Analytical Investigation on the Performance of Tube-In-Tube Structures Subjected to Lateral Loads

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Analytical Investigation on the Performance of Tube-In-Tube Structures Subjected to Lateral Loads

Nimmy Dileep

PG Scholar, Dept. of Civil Engineering Sree Buddha College of Engineering, Pattoor

Nooranad, Alappuzha Dist

Renjith R

Assistant Professor, Dept. of Civil Engineering Sree Buddha College of Engineering, Pattoor Nooranad, Alappuzha Dist

Abstract Over the past few years tubular structures are becoming a common feature in tall buildings. Tube in tube structures is particularly suitable for all tall buildings. A tube – in tube structure comprises of a peripheral framed tube and a core tube interconnected by floor slabs. The entire building act as a huge tube with a smaller tube in middle of it. Lateral loads are shared between the inner and outer tubes .In order to study the seismic performance of tube in tube structures three different models were developed in SAP2000 software by varying the location of the inner tubes. The structures are analyzed using continuum approach in which the horizontal slabs and beams connecting vertical elements are assumed as continuous connecting medium having equivalent distributed stiffness properties. Equivalent static and Time history analysis is done and the output of three models are evaluated to have a comparative study of their seismic performance.

Keywords Tube in- Tube, Static analysis, Time history analysis

  1. INTRODUCTION

    Nowadays, the advancements in structural systems, increase in building height and slenderness, use of high strength materials, reduction of building weight etc has necessitated the consideration of lateral loads such as wind and earthquake in the design process. Lateral forces resulting from wind and seismic activities are now dominant in design considerations. Lateral displacement of such buildings must be strictly controlled, not only for occupants comfort and safety, but also to control secondary structural effects. Currently, there are many structural systems such as rigid frame, braced frame, shear-walled frame, frame-tube, braced- tube, bundled-tube and outrigger systems that can be used to enhance the lateral resistance in tall buildings.

    Tubular structures have been successfully utilized and are becoming a common feature in tall buildings. Basic forms of tubular systems are the framed tube, core tube, tube-in-tube and bundled tube. A tube-in-tube structure comprises of a peripheral framed tube and a core tube interconnected by floor slabs. For each of these vertical components, various simplified models have been developed that analyze structures behavior under lateral loads. Approximate techniques for a single tube and multi-tube systems have been developed by many researchers over the past decades.

    The exterior and interior columns of a tube-in-tube structure are placed so closely together that they not only appear to be solid, but they act as a solid surface as well. The entire building acts as a huge hollow tube with a smaller tube in the middle of it. Lateral loads are shared between the inner and outer tubes.

  2. LITERATURE RIVEW

    Peter C. Chang(1) (1985) analyzed Tube-in-tube structures using a continuum approach. Flexural deformation, shear deformation, and shear-lag effects are studied. The beams are forced to have equal lateral deflections, and the amount of load carried by each beam is a function of its relative stiffness The analyses are performed using the Minimum Potential Energy principle, and the results are compared with results of finite element analyses. An efficient method for determining the global deflection behavior of a tube-in-tube structure was presented.. Displacement compatibility of lateral deflections between the two tubes is enforced, thereby reducing the two sets of differential equations to a set of 10 first-order differential equations.

    J. J, Connor and C. C. Pouangare(2) (1991) proposed a very simple model for the analysis and design of framed-tube structures subjected to lateral loads. The structure is modeled as a series of stringers and shear panels. The analytical expressions for the stresses and displacements are done to attain the desired results. The model can be used directly for the analysis of structures that incorporate different materials and different properties along the height of the structure

    1. R. Jahanshahi, R. Rahgozar, M. Malekinejad (3)( 2012) They presents parametric functions for static analysis of tall buildings with combined system of tube in- tube and outrigger-belt truss system subjected to three separate load cases of concentrated load at top of the structure, uniformly and triangularly distributed loads along the height of the structure. The formulas proposed here have been validated by comparing them to the computer static analysis results obtained from three-dimensional studies using the finite element method. It has been shown that results computed by the energy method correlate well with those obtained by means of SAP2000 analysis.

      Kang-Kun Lee, Yee-Chaye Loo, Hong Guan(4) (2001) A simple mathematical model is proposed for the approximate analysis of framed-tube structures with multiple internal tubes. The accuracy, simplicity, and reliability of the proposed method are verified through the comparisons with the two existing simplified methods and a 3D frame analysis program. The additional lateral stiffness due to the tube-tube interaction is also accounted for in the analysis. The additional bending stresses are observed to have significant effect on the shear-lag phenomenon. In comparison with the 3D frame analysis program, the only other approach available for the tubes-in-tube system, the proposed method provides similarly accurate results in predicting the deflection response and the column axial stress distributions.

