Storey Response of G+40 Horizontally Connected Buildings with Dampers

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Storey Response of G+40 Horizontally Connected Buildings with Dampers

Mayuri M. Baviskar

Department of Civil Engineering MGMs Jawaharlal Nehru Engineering College

Aurangabad, Maharashtra, India

Prof. L. G. Kalurkar

Department of Civil Engineering MGMs Jawaharlal Nehru Engineering College

Aurangabad, Maharashtra, India

Abstract Analyzing the response of structure to ground shaking caused by an earthquake is one the most important application of structural dynamics. Tall structures are more exposed to dynamic loads, earthquake and wind effects. Tall buildings are characterized by low natural frequency. Hence, they can vibrate significantly under lateral dynamic earthquake loads. This paper deals with the analysis of G+40 storey buildings connected horizontally with the truss bridge at 21st and 31st storey having fixed base and shows the storey response curves of buildings connected with dampers and without dampers. The building frame type used is ordinary moment resisting frame (OMRF). The dampers used are fluid viscous dampers (FVD) having force capacity of 500KN. The analysis is done using ETABS V16 software.

Keywords Dampers, fluid viscous damper, storey response curve, fixed base, seismic response, ordinary moment resisting frame, ETABS V16.

structure can all collapse or part collapse or wont collapse throughout or after earthquake, time history analysis is required to perform. The results obtained from analysis are studied to know the actual behavior of structure.

I.INTRODUCTION

As the business activities demands to be on the point of one another and at the town centre, tall buildings get a lot of attention in todays life. Also, because they form distinctive landmark, tall buildings are oftentimes developed in town centers as status image for company organization. Due to the speedy increase in population and reduction in accessibility of land, vertical accommodation is obtaining a lot of preference which is resulting in vertical town development. The higher land costs, reduction in urban sprawl and for agricultural production, residential buildings are growing upward. Buildings are designed primarily to serve the needs of occupancy whether residential or commercial. At the same time, clients requirement regarding aesthetic qualities plays important role.

The modeling of high rise structure for analysis is depends on the approach of research. The bottom shaking that occurs in an earthquake are often represented as a series of multidirectional random acceleration pulses. The seismal response of tall building will depend on the dynamic properties of the structure, ground motion at the foundation and mode of soil structure interaction. Response spectrometry shows that how the structure will respond if damping is elicited. Various curves are developed with different levels of damping. As damping increases, response spectra shift downward. As per typical earthquake resistant design, structure is designed for forces which are much less than the actual design earthquake forces. Therefore, throughout earthquake event, structure undergoes severe non resilient deformation with non repairable damages. RCC structure can be made ductile with the help of reinforcing steel. Thus, to grasp whether or not the

Fig 1: Real horizontally connected structures.

  1. EXAMPLE BUILDING

    Building set up chosen for this project is as shown in figure below. Two buildings are connected by a truss bridge of 50m length at twenty first floor and thirty first floor. The structure is built with ordinary moment resisting frame (OMRF). Both buildings are symmetric to each other and considered to be served as residential building. Building is having forty storeys for accommodation purpose and top story as terrace. The columns are fixed at base. Two column sizes are utilized in

    structure. Column of size 0.85m x 0.65m are used up to 10th storey and 0.75m x 0.55m are used for rest of the storey. Beams having cross sectional size 0.3m x 0.6m. The floor to floor height is kept constant as 3m and slab thickness as 0.18m throughout the structure. 4 lifts are provided at each floor per building. Shear wall of 0.3m thick are used for the lift sections. Concrete grades used are M35 and M40 while steel used is of grade HYSD500. Instead of traditional brick wall Autoclave Aerated Concrete (AAC) Blocks are used as wall having unit weight ranging from 4.6 kN/m3 to 7.5 kN/m3 which is almost 1/3rd of normal concrete. Building is analyzed for all zones for earthquake. Load combinations are taken as per IS 456:2000 and earthquake loading is taken as per IS 1893:2002. Load combinations used are listed below: 1.5(DL+LL)

    1.5(DL±EQx)

    1.5(DL±EQy)

    1.5(DL±WLx)

    1.5(DL+±WLy)

    1.2(DL+LL±EQx)

    1.2(DL+LL±EQy)

    1.2(DL+LL±WLx)

    1.2(DL+LL±WLy)

    0.9DL±1.5EQx

    0.9DL±1.5EQy

    Fig 2: 3-D view of G+40 building.

