MINISTRY OF EDUCATION AND TRAINING

THE UNIVERSITY OF DANANG

BUI THIEN LAM

RESEARCH ON CALCULATION OF WIND LOADS ACTING ON

WALL-FRAME HIGH-RISE BUILDINGS

Major subject: Technical Mechanics

Code: 62 52 01 01

COMPENDIUM OF TECHNICAL DOCTORAL THESIS

DANANG / 2018

The work has been conducted at

THE UNIVERSITY OF DANANG

Academic supervisors: Prof. Dr. Phan Quang Minh

Assoc. Prof. Dr. Le Cung

Reviewer 1: Prof. Dr. Pham Van Hoi

Reviewer 2: Assoc. Prof. Dr. Ngo Huu Cuong

Reviewer 3: Dr. Tran Dinh Quang

The thesis is reviewed and marked by the PhD thesis Examiners at the

University of Danang in 14h30 day 10 month 03 year 2018

Thesis can be found at

- Center for Information- Learning, The University of Danang

- National Library of Vietnam

1

INTRODUCTION

There are three methods which are mostly used in the world to

determine the wind load i.e., simplified procedure, analytical procedure and

wind-tunnel procedure. The Vietnamese standard TCVN 2737:1995 is

compiled in accordance with Russian standard SNiP 2.01.07-85* that does

not mention the wind-tunnel method.

For symmetric plan highrise buildings , the dynamic component of wind

load is crucially governed by the first mode shape. As a result, the

approximate formula with respect to the first mode shape is exerted to

calculate the dynamic componet of wind load in practice. Hence the

approximate approach applied into wind code is prefered by the most

nations. In which, the dynamic wind acting on highrise buildings is

computed from the static wind by multiplying with gust loading factor. The

dynamic wind in TCVN 2737:1995 is also computed by taking the static

component of wind load multiplying with a factor that reflect the effects of

the velocity pulses and inertia forces.

TCVN 2737:1995 introduced an approximate formula to determine the

dynamic wind. This formula is simply and useful. However, it is only

consistent with the buildings that transverse displacements adheres to

linear rule with respect to z level. In fact the number of buildings conform

to this condition limitted due to artchitectural requirements and economic

efficiency. Therefore, the applicable area of this formula must be clearly

distinguished to eliminate the big errors. On the other hand, the

computational procedure of the wind load according to Vietnamese

standard is very complicated. This inspires to the present study in order to

pursuit the complementation for computational procedure of dynamic wind

acting on the highrise buildings conforming with conditons in Vietnam.

Further, the present study approaches to standards of advanced countries,

2

this is essential and practical.

Aims of the research

- Formulate an approximate formula for dynamic wind according to

TCVN 2737:1995 with acceptable error.

- Propose a simplified fomula to compute the dynamic wind based on

the gust loading factor applied for the wall-frame system of a highrise

buildings with 35 stories and symmetric plane.

Đối tượng và phạm vi nghiên cứu

- Study subjects: the dynamic wind load on highrise buildings

- Scope of research: the wall-frame system of a highrise buildings with

35 stories and symmetric plane.

Research objectives

- Study the transverse displacement of wall-frame buildings; evaluate

the error of approximate formula determined the dynamic wind in

Vietnamese standard.

- Formulate an approximate and simplified formula in similarity with

approximate formula in TCVN 2737:1995 with acceptable error.

- Study the gust loading factor G corresponding with structural systems

are altered the stiffnesses based on TCVN 2737:1995.

- Propose a simplified fomula to compute the dynamic wind based on

the gust loading factor applied to highrise buildings up to 35 stories,

symmetric plane and using the wall-frame system located in Danang city.

Contributions and innovativeness of the thesis

- Clarified the applicable area of the approximate formula to compute

the dynamic wind in TCVN 2737:1995.

- Proposed the approximate fomula to compute the dynamic wind for

highrise buildings using the wall-frame system based on Vietnamese

standard.

3

- Propose a simplified fomula to compute the dynamic wind based on

the gust loading factor G applied for highrise buildings up to 35 stories,

located in Danang city and similar topographies with appropriate accuracy

in comparison to the analytical method in TCVN 2737:1995.

Thesis layout

The thesis consists of 123 pages including 5 pages of Introduction

section. Chapters 1, 2 and 3 consist of 41 pages, 40 pages and 35 pages

respectively. Eventually, conclusions and recommendation section includes

2 pages; publication section has 1 page and References section has 7 pages.

