Effect of Column Shortening on the Behavior of Tubular Structures

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Abstract

This paper presents the column shortening effect on the behavior of Tubular, Tube in tube and Bundled tube structure.

Frame tube buildings consist of closely spaced column connected by deep spandrel beams placed on the perimeter in plan.

A Tube in tube and Bundled tube structure of 50 storeys with storey height of 4 m is considered for the study, RC columns and spandrel beams are modelled with M70 and M110 concrete mix. Models are developed using ETABS software and the effect of elastic shortening of the RC column is included in the analysis to study the behavior by calculating member forces.

From the analysis, the effects due to elastic shortening in parameters such as axial force, shear force, bending moment and time period are obtained and compared between the tubular, tube in tube structure and bundled tube structure, there is a variation of about 25%, 20%, 23% and 74% and 23%, 17%, 25% and 57%. 19%, 15%, 31% and 60% respectively, which results in the reduction of member size, which ultimately reduces the dead load and the cost of construction.

Effect of Column Shortening on the Behavior of Tubular Structures

J. S. Arvind

^*

and M. Helen Santhi

SMBS, VIT University Chennai Campus, Chennai - 600127, Tamil Nadu, India; [email protected],

[email protected]

Keywords: Bundled Tube Structure, Elastic Column Shortening, Tube in Tube Tall Structure, Tubular Structure

1. Introduction

The vertical city concept has been manifested due to increase in population density and demand on cultivation land. The advancement of technology and the develop- ment of economy of the world have made the vertical city concept dream become true in the way of tall buildings/

towers. Fazlur Khan of Bangladesh has introduced the tall buildings concept and he had addressed many structural systems for the high-rise buildings. Some of the structural systems adopted for tall buildings are wall-frame structure, framed tube structures, outrigger-braced structures, suspended structures, core structures, space structures and hybrid structures for lateral loads supports¹.

The framed-tube of many type have being developed for lateral load resisting systems. Some of them are multiple tube systems, Bundled tube systems and tube-in-tube systems^2,3. The Tube in tube and Bundled tube structure is being taken for the current study. A typical form of framed tube structure is shown in Figure 1.

Taranath et al. tubular system structure is a structure with closed column space between two to four meters and jointed by a deep spandrel beams at the floor level as shown in Figure 2. A group of columns perpendicular to the direction of the horizontal load is called flanged frame and a group of columns parallel to the direction of the horizontal load is called web frames⁴.

Since the columns are closed to each other and the spandrel beams are deep, the structure can be considered as perforated tube and behaves as a cantilever tube. The flanged frame columns will resist the axial forces (tension and compression) and the web columns will resist the shear forces⁴. Coull et al. it has been proved that the tubular structure is an efficient structural system to resist the horizontal loads. However, in the actual tubular structure, the distribution of axial forces along the flanged frame columns at one floor is not uniform and the distribution of shear forces along the web is not linear. This is mainly due to the flexibility of the structure. This phenomenon

*Author for correspondence

Indian Journal of Science and Technology, Vol 8(36), DOI: 10.17485/ijst/2015/v8i36/87533, December 2015 ISSN (Online) : 0974-5645

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Effect of Column Shortening on the Behavior of Tubular Structures

Indian Journal of Science and Technology 2 Vol 8 (36) | December 2015 | www.indjst.org

suited for story height from 40-100. Thus considering the shear lag effect and the seismic effect on the buildings, the models for this study are square in plan. Table 1 shows the details of tabular structure under study.

In this analysis of Tube in tube structure, the inner tube is assumed to be of closely spaced column. The connection of secondary beams to the core columns is hinged connection and the connection of spandrel beams to columns is rigid connection. The floor plan of tubular structure is shown in Figure 3 and Tube in tube structure is shown in Figure 4. In the case of Bundled tube structure, the closely spaced core columns are placed on the four corners of the building as shown in the Figure 5.

Figure 1. A typical form of framed tube structure.

8.

9.