  3. SCOPE OF WORK

    The main objective of this thesis is to investigate the performance of a tube in tube structure with different positioning of the internal tube. The study is done in 3D models developed in SAP 2000. Static and Time history analysis of each sets of models and the comparison of these two methods is done. The effect of different positions of the internal tube during the seismic loading is included in studied.

    The displacement parameters at each floor level for Equivalent static and Time history are plotted and a comparative study is conducted which is expected to present the effect of torsion and pounding gap of adjacent building.

  4. MODEL DETAILS

    Three sets of 15 storied building are modeled with story height 4m. the total base area of the building is 51 x 51 m2. All models have the same plan but the interior positioning of the inner tubes are varied to compare the result of their seismic performance. The building consists of rectangular columns with dimensions 1200 x 600 and beams with dimension 600 x 250. The floor slabs are of 280mm thick and the tube side walls are of 250mm thick. The modulus of elasticity (E) and the shear modulus (G) are taken as 2.73x 107 KN/m2 and 1.14 x 107 KN/m2.

    In the present study a commercial building under seismic zone V is adopted with varying the positioning of the internal tube. The base plan and various positioning are shown in Fig. 1and 2.

    The gravity loads include beam, column, slab, wall and other permanent members. The self weight of the beams, columns (frame members) and slab (area element) is automatically considered by the program itself. The wall loads are calculated separately and applied as uniformly distributed load on beams. Live loads are assigned as uniform area load on slab element as per IS 1893 (Part 1) 2002 Live load on roof is taken as 4 KN/ m2 and that on floors are taken as 5 KN/ m2.

    Fig. 1. Base plan

    Fig.2. Positioning of internal tubes

    v. ANALYSIS DONE

    Two types of analysis procedures are carried out to determine the behavior of the structure under the effect of seismic loads.

    The analyses carried out are

      1. Equivalent static analysis

      2. Time history analysis

    Analysis type

    Usual name

    Dynamic effect

    Non linearity

    Linear static

    Equivalent static analysis

    No

    No

    Non linear dynamic

    Time history analysis

    Yes

    Yes

    1. Equivalent static analysis:

      This procedure is carried according to IS 1893 (Part 1) 2002. First the design base shear is computed for the building and then it is distributed along the total height. Thus the lateral force at each floor level is distributed to individual lateral load resisting element. Since the live load coming in each floor is greater than 3 KN/m2 the seismic weight is taken as dead load plus 50% live load. Hence the lateral load resisting system adopted is ductile shear wall with SMRF accordingly response reduction factor is adopted is 5.

    2. Time history analysis

      Mathematical models of the building are developed and they are subjected to accelerations from previous earthquake records. The method consist of step by step direct integration over a time interval: equations of motion are solved with displacement, velocities and accelerations of previous step serving as initial functions. The equation of motion is represented in equation 1.

      ( ) + ()+ () = () (1)

      Where m is the diagonal mass matrix, k is the stiffness matrix and c is the damping matrix. ( ), ( ), (), are the acceleration, velocity and displacement and applied load respectively.

      The analysis is carried out using Lacc North 1 earthquake for obtaining various floor responses. Ritz vector model is assigned and modal analysis is done to get the response.

      1. RESULTS

        The results of equivalent static and time history analysis for all the 3 models are listed below:

        1. Table 1 and Fig.3 illustrates the comparison of story drift with respect to story height done in static analysis.

        2. Table 2 and Fig.4 illustrates the comparison of story drift with respect to height done in time history analysis.

        3. Table 3 and Fig.5 illustrates the difference in results of static and time history analysis.

    The comparison results are tabulated in tables 1 to 3.

    Height(m)

    Deflection(mm)

    Model 1

    Model 2

    Model 3

    4

    0.328

    0.25

    0.275

    8

    1.075

    0.811

    0.902

    12

    2.068

    1.574

    1.735

    16

    3.225

    2.458

    2.711

    20

    4.514

    3.449

    3.807

    24

    5.917

    4.544

    5.014

    28

    7.418

    5.738

    6.327

    32

    9.006

    7.026

    7.74

    36

    10.683

    8.398

    9.239

    40

    12.428

    9.834

    10.802

    44

    14.193

    11.305

    12.394

    48

    15.923

    12.77

    13.971

    52

    17.557

    14.177

    15.474

    56

    19.005

    15.463

    16.836

    60

    20.224

    16.573

    17.996

    64

    21.204

    17.515

    18.964

    Height(m)

    Deflection(mm)