Chapter 1 LITERATURE REVIEW

1.1. Wind and its action on buildings

1.1.1. Concepts of wind, storm, cyclone

1.1.2. Wind action on buildings and structures

1.1.3. Structures and its typical parameters affecting to wind load

1.1.4 Investigating of the effect of parameters on wind load on buildings

1.2 Overview of wind load studies

1.2.1. Overseas studies

Many theoritical and experimental studies have conducted so far, in

which an outstanding study is the gust loading factor methos of Davenport

published in 1967. According to Davenport, the wind load is computed by

multiplying the average wind load with an factor that takes into account the

gust load of wind. Recently, this method has been applied into the most

countries’ standards by regulating to conform with conditions of each

country. 1.2.2. Domestic studies

Vietnamese standards of wind loads were compiled based upon Russian

standards. But it has been regulated to conform to the conditions in Vietnam

e.g., time average interval to measure the wind velocity, time return period,

4

division of wind zones. Recently, some theoretical, computational and

practical studies have been performed in the wind-tunnel.

1.3. Standards for determination of wind loads

1.3.1. American standard ASCE/SEI 7-16

Wind pressure acting on main structures of builddings is given as

following formula,

p = q.G.Cp - qi.(GCpi) (N/m2) (1.27)

G: Gust loading factor

1.3.2 European standard EN 1991-1.4 (2005)

- Wind load acting on buildings is described as equation (1.41):

Fw = CsCd. Cf. qp(ze) .Aref (1.41)

CsCd : factors counting to dynamic actions.

1.3.3. Vietnamese standard TCVN 2737:1995

- Static wind

���� = ��. �. �(���/�

�) (1.46) - Dynamic wind

�� ≥ ��:����� = ��

��. z�.n(���/��) (1.48)

�� < ��:��(��)�� = ��. x� .y����(���/�

�) (1.50)

Approximate formula: ���� = 1.4

�

�. �.���

�� (1.52)

From (1.46) and (1.48), the total wind load (when f1>fL) is calculated:

��� = ���� +���

�� = �1 + z�n���

�� (1.53)

Then � = 1 + z�.n is the gust loading factor (1.54)

1.4. Conclusions

Most wind load standards in the world based upon the gust loading

factor method of Davenport to estimate the wind load acting on buildings

along wind direction.

5

Basing on the analyses of some standards, it can be seen that TCVN is

different from ASCE-7 and EN when consideration of dynamic component

of wind loads. The standards ASCE-7 and EN determined the dynamic

wind through the gust loading factor. Meanwhile Vietnamese standard

divided dynamic wind into static and dynamic components, it becomes very

complicated so that it needs to continue studying.

Chapter 2- CALCULATION OF THE DYNAMIC WIND LOAD

FOR THE SYMMETRIC WALL-FRAME BUILDINGS

2.1. The priciples of the wall-frame system

Wall-frame system ultilizes the advantages of each component, it both

enlarges using space effectively according to requirements of architectual

arrangement and strongly resist against transverse loads.

2.1.1. Interaction within braced frame under distributed load.

Since frame-diaphragm structures subjected by transverse loads. The

diaphragm and frame will undergo a transverse displacement. But due to

the stiffnesses of diaphragm and frame are different, hence the transverse

displacements of diaphragm and frame are also different. As a result,

diaphragm and frame will interact each others through slab and beam

systems.

2.1.2. Analyses of the braced frame structures

2.1.2.1. Basic differential equation

The differntial equation characterizes for the transverse displacement of

frame-diaphragm structures. ���

���− ��

���

���=�(�)

�� (2.4)

2.1.2.2. Case of subjecting to uniformly distributed loads

From equation (2.4), the equation of transverse displacement is written

as follows,

6

�(�) =���

���

�

(��)��(����������)

������(���ℎ�� − 1) − �����ℎ�� +

(��)� ��

�−�

���

������ (2.13)

The equation (2.13) can be written in the compact form as given in

equation (2.16)

�(�) =���

�����(��, �/�) (2.16)

�� = ��

(��)��(����������)

������(���ℎ�� − 1) − �����ℎ�� + (��)� �

�

�−

�

���

������ (2.17)

2.1.2.3. Case of subjecting triangular distributed loads

�(�) =�����

�

�������(��, �/�) (2.23)

�� = ����

��(��)�����������

�−������

��+ 1� �

��������

������� + �

�

�−

������

��� �(��)�

�− 1� −

(��)�

���

���� (2.24)

Figure 2.7- K1, since subjected triangular distributed loads

Figure 2.6- K1, since subjected uniformly distributed loads

7

2.1.2.4. Discussions

Since αH >2, displacement diagram is approximately linear in z-

direction, in similarity with the strains of frame subjected transverse loads.

Since αH ≤ 2, displacement diagram is a curve in z-direction.

In Vietnam, the most high-rise buildings from 15 to 35 stories are

mostly used wall-frame system and diaphragm. Their role in the buildings

resists agianst transverse loads. Therefore the dimensions of column are

minimized to increase the using space, in this situation corresponding with

the case of αH ≤ 2.