10

11 12

Smith BS, C Wiley Inters Soegiarso R loads. Journ 0. Coull A, A

Structural D May. 104(ST 1. Taranath B

analysis and 2. Lee KK, L internal tube

Coull A. Text science Public R, Tjendera E.

nal Teknik Sip Ahemed AK. D Division. Proc

T5). p. 875–6 BS. Text book d design. New Loo YC, Guan es. The Struct

book on tall cation. New Y . Behavior of pil F.T. Untar

Deflection of ceedings of Th

61.k on wind and w York: Marc

n H. Simple a tural Design o

7

building stru York; John W f high-rise Tu

r/No.2 Tahun f framed tube he American d earthquake cel Dekker; 20

analysis of fra of Tall and S

uctures: Analy Wiley and Son ubular structur nKe III; 1997 e structures. J Society of C resistant buil 004.

amed-tube str pecial Buildi

ysis and desig ns; 1st ed. 19 res due to hor . p. 73–85.

Journal of the Civil Engineer ldings: Struct ructures with ings. 2001; 8:

gn. A 91.rizontal

rs; 1978 tural

multiple :97–103.

Figure 2. Components in tall structure.

8.

9.

10

11 12

Smith BS, C Wiley Inters Soegiarso R loads. Journ 0. Coull A, A

Structural D May. 104(ST 1. Taranath B

analysis and 2. Lee KK, L internal tube

Coull A. Text science Public R, Tjendera E.

nal Teknik Sip Ahemed AK. D Division. Proc

T5). p. 875–6 BS. Text book d design. New Loo YC, Guan es. The Struct

book on tall cation. New Y . Behavior of pil F.T. Untar

Deflection of ceedings of Th

61.k on wind and w York: Marc

n H. Simple a tural Design o

7

building stru York; John W f high-rise Tu

r/No.2 Tahun f framed tube he American d earthquake cel Dekker; 20

analysis of fra of Tall and S

uctures: Analy Wiley and Son ubular structur nKe III; 1997 e structures. J Society of C resistant buil 004.

amed-tube str pecial Buildi

ysis and desig ns; 1st ed. 19 res due to hor . p. 73–85.

Journal of the Civil Engineer ldings: Struct ructures with ings. 2001; 8:

gn. A rizontal91.

rs; 1978 tural

multiple :97–103.

reduces the efficiency of the tubular structures and it is called shear lag effect. The efficiency of the tubular structure is measured by the shear lag factor. The shear lag factor can be defined as the ratio of the stress at the centre of the flanged and the stress at the corner of the flange⁵.

Mola et al. observed that the tubular structure was efficient if the shear lag factor of 0.7 is achieved. In the design of tall buildings the challenge for the engineer is to maximize the shear lag factor with minimum weight.

When the shear lag is equal to one, the axial forces are distributed equally along the flange. In tubular structural system, there are several parameters contribute to the shear lag factors, among them all the size of the spandrel beams and columns along the flange, the bending stiffness of the web and the shape of the structures⁶.

2. Modelling of Tubular Structure

Structure consists of closely spaced column connected by deep spandrel beams placed on the perimeter in plan.

Tubular, Tube in tube and Bundled buildings are generally

Table 1. Details of Structure

Number of Storey

Concrete Mix

Column size (m)

Spandrel beam size (m)

Spacing of columns (m)

Storey height (m)

50 M70 1.00×1.00 0.50×0.50 2.00 4

50 M100 1.00×1.00 0.50×0.50 2.00 4

Figure 3. Floor plan of tubular structure figure Figur

Comp

Table

Figur plan o

re 1. A typica ponents in tal

e 1. Details o Number

ofStorey 50

50

re 3. Floor pl of tube in tub

al form of fra ll structure.

of Structure

y Concrete Mix M70

M100

lan of tubular be structure.

amed tube stru

e Column

size(m) 1.00x1.00

1.00x1.00

r structure fig

8

ucture.

Spandrel

beam

size(m) 0.50x

0.50 0.50x

0.50

gure,

Spacingof

columns

(m) 2.00

2.00

Figure 2.

Storey height(m) 4

4

Figuree 4. Floor

Figure 4. Floor plan of tube in tube structure.

