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

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