2.2. Determination of dynamic wind load for symmetric wall-frame

structures buildings

2.2.1. Evaluation of errors in approximate formula of TCVN

The errors are evaluated base on investigation of the dynamic wind with

resoect to some of buildings that located in zone IIB with various values of

αH according to the approximate and exact formula in TCVN.

2.2.1.1. Buildings with 20 stories: Considering 5 cases where the frame-

diaphragm system has αH between 0.50 and 2.50. The plan is shown in

Figure 2.8, and its data given in Table 2.1.

Table 2.1. Dimensions of structural components in 20 stories building

Models Colunms Beams Diaphragm Slab

thicknesses (m)

Story hieght

(m) (m2) (m2) (m)

Model 1 0.50x0.50 0.25x0.50 0.5 0.2 3.6

Model 2 0.60x0.60 0.30x0.60 0.3 0.2 3.6

Model 3 1.00x1.00 0.40x0.60 0.2 0.2 3.6

Model 4 1.00x1.00 0.40x0.70 0.2 0.2 3.6

Model 5 1.00x1.00 0.45x0.80 0.2 0.2 3.6

8

Using dynamic analysis to calculate the dynamic wind (the wind zone is

IIB, type of Danang topography is B), according to approximate formula

(1.52) and formula (1.50), the obtained results are compared and given in

the Table 2.3.

Figure 2.8-Structural plan of building 20 and 30 stories.

Table 2.3. Comparison of the dynamic wind according to formulas (1.52)

and (1.50) for buildings with 20 stories.

2.2.1.2. Buildings with 30 stories: Considering 5 cases where the frame-

diaphragm system has αH between 1.00 and 3.00. The input data is given in

Table 2.4 and obtained results are given in Table 2.6.

CT1.50 CT1.52 CT1.50 CT1.52 CT1.50 CT1.52 CT1.50 CT1.52 CT1.50 CT1.52

Sum 1869.4 2155.8 1923.9 2163.3 2004.3 2165.8 2016.8 2153.3 1961.3 2077.0

Error 15.32% 12.45% 8.06% 6.77% 5.90%

Model 5,

αH=2.45

T=1.645Models

Model 1,

αH=0.54

T=1.746

Model 2,

αH=1.01

T=1.879

Model 3,

αH=1.53

T=1.916

Model 4,

αH=1.92

T=1.783

9

Table 2.4. Dimensions of structural components in building

with 30 stories

Models Colunms Beams Diaphragm Slab

thicknesses (m)

Story hieght

(m) (m2) (m2) (m)

Model 1 0.70x0.70 0.30x0.50 0.5 0.2 3.6

Model 2 0.80x0.80 0.40x0.50 0.3 0.2 3.6

Model 3 1.00x1.00 0.35x0.60 0.25 0.2 3.6

Model 4 1.00x1.00 0.45x0.60 0.2 0.2 3.6

Model 5 1.00x1.00 0.45x0.70 0.2 0.2 3.6

Table 2.6. Comparison of the dynamic wind according to formulas (1.52)

and (1.50) for buildings with 30 stories.

Table 2.3 and Table 2.6 describe the errors between approximate

formula (1.52) and exact formula (1.50). The error degree depends on the

values of αH factor. Since αH is smaller then the error degree is larger. For

high-rise buildings from 15-35 stories using wall-frame system then αH is

often small. If the approximate formula (1.52) is used to determine the

dynamic wind then the error degree will increase. As a result, the designs

cause waste, hence there needs to additional studies.

2.2.2. Correction of the approximate formula for calculating the dynamic

wind

2.2.2.1. Proposal formula to express K1 function

(CT1.50) (CT1.52) (CT1.50) (CT1.52) (CT1.50) (CT1.52) (CT1.50) (CT1.52) (CT1.50) (CT1.52)

Sum 3132.63 3565.75 3223.49 3565.75 3298.55 3565.75 3333.12 3547.47 3290.22 3476.15

Error 13.83% 10.62% 8.10% 6.43% 5.65%

Model 5,

αH=2.88

T=3.048Models

Model 1,

αH=0.95

T=3.31

Model 2 ,2

αH=1.42

T=3.311

Model 3,

αH=1.93

T=3.310

Model 4,

αH=2.44

T=3.286

10

From theoretical analysis in section 2.1, for the buildings using the

symmetric braced frame system subjected transversely triangular distributed

loads then the transverse displacement yz determined in formula (2.23)

distributes as curve rule depending on interaction between frame and

diaphragm (as seen Figure 2.7). However, K1 calculated in formula (2.24)

is very complicated. By using the fitting curve technique corresponding

with αH<2.0, the curve K1 is approximated as a parabolic curve.