Figur Comp

Table

Figur plan o

re 1. A typica ponents in tal

e 1. Details o Number

ofStorey 50

50

re 3. Floor pl of tube in tub

al form of fra ll structure.

of Structure

y Concrete Mix M70

M100

lan of tubular be structure.

amed tube stru

e Column

size(m) 1.00x1.00

1.00x1.00

r structure fig

8

ucture.

Spandrel

beam

size(m) 0.50x

0.50 0.50x

0.50

gure,

Spacingof

columns

(m) 2.00

2.00

Figure 2.

Storey

height(m) 4

4

Figuree 4. Floor

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3.4 Elastic Shortening of RC Columns

A column in a tall building undergoes axial shortening considerably more than its lower brethren required that special attention be paid in column design⁸. A related problem, by no means unique to tall buildings, but one that gets aggravated to a great extent, is the levelness of floors^9,10. Similarly, the problem of human response to transient vibration of floors is not unique to tall buildings but needs careful study because the cost of correcting the problem in a tall building with several floors is phenom- enally more expensive than correcting the relatively fewer floors of a low-rise building. Column in tall building subjected to larger axial displacement due to the accumu- lated load from a large number of floors and also from the larger length is known as axial elastic shortening¹¹. It depends on material properties of columns and the stress induced strains due to axial load^11,12.

4. Results and Discussion

The models for this study are square in plan having 50 storeys. The parameters like axial force, shear force, bending moment and time period is considered and compared and the variation in these parameters due to column shortening is discussed below. The change in axial force due to column shortening in Tubular, Tube in tube and Bundled tube structure are shown in Figure 6. The column shortening effect in structure with M70, M110 grades and structure without column shortening is compared.

The result shows a variation of about 20%, 23% and 19% decrease in the axial force in the Tubular, Tube in tube and Bundled tube structure respectively with column shortening to the structure without column shortening.

Figure 5. Floor plan of Bundled tube structure.

Figur

50 100 150 200 250

MaxAxialForce(kN)

re 5. Floor pl

0 000 000 000 000 000

WITHCOLUMN

SHORTENING

(M70)

lan of Bundle

WITHCOLUMN

SHORTENING

(M110) WITH SHORTCOL

ed tube structu

HOUT

TENINGUMN

TUBULAR TUBEINTUBE BUNDLED

TUBE

ure.

0 50 100 150 200 250 300

WITHC SHORT (M

MaxShearForce(kN)

OLUMN

TENING

70)

WITHCOLUM SHORTENING (M110)

N

G WITHOUT

COLUMN

SHORTENING TUBU TUBE BUN TUBE ULAR EINTUBE

DLED

E

3. Analysis of Framed Tubular Frames

The 3D analysis of the structure is carried out using the ETABS software which is based on the stiffness approach.

The calculations made are mentioned below:

3.1 Load Patterns

Dead load is calculated by taking the self weight of each members. Imposed load is taken to be as 3 kN/m² and wind load is calculated as per IS 875 part-3⁷.

3.2. Wind Load

Wind load is calculated as per IS 875 Part- 3⁷ where the location is considered as Chennai and the following parameters are calculated. The calculated wind pressure is distributed based on the height of floor and number of columns in that floor:

Design wind speed (V_z) = 70 m/s Design Wind Pressure (P_z) = 2597 N/m²

3.3 Analysis

The analysis is performed using ETABS. The analysis is performed with elastic shortening when the properties of the columns and beams are modelled and load is applied.

The member properties like area and moment of inertia of columns and moment of inertia of spandrel beams are given as explicit input then analysis is performed for obtaining column and beam forces without effect of

elastic shortening of the RC columns. Figure 6. Comparison of Max Axial force.

Figur

50 100 150 200 250

MaxAxialForce(kN)

re 5. Floor pl

0 000 000 000 000 000

WITHCOLUMN

SHORTENING

(M70)

lan of Bundle

WITHCOLUMN

SHORTENING

(M110) WITHCOL SHORT

ed tube structu

HOUT

UMN

TENING TUBULAR TUBEINTUBE BUNDLED

TUBE

9

ure.

