In present scenario, we have seen that whenever there is an earthquake a lot of damage occurs. Even if the probability of occurrence of earthquake within the life span of structures is very less, strong ground motion would generally cause greater damage to the structure. Hence, it becomes important that the building must be adequate in resisting earthquake. So building with shear wall helps in resisting lateral load. The Non-linear static analysis of shear wall gives the desired base shear and the story drift which it can encounter during its life.
Non-linear Static Pushover analysis
Pushover analysis is a term used for the non-linear static analysis of frames. The practical method used for evaluating the displacement, time period etc is most done by pushover analysis. It is the procedure in which the magnitude of the structural loading is incrementally increased in accordance with a certain predefined pattern. With the increase in the magnitude of the loading, weak links and failure modes of the structure are found. The loading is monotonic with the effects of the cyclic behaviour and load reversals being estimated by using a
modified monotonic force-deformation criteria and with damping approximations.
The static pushover analysis is becoming a popular tool for seismic performance evaluation of existing and new structures. The expectation is that the pushover analysis will provide adequate information on seismic demands imposed by the design ground motion on the structural system and its components. Further, Indian buildings built over past two decades are seismically deficient because of lack of awareness regarding seismic behaviour of structures. The widespread damage especially to RC buildings during earthquakes exposed the construction practices being adopted around the world, and generated a great demand for seismic evaluation and retrofitting of existing building stocks.
The pushover analysis of a structure is a static non-linear analysis under permanent vertical loads and gradually increasing lateral loads. The equivalent static lateral loads approximately represent earthquake induced forces. A plot of the total base shear versus top displacement in a structure is obtained by this analysis that would indicate any premature failure or weakness. The analysis is carried out up to failure, thus it enables determination of collapse load and ductility capacity.
Purpose of Pushover analysis
The purpose of pushover analysis is to evaluate the expected performance of structural systems by estimating performance of a structural system by estimating its strength and deformation demands in design earthquakes by means of static
inelastic analysis, and comparing these demands to available capacities at the performance levels of interest.
The evaluation is based on an assessment of important performance parameters, including global drift; inter story drift, inelastic element deformations (either absolute or normalized with respect to a yield value), deformations between elements, and element connection forces (for elements and connections that cannot sustain inelastic deformations).
The inelastic static pushover analysis can be viewed as a method for predicting seismic force and deformation demands, which accounts in an approximate manner for the redistribution of internal forces that no longer can be resisted within the elastic range of structural behavior.
3.2 Problem Formulation
Different shear wall models having edge column and without edge column are consider with different thickness and story height. The models which are having edge column are confined with high reinforcement whereas those without edge column are unconfined.
Materials properties
Concrete: The concrete has a uniaxial compressive strength fc’. Under uniaxial compression, the concrete strain εo corresponding to the peak stress fc’ is usually around the range of 0.002–0.003 and used in the analysis is εo 0.003. The Poisson’s ratio νc of concrete under uniaxial compressive stress ranges from
about 0.15-0.22, with a representative value of 0.19 or 0.20. In this study, the Poisson’s ratio of concrete is assumed to be νc 0.2. The uniaxial tensile strength fc’ of concrete is difficult to measure. For this study the value is taken as
ft’= 0.25 √ fc’ MPa
The initial modulus of elasticity of concrete E’is highly correlated to its compressive strength and can be calculated
Ec= 5000 √ fc’ MPa
Table 3.1: Properties of concrete
S.No.
Notations
Value
1.
M-25
25 N/mm2
2.
Ec
25000 N/mm2
3.
fc’
25N/mm2
4.
ft’
1.25 N/mm2
5.
νc
.3
6.
εcrushing
.004
7.
εu
.001
Steel: The elastic modulus, Es, and yield stress, fy, are taken and these values are used in the model. A Poisson’s ratio of 0.3 is used for the steel.
Table 3.2: Steel Properties
Fe-415
415 N/mm2
Es
210000 N/mm2
νs
.3
Location of Shear Wall:
Shear walls are located on the exterior central portion in all direction. The location is so selected so as to give symmetry to the building. The location of shear wall affects the performance of the building.
Load Considerations:
The dead load is calculated according the self-weight of the slab and is distributed uniformly. The unit weight of the slab is considered as 25 KN/m3. The live load is assumed to be uniformly distributed on slab and is taken as 2 KN/m2. These loads are applied in vertical direction. The live load is assumed to be taken as 25 % of the total load.