Consequently, it can express as second degree polynomial function or

sinusoidal function. This study recommends K1 curve described under

sinusoidal rule (as given in equation (2.25)).

�� = ��(�)�

�sin(

�

�

�

�) (2.25)

Figure 2.10. K1 curve vs. CT 2.24, CT 2.25 with αH=0.5; 1.0; 1.5; 2.0

Graph in Figure 2.10 demonstrates that for buildings using the wall-

frame structure with K1 curve corresponding with αH ≤ 2.0 then the K1

curve expressed in formula (2.25) is acceptable, its error is sufficient small.

11

2.2.2.2. Establishment of formula to calculate the dynamic wind

The value of relative displacement yji in formula (1.50) and (1.51) is

ratio of y(z)/y(H), from equation (2.25) it is obtained:

��� =�

�sin(

�

�

�

�)�� (2.29)

Dynamic wind pressure acting on buildings at z-leval is ���

W�� = M�. ξ.∫ ���.��.���

�

∫ ���� .

�

���.��

y�� (2.30)

W�� = M�. ξ.∫ y��.W��. z�. n. dz�

�

∫ y���.

�

�M�dz

y�� (2.31)

Substitute Wmz in formula (1.46) into equation (2.31), it obtains the equation (2.32)

W�� = M�. ξ.∫ ���.��.��.�.z�.n.���

�

∫ ���� .

�

�����

y�� (2.32)

��� = ��x���� ∫ �

�

�����

�

�

�

���������

�

������

z����

������

���

�

�� ∫ ��

�����

�

�

�

�����

��

���

��

���� �

�

�

�

�� ��� (2.35)

From equation (2.35) combination with type A of topography (mt=0.07),

it can infer the equation (2.36):

��� = 1,47�

���� �

�

2

�

������ (2.36)

In the same manner, with type B of topography (mt = 0,09), we have:

��� = 1,46�

���� �

�

�

�

�� ���� (2.37)

with type C of topography (mt = 0,14), we also have:

��� = 1,43�

���� �

�

2

�

�� . �.��� (2.38)

12

2.3. Evaluating errors of proposal formula

In order to evaluate the proposal formula is either appropriate or not,

four types of the buildings with various top-plans and number of stories are

computed. The buildings in this computation located of wind zone IIB, type

B of topography. The top plans are presented in Figure 2.11, 2.18, 2.21 and

2.24. The input data of structural components in buildings is given in Table

2.8. The results of dynamic wind computed in formula (1.50), (1.52) of

TCVN and in proposal formula (2.37) are shown in Figures 2.12 and 2.16;

Table 2.16 and 2.17.

Figure 2.11 Structural plan of building: type 1

Figure 2.18 Structural plan of building: type 2

Figure 2.24. Structural plan of

building: type 4 Figure 2.21 Structural plan of building:

type 3

13 Table 2.6. The input data of four types of buildings from 20-30 stories

Figure 2.12. Dynamic wind of building-type 1, 20 stories, diaphragm

thickness 200

Figure 2.16. Dynamic wind of building-type 1, 30 stories, diaphragm

thickness 300

20 30

8.0x8.0 8.0x8.0

3.6 3.6

200 200

Model 1-2 700x700 1000x1000

Model 3-4 800x800 1000x1000

200-250-300 250-300-350

B30 B30Concrete strength

Section

colunms

(mm)

Diaphragm thichnesses

(mm)

Story of numbers

Colunm grids (m)

Story hieghts (m)

Slab thicknesses (mm)

14

Table 2.16. Comparing the bottom shear forces induced by dynamic wind

according to four types of buildings with 20 stories.

2.4. Discussion

From the computational results of dynamic wind as given in Table 2.16

and 2.17 for the buildings with αH≤ 2.0, and after comparison between

results were calculated in exact and approximate formulas (1.50) and (1.52)

of TCVN 2737:1995 and proposal formula (2.37) demonstrate that,

- The error of the results computed between formula (1.52) and

(1.50) is quite large, it is about 13-17%.

- The error of the results computed between proposal formula (2.37)

and (1.50) is sufficient small, it is less than 4.5%.

- The proposal formula (2.37) is simply and useful, it is similar to the

approximate formula (1.52) in TCVN 2737:1995. But its accuracy

approximates with exact formula (1.50) in TCVN as well.

