mathbf{e} \mathbf{f}\mathbf{r}\mathbf{a}\mathbf{m}\mathbf{e}\mathbf{s}}$$
From the above, Table 9:10 The multiplication factor for column shear and column moment varies accordingly for ground, first and second floor soft story. Values of multiplication factor does not increase 1.2 either. Hence no multiplication factor of 2.5 should be implied for low rise building.
Comparison of Performance Point
Table 9:11
Comparison of Performance point along X-direction
Model
|
Base Shear KN
|
Displacement mm
|
Bare Frame
|
1021.57
|
48
|
Ground floor soft story
|
1066.5
|
25
|
First floor soft story
|
1212.6
|
20.51
|
Second floor soft story
|
633.24
|
4.9
|
Table 9:12
Comparison of Performance point along Y-direction
Model
|
Base Shear KN
|
Displacement mm
|
Bare Frame
|
1002.78
|
49
|
Ground floor soft story
|
1064.41
|
29
|
First floor soft story
|
1226.28
|
24.3
|
Second floor soft story
|
790.5
|
6.9
|
Comparison of Displacement at Performance Point
Table 9:13
Comparison of Displacement at Performance point
Story No
|
Bare frame mm
|
Ground floor soft story mm
|
First floor soft story mm
|
Second floor soft story mm
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
Along-x
|
Along-y
|
4
|
54.66
|
48
|
22.91
|
24.99
|
19.96
|
21.02
|
11.25
|
12.36
|
3
|
51.5
|
44.71
|
20.78
|
22.68
|
17.72
|
18.77
|
7.73
|
8.57
|
2
|
42.75
|
36.8
|
19.68
|
20.96
|
16.15
|
16.61
|
1.28
|
2.29
|
1
|
23.68
|
19.66
|
16.96
|
16.97
|
3.71
|
4.86
|
0.69
|
1.2
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
Formation of Hinges
Figure 5,6,7,8 shows the sequential steps for the formation of Non-linear linear hinges in the structural elements. In first step of pushover analysis, bare frame model has formed 10 basic level hinges from base to second story but ground floor soft story has formed one basic hinge in column, first floor soft story has no hinges formed and second floor soft story has formed one basic hinge in beam. Similarly in fourth step, bare frame model has formed 15 basic level hinges in beam and column from base to second floor while ground floor soft story has formed 8 basic hinges in column in ground floor, first floor soft story has formed 11 basic hinges in first floor column and beam and second floor soft story has formed 12 basic hinges in second story columns and beams. Similarly in seventh step, bare frame model has formed 21 hinges in which 8 immediate occupancy hinge is formed in ground floor column whereas 13 basic hinges at upper floor levels while ground floor soft story has formed 9 hinges in which 8 immediate occupancy hinges are formed column in ground story and one basic hinge in beam level, in first floor soft story has formed 12 hinges out of which 5 hinges are beyond collapse hinges at level “D” hinge 3 is life safety hinge in first floor column 4 is basic hinge in beam and in second floor soft story has formed 14 hinges out of which 1 is life safety and 7 immediate occupancy hinge in second floor column 6 basic hinges in beam. Comparing step 10, bare frame model has formed 22 hinges in which 1 hinge is beyond collapse hinge at level “D” hinge 2 hinge is life safety hinge 5 immediate occupancy hinge is formed in ground floor column whereas 14 basic hinges at upper floor levels while ground floor soft story has formed 11 hinges in which 4 hinge is beyond collapse hinge at level “D” hinge 3 hinge is life safety hinge 1 immediate occupancy hinges are formed column in ground story and 3 basic hinge in beam level, in first floor soft story has formed 12 hinges out of which 5 hinges are beyond collapse hinges at level “D” hinge 3 is life safety hinge in first floor column 4 is basic hinge in beam and in second floor soft story has formed 22 hinges out of which 1 is beyond collapse prevention hinge at level “D” hinge 4 life safety and 3 immediate occupancy hinge in second floor column 6 basic hinges in second floor beam level while 2 life safety and 2 basic hinge at top story column and 2 basic hinges at roof level beam.