    1. Fluid Viscous Dampers:

      The fluid viscous dampers are hydraulic devices that dissipate the mechanical energy of seismal events and cushion the

      impact between structures. Theyre versatile and might be designed to permit free movement in addition as controlled damping of a structure to safeguard from wind load, thermal motion or seismic events. The fluid viscous damper is consisting of oil cylinder, piston, piston rod, lining, medium, pin head and other main parts. The piston may create mutual motion within the oil cylinder. The piston is provided with damping structure and therefore the oil cylinder is jam-packed

      with fluid damping medium. Once the external stimulation (such as earthquake, wind vibration) reaches to the engineering structure, itll be deformed and drive the damper to move, which will occur the pressure difference on the different side of the piston. Then the medium can undergo the damping structure and make damping power, which will occur the exchange of power (the mechanical power exchange to heat power). All which will reach the aim of reducing the engineering structures vibration.

      Fig 3: schematic diagram of Fluid Viscous Damper

      Damper system are designed and made to safeguard structural integrities, management and stop structural damages by fascinating seismic energy and reduces deformations within the structure. Due to easy installation, adaptability, coordination with other members and variety in their sizes, viscous dampers have several applications in planning and retrofitting..

      In this project, each building is connected with 6 fluid viscous dampers at alternate floors. Dampers having capacity of 500kN are used. Table showing damper capacity is shown below:

      TABLE 1: FVD WITH DIFFERENT CAPACITIES FORCES (KN)

      Force (kN)

      Spherical Bearing Bore Diameter (mm)

      Stroke (mm)

      Clevis Thickness (mm)

      Weight (kg)

      250

      38.10

      ±75

      43

      44

      500

      50.80

      ±100

      55

      98

      750

      57.15

      ±100

      59

      168

      1000

      69.85

      ±100

      71

      254

      1500

      76.20

      ±100

      77

      306

      2000

      88.90

      ±125

      91

      500

      3000

      101.60

      ±125

      117

      800

      4000

      127.00

      ±125

      142

      1088

      6500

      152.40

      ±125

      154

      1930

    2. Response Spectrum Analysis:

      Response spectra are curves plotted between maximum response of system subjected to specified earthquake ground motion and its time period (or frequency). Response spectrum can be interpreted as the locus of maximum response of a system for given damping ratio. Response spectra thus helps in obtaining the peak structural responses under linear range, which can be used for obtaining lateral forces developed in structure due to earthquake thus facilitates in earthquake-