Example Problem:
Table 3.3: 4 Story shear wall with edge column
S. No.
hs (m)
tw
(mm)
Lw
(m)
hw
(m)
Percentage of reinforcement in edge column
Ac
(mm2)
ρ
As
(mm2)
SWE1*
3.5
150
4.0
14
1 %
785
.175
1050
SWE2
3.5
150
4.0
14
2%
1582
.175
1050
SWE3
3.5
200
4.0
14
1%
1099
.131
1048
SWE4
3.5
200
4.0
14
2%
2034
.131
1048
SWE5
3.5
250
4.0
14
1%
1356
.105
1050
SWE6
3.5
250
4.0
14
2%
2814
.105
1050
* SWE stands for Shear wall with edge column
Table 3.4: 6 Story shear wall with edge column
S. No.
hs (m)
tw
(mm)
Lw
(m)
hw
(m)
Percentage of reinforcement in edge column
Ac
(mm2)
ρ
As
(mm2)
SWE7
3.5
150
6.0
21
1 %
785
.308
2772
SWE8
3.5
150
6.0
21
2 %
1582
.308
2772
SWE9
3.5
200
6.0
21
1 %
1099
.224
2688
SWE10
3.5
200
6.0
21
2%
2034
.224
2688
SWE11
3.5
250
6.0
21
1%
1356
.165
2475
SWE12
3.5
250
6.0
21
2%
2814
.165
2475
SWE13
3.5
300
6.0
21
1%
1582
.131
2358
SWE14
3.5
300
6.0
21
2%
3216
.131
2358
Table 3.5: 8 Story shear wall with edge column
S. No.
hs (m)
tw
(mm)
Lw
(m)
hw
(m)
Percentage of reinforcement in edge column
Ac
(mm2)
ρ
As
(mm2)
SWE15
3.5
150
8.0
28
1 %
785
.524
6288
SWE16
3.5
150
8.0
28
2 %
1582
.524
6288
SWE17
3.5
200
8.0
28
1 %
1099
.343
6288
SWE18
3.5
200
8.0
28
2%
2034
.343
6288
SWE19
3.5
250
8.0
28
1%
1356
.302
6040
SWE20
3.5
250
8.0
28
2%
2814
.302
6040
SWE21
3.5
300
8.0
28
1%
1582
.251
6024
SWE22
3.5
300
8.0
28
2%
3216
.251
6024
Table 3.6: 8 Story shear wall without edge column
S. No.
hs
(m)
tw
(mm)
Lw
(m)
hw
(m)
ρ
As
(mm2)
SWN1*
3.5
150
8.0
28
.524
6288
SWN3
3.5
200
8.0
28
.343
6288
SWN5
3.5
250
8.0
28
.302
6040
SWN7
3.5
300
8.0
28
.251
6024
*SWN stands for Shear wall without edge column
Table 3.7: 6 Story shear wall without edge column
S. No.
hs
(m)
tw
(mm)
Lw
(m)
hw
(m)
ρ
As
(mm2)
SWN9
3.5
150
6.0
21
.308
2772
SWN11
3.5
200
6.0
21
.224
2688
SWN13
3.5
250
6.0
21
.165
2475
SWN15
3.5
300
6.0
21
.131
2358
Table 3.8: 4 Story shear wall without edge column
S. No.
hs
(m)
tw
(mm)
Lw
(m)
hw
(m)
ρ
As
(mm2)
SWN17
3.5
150
4.0
14
.175
1050
SWN19
3.5
200
4.0
14
.131
1048
SWN21
3.5
250
4.0
14
.105
1050
Non-Linear Static Analysis using SAP 2000
Static pushover analysis is an attempt by the structural engineering profession to evaluate the real strength of the structure and it promises to be a useful and effective tool for performance based design. The ATC-40 and FEMA-273 documents have developed modelling procedures, acceptance criteria and analysis procedures for pushover analysis. These documents define force deformation criteria for hinges used in pushover analysis.
The SAP2000 static pushover analysis capabilities, which are fully integrated into the program, allow quick and easy implementation of the pushover procedures prescribed in the ATC-40 and FEMA-273 documents for both two and three-dimensional buildings.
