estimation method of tall building structure system in architecture project design

Estimation method of tall building structure system in architecture project design

Jianguang Shi*,†, Linlin Hua and Tong Han

School of Architecture and Civil Engineering, Xiamen University, Xiamen, China

SUMMARY

Architecture project design is a key stage to tall building design because its structure form, structure system and main member dimension may be determined, and the possibility to infl uence construction cost may attain 70–80% in this stage. Based on building conditions in architecture project design, such as building function, storeys, height, length/width ratio, height/width ratio, fl oor height and the maximum wind pres-sure, seismic intensity and site type, one of the estimation methods for building structure behaviour under these combined action is presented. In this method, every storey in the building is taken as a macro-element. The member in the building, such as beams, columns, walls and slabs, are included in the macro-element. Considering the contribution of each member, the macro-element stiffness is established for each storey. Then, the estimation analysis of the building structure is carried out following the fi nite element method. Comparing the analysis results, such as internal force and storey deformation with the usual analysis method, it is known that this estimation analysis method can be used to estimate the behaviour of the building structure system in architecture project design. It is also a useful tool to architects and structure engineers in estimating the applicability of the structure system. Copyright © 2009 John Wiley & Sons, Ltd.

1. INTRODUCTION

The possibility of determining the cost of building in architecture project design is 70∼80% (Hsu and Liu, 2000). Improper structure collocation or element dimension in this stage may cause impairment, such as a weak lower storey or element with high reinforcement ratio and small dimension were often the cause of structure damage (Otani, 1997). In previous earthquakes, such as the China Tongshan earthquake in 1976, the Romania earthquake in 1977, the Mexico earthquake in 1985, the Armenia earthquake in 1988, the Japan Hanshin earthquake in 1995 and the Chi-Chi earthquake in 1999, the damage and collapse of a reinforced concrete building is associated with the poor resistance of hori-zontal elements, such as smaller column dimension and a large difference in stiffness distribution. These problems can be avoided in an architecture project. Despite recognizing the importance of the structure system design of a tall building in an architecture project, the computer-aided design for structure system is less important because the possible variables are high, and there are many inde-terminacy factors.

The computer-aided design can be divided into two kinds: artifi cial intelligence and computer-aided design. The differences are initiative and passiveness. Various expert systems, such as those based on knowledge, based on instance and based on regulation, used fuzzy reasoning, nerve network, inherit arithmetic or the combine to solve the problem of the structure system determining (Zhang 2001; Wang et al., 2003). In fact, due to many artifi cial factors in tall building projects, the computer-aided design cannot be automated. For displaying human creativity and judgement it is an appropriate approach to increase the scientifi calness through computer-aided calculation and analysis. For the structure system design of tall buildings, the estimation method is presented in this paper to aid the architect into obtaining the proper structure system in the project plan.

THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGSStruct. Design Tall Spec. Build. 20, 661–668 (2011)Published online 30 October 2009 in Wiley Online Library (wileyonlinelibrary.com/journal/tal). DOI: 10.1002/tal.550

Copyright © 2009 John Wiley & Sons, Ltd.

* Correspondence to: Jianguang Shi, School of Architecture and Civil Engineering, Xiamen University, 361005 Xiamen, China

† E-mail: [email protected]

662 J. SHI, L. HUA AND T. HAN

Copyright © 2009 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 20, 661–668 (2011) DOI: 10.1002/tal

Architecture project design

Function, storey number, height, plane shape, vertical shape, interspace

Ratio of length with width, ratio of height with width, story height and distribute

Maximum earthquake, maximum wind pressure, site category

Figure 1. Structure parameters in the architecture project design.

The structure design in architecture project stage

shape dividing

choice of the structure system

collocation of the structure member

Figure 2. The structure design in the architecture project stage.

Figure 3. The formation process of the structure (project concept, space dividing, inter-part dividing).

2. THE FORMATION PROCESS OF THE BUILDING STRUCTURE

The architecture and structure design of tall buildings can be divided into four parts: architecture project, architecture design, structure project and structure design. The important work in the structure project stage is determining the structure system, the layout and the dimension of the main members of a tall building. The main factors infl uencing the structure project has already been determined in the architecture project stage, because while the design process of a tall building is a consultation process, it is also a gradually clear process.

For bigger tall buildings, the formation of the structure system may be the result of the comparison of many projects. But for the normal building, especially the frame structure, the structure parameters have already been made sure at the architecture design stage. The main parameters infl uencing struc-ture in the architecture project stage are those as shown in Figure 1. If the architect reasonably set these parameters, the rationality of the structure project can get assurance from the beginning.

The structure design in the architecture project stage involves three parts, as shown in Figure 2. The shape dividing depends on the shape regulation, building dimension and foundation condition. The choice of the structure system is decided by function, the number of storeys, building height, interspace dividing, length/width ratio, height/width ratio, storey height and distribution, etc. The collocation of the structure member needs contented function, strength, stiffness, stability etc. The formation process of the structure is the process shown in Figure 3 that the building interspace is divided into different spaces and the inner parts.