      25th floor

      41.141

      50.107

      24th floor

      39.152

      47.836

      23rd floor

      37.285

      45.539

      22ndfloor

      35.258

      43.221

      21st floor

      33.373

      40.888

      20th floor

      31.328

      38.545

      19th floor

      29.446

      36.199

      18th floor

      27.405

      33.859

      17th floor

      25.545

      31.533

      16th floor

      23.534

      29.226

      15th floor

      21.718

      26.941

      14th floor

      19.75

      24.68

      13th floor

      17.997

      22.449

      12th floor

      16.093

      20.254

      11th floor

      14.426

      18.102

      10th floor

      12.608

      15.998

      9th floor

      11.054

      13.951

      8th floor

      9.348

      11.968

      7th floor

      7.94

      10.059

      6th floor

      6.377

      8.236

      5th floor

      5.17

      6.511

      4th floor

      3.793

      4.901

      3rd floor

      2.82

      3.479

      2nd floor

      1.743

      2.203

      1st floor

      1.067

      1.13

      PL

      0.298

      0.343

      GL

      0.105

      0.044

      Base

      0

      0

      25th floor

      41.141

      50.107

      24th floor

      39.152

      47.836

      23rd floor

      37.285

      45.539

      22ndfloor

      35.258

      43.221

      21st floor

      33.373

      40.888

      20th floor

      31.328

      38.545

      19th floor

      29.446

      36.199

      18th floor

      27.405

      33.859

      17th floor

      25.545

      31.533

      16th floor

      23.534

      29.226

      15th floor

      21.718

      26.941

      14th floor

      19.75

      24.68

      13th floor

      17.997

      22.449

      12th floor

      16.093

      20.254

      11th floor

      14.426

      18.102

      10th floor

      12.608

      15.998

      9th floor

      11.054

      13.951

      8th floor

      9.348

      11.968

      7th floor

      7.94

      10.059

      6th floor

      6.377

      8.236

      5th floor

      5.17

      6.511

      4th floor

      3.793

      4.901

      3rd floor

      2.82

      3.479

      2nd floor

      1.743

      2.203

      1st floor

      1.067

      1.13

      PL

      0.298

      0.343

      GL

      0.105

      0.044

      Base

      0

      0

      resistant design of structures. The three spectra i.e. displacement, pseudo velocity and pseudo acceleration provide the same information on the structural response. However, each one of them provides a physically meaningful quantity and therefore, all three spectra are useful in understanding the nature of an earthquake and its influence on the design. A combined plot showing all three of the spectral quantities is possible because of the relationship that exists between these three quantities.

    3. Time History Analysis:

      The actual method of mixing the various modal contributions is a probabilistic averaging technique and in some cases, results will not represent the actual behaviour of structure. Time history analysis overcomes this. However, it needs massive procedure efforts. The tactic consists of a step by step direct integration in which the time domain is discretized into a number of tiny increments and for every quantity the equation of motion is solved with the displacements and velocities of the previous step serving as initial functions. The tactic is applicable to both elastic and inelastic analyses. In elastic analysis, the stiffness characteristics of structure are assumed to be constant for whole duration of the earthquake. In inelastic analysis, the stiffness is assumed to be constant through the progressive time solely.

      The proposed building in Zone V with site condition III is analysed for both response spectrum and time history analysis with time history data of El-Centro earthquake in 1940. The analysis is done for with damper condition and without damper condition also. 5% damping is allowed in the structure. The graphs of Spectral Displacement Vs Period, Pseudo Spectral Velocity Vs Period and Pseudo Spectral Acceleration Vs Period are obtained which are shown in result section.

  2. RESULTS

    The proposed building in analyzed in different zones of earthquake and the displacement value of each storey are tabulated for with damper and without damper condition for each zone. Chart 1 shows the displacement values of building in Zone II with site type I. Chart 2 shows the displacement values of building in Zone III with site type III. Chart 3 shows the displacement values for Zone IV with site type II and chart 4 shows displacement values for Zone V with site type III.

    Storey

    With Damper

    Without Damper

    top

    66.266

    79.234

    40th floor

    65.392

    77.96

    39th floor

    64.115

    76.563

    38th floor

    62.787

    75.087

    37th floor

    61.397

    73.549

    36th floor

    59.954

    71.944

    35th floor

    58.478

    70.269

    34th floor

    56.919

    68.524

    33rd floor

    55.357

    66.709

    32ndfloor

    53.686

    64.828

    31st floor

    52.042

    62.884

    30th floor

    50.269

    60.88

    29th floor

    48.551

    58.82

    28th floor

    46.69

    56.707

    27th floor

    44.907

    54.548

    26th floor

    42.974

    52.346

    Storey

    With Damper

    Without Damper

    top

    66.266

    79.234

    40th floor

    65.392

    77.96

    39th floor

    64.115

    76.563

    38th floor

    62.787

    75.087

    37th floor

    61.397

    73.549

    36th floor

    59.954

    71.944

    35th floor

    58.478

    70.269

    34th floor

    56.919

    68.524

    33rd floor

    55.357

    66.709

    32ndfloor

    53.686

    64.828

    31st floor

    52.042

    62.884

    30th floor

    50.269

    60.88

    29th floor

    48.551

    58.82

    28th floor

    46.69

    56.707

    27th floor

    44.907

    54.548

    26th floor

    42.974

    52.346

    TABLE 2: STOREY DISPLACEMENT IN ZONE II (X-DIRECTION)

    Chart -1(a): Comparison of storey displacement in Zone II (x-direction)

    Storey

    With Damper

    Without Damper

    top

    144.194

    172.414

    40th floor

    142.293

    169.641

    39th floor

    139.513

    166.601

    38th floor

    136.626

    163.389

    37th floor

    133.599

    160.042

    36th floor

    130.46

    156.549

    Storey

    With Damper

    Without Damper

    top

    144.194

    172.414

    40th floor

    142.293

    169.641

    39th floor

    139.513

    166.601

    38th floor

    136.626

    163.389

    37th floor

    133.599

    160.042

    36th floor

    130.46

    156.549

    Chart -1(b): Comparison of storey displacement in Zone II (y-direction) TABLE 3: STORY DISPLACEMENT IN ZONE III (X-DIRECTION)