3.3 Modeling in SAP 2000
Modeling and analysis is done using the SAP 2000, 16 models of shear wall with and without edge column are generated and there pushover curves are obtained. Models with different thickness and reinforcing ratio are taken for parametric study and to obtain the base shear and displacement for different story height.
Procedure
I. The basic computer model (without the pushover data) in the usual manner using the graphical interface of SAP2000 is created.
II. Defining the material properties and assigning the concrete as confined and unconfined concrete.
III. The confined and unconfined concrete are now assigned with the reinforcement in longitudinal and transverse direction.
IV. After that, the sections are assigned with confined and unconfined concrete.
V. Load Case (Gravity Load) is generated i.e. dead load and live load are applied (live load will take 25% of load). Pushover load case is created after the gravity load.
VI. The model is run for the Non-linear static pushover analysis. And the pushover curve is obtained
4
RESULTS
—————————————————————————————————
The Non-linear static analysis of shear wall results is obtained in the form of base shear and displacement curves. The different pushover curves for different story height of shear wall is obtained that are drawn for different thickness. It is to be noted that the results obtained are within the permissible limits and as those given in different codes.
The results are displayed in the form of curve. The
curves are divided into three sections that is in the first section the shear wall with edge column for different story i.e. 4, 6 and 8 story is drawn for different thickness having the percentage of reinforcement varying as 1% and 2%. In the second section the shear wall without edge column is drawn for different height. Finally the base shear obtained is compared with the design value.
Hence, from the results it is tried to give an idea to select the required thickness that is suitable for a particular story height of the building.
0
100
200
300
400
500
600
700
0 10 20 30 40 50 60
BASE SHEAR (KN)
DISPLACEMENT (mm)
BASE SHEAR VS DISPLACEMENT
150 MM
200 MM
250 MM
0
200
400
600
800
1,000
1,200
0 10 20 30 40 50 60
BASE SHEAR (KN)
DISPLACEMENT
BASE SHEAR VS DISPLACEMENT
150 MM
200 MM
250 MM
Section 1: Pushover curves for different thickness
Fig. 4.1 Base shear and displacement curve for 4 story shear wall with edge column having 1% reinforcement
Fig. 4.2 Base shear and displacement curve for 4 story shear wall with edge column having 2% reinforcement
From the above figures it is evident, as the thickness increases the base shear increases but after a particular point it varies constantly.
Fig. 4.3 Base shear and displacement curve for 6 story shear wall with edge column having 1% reinforcement
Fig. 4.4 Base shear and displacement curve for 6 story shear wall with edge column having 2% reinforcement
0
200
400
600
800
1000
1200
1400
0
20
40
60
80
100
BASE SHEAR (KN)
DISPLACEMENT (mm)
BASE SHEAR VS DISPLACEMENT
150 MM
200 MM
250 MM
300 MM
0
200
400
600
800
1000
1200
1400
1600
1800
0
20
40
60
80
100
BASE SHEAR (KN)
DISPLACEMENT (mm)
BASE SHEAR VS DISPLACEMENT
150 MM
200 MM
250 MM
300 MM
Fig. 4.5 Base shear and displacement curve for 8 story shear wall with edge column having 1% reinforcement
Fig. 4.6 Base shear and displacement curve for 8 story shear wall with edge column having 2% reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
20
40
60
80
100
120
BASE SHEAR (KN)
DISPLACEMENT (mm)
BASE SHEAR VS DISPLACEMENT
150 MM
200 MM
250 MM
300 MM
0
500
1000
1500
2000
2500
0
20
40
60
80
100
120
BASE SHEAR (KN)
DISPLACEMENT (mm)
BASE SHEAR VS DISPLACEMENT
150 MM
200 MM
250 MM
300 MM
Fig. 4.7 Base shear and displacement curve for 4 story shear wall without edge column
Fig. 4.8 Base shear and displacement curve for 6 story shear wall without edge column
0
100
200
300
400
500
600
700
0
10
20
30
40
50
60
BASE SHEAR (KN)
DISPLACEMENT (mm)
BASE SHEAR VS DISPLACEMENT
150 MM
200 MM
250 MM
0
200
400
600
800
1000
1200
1400
0
20
40
60
80
100
BASE SHEAR (KN)
DISPLACEMENT (mm)
BASE SHEAR VS DISPLACEMENT
150 MM
200 MM
250 MM
300 MM
Fig. 4.9 Base shear and displacement curve for 8 story shear wall without edge column
The pushover curve for shear wall without edge column shows that the base shear increase linearly up to reaching its peak value then, there is fall in the base shear as the thickness increases. As we can see that after that the base shear remains constant for different thickness.