The choice of the structure system is at the space dividing stage, but the collocation of the structure member is at the inner part dividing stage. The formation process of the structure is illustrated in

TALL BUILDING STRUCTURE SYSTEM 663


Figure 4. The process from whole body to structure system to member.

Figure 4. The structure engineering causes a lot of strenuous efforts and energy to the design of the member rather than the structure system. The creation of the structure system usually begins in the exchanges of the architect and the structure engineer.

At present, there are many analytical methods and software available to solve the problem in the structure collocation stage. The choice of structure system mainly depends on experience and concept because the structure information is not complete and undecided, or there are more factors to be considered. Its core problem of structure system choice is to satisfy the building function request, safety and usage. In general, fi rst, choose a project that satisfi es the building function request, then check whether the content structure request is satisfactory; if not, then re-choose. It is a trial-and-error process. The structure design is very passive. If revising the thinking process we can get a structure system directly after the demand that satisfi es structure request is determined. From the architecture to the structure system, the estimation method, based on incomplete information, is needed. There is the cantilever beam model (Li and Liu, 1998) suited to tall structures that satisfi es the beam characteristics.

3. ESTIMATION METHODS OF TALL BUILDINGS

The building form in the project stage decides the structure characteristics under force. The variety of building form infl uences structure behaviour more than the choice or adjustment of the member. If the building form or shape is associated with structure behaviour, the specifi c architecture of a building can obtain the reference and the structure engineer can be clear to the structure system.

The loads on the building will be gravity, wind, earthquake, etc. The building should have the car-rying ability, stiffness and deformation as shown in Figure 5. The structure system can be frame, wall, frame–wall, tube, plate–column-wall, etc. The structure formation can be considered as a one-layer process adding to other layers, as shown in Figure 6. Every fl oor slab may be stronger than the inter-space between fl oors. The complicated form can consist of simple forms.

Every storey of the structure is taken as an element. The members in the storey are the contributors of this element. The fi nite element method can be used to analyse the behaviour of the structure. The stiffness of every storey can be obtained by adding the contribution of every column in its fl oor, shown in Figure 7.

Figure 5. The load on the building.



Figure 6. The formation of the building.

Figure 7. The consistency of storey element and its member contribution.

Applying equal-parameter deformation interpolation, the deformation at one point can be expressed by element nodes as follows:

uvw

Nuvw

i

i

i

ii

n⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪=

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪=∑

1

(1)

in which u, v and w are the deformations in the X-, Y- and Z-directions, respectively; n is the number of element nodes; and Ni is the shape function of an element. Under small deformation assumption, the rotation angle at one point is:

θθθ

x

y

z

w

y

v

zu

z

w

xv

x

u

y

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪=

∂∂

− ∂∂

∂∂

− ∂∂

∂∂

− ∂∂

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

⎫

⎬

⎪1

2

⎪⎪⎪

⎭

⎪⎪⎪

(2)

Applying Equation (1) to Equation (2), the following equation can be obtained:

θθθ

x

y

z

i i

i i

i i

N

z

N

yN

z

N

xN

y

N

x

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪=

− ∂∂

∂∂

∂∂

− ∂∂

− ∂∂

∂∂

02 2

20

2

2 200

1

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪=∑i

n i

i

i

uvw

(3)



Combining Equations (1) and (2), the deformation at point A can be obtained by the equation:

uvw

NN

NN

z

a

a

a

ax

ay

az

ia

ia

ia

ia

θθθ

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

⎫

⎬

⎪⎪⎪

⎭

⎪⎪⎪

=− ∂

∂

0 00 00 0

02

∂∂∂

∂∂

− ∂∂

− ∂∂

∂∂

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥N

yN

z

N

xN

y

N

x

ia

ia ia

ia ia

2

20

2

2 20

⎥⎥⎥⎥⎥⎥⎥

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪=∑i

n i

i

i

uvw1

(4)

in which Nia is the value of the shape function at point A. The deformation at the nodes of line element ij in element body is expressed as:

δ θ θ θ θ θ θij i i i ix iy iz j j j jx jy jzxTu v w u v w{ } = { }

For the eight nodes body element, the node deformation vector of body element is:

δe u v w u v w u v w u v w u v w u v w

u v w u v w

{ } = {}

1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6

7 7 7 8 8 8

The relationship of the inside deformation vector of the line element with the node deformation vector of body element is:

δ δij eR{ } = [ ]{ } (5)

in which [R] can be obtained through the derivative of the element shape function. If the node force vector is:

F X Y Z M M M X Y Z M M Mij i i i ix iy iz j j j jx jy jz{ } = { }

the stiffness equation of element can be expressed as:

