 Open Access
 Authors : Malavika G Babu
 Paper ID : IJERTV10IS060215
 Volume & Issue : Volume 10, Issue 06 (June 2021)
 Published (First Online): 23062021
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Reliability Analysis for Buckling Restrained Braced Frame (BRBF)
Malavika G Babu
M. tech Student [Structural Engineering] Dept of Civil Engineering
Younus College of Engineering and Technology Kollam, India
AbstractStructural demands in high seismic zones require the use of strong lateral framing systems. The structure must have adequate strength and stiffness to resist smaller, frequent earthquakes with limited damage, but must also be able to sustain large inelastic cyclic deformations to economically assure safety and stability during large, infrequent earthquakes. To overcome these problems, a new type of braces called buckling restrained braces (BRBs) was introduced. They are structural steel frame that provide lateral resistance to buckling during seismic activity. This study aims to assess the seismic performance of buckling restrained braced frames (BRBFs) by Eigen value modal analysis, equivalent static analysis and time history plots should be created by spectral matching to find out peak response of the building. The reliability index can be calculated by varying building height and plotting the safety margin curves. The modeling and analysis of building is carried out using ETABS software.
Keywords Buckling restrained braced frames (BRBFs), Eigen value modal analysis, ETABS software, Reliability index.

INTRODUCTION
Earthquake causes economic losses as well as losses of lives due to the collapse of structures. During strong seismic waves structural elements like beams and columns are seriously affected. Under moderate to severe earthquakes conventional lateral load resisting systems are not effective to overcome these problems, a new type of braces called buckling restrained braces (BRBs) were introduced. They are structural steel frame that provide lateral resistance to buckling during seismic activity. The main components of braces are steel core, bondpreventing layer and outer casing. The steel core is able to resist axial force acting on bracings. Core is divided into three parts, central yielding part and rigid non yielding parts at both ends. The bond preventing layer separates core and casing. It allows free expansion and contraction of core during tension and compression. The casing envelops the inner parts and restraining the steel core from buckling
In this work the seismic performance of a10 storey I shaped BRBF building is evaluated by equivalent static analysis, Eigen value model analysis. Time history data collected for spectral matching and peak response of building is obtained. Reliability index of structure can be calculated by plotting safety margin curves for different building height.

METHODOLOGY DATA COLLECTION
LITERATURE REVIEW
SOFTWARE STUDY MODELLING
CONCLUSIONS
CONCLUSIONS
ANALYSIS RESULTS & DISCUSSION

MODELLING
A 10 storey I shaped building is modelled using etabs software. The materials used are M30 grade concrete and Fe415 grade steel. Height of each storey is 3 m. Number of bays in X and Y direction are 7 and 4 respectively. The span of each bay is 3m.The beam section of size 250 mm x 250 mm and Column of size 500 mm x 500 mm is used. Here the provided Slab thickness is 120 mm.
Fig 1.Plan and elevation of building
TABLE I. .DEAD LOAD (IS 875: 1987 PART 1)
Parapet
2kN/m
Wall Load
12 kN/m
Floor finish
1KN/m2
TABLE II. LIVE LOAD (IS 875: 1987 PART 2)
Residential building
2 KN/m2
Roof
1.5 KN/m2
TABLE III. WIND LOAD (IS 875: PART 3)
Risk factor,(k1)
1.0
Topography factor,(k2)
1.0
Terrain factor,(k3)
1.0
Terrain category
2
Building class
B
TABLE IV. SEISMIC LOAD (IS1893:2002)
Seismic zone factor, Z
0.16
Importance factor, I
1
Response reduction factor ,R
5
TABLE V. LOAD COMBINATIONS (IS 1893: 2002 PART 1)
1.5 DL
0.9 DL + 1.5 WLY
1.5 ( DL + LL)
1.2 ( DL + LL + EQX )
1.2 (DL + LL + WLX )
1.2 ( DL + LL + EQX )
1.2 ( DL + LL + WLX )
1.2 ( DL + LL + EQY )
1.2 ( DL + LL + WLY )
1..2 ( DL + LL + EQY )
1.2 ( DL + LL + WLY )
1.5 ( DL + EQX )
1.5 ( DL + WLX )
1.5 ( DL + EQX )
1.5 ( DL + WLX )
1.5 ( DL + EQY )
1.5 ( DL + WLY)
1.5 ( DL + EQY )
0.9 ( DL + 1.5 WLX )
0.9 ( DL + 1.5 EQX )
0.9 ( DL + 1.5 WLX )
0.9 ( DL + 1.5 EQX )
0.9 ( DL + 1.5 WLY )
0.9 ( DL + 1.5 EQY )
1.5 ( DL + WLY )
0.9 ( DL + 1.5 EQY )

