Manual 21262523

Manual 21262523

Tenth U.S. National Conference on Earthquake Engineering

Frontiers of Earthquake Engineering

July 21-25, 2014

Anchorage, Alaska

10NCEE

INFLUENCE OF MINIMUM BASE SHEAR

FORCE ON THE COLLAPSE RESISTANCE

OF SUPER-TALL BUILDINGS

Xiao Lu

1

, Xinzheng Lu

2

and Lieping Ye

2

, Mengke Li

3

ABSTRACT

The minimum base shear force in the seismic design of super-tall buildings is a key issue and a considerable amount of attention has been given to it. In this paper, based on a super-tall building located in high seismic zone of China with the maximum spectral acceleration of 0.9

g

(

g

represents the gravity acceleration), two building models with different base shear forces are designed according to the Chinese codes and the alternative method proposed in the U.S. specifications, respectively. The differences in the components dimensions and the dynamic characteristics of these two buildings are compared correspondingly. The seismic performance and collapse resistances of these two buildings are discussed in detail. The study indicates that

Model B, whose base shear force determined by modal response spectrum analysis (RSA) is scaled to meet the minimum base shear force requirement, performs a higher collapse resistance than that of Model A, whose structural stiffness is adjusted to make the modal base shear force meet the acceptance limit, with less difficulty and at a lower cost to design and construct.

1

Assistant Professor, School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China;

2

Professor, Dept. of Civil Engineering, Tsinghua University, Beijing, 100084, China;

3

Graduate Student Researcher, Dept. of Civil Engineering, Tsinghua University, Beijing, 100084, China.

Lu X, Lu XZ, Ye LP and Li MK. Influence of minimum base shear force on the collapse resistance of super-tall buildings.

Proceedings of the 10 th

National Conference in Earthquake Engineering

, Earthquake Engineering

Research Institute, Anchorage, AK, 2014.

Tenth U.S. National Conference on Earthquake Engineering

Frontiers of Earthquake Engineering

July 21-25, 2014

Anchorage, Alaska

10NCEE

Influence Of Minimum Base Shear Force On The Collapse Resistance

Of Super-Tall Buildings

Xiao Lu

1

, Xinzheng Lu

2

, Lieping Ye

2

, Mengke Li

3

ABSTRACT

The minimum base shear force in the seismic design of super-tall buildings is a key issue and a considerable amount of attention has been given to it. In this paper, based on a super-tall building located in high seismic zone of China with the maximum spectral acceleration of 0.9

g

(

g

represents the gravity acceleration), two building models with different base shear forces are designed according to the Chinese codes and the alternative method proposed in the U.S. specifications, respectively. The differences in the components dimensions and the dynamic characteristics of these two buildings are compared correspondingly. The seismic performance and collapse resistances of these two buildings are discussed in detail. The study indicates that Model

B, whose base shear force determined by modal response spectrum analysis (RSA) is scaled to meet the minimum base shear force requirement, performs a higher collapse resistance than that of

Model A, whose structural stiffness is adjusted to make the modal base shear force meet the acceptance limit, with less difficulty and at a lower cost to design and construct.

Introduction

Among the various aspects of current seismic design methodologies, seismic design force is generally determined based on the acceleration spectra specified in the established design codes.

Because the knowledge of the characteristics of long-period ground motion is inadequate at the current stage, the ground velocity or displacement brought about by long-period ground motion may cause greater than anticipated damage to the structures suffered. Moreover, the seismic design force that is determined by the equivalent lateral force procedure (ELF) or modal response spectrum analysis (RSA) using code-specified acceleration spectra, do not adequately reflect the impact of long-period ground motion on the structural response, especially for supertall buildings. In such buildings, the fundamental periods are very long, while the seismic design force calculated directly by RSA are relatively small. Therefore, from the viewpoint of structural safety, a minimum base shear force requirement is utilized in many seismic design codes and specifications in various countries.

On the other hand, a large number of super-tall buildings have been designed and

1

Assistant Professor, School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China;

2

Professor, Dept. of Civil Engineering, Tsinghua University, Beijing, 100084, China;

3

Graduate Student Researcher, Dept. of Civil Engineering, Tsinghua University, Beijing, 100084, China.