Diaphragm

(mm)αH CT1.50 (kN) CT1.52 (kN) Δ1 (% ) CT2.37 (kN) Δ2 (% )

200 0.902 1543.21 1804.31 16.9% 1546.09 0.2%

250 0.808 1506.46 1766.90 17.3% 1514.03 0.5%

300 0.738 1501.06 1741.71 16.0% 1492.45 -0.6%

200 0.980 1979.69 2300.2 16.2% 1971.0 -0.44%

250 0.877 1880.36 2209.09 17.5% 1892.94 0.67%

300 0.802 1883.3 2201.14 16.9% 1886.13 0.15%

200 1.500 2072.17 2397.91 15.7% 2054.73 -0.84%

250 1.341 2035.86 2368.78 16.4% 2029.77 -0.30%

300 1.224 1998.09 2334.03 16.8% 2000.00 0.10%

200 1.382 2152.52 2468.51 14.7% 2115.23 -1.73%

250 1.235 2111.72 2437.17 15.4% 2088.38 -1.11%

300 1.126 2080.76 2413.02 16.0% 2067.69 -0.63%

Building 20 stories

Ty

pe

1

Notes: - Δ1 (%) is error between formula TCVN (1.52) and TCVN (1.50).

- Δ2 (%) is error between proposal formula (2.37) and formula (1.50)

Ty

pe

2T

yp

e 3

Ty

pe

4

15

Table 2.17. Comparing the bottom shear forces induced by dynamic wind

according to four types of buildings with 30 stories.

Chapter 3

DETERMINATION OF THE GUST LOADING FACTOR OF

SYMMETRICAL WALL-FRAME HIGH-RISE STRUCTURES

BASED ON TCVN

3.1 Gust loading factor Davenport

Davenport proposed the method for determination of the peak load

max( )p z based on the mean wind load (static) p(z) and gust loading factor

G, as given by:

�(�)��� = �. �̅(�)

(3.3)

where

�(�) =�

����

���(�)

Diaphragm

(mm)αH CT1.50 (kN) CT1.52 (kN) Δ1 (% ) CT2.37 (kN) Δ2 (% )

250 1.219 2745.99 3180.93 15.8% 2715.30 -1.1%

300 1.114 2701.95 3141.79 16.3% 2681.89 -0.7%

350 1.032 2658.89 3100.55 16.6% 2646.68 -0.5%

250 1.325 3435.04 3958.82 15.2% 3379.32 -1.62%

300 1.210 3360.99 3914.77 16.5% 3341.72 -0.57%

350 1.121 3366.48 3908.26 16.1% 3336.16 -0.90%

250 2.027 3550.29 4034.30 13.6% 3443.75 -3.00%

300 1.850 3525.58 4030.01 14.3% 3440.09 -2.42%

350 1.711 3487.16 4004.77 14.8% 3418.55 -1.97%

250 1.852 3588.19 4028.28 12.3% 3438.61 -4.17%

300 1.689 3571.45 4035.75 13.0% 3444.99 -3.54%

350 1.561 3553.12 4036.41 13.6% 3445.55 -3.03%

Building 30 stories

Ty

pe

1

Notes: - Δ1 (%) is error between formula TCVN (1.52) and TCVN (1.50).

- Δ2 (%) is error between proposal formula (2.37) and formula (1.50)

Ty

pe

2T

yp

e 3

Ty

pe

416

1V mean wind velocity evaluated at the top height of the structure

According to Davenport, gust loading factor G is given by:

� = 1 + ��√� + � (3.4)

3.2. Proposal of formula for determination of the gust loading factor

based on TCVN 2737:1995

3.2.1. When frequency of vibration in the fundamental mode ��(��) larger

than frequency of vibration ��(��):

From (1.46) and (1.48), the total wind load is given (1.53) and (1.54):

��� = ���� +���

�� = ���� �1 + z

�n�

� = 1 + z�n

In accordance with Davenport, � = 1 + z�n is defined as gust loading

factor

3.2.2. When stiffness, mass, and width of the structure normal to the

oncoming wind height are constant

3.2.2.1. Case 1: αH = 2 ÷ 6 (when the frame structures play primary role in

wall-frame structures)

Equation (1.52) gives:

���� = 1.4

�

�. �.���

��

�ℎ�������� = ��

�� ��

�����

z�� (3.10)

Substituting ����� from (3.10) into (1.52) leads to:

���� = 1,4 �

�

�������

�z����

�� (3.11)

��� = ���� +��

�� = ���� �1 + 1,4 �

�

�������

�z���

(3.12)

Gust loading factor G is given:

� = 1 + 1,4 ��

�������

�z�� (3.13)

17

3.2.2.2. Case αH ≤ 2 (when the wall structures play primary role in wall-

frame structures)

The dymamic wind load is given in Equation 2.37 (see Chapter 2)

���� = 1,4

�

���� �

�

2.�

�� ����

���� = 1,4 �

�

�������

�z����� �

�

2.�

����

��

If: �� = 1,4 ��

�������

�z����� �

�

�.�

�� (3.14)

Then: ���� = ����

��

��� = ���� +��

�� = ���� �1 + 1,4 �

�

�������

�z����� �

�

�.�

���

Gust loading factor: � = 1 + 1,4 ��

�������

�z����� ��

�.�

�� (3.15)