0 50 100 150 200 250 300

WITHC SHORT (M

MaxShearForce(kN)

OLUMN

TENING

70)

GN WITHOUT COLUMN SHORTENING

TUBU TUBE BUN TUBE

ULAR EINTUBE DLED E

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The change in shear force due to column shortening in Tubular, Tube in tube and Bundled tube structure are shown in Figure 7. The column shortening effect in Tube in tube and Bundled tube structure with M70, M110 grades and structure without column shortening is compared. The result shows a variation of about 23%, 17% and 15% decrease in the shear force in the Tubular, Tube in tube and Bundled tube structure respectively with column shortening to the structure without column shortening.

The change in bending moment due to column shortening in Tube in tube and Bundled tube structure are shown in Figure 8. The column shortening effect in Tube in tube and Bundled tube structure with M70, M110 grades and structure without column shortening is compared. The result shows a variation of about 24%, 27% and 31% decrease in the bending moment in the Tube in tube and Bundled tube structure respectively with column shortening to the structure without column shortening.

Figure 7. Comparison of Max Shear force.

Figur

50 100 150 200 250

MaxAxialForce(kN)

re 5. Floor pl

0 000 000 000 000 000

WITHCOLUMN

SHORTENING

(M70)

lan of Bundle

WITHCOLUMN

SHORTENING

(M110) WITH SHORTCOL

ed tube structu

HOUT

TENINGUMN

TUBULAR TUBEINTUBE BUNDLED

TUBE

9

ure.

0 50 100 150 200 250 300

WITHC SHORT (M

MaxShearForce(kN)

OLUMN

TENING

70)

N

G WITHOUT

COLUMN

SHORTENING TUBU TUBE BUN TUBE ULAR EINTUBE

DLED

E

Figure 8. Comparison of Max bending moment.

10

Figure 6. Comparison of Max Axial force. Figure 7. Comparison of Max Shear force.

Figure 8. Comparison of Max bending moment.

Figure 9. Comparison of time period. Figure 10. Comparison of time period.

With Column shortening (M70) With Column shortening (M110)

0 100 200 300 400 500 600 700

WITH

COLUMN

SHORTENING

(M70)

WITH

COLUMN

SHORTENING

(M110)

WITHOUT

COLUMN

SHORTENING

MaxBendingMoment(kNͲm)

TUBULAR TUBEIN

TUBE BUNDLED

TUBE

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0 1 2 3 4 5 6 7 8 9 10 11 12

TimePeriod(Sec)

Mode

TUBULAR TUBEIN

TUBE BUNDLED

TUBE

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0 1 2 3 4 5 6 7 8 9 10 11 12

TimePeriod(Sec)

Mode

TUBULAR TUBEIN

TUBE BUNDLED

TUBE

The change in time period due to column shortening in Tubular, Tube in tube and Bundled tube structure with column shortening with M70, M110 and without column shortening are shown in Figures 9, 10 and 11 respectively. The column shortening effect in Tube in tube and Bundled tube structure with M70, M110 grades and structure without column shortening is compared. The result shows a variation of about 62%, 57% and 60% increase in the time period of the Tubular, Tube in tube and Bundled tube structure respectively with column shortening to the structure without column shortening.

The change in Storey drift in Tubular, Tube in tube and Bundled tube structure with column shortening and without column shortening is shown in Figures 12, 13 and 14 respectively and the result shows a variation

Figure 9. Comparison of time period. With Column shortening (M70).

10

0 100 200 300 400 500 600 700

WITH

COLUMN

SHORTENING

(M70)

WITH

COLUMN

SHORTENING

(M110)

WITHOUT

COLUMN

SHORTENING

TUBULAR TUBEIN

TUBE BUNDLED

TUBE

0 0.5 1 1.5 2 2.5 3 3.54 4.5 5

0 1 2 3 4 5 6 7 8 9 10 11 12

TimePeriod(Sec)

Mode

TUBULAR TUBEIN

TUBE BUNDLED

TUBE

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0 1 2 3 4 5 6 7 8 9 10 11 12

TimePeriod(Sec)

Mode

TUBULAR TUBEIN TUBE BUNDLED TUBE

Figure 10. Comparison of time period. With Column shortening (M110).