Lu X, Lu XZ, Ye LP and Li MK. Influence of minimum base shear force on the collapse resistance of super-tall buildings. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering

Research Institute, Anchorage, AK, 2014.

constructed in China in recent years. The fundamental period of these super tall buildings is very long, and the modal base shear force of the super-tall buildings calculated by RSA does not meet the minimum base shear force requirement specified in the current Chinese seismic design code.

For example, the Goldin Finance 117 Tower that is located in Tianjin has a maximum spectrum acceleration of 0.72

g

(referred to as an 'Intensity 7.5 region' in the seismic hazard map of China; g is the gravity acceleration), while the actual design base shear force is 0.0148

G

(

G

is the effective seismic weight of the building), compared to the acceptance limit of 0.018

G

specified in the Chinese seismic design code. The actual design base shear force of the Ping An Finance

Center, located in Shenzhen, has a maximum spectrum acceleration of 0.5

g

(an 'Intensity 7 region' in the seismic hazard map of China) which is approximately 0.0103

G

, and this is also smaller than the acceptance limit of 0.012

G

. The actual design base shear force of another proposed super-tall building located in Beijing with a maximum spectrum acceleration of 0.9

g

(an 'Intensity 8 region' ), is 0.0172

G

. This is much smaller than the acceptance limit of 0.024

G

[1]. These design cases clearly demonstrate that the seismic design base shear force directly determined by RSA is unable to meet the requirement of minimum base shear force specified in the Chinese seismic design code. This is a key issue in the seismic design of super-tall buildings in China.

To further understand the influence of minimum base shear force on the seismic structural responses, the relevant provisions of the minimum base shear force requirement specified in the Chinese and U.S. seismic design codes were brief reviewed first. Taking a hypothetical super-tall building located in an Intensity 8 region in China as an example, two buildings (referred to as Model A and B) were designed with different base shear forces according to the Chinese codes and the alternative method learned from the U.S. codes, respectively. The impact of minimum base shear force on the seismic performance and collapse resistance is discussed in detail as follows using a large number of time history and collapse analyses.

Review of the Provisions for Minimum Base Shear Force in the Chinese and U.S. Codes

Provisions in the Chinese Design Code

Since the research on the long-period ground motion is inadequate, in order to ensure the structural safety, in Section 5.2.5 of the Chinese seismic design code-

Code for seismic design of buildings (GB 50011-2010)

[2], it is specified that during the seismic evaluation, the seismic shear force of any floor shall be complied with the following equation:

V

EK,

i

λ

n

j

=

i

G j

(1) where,

V

EK

,i

load.

λ

is the seismic shear force of the

i

-th floor corresponding to the horizontal seismic

is the seismic response coefficient.

G j

is the effective seismic weight above the

j

-th floor.

Although the provisions specified in the

Code for seismic design of buildings (GB 50011-2010)

[2] is a universal requirement for all structures, the requirement about the minimum base shear force in the

Technical specification for concrete structures of tall building (JGJ 3-2010)

[3], which is a professional technical specification for tall buildings, is also in accordance with

Section 5.2.5 of the

Code for seismic design of buildings (GB 50011-2010)

[2].

According to the requirement of current Chinese seismic design codes, the seismic base shear force should be adjusted if the base shear force of any floor does not meet the minimum base shear force requirement during the course of a structural seismic evaluation. Although various suggestions regarding the adjustment of the seismic shear force are provided in the

Code for seismic design of buildings (GB 50011-2010)

[2], the stiffness adjustment method is frequently adopted in most actual design to meet this requirement. Meanwhile, many reports of actual design results of super-tall buildings also indicate that it is very difficult to meet this requirement, even when the stiffness adjustment method is adopted [1]. Taking the building located on a Site Class II (

V

eq

=200m/s) in an Intensity 8 seismic region with a characteristic period of 0.35s for example, for which the design spectrum and the corresponding acceptance limit of minimum seismic response coefficients are shown in Figure 1. It is clearly shown that the spectral acceleration is smaller than the acceptance limit of the minimum seismic response coefficients when the fundamental period exceeds 6s. The longer the fundamental period is, the smaller the spectral acceleration is in comparison with the minimum seismic response coefficient.

Generally, the fundamental periods of modern super-tall buildings range from 7s to 10s.