    35th floor

    127.249

    152.905

    34th floor

    123.855

    149.107

    33rd floor

    120.457

    145.16

    32ndfloor

    116.821

    141.066

    31st floor

    113.243

    136.835

    30th floor

    109.386

    132.474

    29th floor

    105.647

    127.992

    28th floor

    101.597

    123.395

    27th floor

    97.719

    118.696

    26th floor

    93.511

    113.905

    25th floor

    89.523

    109.033

    24th floor

    85.194

    104.092

    23rd floor

    81.131

    99.093

    22ndfloor

    76.721

    94.049

    21st floor

    72.62

    88.971

    20th floor

    68.17

    83.873

    19th floor

    64.074

    78.769

    18th floor

    59.632

    73.677

    17th floor

    55.587

    68.616

    16th floor

    51.21

    63.597

    15th floor

    47.258

    58.623

    14th floor

    42.975

    53.703

    13th floor

    39.162

    48.849

    12th floor

    35.018

    44.073

    11th floor

    31.392

    39.39

    10th floor

    27.435

    34.812

    9th floor

    24.054

    30.357

    8th floor

    20.34

    26.042

    7th floor

    17.277

    21.888

    6th floor

    13.876

    17.921

    5th floor

    11.25

    14.168

    4th floor

    8.254

    10.665

    3rd floor

    6.136

    7.57

    2nd floor

    3.793

    4.793

    1st floor

    2.321

    2.459

    PL

    0.648

    0.746

    GL

    0.229

    0.096

    Base

    0

    0

    Chart 2(a): Comparison of story displacement in Zone III (x-direction)

    Chart 2(b): Comparison of storey displacement in Zone III (y-direction)

    TABLE 4: STOREY DISPLACEMENT IN ZONE IV (X-DIRECTION)

    Storey

    With Damper

    Without Damper

    top

    265.593

    317.571

    40th floor

    262.092

    312.463

    39th floor

    256.971

    306.865

    38th floor

    251.652

    300.949

    37th floor

    246.078

    294.783

    36th floor

    240.296

    288.35

    35th floor

    234.381

    281.637

    34th floor

    228.131

    274.643

    33rd floor

    221.872

    267.371

    32ndfloor

    215.173

    259.832

    31st floor

    208.584

    252.038

    30th floor

    201.48

    244.005

    29th floor

    194.592

    235.75

    28th floor

    187.133

    227.283

    27th floor

    179.989

    218.627

    26th floor

    172.239

    209.802

    25th floor

    164.894

    200.829

    24th floor

    156.92

    191.728

    23rd floor

    149.437

    182.521

    22ndfloor

    141.313

    173.23

    21st floor

    133.761

    163.877

    20th floor

    125.564

    154.487

    19th floor

    118.019

    145.086

    18th floor

    109.838

    135.706

    17th floor

    102.386

    126.384

    16th floor

    94.324

    117.14

    15th floor

    87.046

    107.978

    14th floor

    79.156

    98.916

    13th floor

    72.133

    89.976

    12th floor

    64.499

    81.179

    11th floor

    57.821

    72.552

    10th floor

    50.532

    64.121

    9th floor

    44.306

    55.915

    8th floor

    37.465

    47.967

    7th floor

    31.823

    40.316

    6th floor

    25.559

    33.008

    5th floor

    20.721

    26.096

    4th floor

    15.204

    19.644

    3rd floor

    11.302

    13.943

    2nd floor

    6.987

    8.828

    1st floor

    4.275

    4.529

    PL

    1.193

    1.374

    GL

    0.422

    0.176

    Base

    0

    0

    Chart 3(a): Comparison of storey displacement in Zone IV (x-direction)