    Model 1

    Model 2

    Model 3

    4

    0.328

    0.25

    0.275

    8

    1.075

    0.811

    0.902

    12

    2.068

    1.574

    1.735

    16

    3.225

    2.458

    2.711

    20

    4.514

    3.449

    3.807

    24

    5.917

    4.544

    5.014

    28

    7.418

    5.738

    6.327

    32

    9.006

    7.026

    7.74

    36

    10.683

    8.398

    9.239

    40

    12.428

    9.834

    10.802

    44

    14.193

    11.305

    12.394

    48

    15.923

    12.77

    13.971

    52

    17.557

    14.177

    15.474

    56

    19.005

    15.463

    16.836

    60

    20.224

    16.573

    17.996

    64

    21.204

    17.515

    18.964

    TABLE 1 VARIATION OF STORY HEIGHT WITH TO STATIC ANALYSIS

    FIG.3. VARIATION OF STORY DRIFT WITH RESPECT TO STORY HEIGHT IN STATIC ANALYSIS

    TABLE 2 VARIATION OF STORY HEIGHT WITH RESPECT TO TIME HISTORY ANALYSIS

    Height(m)

    Deflection (mm)

    Model 1

    Model 2

    Model 3

    4

    4.058

    5.331

    2.408

    8

    8.623

    10.114

    6.998

    12

    13.942

    14.784

    12.449

    16

    19.706

    19.327

    18.258

    20

    25.739

    23.793

    24.139

    24

    31.912

    28.183

    29.906

    28

    38.104

    32.466

    35.049

    32

    44.187

    36.606

    39.576

    36

    50.039

    40.571

    44.037

    40

    55.569

    44.328

    49.095

    44

    60.735

    47.83

    53.01

    48

    65.525

    51.016

    56.642

    52

    69.941

    53.852

    61.001

    56

    74.052

    56.34

    64.708

    60

    77.884

    58.455

    68.596

    TABLE 3 DIFFERENCE IN THE RESULTS OF STATIC AND TIME HISTORY ANALYSIS

    Model 2

    Height (m)

    Deflection Difference (mm)

    Model 1

    Model 3

    4

    3.73

    5.081

    2.133

    8

    7.548

    9.303

    6.096

    12

    11.874

    13.21

    10.714

    16

    16.481

    16.869

    15.547

    20

    21.225

    20.344

    20.332

    24

    25.995

    23.639

    24.892

    28

    30.686

    26.728

    28.722

    32

    35.181

    29.58

    31.836

    36

    39.356

    32.173

    34.798

    40

    43.141

    34.494

    38.293

    44

    46.542

    36.525

    40.616

    48

    49.602

    38.246

    42.671

    52

    52.384

    39.675

    45.527

    56

    55.047

    40.877

    47.872

    60

    57.66

    41.882

    50.6

    64

    60.218

    42.657

    53.12

    Fig.4. Variation of story drift with respect to story height in time history analysis

    Fig.5. Comarison of results of static and dynamic analysis

    1. CONCLUSION

The results of two methods of analysis are compared between the three sets of models to study the effect of lateral load pattern on displacements of buildings. From the above study it is concluded that time history analysis predicts the structural response more accurately than equivalent static analysis. It is seen that for a regular structure with seismic loading, the model with inner core located at the middle (model 2) yielded better results. Large displacements are seen in model 3 in which the positioning of the inner cores are in four corners and hence this type of arrangement is least recommended.

REFERENCES

  1. Peter C. Chang, Analytical modeling of tube-in-tube structure

    ASCE Journal of Structural Engineering, Vol. I l l , No. 6, June

  2. J. J, Connor and C. C. Pouangare Simple model for design of framed- tube ASCE Journal of Structural Engineering, Vol. 117, No. 12,December, 1991

  3. M. R. Jahanshahi, R. Rahgozar, M. Malekinejad A simple approach to static analysis of tall buildings with a combined tube-in tube and outrigger-belt truss system subjected to lateral loading Ije TransactionsA: Basics Vol. 25, No. 3, July 2012

  4. Kang-Kun Lee, Yee-Chaye Loo, Hong Guan Simple Analysis of Framed-Tube Structures with Multiple Internal Tubes Journal of Structural Engineering, Vol. 127, No. 4, April, 2001.

  5. .Myoungsu Shin1, Thomas H.-K. Kang ,James M. LaFave and Jacob S. Grossman Design and behavior of a reinforced concrete high-rise tube

    building with belt walls Struct. Design Tall Spec. Build. 2010

  6. Mir M. Ali Performance characteristic of tall framed tube buildings in seismic zones Eleventh World Conference Of Earthquake Engg 1996

  7. Wang Hi Bo, Shen Pu Sheng Nonlinear seismic response analysis of reinforced concrete tube in tube structures J Cent South Univ Technol Vol 12 October 2005

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