+ GIS shape A: mt = 0.07

� = 1 + 1,4 ��

���.��

�z����� �

�

�

�

�� (3.16)

+ GIS shape B: mt = 0.09

� = 1 + 1,4 ��

���.��

�z����� �

�

�

�

�� (3.17)

+ GIS shape C: mt = 0.14

� = 1 + 1,4 ��

���.��

�z����� �

�

�

�

�� (3.18)

3.2.2.3. Approximate determination of gust loading factor G of 15 to 35

story high rise buildings

From (3.16), (3.17), (3.18), we can see that the determination of gust

loading factor G is complicated depending on many varied factors.

Therefore, gust loading factor G is studied basing on some factors which

can establish the simple formulation for approximate determination of G

with acceptable precision.

a. Power law coefficient ξ: Power law coefficient ξ is determined in accordance with TCVN,

depending on � =����

����� , and lôga reduction of vibration δ

18

f1 can be calculated as T1=0.08n, where n is the number of stories

b. Fluctuating pressure coefficent ζ:

Calculated in accordance with TCVN, depending on height z and GIS

shape.

c. Space correlation of fluctuating pressure coefficient ν: Determined in

accordance with TCVN.

d. Formulation of the equation:

Wind load direction is perpendicular to ZOY plane, width of structures

normal to oncoming wind load, b = 30-50m, 15 to 35 stories, H=40-100m.

- Space correlation of fluctuating pressure coefficient �: From TCVN, �

is in the range of 0,66 to 0,61, and the mean value � = 0.63.

- Fluctuating pressure coefficent z : depending on height z, is given:

z�= z

�� ���

����

(3.19)

For GIS shape B, at z=H:

z�= z

�� ���

���.��

= 0.486 ���

���.��

(3.20)

- Power law coefficient ξ:

For time period: � = 0.08�

safety coefficient γ =1.2

Then ε for buildings in wind zone IIB (W0 = 950N/m2):

� =����

�����=

√�,�×���

���×(�

�,���)= 0.00287� (3.21)

For 15, 20, 25, 30 and 35 story buildings, and T=0,08n, the frequency f1,

ε value and power law coefficient ξ respectively are given in Table 3.3.

From ξ in Table 3.3, we can calculate ξ in accordance with the following

equation:� = 1.3 + 0.2� = 1.3 + 0.016� (3.22)

19

Table 3.3. f1 , ε , ξ

Number of story 15 20 25 30 35

f1 (Hz) 0.833 0.625 0.500 0.417 0.357

ε 0.043 0.057 0.072 0.086 0.101

ξ 1.513 1.633 1.737 1.826 1.901

GIS shape B: mt = 0.09, rewrite (3.14):

�� = 1,4 ��

���.��

�z����� �

�

2

�

��

As we can see:��

���.��

��� ��

�

�

�� ≈ �

�

���.�

(3.23)

Substituting (3.20), (3.22), (3.23) and � ≈ 0.63 into (3.14), leads to:

�� = 1,4 ��

���.�(1.3 + 0.016�) �0.486 �

��

���.��� 0.63 (3.24)

When safety coefficent γ =1.2, (3.24) becomes:

�� =�.����.����

��.����

���.�

(3.25)

Gust loading factor:

� = 1 +�.����.����

��.����

���.�

(3.26)

Dynamic wind load Wpz: ��� = ����� (3.27)

Total wind load Wz: �� = ���� (3.28)

For the upto 35 storey braced frame structures, time period T≈0,08n, Kp

and gust loading factor G at height z can be determined approximately in

accordance with simple equations (3.25) and (3.26),

3.3 Evaluation the error of propsed formula of wind load

In order to evaluate the accurateness of equations (3.25 to (3.28), the

dynamic of wind load and total wind load of some high-rise buildings in

wind zone IIB, type B of topography with different plan and height is

calculated in accordance with 3.25 to 3.28 and compared with those

calculated in accordance with equation (1.50) of TCVN.

20

3.3.1. Building types 1, 2, 3: The dynamic wind loads were calculated in

accordance with equation (1.50) and (3.27) (data from chapter 2). The

results are given in the Figures 3.5 and 3.9 and Tables 3.4.

3.3.4. Building types 1a, 2a và 3a

3 cases of 20 storey building with wall thickness of 200, 250, 300 and 3

cases of 20 storey building with wall thickness of 250, 300, and 350 were

investigated. The results of dynamic wind load calculated by equation

(1.50) TCVN and proposed equation (3.27) are similar to building types 1,

2, 3.