    Storey

    With Damper

    Without Damper

    top

    430.305

    524.387

    40th floor

    424.678

    516.047

    39th floor

    416.464

    506.927

    38th floor

    407.940

    497.3

    37th floor

    399.004

    487.273

    36th floor

    389.745

    476.814

    35th floor

    380.265

    465.902

    34th floor

    370.256

    454.533

    33rd floor

    360.223

    442.712

    32ndfloor

    349.494

    430.453

    31st floor

    338.926

    417.775

    30th floor

    327.539

    404.701

    29th floor

    316.483

    391.258

    28th floor

    304.514

    377.458

    27th floor

    293.033

    363.339

    26th floor

    280.580

    348.931

    25th floor

    268.760

    334.265

    24th floor

    255.925

    319.373

    23rd floor

    243.863

    304.289

    22ndfloor

    230.761

    289.049

    21st floor

    218.566

    273.687

    20th floor

    205.320

    258.241

    19th floor

    193.112

    242.758

    18th floor

    179.861

    227.285

    17th floor

    167.779

    211.885

    16th floor

    154.689

    196.588

    15th floor

    142.863

    181.403

    14th floor

    130.021

    166.357

    13th floor

    118.580

    151.486

    12th floor

    106.121

    136.829

    11th floor

    95.215

    122.426

    10th floor

    83.285

    108.324

    9th floor

    73.092

    94.57

    8th floor

    61.861

    81.223

    7th floor

    52.589

    68.349

    6th floor

    42.272

    56.027

    5th floor

    34.310

    44.347

    4th floor

    25.189

    33.421

    3rd floor

    18.756

    23.749

    2nd floor

    11.610

    15.054

    1st floor

    7.116

    7.732

    PL

    1.988

    2.344

    GL

    0.703

    0.301

    Base

    0

    0

    Storey

    With Damper

    Without Damper

    top

    430.305

    524.387

    40th floor

    424.678

    516.047

    39th floor

    416.464

    506.927

    38th floor

    407.940

    497.3

    37th floor

    399.004

    487.273

    36th floor

    389.745

    476.814

    35th floor

    380.265

    465.902

    34th floor

    370.256

    454.533

    33rd floor

    360.223

    442.712

    32ndfloor

    349.494

    430.453

    31st floor

    338.926

    417.775

    30th floor

    327.539

    404.701

    29th floor

    316.483

    391.258

    28th floor

    304.514

    377.458

    27th floor

    293.033

    363.339

    26th floor

    280.580

    348.931

    25th floor

    268.760

    334.265

    24th floor

    255.925

    319.373

    23rd floor

    243.863

    304.289

    22ndfloor

    230.761

    289.049

    21st floor

    218.566

    273.687

    20th floor

    205.320

    258.241

    19th floor

    193.112

    242.758

    18th floor

    179.861

    227.285

    17th floor

    167.779

    211.885

    16th floor

    154.689

    196.588

    15th floor

    142.863

    181.403

    14th floor

    130.021

    166.357

    13th floor

    118.580

    151.486

    12th floor

    106.121

    136.829

    11th floor

    95.215

    122.426

    10th floor

    83.285

    108.324

    9th floor

    73.092

    94.57

    8th floor

    61.861

    81.223

    7th floor

    52.589

    68.349

    6th floor

    42.272

    56.027

    5th floor

    34.310

    44.347

    4th floor

    25.189

    33.421

    3rd floor

    18.756

    23.749

    2nd floor

    11.610

    15.054

    1st floor

    7.116

    7.732

    PL

    1.988

    2.344

    GL

    0.703

    0.301

    Base

    0

    0

    Chart 3(b): Comparison of storey displacement in Zone IV (y-direction) TABLE 5: STOREY DISPLACEMENT IN ZONE V (X-DIRECTION)

    Chart 4(a): Comparison of storey displacement in Zone V (x-direction)

    Chart 4(b): Comparison of storey displacement in Zone V (y-direction)

    TABLE 6: COMPARISON OF MAXIMUM DISPLACEMENTS OF BUILDING (X-DIRECTION)

    ZONE

    II

    III

    IV

    V

    with damper

    66.266

    144.195

    267.07

    430.3

    without damper

    79.234

    172.41

    317.57

    524.387

    Chart 5(a): Comparison of maximum displacements of building (x-direction)

    TABLE 7: COMPARISON OF MAXIMUM DISPLACEMENTS OF BUILDING (Y-DIRECTION)

    ZONE

    II

    III

    IV

    V

    with damper

    66.636

    145

    265.59

    434.029

    without damper

    90.069

    195.96

    360.99

    601.809

    Chart 5(b): Comparison of maximum displacements of building (y-direction)

    Building in Zone V is again analysed for time history analysis with time history data of El-Centro earthquake in order to compare the difference in spectral acceleration, spectral velocity and spectral displacement of building for with damper and without damper condition. The obtained response spectrum curves having 5% damping are shown below. Table 7 summarizes maximum and minimum values of acceleration, velocity and displacement at 0% damping and 0.1% damping.