ANALYSIS

Buckling Analysis
Buckling analysis is carried out to predict the maximum load a structure can support prior to instability or Collapse The colored portions indicates regions with buckling load is maximum. The buckling load factors can be obtained from the software.
Fig 2.Column axial load
In conventional method, to avoid buckling we should multiply these buckling load factors as factor of safety to the loads acting on the building and design as per the resultant loads. Instead of this, the provision of using
buckling restrained braced frame on the building should be analyzed.
BUCKLING RESTRAINED BRACED FRAME
Star Seismic is an international manufacturer of Buckling restrained braces. The details of braces can be collected from star seismic manual. Star Seismic sections of size 1 incp to 52 incp are available. By selecting auto selection option the software itself select the suitable section for the structure. Here Star BRB of cross section 26.5 incp is selected. This process is called optimization of BRB.
TABLE VI. BRBF MATERIAL PROPERTIES
Core Material Density
7850 KN/m3
Modulus of Elasticity
2×105 MPa
Poissons Ratio
0.3
Shear Modulus
76903.07 Mpa
Minimum Yield stress
262 Mpa
Minimum Tensile Stress
399.9 Mpa
Effective Yield Stress
327.5 Mpa
Effective Tensile Strength
499.87 Mpa
TABLEVII. BRBF SECTION DETAIL
Weight
25.54 kN
Depth
406.4 mm
Width
304.8 mm
Area of yielding core
171 cm2
Stiffness of elastic segment
4334353.557 kN/m
Length of yielding core
4.2672
Length of elastic segent
2.2713
Linear Effective Axial Stiffness
676133.98 kN/m

Equivalent Static Analysis
Here parameters like storey displacement, storey drift and storey shear values of Conventional Buckling resistance building and BRBF building are compared.
Fig 3. Storey displacement Without BRB and With BRB Maximum value of storey displacement for conventional building is 29.57 Mm and for building with BRB the maximum storey displacement is 12.02 mm.
Fig 4. Storey drift Without BRB and with BRB
Maximum value of storey drift for building without is 29.5mm and maximum value of storey drift for building with BRB is 4.92 mm.
Fig 5. Storey shear Without BRB and with BRB Maximum storey shear for building Without BRB is 726.78 KN and Maximum storey shear for building with BRB 1990 kN. Maximum Displacement and Story Drift get reduced when BRB sections wereprovided.The Base shear increases with increase in weight.

Eigen Value Modal Analysis
Fig 6 .Building With BRBF
Fig 7 .Building Without BRBF
For building without BRBF, the modal participating mass ratio becomes 99% atMode 20 andfor building with BRBF the modal participating mass ratio becomes99% atMode

Less the number of modes, less will be the distortion of building.Circular frequency zero means applied load is close to critical buckling load.
TARGET RESPONSE SPECTRUM
According to IS 1893 there are four seismic zones in India.Code provide acceleration time graph for each seismic zone based on previousearthquake datas.
TIME HISTORY DATA FROM STRONG MOTION VIRTUAL DATA CENTRE
Collect datas of past 12earthquake occurredin India from strong motion virtual data centre.
SPECTRAL MATCHING
In spectral matching the response spectrum for different seismic zones provided by the code combines with acceleration time graph of various earthquakes collected from strong motion virtual data centre
Fig 8. Matched Response Spectrum
RELIABILITY INDEX
As per IS1893, total drift of the building should not exceed
0.004 times the buildingheight.The reliability index is typically used to measure the reliability of the building ,by using the maximum roof displacement of the building. MARGIN OF SAFETY

