Reliability Analysis for Buckling Restrained Braced Frame (BRBF)

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.

1. 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, bond-preventing 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.

2. METHODOLOGY DATA COLLECTION

   LITERATURE REVIEW

   SOFTWARE STUDY MODELLING

   CONCLUSIONS

   CONCLUSIONS

   ANALYSIS RESULTS & DISCUSSION

3. 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 WL-Y
   1.5 ( DL + LL)	1.2 ( DL + LL + EQX )
   1.2 (DL + LL + WLX )	1.2 ( DL + LL + EQ-X )
   1.2 ( DL + LL + WL-X )	1.2 ( DL + LL + EQY )
   1.2 ( DL + LL + WLY )	1..2 ( DL + LL + EQ-Y )
   1.2 ( DL + LL + WL-Y )	1.5 ( DL + EQX )
   1.5 ( DL + WLX )	1.5 ( DL + EQ-X )
   1.5 ( DL + WL-X )	1.5 ( DL + EQY )
   1.5 ( DL + WL-Y)	1.5 ( DL + EQ-Y )
   0.9 ( DL + 1.5 WLX )	0.9 ( DL + 1.5 EQX )
   0.9 ( DL + 1.5 WL-X )	0.9 ( DL + 1.5 EQ-X )
   0.9 ( DL + 1.5 WLY )	0.9 ( DL + 1.5 EQY )
   1.5 ( DL + WLY )	0.9 ( DL + 1.5 EQ-Y )

4. ANALYSIS

   1. 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

   2. 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.

   3. 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

      1. 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

      1. 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 y-direction (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.

         REFERENCES

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         3. Arunraj E, Vincent Sam Jebadurai S, Samuel Abraham D, Daniel C, Hemalatha G. Analytical Investigation of Buckling Restrained Braced Frame Subjected To Non-Linear Static Analysis ,

            Volume-8 Issue-5, June 2019

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5. 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