    Characteristics

    With damper

    Without damper

    Pseudo spectral Acceleration (mm/sec²)

    0%

    damping

    0.10%

    damping

    0%

    damping

    0.10%

    damping

    4060.08

    440.9

    7206.58

    497.55

    Pseudo spectral velocity (mm/sec)

    1092.26

    2.35

    1485

    2.5

    Spectral displacement(mm)

    968.5

    0.011

    1492.238

    0.012

    Characteristics

    With damper

    Without damper

    Pseudo spectral Acceleration (mm/sec²)

    0%

    damping

    0.10%

    damping

    0%

    damping

    0.10%

    damping

    4060.08

    440.9

    7206.58

    497.55

    Pseudo spectral velocity (mm/sec)

    1092.26

    2.35

    1485

    2.5

    Spectral displacement(mm)

    968.5

    0.011

    1492.238

    0.012

    TABLE 8: MAXIMUM AND MINIMUM VALUES OF RESPONSE SPECTRUM CHARACTERISTICS

    Fig 4(b): PSA Vs Time period (without damper condition)

  3. CONCLUSION

    From Table 6 and Table 7 it is observed that by providing dampers overall displacement of building in each zone is considerably reduced. Percentage reduction in displacement for Zone II, Zone III and Zone IV is approximately 16% whereas for Zone V it is approximately 18% for x-direction. On other hand, for y-direction percentage reduction in displacement for Zone II, Zone III and Zone IV is approximately 26% and for Zone V is approximately 28%. From Table 7 it is observed that although having 5% damping in the building, the response spectrum characteristics such as pseudo spectral acceleration, pseudo spectral velocity and spectral displacement are much reduced after the application of dampers in the building. For 0% damping, pseudo spectral acceleration is reduced by approximately 44% while for 0.1% damping it is reduced by approximately 11%. It may be possible to increase the percentage reduction in displacement by increasing the capacity of fluid viscous dampers and the dampers are found to be very effective in reducing earthquake responses.

    Fig 4(a): PSA Vs Time period (with damper condition)

  4. REFERENCES

    1. Pramodini Naik, Satish Annigeri. Performance Evaluation Of 9 Storey RC Building Located In North Goa. 11th International Symposium On Plasticity And Impact Mechanics, Implast 2016.

    2. Savita C. Majage, Prof. N. P. Phadtare. Dynamic Analysis And Design of G+8 Storey RC Structure By Providing Lead Rubber Bearing as Base Isolation System. International Research Journal of Engineering and Technology. Volume 05 Issue: 08. Aug 2018.

    3. Sayed Mahmoud. Horizontally Connected High Rise Building Under Earthquake Loading. Ain Shams Engineering Journal 10 (2019) 227-241.

    4. Ji Dongyu, Li Xiaofen. Seismic Behaviour Analysis of High Rise Connected Structure. International Conference on Mechatronics, Electronic, Industrial and Control Engineering (MEIC 2014).

    5. Surendra Chaurasiya, Sagar Jamle. Twin Tower High Rise Building Subjected To Seismic Loading: A Review. International Journal of Advanced Engineering Research And Science. Vol-6, Issue-4, Apr-2019.

    6. A.V. Bhaskararao, R. S. Jangid. Seismic Response Of Adjacent Buildings Connected With Dampers. 13th World Conference on Earthquake Engineering. Vancouver, B.C., Canada. August 1-6, 2004. Paper No. 3143.

    7. S. Shamshad Begum, Dr. G. Vani. Analysis of a High Rise Unsymmetrical Building with Dampers Using Etabs. 2016 Ijsrst, Volume 2, Issue 3.

    8. Wensheng LU and Xilin LU, (2000). Seismic Modal Test And Analysis Of Multi-Tower High-Rise Buildings. 12th World Conference on Earthquake Engineering, Pp. 0281.

    9. Bryan Stafford Smith, Alex Couli.Tall Building Structures, Analysis and Design.

    10. Bungale S. Taranath. Structural Analysis and Design Of Tall Buildings.

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