Therefore, during the seismic evaluation, the seismic base shear forces determined by RSA are not large enough to meet the minimum base shear force requirement specified in the current

Chinese seismic design code. To meet such a requirement, the lateral stiffness should be increased until the fundamental period is smaller than 6s on the site of Figure 1. Clearly, this would not be economical and thus is difficult to achieve.

Figure 1. The design spectrum at Site II and the corresponding minimum seismic response coefficients.

Provisions in the U.S. Design Code

Similarly, there are also some provisions about the minimum base shear force requirement in U.S. seismic design codes and ASCE 7-10 [4] is the typical one. The seismic base shear force determined by ELF procedure is described in Section 12.8 in ASCE 7-10. It clearly specifies that the seismic base shear,

V

, in a given direction shall be determined in accordance with the following equation:

where,

C

s

C

V

=

C

s

W

(2) s

is the seismic response coefficient and

W

is the effective seismic weight. The value of

shall not less than the Eq. 3a. Where,

I

is the important factor of building.

C

s

= 0.044

S

DS

I

0.01

/ (

R

/

I

)

(3a)

C

s

≥ 0.5

S

l

In addition, for structures located where

S

1

is equal to or greater than 0.6

g

,

C

not be less than Eq. 3b. Where,

R

is response modification coefficient.

(3b) s

also shall of

C

s

When the ELF procedure is adopt to implement the structural seismic design, if the value

calculated from the code-specified design spectrum is smaller than the minimum value of

C

s

, the design seismic base shear force,

V

, is determined with the minimum value of

C

s

. However, for tall buildings, the RSA procedure is widely adopted to calculate the base shear force.

Therefore, besides the RSA procedure, the ELF procedure in Section 12.8 of ASCE 7-10 shall also be implemented to calculate the base shear force

V

in each of the two orthogonal horizontal directions using the corresponding fundamental period of the structure

T

. If the modal base shear force,

V

t

, calculated by RSA is smaller than 0.85

V

, the design modal base shear force should be scaled by 0.85

V

/

V

t and then conduct the load combination and design. Comparing to the Chinese design procedure, U.S. design procedure is a method to ensure the structural safety from the viewpoint of structural strength instead of structural stiffness. Furthermore, recently published the

Guidelines for Performance-Based Seismic Design of Tall Buildings

[5] has already eliminated such a minimum base shear force requirement. Alternatively, structural safety is ensured by the seismic performance objectives at different seismic hazard levels, including the service level and Maximum Considered Earthquake (MCE) level for local components and global structure.

Building Design and Comparison

In order to discuss the impact of minimum base shear force on the seismic performance and collapse resistance capacity of super-tall buildings, a hypothetical super-tall building located in an Intensity 8 high seismic region in China is taken as the basic research object in this paper.

Two different buildings (referred to as Model A and B) are designed according to two different methods of adjusting the structural base shear force determined by RSA. The details of these two methods of adjusting the modal base shear force are shown in Table 1. Model A: in this model, the structural lateral stiffness is adjusted so as to make the seismic base shear forces

V

t

, as determined by RSA, meet the minimum base shear force requirement specified in Chinese design codes-

Code for seismic design of buildings (GB 50011-2010)

[2] and the

Technical specification for concrete structures of tall building (JGJ 3-2010)

[3]. Model B: the seismic base shear force

V

t

determined by RSA is smaller than the code-specified minimum base shear force; so the design shear force at the floors, in which the minimum shear force requirement is not satisfied, are scaled to the minimum shear force required for the building design.

The hypothetical super-tall building locates on a Site Class II (

V

eq

=200m/s) with a characteristic period of 0.35s. The total height of the building is about 439m, with 97 stories. The

top 4 stories are used for tourists and the basement is approximately 18m in height, with 4 stories.

The planar dimension of this building is about 36.1 m×53.7 m. The 16 concrete filled rectangular steel tube (CFST) mega columns constitute the external frame and the internal core tube is a 21 m×37 m rectangular concrete tube. The hybrid lateral-force-resisting system referred to as ‘mega column-core tube-outrigger’ is adopted in the

x

direction to resist the corresponding seismic forces; and in the orthogonal

y

direction, 5 mega steel braces are used to enhance the lateral stiffness so as to resist the seismic lateral loads. 5 outrigger systems are distributed along the building height and each outrigger is about 8.3 m high. The three-dimensional diagrams of this super-tall building are shown in Figure 2.

