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.