0
200
400
600
800
1000
1200
1400
1600
1800
0
20
40
60
80
100
120
BASE SHEAR (KN)
DISPLACEMENT (mm)
BASE SHEAR VS DISPLACEMENT
150 MM
200 MM
250 MM
300 MM
Section 2: Base Shear comparison with design value for edge column
Fig. 4.10 Base shear Comparison with Design Value for 4 story shear wall
Fig. 4.11 Base shear Comparison with Design Value for 6 story shear wall
From figure 4.10, it is clear that for 4 story shear with edge column 150 mm thickness can be used. And from figure 4.11, i.e. for 6 story height the thickness required is 200 mm ,250 mm thickness can also be used.
0
200
400
600
800
1000
1200
1400
150
200
250
BASE SHEAR (KN)
THICKNESS (mm)
With Edge column
Design Value
0
500
1000
1500
2000
2500
150
200
250
300
BASE SHEAR (KN)
THICKNESS (mm)
With Edge Column
Design value
Fig. 4.12 Base shear Comparison with Design Value for 8 story shear wall for 1 % reinforcement
Fig. 4.13 Base shear Comparison with Design Value for 8 story shear wall for 2 % reinforcement
For 8 story height the thickness requirement 250mm and 300 mm as shown in above figures.
0
500
1000
1500
2000
2500
3000
3500
4000
150
200
250
300
BASE SHEAR (KN)
THICKNESS (mm)
With Edge Column
Design Value
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
150
200
250
300
BASE SHEAR (KN)
THICKNESS (mm)
With Edge Column
Design Value
Section 3: Base Shear comparison with design value without edge column
Fig. 4.14 Base shear Comparison with Design Value for 4 story shear wall without edge column
Fig. 4.15 Base shear Comparison with Design Value for 6 story shear wall without edge column
0
200
400
600
800
1000
1200
1400
150
200
250
BASE SHEAR (KN)
THICKNESS (mm)
Without Edge Column
Design Value
0
500
1000
1500
2000
2500
150
200
250
300
BASE SHEAR (KN)
THICKNESS (mm)
Without Edge Column
Design Value
Fig. 4.16 Base shear Comparison with Design Value for 8 story shear wall without edge column
From figure 4.14, we can see that the base shear value without edge column and design values are approximately equal for 150 mm thickness. It means that if shear wall without edge column is to be used for 4 story then, 150 mm thickness is sufficient. Similarly, we can say for 6 story and 8 story the thickness requirement are 250 mm and 300 mm respectively.
0
500
1000
1500
2000
2500
3000
3500
4000
150
200
250
300
BASE SHEAR KN)
THICKNESS (mm)
Without Edge Column
Design Value
5
Conclusion and FUTURE SCOPE
——————————————————————————————————-
5.1 Conclusion
It is evident that with the use of shear wall lateral stiffness of the structure increases. The building having shear wall performs better in earthquake. The displacement also reduces with the use of shear wall. Hence, it becomes very important to design the shear wall correctly and its location so as to fully utilized it to resist the lateral forces.
Now a days multi storied building are constructed using shear wall so its proper analysis and design must be done so that structure performance increases.
Provision of shear wall results in a huge decrease in base shear and roof displacement both symmetrical building and un-symmetrical building. Pushover curves show non-ductile behavior of the building, because almost all the seismic load is carried by the shear walls and at very small displacement, hinges start forming in shear walls. This indicates that strengthening of the shear walls in the building is required.
The present study done on shear wall with and without edge column concludes that:
When the thickness of the shear wall increases the base shear increases but the displacement decreases.
For lower height of building, minimum thickness can be taken as 150mm as we have seen in 4 story shear wall thickness less than 150 mm can be taken and higher thickness will not be economical.
While changing the percentage of reinforcement in edge column, it is clear that as the percentage increases the base shear obtained matches with design value.
There is a need of modification in percentage of reinforcement in edge column as given in codes.
5.2 Future Scope:
It is the part of research to analyse the shear wall with different width and thickness of the edge column. Since the whole study is based on uniform thickness of wall it would be part of research to take different thickness of wall section. Also, work can be done on location of shear wall, number of shear wall.