Table 1. Two methods of adjusting the design shear force.

The values of base shear force Model A Model B

V

d ,

i

=

V

t ,

i

λ min

j n

=

i

G j

Yes No

V

t

<

λ min

n

i

=

1

G i

and

V

d ,

i

= max(

λ min

j n

=

i

G

*Note

V

d,

i

is the design shear force at

i

th

j

,

V

t ,

i

)

floor;

V

t,

i

base shear force determined by RSA respectively; seismic response coefficient; and

G

λ

- Yes

and

V

t

are the shear force at

i

th

floor and total min

is the acceptance limit of minimum

i

is the effective seismic weight above the

i

th

floor.

y z x

Three-dimensional view

xz

plane view

yz

plane view

Figure 2. Three-dimensional view of the hypothetical super-tall building.

Model A and B have similar overall structural layout. In order to make the modal base shear force of Model A,

V

t

, determined by RSA meet the minimum base shear requirement specified in Chinese seismic design code, the structural stiffness should be increased to make the fundamental period smaller than 6.0s. Although a series of measures including the enlarging the cross section of the external mega columns, increasing the thickness of the shear walls, embedding steel plates in the shear walls and so on, are adopted, the minimum base shear force requirement is still not achieved. Therefore, for the research purpose, the steel fiber reinforced high performance concrete with the strength of 82MPa has been adopted for the design of the

core-tube in Model A in order to increase the lateral stiffness to the greatest extent possible. The comparison of the cross-sectional dimensions of typical components of Model A and B is shown in Table 2. Clearly, the component cross-sectional dimensions of Model A are far larger than those of Model B and the maximum shear wall thickness of Model A is 1.52 times as thick as the shear wall in Model B. Moreover, steel plate is embedded and steel fiber reinforced ultra-high performance concrete is adopted in the shear wall of Model A to increase the lateral stiffness.

The cross-sectional dimension of external mega columns of Model A is also larger than that of

Model B and the maximum cross section is 1.25 times as large as the one in Model B.

Table 2. The typical components sections of Model A and B (unit: mm).

Components dimension

Thickness of external wall in the

x

direction

Thickness of external wall in the

y

direction

Shear wall Concrete strength

Model A Model B

2900 1900

1800 1200 steel fiber reinforced ultrahigh performance concrete with the strength of 82 MPa

Yes

50.2 MPa

Mega column

Embedded steel plate

Typical boundary elements for shear wall

Column in

Column in

x y

direction

direction

Column in the corners

650×1300×50×70 650×1300×50×70

3700×3150×45

2850×2850×40

4950×3300×50

No

3200×2650×45

2350×2350×40

3950×2700×50

*Note

The unit of the cross-sectional dimension is in

mm

. The boundary element for shear wall is made up of an H-shaped steel beam and the section is described as the width × height × web thickness × flange thickness; The mega column is made up of a concrete filled steel tube and is described as the height × width × tube thickness.

Table 3. The comparison of the dynamic characteristics of Model A and B.

T

1

(s)

T

2

(s)

T

3

(s)

Effective Design base

Model translation in

x

direction translation in

y

direction torsion seismic shear force weight (ton)

7.12×10

5

(N)

1.67×10

8

5.76×10

5

1.13×10

8

The dynamic characteristics of Model A and B are compared in Table 3. The fundamental period of Model A, whose lateral stiffness is adjusted to make the modal base shear force meet the code-specified requirement, is 5.51s. This is obviously shorter than the fundamental period of Model B. The lateral stiffness of Model A is thus evidently much larger than the stiffness of Model B. Meanwhile, the effective seismic weight of Model A also increases significantly and it is 1.24 times as much as the weight of Model B. This shows that the amount of construction materials in Model A is obviously greater than the materials in Model B, which will be reflected in construction cost. For this reason, more construction and effort is

needed to make the base shear force of a super-tall building meet the minimum base shear force requirement specified in Chinese seismic design code-

Code for seismic design of buildings (GB

50011-2010)

[2]. Moreover, these design measures are very difficult to implement in the actual super-tall building design and construction. Furthermore, even achieved, the economic efficiency and practicability is still poor.