10

0 100 200 300 400 500 600 700

WITH

COLUMN

SHORTENING

(M70)

WITH

COLUMN

SHORTENING

(M110)

WITHOUT

COLUMN

SHORTENING

TUBULAR TUBEIN

TUBE BUNDLED

TUBE

0 0.51 1.5 2 2.5 3 3.5 4 4.5 5

0 1 2 3 4 5 6 7 8 9 10 11 12

TimePeriod(Sec)

Mode

TUBULAR TUBEIN

TUBE BUNDLED

TUBE

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0 1 2 3 4 5 6 7 8 9 10 11 12

TimePeriod(Sec)

Mode

TUBULAR TUBEIN

TUBE BUNDLED

TUBE

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J. S. Arvind and M. Helen Santhi

Figure 11. Comparison of time period - without column

shortening. Figure 11. Comparison of time period - without column shortening.

0 0.5 1 1.5 2

0 1 2 3 4 5 6 7 8 9 10 11 12

TimePeriod(Sec)

Mode

TUBULAR

TUBEIN

TUBE BUNDLED

TUBE

Figure 12. Comparison of storey drift in tubular structure with and without column shortening effect.

12

Figure 12. Comparison of storey drift in tubular structure Figure 13.

Comparison of storey drift in Tube in tube structure

with and without column shortening effect. with and without column shortening effect.

Figure 14. Comparison of storey drift in Bundled tube structure Figure 15.

comparison of storey drift in Tubular, Tube in tube and

with and without column shortening effect Bundled tube structure with column shortening effect.

0 10 20 30 40 50

0 2 4 6

STOREYLEVEL

DRIFTmm)

TUBULAR

STRUCTURE

WITH

COLUMN

SHORTENING

TUBULAR

STRUCTURE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3 4

STOREYLEVEL

DRIFT(mm)

TUBEINTUBE

WITHCOLUMN

SHORTENING

TUBEINTUBE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3

STOREYLEVEL

DRIFT(mm)

BUNDLED

TUBEWITH

COLUMN

SHORTENING

BUNDLED

TUBE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3 4 5

STOREYLEVEL

DRIFT(mm)

TUNULAR

STRUCTURE TUBEINTUBE

STRUCTURE BUNDLEDTUBE

STRUCTURE

Figure 13. Comparison of storey drift in Tube in tube structure with and without column shortening effect.

12

0 10 20 30 40 50

0 2 4 6

STOREYLEVEL

DRIFTmm)

TUBULAR

STRUCTURE

WITH

COLUMN

SHORTENING

TUBULAR

STRUCTURE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3 4

STOREYLEVEL

DRIFT(mm)

TUBEINTUBE

WITHCOLUMN

SHORTENING

TUBEINTUBE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3

STOREYLEVEL

DRIFT(mm)

BUNDLED

TUBEWITH

COLUMN

SHORTENING

BUNDLED

TUBE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3 4 5

STOREYLEVEL

DRIFT(mm)

TUNULAR

STRUCTURE

of about 74%, 70% and 60% decrease in Tubular, Tube in tube and Bundled tube structure with column shortening and without column shortening. The change in Storey drift in Tubular, Tube in tube and Bundled tube structure with column shortening is shown in Figure 15.

Figure 14. Comparison of storey drift in Bundled tube structure with and without column shortening effect.

12

0 10 20 30 40 50

0 2 4 6

STOREYLEVEL

DRIFTmm)

TUBULAR

STRUCTURE

WITH

COLUMN

SHORTENING

TUBULAR

STRUCTURE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3 4

STOREYLEVEL

DRIFT(mm)

TUBEINTUBE WITHCOLUMN SHORTENING

TUBEINTUBE WITHOUT COLUMN SHORTENING

0 10 20 30 40 50

0 1 2 3

STOREYLEVEL

DRIFT(mm)

BUNDLED

TUBEWITH

COLUMN

SHORTENING

BUNDLED

TUBE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3 4 5

STOREYLEVEL

DRIFT(mm)

TUNULAR STRUCTURE TUBEINTUBE STRUCTURE BUNDLEDTUBE STRUCTURE

Figure 15. comparison of storey drift in Tubular, Tube in tube and Bundled tube structure with column shortening effect.