The margin of safety of a building is given by the following equation:

M = – (1)
where,
= allowable drift
= maximum roof displacement
maximum roof displacement for building at different heights are Plotted
30m 24m 18m 12m 6m
Figure 11.Safety margin curve for (6m)
Safety margin curve for 6 m height building is plotted.The standard deviation value is .004 and mean value is .021 and reliability index value is 5.27 along X direction.For Y direction the standard deviation value is .003 mean value is

and reliability index is 8.05.
ROORKEE UTTARKASHI
TEHRI SHILLONG PANIMUR JELLALPUR GHANSIALI
DAUKI CHERRAPUNJI
CHAMOLI CHAMBA
BHUJ
0 200 400 600 800
Figure 12. Safety margin curve for 12 m building
Safety margin curve for 12 m height building is plotted.The standard deviation value is .015 and mean value is .037 and reliability index value is 2.41 along X direction.For Y direction the standard deviation value is .035 mean value is
.026 and reliability index is .76.
Fig 9. Roof displacement in x direction(mm)
For building with more height ,displacement is less because lateral load get diminished along the height. The Cherrapunji earthquake induce more roof displacement and Shillong earthquake induce least roof displacement.
30m 24m 18m 12m 6m
30m 24m 18m 12m 6m
UTTARKASHI SHILLONG JELLALPUR
DAUKI CHAMOLI
BHUJ
UTTARKASHI SHILLONG JELLALPUR
DAUKI CHAMOLI
BHUJ
0
200
400
600
800
0
200
400
600
800
Fig 10.Roof displacement in ydirection (mm)
The Cherrapunji earthquake induce more roof displacement and Shillong earthquake induce least roof displacement.
Fig 13.Safety margin curve for 18 m
Safety margin curve for 18 m height building is plotted.The standard deviation value is .011 and mean value is .059 and reliability index value is 5.34 along X direction.For Y direction the standard deviation value is 0.086 mean value is .016 and reliability index is .18.
Fig 14.Safety margin curve for 24 m height building
Safety margin curve for 18 m height building is plotted.The standard deviation value is .142 and mean value is .029 and reliability index value is .20 along X direction.For Y direction the standard deviation value is 0.088 mean value is .005 and reliability index is .05.
Fig 15.Safety margin curve for 30 m height building
Safety margin curve for 30 m height building is plotted.The standard deviation value is .043 and mean value is .063 and reliability index value is 1.47 along X direction.For Y direction the standard deviation value is 0.091 mean value is .010 and reliability index is .11.
TABLE VIII. DEVELOPED RELIABILTY INDEX FOR BRBF
Storey Height(m)
Minimum Range
Maximum Range
30
0.11
1.70
24
0.05
0.20
18
0.18
5.34
12
0.76
2.41
6
5.27
8.05
time period, higher circular frequency and higher eigenvalue, so BRBF is more buckling resistant.The reliability index of a structure increases when the probability of failure reduces.Here for 30 m building reliability index ranges from .11 to 1.7 and for 24 m building reliability index ranges from .50 to .2. For 18 m building reliability index varies from .18 to 5.34 and for 12 m building reliability index is from .76 to 2.41.In the case of 6 m heigh buiding the value varies from 5.27 to 8.05.
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CONCLUSION
By using Buckling restrained braced frames 40% reduction in storey displacement and storey drift value became negligible when compared with conventional building.The storey shear of structure increases due to increase in weight. So BRBF is better than conventional buckling resisting buildings . FEMA356 recommends 99% mass participation is required to obtain requirednumber of modes in modal analysis.Less the number of modes, less will be the distortion of building. BRBF have less fundamental