Discussion of the Structural Collapse Resistance

Seismic Performance at MCE Level

The commercial finite element software MSC.Marc, which has an excellent nonlinear computational capacity, was adopted for the nonlinear time history analysis. Based on this analysis platform, the modeling method proposed in Ref. [6-8], including fiber-beam element, multi-layer shell element, and membrane element, is adopted to build up the 3-dimensional finemeshed finite element model of Model A and B. The widely used fiber-beam element model is adopted to simulate these steel braces, CFST columns and secondary steel frame. The core tube is simulated by multi-layer shell element which has outstanding nonlinear performance on replicating the bending and shear coupling behaviors both in-plane and out-plane. According to the actual reinforcement, the vertical and horizontal rebar are treated as the equivalent rebar layers and totally the multi-layer shell element model is divided into 21 layers in the thickness direction. The concentrated reinforcement H-shaped steel in the boundary zones in shear wall is simulated by beam elements which are incorporated into the shell model with sharing the nodes.

The floor slabs are simulated by the membrane element.

7 ground motion records including 5 natural ground motion records selected in NGA ground motion database [9] and 2 artificial ground motion records are selected according to the ground motion selection procedure specified in the Chinese seismic design code. This selected ground motion set refers to as ‘EQ-7’ in the following discussion. The final mean spectrum of scaled EQ-7 and the target code-specified spectrum at the MCE level are shown and compared in

Figure 3. Clearly, the mean spectrum of EQ-7 is more compatible with the target code-specified spectrum at the MCE level and the deviations for the considered periods are within 20% which meets the ground motion selection requirement in Chinese seismic design code.

1.5

1.2

Median spectrum of EQ-7

Code-specified spectrum

Acceptance limit

KOCAELI_DZC180

0.9

0.6

T

1,A

=5.51s

T

1,B

=6.91s

0.3

0.0

0 1 2 3 4 5 6 7 8

Period (s)

Figure 3. The individual, median spectrum of EQ-7 and the target code-specified spectrum.

100

80

60

40

100

80

60

40

20 20

Model B

Model A

Model B

Model A

0 0

-2.0

-1.5

-1.0

-0.5

0.0

0.5

Displacment (m)

(a)

1.0

1.5

2.0

-0.010

-0.005

0.000

Story drift ratio (rad)

(b)

0.005

0.010

Figure 4. The average displacement responses of Model A and B subjected to EQ-7 at MCE level; (a) the average of maximum story displacement; (b) the average of maximum story drift. cm/s

2

During the seismic performance evaluation process, the PGA of EQ-7 is scaled to 400

that is specified in the Chinese seismic design codes corresponding to the MCE seismic hazard level of an Intensity 8 seismic region. The scaled ground motion record is input along the

x

direction, which is the direction of fundamental vibration mode, and the classical Rayleigh damping is adopted with the damping ratio of 5% for the nonlinear time history analysis. The displacement responses of Model A and B subjected to EQ-7 are shown in Figure 4. Figure 4a clearly shows that both the positive and negative envelope displacement responses of Model A and B have a similar tendency with small discrepancy, which is that the story displacement response of Model B is slightly smaller. Figure 4b indicates that both the maximum positive story drift ratio and the minimum negative story drift ratio of Model A are larger than that of

Model B. The story drift ratio of Model A has an obvious change above the 78th story and the maximum story drift ratio occurs at the 85th story with a value of 1/92, which slightly exceeds the acceptance limit of 1/100 specified in the Chinese design code-

Technical Specification for

Structures of Tall Building

(

JGJ 3-2002

) at the MCE level. In contrast, the distribution of the story drift ratio of Model B along the building height is relatively uniform and the abrupt change on story drift ratio does not appear above the 78th story. The maximum story drift ratio occurs at the 84th story with the value of 1/109, which meets the code-specified acceptance limit.

However, the story drift ratios of Model B located from 30th story to 75th story are larger than that of Model A and smaller than that of Model A below the 30th story. Generally speaking,

Model A and B have a generally similar seismic performance at the MCE level subjected to EQ-

7 and Model B even displays a slightly better seismic performance than Model A.

Structural Collapse Resistance

Collapse prevention is the most important design object in earthquake engineering. Collapse simulation is a powerful numerical method to evaluate the structural collapse resistance.