12

0 10 20 30 40 50

0 2 4 6

STOREYLEVEL

DRIFTmm)

TUBULAR

STRUCTURE

WITH

COLUMN

SHORTENING

TUBULAR

STRUCTURE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3 4

STOREYLEVEL

DRIFT(mm)

TUBEINTUBE

WITHCOLUMN

SHORTENING

TUBEINTUBE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3

STOREYLEVEL

DRIFT(mm)

BUNDLED

TUBEWITH

COLUMN

SHORTENING

BUNDLED

TUBE

WITHOUT

COLUMN

SHORTENING

0 10 20 30 40 50

0 1 2 3 4 5

STOREYLEVEL

DRIFT(mm)

TUNULAR

STRUCTURE

5. Conclusion

The columns in a tall building undergoes axial shortening considerably more than columns in the low and medium rise buildings. This leads to the uneven settlement of the floor levels. In this paper, the Tubular, Tube in tube and Bundled tube structure are analysed and the following conclusions are drawn:

Decrease in the maximum bending moments, Axial

• force, Shear Force of about 25%, 20% and 23%

respectively while comparing the Tubular structure without column shortening to the structure with column shortening.

• force, Shear Force of about 23%, 17% and 25% respectively while comparing the Tube in tube structure without column shortening to the structure with column shortening.

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•

force, Shear Force of about 19%, 15% and 31% respectively while comparing the Bundled tube structure without column shortening to the structure with column shortening.

Increase in the time period of about 62%, 57% and

• 60% while comparing the Tubular, Tube in tube structure and Bundled tube structure without column shortening to the structure with column shortening.

Decreases in Storey Drift of about 74%, 70% and 60%

• in the Tubular, Tube in tube structure and the Bundled tube structure without column shortening to the structure with column shortening.

Due to reduction of forces the dimension of the

• structural elements can be reduced which directly reduces the dead load of the structure and also the cost of construction.

6. References

1. Khan FR, Amin NR. Analysis and design of framed tube structure for all tall buildings. ACI Publications SP-36:

Response of multistorey concrete structures to lateral forces. 1973; 51(3):39–60.

2. Fintal M, Ghosh SK, Iyengar H. Column shortening in tall structures: Prediction and compensation. Illinois, Chicago:

Portland Cement Associations; 1987 Jun.

3. Urs A. Stability analysis of frame tube tall buildings. [Thesis of Master of Science]. Department of Civil Engineering, Worcester Institute; 2002 Oct.

4. Taranath BS. Text book on reinforced concrete design of tall buildings. New York: CRC Press, Taylor and Francis Group; 2010.

5. Coull A, Subedi NK. Framed-tube structure for high rise buildings. Journal of the Structural Division. Proceedings of the American Society of Civil Engineers. Proc Paper 11696; 1975 Nov. 101(ST11). p. 2223–40.

6. Mola F, Pellegrini LM. Effects of column shortening in Tall R.C Buildings. 35th Conferences on our world in concrete and structure; Singapore. 2010 Aug 25-27. p. 1–15.

7. Code of practice for design loads (Other than earthquake) for building and structures. New Delhi: Bureau of Indian Standards; IS 875 (Part 3) – 1987.

8. Smith BS, Coull A. Text book on tall building structures:

Analysis and design. A Wiley Interscience Publication.

New York; John Wiley and Sons; 1st ed. 1991.

9. Soegiarso R, Tjendera E. Behavior of high-rise Tubular structures due to horizontal loads. Journal Teknik Sipil F.T.

Untar/No.2 TahunKe III; 1997. p. 73–85.

10. Coull A, Ahemed AK. Deflection of framed tube structures.

Journal of the Structural Division. Proceedings of The American Society of Civil Engineers; 1978 May. 104(ST5).

p. 875–61.

11. Taranath BS. Text book on wind and earthquake resistant buildings: Structural analysis and design. New York: Marcel Dekker; 2004.

12. Lee KK, Loo YC, Guan H. Simple analysis of framed-tube structures with multiple internal tubes. The Structural Design of Tall and Special Buildings. 2001; 8:97–103.