Figure 3.9 Dynamic wind load- plan shape 1 (30 story, wall thickness of 300)

Figure 3.5 Dynamic wind load- plan shape 1 (20 story, wall thickness of 200)

21

The errors of dynamic wind load are less than 5% while the errors of

total wind load are less than 1.4% (Table 3.12 and 3.13)

20 STORY BUILDING

Wall thickness

(mm) T1(s)

Wj (kN)

Wpz (kN)

KpWj (kN)

Error Δ(%)

(dynamic wind load)

Error Δ(%) (total wind load)

Ty

pe

1

200 2.00 4520.52 1543.21 1575.30 -2.08% -0.53%

250 1.86 4520.52 1506.46 1575.30 -4.57% -1.14%

300 1.77 4520.52 1501.06 1575.30 -4.95% -1.23%

Ty

pe

2

200 2.33 5650.66 1979.69 1969.11 0.53% 0.14%

250 2.07 5650.66 1880.36 1969.11 -4.72% -1.18%

300 2.05 5650.66 1883.3 1969.11 -4.56% -1.14%

Typ

e 3

200 2.69 6780.79 2430.48 2362.94 2.78% 0.73%

250 2.55 6780.79 2387.89 2362.94 1.04% 0.27%

300 2.43 6780.79 2343.59 2362.94 -0.83% -0.21%

30 STORY BUILDING

Wall thickness

(mm) T1(s)

Wj (kN)

Wpz (kN)

KpWj (kN)

Error Δ(%)

(dynamic wind load)

Error Δ(%) (total wind load)

typ

e 1

250 3.84 7275.47 2745.99 2635.40 4.03% 1.10%

300 3.67 7275.47 2701.95 2635.40 2.46% 0.67%

350 3.53 7275.47 2658.89 2635.40 0.88% 0.24%

typ

e 2

250 4.39 9171.83 3435.04 3294.25 4.10% 1.12%

300 4.06 9171.83 3360.99 3294.25 1.99% 0.53%

350 4.03 9171.83 3366.48 3294.25 2.15% 0.58%

typ

e 3

250 4.93 10886.2 4157.31 3953.10 4.91% 1.36%

300 4.77 10886.2 4138.3 3953.10 4.48% 1.23%

350 4.63 10886.2 4093.2 3953.10 3.42% 0.94%

Wj: static wind load calculated in accordance with TCVN (1.46) Wpz: dynamic wind load calculated in accordance with TCVN (1.50). KpWj: dynamic wind load calculated in accordance with the proposed method (3.27)

3.3.5. Building types 4, 5, 6

Table 3.4: Comparation of wind load calculated in accordance with TCVN and propsed method (3.27)

22

Table 3.14: Some properties of building type 4, 5 and 6 Types

of building

Number of story

Column Grid (m)

Story height

(m)

Width (m)

Slab thickness

(mm)

Wall thickness

(mm)

Column section

(mmxmm)

Beam section

(mmxmm)

4 20 8x8 3.6 24 200 300 800x800 500x700

5 25 8x8 3.6 32 200 350 800x800 400x700

6 30 8x8 3.6 40 200 450 1000x1000 700x900

The results of dynamic and total wind loads for building types 4, 5, 6 are

given in Table 3.18

Table 3.18: Wind load calculated in accordance with TCVN and proposed

equation 3.27

Building type

Static Wind load

Wj (kN) TCVN (1.46)

Dynamic wind load Wpz (kN)

TCVN (1.50)

Total wind load Wz

(kN) (TCVN)

Proposed dynamic

wind load KpWj (kN)

(3.27)

Proposed total wind

load Wz (kN)

(3.28)

Error Δ1(%)

(dynamic wind load)

Error Δ2(%) (total wind load)

Type 4 3060.42 1060.56 4120.97 1074.86 4135.28 -1.35% -0.35%

Type 5 5293.91 1826.51 7120.43 1893.68 7187.59 -3.68% -0.94%

Type 6 8191.28 2886.09 11077.37 2998.71 11189.98 -3.90% -1.02%

3.3.6. Case studies: Danang Plaza and Danang Customs Department

Table 3.19: Some properties of Danang Plaza và Danang Customs

department

Building Height

(m)

Column cross

section (mxm)

Beam cross

section (mxm)

Slab thickness

(m)

Wall thickness

(m)

Concrete class

Danang Plaza 3.6 0.7x0.7 0.3x0.6 0.2 0.3 B30

DN Customs 3.6 0.7x0.7 0.3x0.5 0.2 0.3 B30

Dynamic wind load and the error of wind load calculated by two

methods are given in Table 3.22.