F Kij ij ij{ } = [ ]{ }δ (6)

Further it can become:

δ δ δijT

ij ijT

ij ijF K{ } { } = { } [ ]{ } (7)

Taking {δij} = [R]{δe}, δ{δij} = [R]δ{δe} and δ{δij}T = δ{δe}T[R]T into the above equation, the follow-ing equation is obtained:

δ δ δ δ δeT T

ij eT T

ij eR F R K R{ } [ ] { } = { } [ ] [ ][ ]{ } (8)

Taking off the virtual deformation, the equation becomes:

R F R K RTij

Tij e[ ] { } = [ ] [ ][ ]{ }δ (9)

which is shortened as:

F Kc c e{ } = [ ]{ }δ (10)

in which {Fe} is the equal node force. [Kc] is the contribution stiffness of line element to body element, [Kc] = [R]T [Kij] [R].



Figure 8. Frame structure plane.

The overall stiffness matrix of the body element is the sum of the stiffness matrix of the body element and the contribution stiffness element of all line elements in the body element:

K K Ke v ci[ ] = [ ] + [ ]∑ (11)

After calculating stiffness of every storey using Equation (11), the entire building can be modelled as storey element plus storey element. This kind of estimation method is suitable to estimate the force action of tall buildings in the project design or the preliminary design stage.

4. STRUCTURE ANALYSIS

Applying the entire analysis method to calculate the deformation of the frame and frame–wall struc-tures, the results are listed below. The dead load, live load, wind and earthquake action are calculated according to the China code. Its period and member dimension are determined by the corresponding method (Goel and Chopra, 1997; Hong and Hwang, 2000; Glaister and Pinho, 2003; Crowley and Pinho, 2004; Liu and Jiang, 2002).

4.1. Frame structure

The structure plane is shown in Figure 8. The height of the fi rst fl oor is 4 m, and the height of the second to fi fth fl oors 3.75 m and sixth to eighth fl oors 3.7 m. The reinforced concrete frame will act under the earthquake degree 7 (0.15 g), the wind pressure 0.9 kN/m2 and the site ground sort is II. The deformation obtained by the PKPM software, the estimation method and the D-value method is shown in Figure 9 and Table 1.

4.2. Frame–wall structure

The structure plane is shown in Figure 10. The height of the fi rst to third fl oors is 4 m, and the thick-ness of the wall is 0.3 m. The height of the 4th to 10th fl oors is 3.6 m, and the thickness of the wall is 0.22 m. The height of the 11th to 15th fl oors is 3.6 m, and the thickness of the wall is 0.16 m. The reinforced concrete frame–wall structure will act under the earthquake degree 8 (0.30 g), wind pres-sure 0.6 kN/m2 and site ground sort α. The deformation obtained by estimation method and reference (Zhao, 2005) is shown in Figure 11 and listed in Table 2.

5. CONCLUSION

The determination of the structure system in the preliminary design stage is key work to tall building design. A calculation method for the structure system choice is presented. The method is based on



Figure 9. Deformation of the frame structure.

Figure 10. Frame–wall structure plane.

Figure 11. Deformation of the frame–wall structure.

Table 1. The deformation calculated by various methods.

Top shift (m)Max. inter-fl oor shift

(m)Max. inter-fl oor

angleThe fl oor of maximum

deformation

PKPM software 0.02673 0.00424 1/825 SecondEstimation method 0.0279 0.00507 1/690 SecondD-value method 0.029 0.005 1/700 Second



Table 2. The deformation by various methods.

Top shift (m)Max. inter-fl oor

shift (m)Max. inter-fl oor

angleThe fl oor of maximum

deformation

Reference (Zhao, 2005) 0.07613 0.00636 1/566 10th fl oorEstimation method 0.093 0.00636 1/566 12th fl oor

building conditions in the preliminary design stage, such as building function, storeys, height, length/width ratio, height/width ratio, fl oor height and the maximum wind pressure, seismic intensity and site type. In this method, every storey in the building is taken as the macro-ultra-element. The members in a building, such as beams, columns, walls and slabs, are included in the macro-ultra-element. The macro–ultra-element stiffness is established for each storey after considering the con-tribution of each member. Then, the estimation analysis of the building structure is carried out following the fi nite element method. Comparing the analysis results with the usual analysis method, it is known that this estimation analysis method can be used to estimate the behaviour of the building structure in the preliminary design stage. It is a useful tool to architects and structure engineers for the estimation of the applicability of the structure layout.

REFERENCES

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Goel RK, Chopra AK. 1997. Period formulas for moment-resisting frame buildings. Journal of Structural Engineering ASCE 123(11): 1454–1461.

Hong L, Hwang W. 2000. Empirical formula for fundamental vibration periods of reinforced concrete buildings in Taiwan. Earthquake Engineering and Structural Dynamics 29: 327–337.

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estimation method of tall building structure system in architecture project design

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