However, collapse is a complicated nonlinear process, in which the components may reach their ultimate deformation capacities or load bearing capacities. This phenomenon is a complex elemental nonlinear process and can be simulated by elemental deactivation technology [6-8]. If the specified elemental failure criteria are reached, the elements will be treated as failed and will

be deactivated from the entire model. The deformation-based criteria are adopted as the elemental failure criteria. For example, the concrete crushing strain and the steel facture strain can be adopted as the failure criteria for the concrete layers and rebar layers in multi-layer shell elements, and similarly the rebar fracture strain can be adopted as the failure criteria for fiber beam elements.

A typical natural ground motion record, named Kocaeli_DZC180, was chosen from the

EQ-7 as a typical seismic input. The 5% damped acceleration spectrum and the code-specified spectrum at the MCE level are compared in Figure 3. During the collapse simulation, the classical Rayleigh damping is adopted with 5% damping ratio. The ground motion is input along the

x

direction of the building and the ground motion intensity was increased gradually until collapse occurred. Consequently, the critical ground motion intensity that caused the structural collapse is obtained and used to quantify the collapse resistance capacity of the building.

For Model A, the building collapses when the PGA of Kocaeli_DZC180 increases to 1.4

g

.

Similarly, for Model B, the building collapses when the PGA increases to 2.0

g

. The collapse margin ratio (

CMR

) proposed in FEMA P695 [10] is adopted to quantify the structural collapse resistance capacity. In this paper, PGA is used as the basic ground motion intensity measure to calculate the

CMR

with the following equation:

CMR

=

PGA

Collapse

PGA

MCE

(4) where,

PGA

collapse

PGA

MCE

is the critical ground motion intensity that caused the building collapse; and

is the ground motion intensity corresponding to the MCE level. Because this hypothetical super-tall building is located in an Intensity 8 region, the corresponding

PGA

MCE

is equal to 0.4

g

according to the Chinese seismic design code. Consequently, the

CMR

of Model A subjected to Kocaeli_DZC180 is 3.5 (1.4

g

/0.4

g

) and that of Model B is 5.0 (2.0

g

/0.4

g

). It is evident that both the lateral stiffness and the load carrying capacity of the components of Model

A, whose lateral stiffness was adjusted to make the modal base shear force meet the codespecified requirement, are higher than Model B, whose lateral design shear force was scaled to meet the code-specified minimum base shear force requirement. Because the stiffer the structure the larger the seismic force when the building is subjected to a given ground motion, the seismic demand of Model A increases significantly, which results in a smaller increase on the seismic capacity-demand ratio. In contrast, though the seismic base shear force calculated by RSA of

Model B does not meet the code-specified requirement, the building was alternatively designed with a scaled seismic shear force (80% of the minimum base shear force). This design method results in a great increase in the structural seismic capacity without changing the structural seismic demand, so the seismic capacity-demand ratio of Model B has been improved substantially. For the above reasons, Model B exhibits a higher collapse margin ratio than that of

Model A when subjected to the given ground motion Kocaeli_DZC180.

Conclusions

In this paper, the minimum base shear force requirements the in Chinese and U.S. seismic design codes are compared. The comparison indicates that in U.S. design procedure, the minimum base shear force is used to scale the design strength. On the contrary, in most actual design procedure

for tall buildings in China, the stiffness of the buildings is adjusted so as to make the modal base shear force conform to the code-specified requirement. Then two super-tall buildings with different design base shear force are designed and evaluated. The results indicate that the components sectional dimensions and the amount of the constructional materials of Model A, whose stiffness is adjusted, are significantly larger than that in Model B, whose modal base shear force is scaled to meet the code-specified requirement. However, Model A and B have similar seismic performance at the MCE level and both perform well to meet the seismic performance objectives specified in the seismic codes. Furthermore, since Model A has a smaller capacitydemand ratio than Model B, the collapse resistance of Model A is smaller than Model B, even though much more materials is used in Model A. Note that the collapse margin ratios of Model A and B are evaluated for a given ground motion record. In future work, an increased amount of ground motion records will be utilized in order to more precisely determine the collapse margin ratio.

Acknowledgments

The authors are grateful for the financial support received from the National Nature Science

Foundation of China (No. 51222804

91315301

51261120377), and the Fok Ying Dong

Education Foundation (No. 131071).

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6.

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