23

Table 3.22: Wind load calculated in TCVN and proposed equation 3.27 Building types

Static wind load Wj (kN) TCVN (1.46)

Dynamic wind load Wpz (kN) TCVN (1.50)

Total wind load Wz(kN) TCVN

Proposed Dynamic wind load KpWj (kN) (3.27)

Proposed Total wind load Wz(kN) (3.28)

Error

(%)1

(dynamic wind load) (%)

Error (%)2

(total wind load) (%)

DN Plaza 4804.39 1725.26 6529.66 1674.21 6478.61 2.96 0.78

DN Customs 3857.65 1396.41 5254.06 1344.29 5201.94 3.73 0.99

3.4 Discussion

The gust loading factors G of different high rise building structures were

studied basing on TCVN 2737: 1995. Eleven types of building and 41 case

studies were investigated. The results show that the relationships between

the dynamic wind load calculated in accordance with TCVN and proposed

equation are similar. The errors of dynamic wind load calculated basing on

two methods are less than 5% while the errors of total wind load calculated

basing on two methods are less than 1.4%, an acceptable error.

CONCLUSION AND RECOMMENDATIONS 1. Conclusion

The main conclusions from the results reported in the thesis are as follow:

1. Vietnam standard TCVN 2737:1995 divides the wind load into static and

dynamic wind load. This method is more complicated than GLF method of

Davenport that using the gust loading factor (ASCN, EN Standard…)

Approximate formula (1.52) in accordance with TCVN 2737:1995 is quite

simple, however this approximate can be only applied to frame structures.

For wall-frame structures (αH≤ 2.0), the error of dynamic wind load

calculated basing on equation (1.52) and equation 1.50 is quite large, about

13-17%

2. Analysis of the lateral displacement of symmetrical wall-frame high rise

buildings proposed the approximate formula (2.37) for determination of

24

dynamic wind load. The errors of dynamic wind loads (Tables 2.16 and

2.17) calculated basing on proposed equation (2.37) and equation (1.50) in

accordance with TCVN 2737:1995 are quite small, less than 4.5%.

3. Basing on the Vietnam standard TCVN 2737:1995 and the results from

Chapter 2, the authors has summarised formulas of standards to determine

the gust loading factor G which is similar to the gust loading factor

Davenport in different high rise buildings when lateral loads are applied.

The approximate formula of gust loading factor G Davenport is proposed

for 15 to 35 storey symmetrical wall-frame reinforced concrete high-rise

buildings in Danang and similar GIS shape as follow:

� = 1 +�.����.����

��.����

���.�

Basing on the analysis of some highrise buildings, the error of dynamic

wind loads calculated in accordance with TCVN 2737:1995 and above

proposed formula is quite small, less than 5%. Similarly the error of total

wind load calculated basing on two above methods is quite small, less than

1.4%. Therefore, it is reliable to apply the porposed formula for

determination of wind load.

The approximate fomula gust loading factor is quite simple. It can be used

to determine the wind load without dynamic analysis. It can be used for

design, inspection of high rise building

2. Recommendations

Within the scope of the thesis, some problems are not studied and needs

further research in the future:

Gust loading factor for asymmetrical wall-frame structures.

Experimental research on wind tunnel for improve the reliability.

Experimental research on wind tunnel for investigation of the torsion

wind loading on high rise building.

LIST OF SCIENTIFIC WORKS PUBLISHED

1. Phan Quang Minh, Bui Thien Lam (2017), Study and proprosal

of gust loading factor to calculate wind load on frame-wall

buildings according to Vietnamese standard TCVN 2737:1995,

Journal of Construction, 7-2017, ISSN 0866-0762, trang 274-277

2. Bui Thien Lam (2016), An improved approximate formula for

calculating the dynamic component of wind load in the

Vietnamese standard TCVN 2737:1995, Journal of Construction,

5-2016, ISSN 0866-0762, trang 47-51.

3. Bui Thien Lam, Dang Cong Thuat (2016), Dynamic response and

reliability analysis of structures under wind loading, The 2nd

National Conference on Transport Infracstructure with

Sustainable Development, Construction Publissher, ISBN 978-

604-82-1809-6, trang 619-624.

4. Bui Thien Lam (2016), Study about approximate distribution of

wind load on storeys of multi-storey building from bottom shear

forces, The 2nd Conference on Advanced Technology in Civil

Engineering Towards Sustainable Development, Construction

Publissher, ISBN 978-604-82-2016-7, trang 1-5.

5. Bui Thien Lam (2015), Analysis of some factors affecting the

ratio of dynamic and static component of wind loads under TCVN

2737-1995, The 1st Conference on Advanced Technology in Civil

Engineering Towards Sustainable Development, Construction

Publissher, ISBN 978-604-82-1805-8, trang 32-38.

6. Bui Thien Lam (2014), A Novel Approach for Preliminary

Determination of Dynamic Wind in Design Problem, Journal of

Science and Technology - The University of Danang 12(85)-

2014, ISSN 1859-1531, trang 47-51.