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© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
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© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
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© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
© The Hong Kong Polytechnic University
(04001)
PgS in Construction and Land Use (04001)
(04001)
THE HONG KONG POLYTECHNIC POLYTECHNIC UNIVERSITY DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING 2016/2017 SEMESTER I EXAMINATION POSTGRADUATE POSTGRADUA TE SCHEMES
Program:
MSc
Subject:
Wind Engineering
Subject Code:
CSE531
Session:
2016/17
Date:
12 December 2016
Time:
19:00 – 22:00
Time allowed:
THREE hours
(04001)
This question paper has 6 pages.
Instructions to Candidates : 1. 2 3. 4. 5.
THIS IS AN OPEN BOOK EXAMINATION .
This paper contains 5 questions. Answer any 4 questions. All questions carry equal marks. Students are allowed to bring lecture notes and Hong Kong Wind Code 2004 into the examination venue.
DO NOT TURN OVER THE PAGE UNTIL YOU ARE TOLD TO DO SO
1. a) Table 1 lists the annual maximum hourly mean wind speed recorded at Waglan Island from 1983 to 2012 regardless of wind direction. Assume that the Gumbel distribution can be used to describe the extreme wind conditions in Hong Kong, determine the mean value and the standard deviation of the annual maximum hourly mean wind speed at Waglan Island. The measurement station at Waglan is at a level of 90m. Determine the design hourly mean wind speed and wind pressure at a level of 90m for a special structure of which the design life is 100 years and the accepted risk is 10%. The air density is 1.23kg/m 3.
Year
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
44
24.5
22
29
23.5
19
26
20.2
26.8
25.8
Year
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
U(m/s)
33.3
18.9
27.9
19.2
30.1 30. 1
22.5
42.3
21.1
23.9
21.9
Year
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
23
24.4
22.3
23.1
22.2
32.2
30.8
20.4
22.9
29.7
U(m/s)
U(m/s)
(18 marks) b) The wind data have have been grouped into different different direction direction sectors sectors and the the extreme extreme values analysis analysis gives the following direction multiplier in accordance with the method used in BS6399. Angle from North (Degree) Direction Multiplier
0
45
90
135
180
225
270
315
0.82
0.97
1.00
0.92
0.89
0.90
0.81
0.65
Describe the effect of orientation of a building on the reduction in wind load. What is the maximum amount of reduction in wind load that can be achieved if directional effect is considered? What are the other factors that will affect the wind load reduction due to direction effect? (7 marks)
1
2. a) Briefly describe the pressure distribution over a rectangular building with the width triple the depth along the wind flow direction. What is the change in the wind pressure distribution if the depth of the building is triple its width? (6 marks) b) A building with porous surfaces surfaces can can be treated treated in the the same way as a building with with one opening opening in the windward wall and one opening in the leeward wall. Prove that the internal pressure C pi of the building can can be given given by
C pi
b1 C p
e ,1
b 2 C p
e, 2
b1 b 2
Where b1 represents the total effective volume of windward openings, b 2 represents the total effect volume of suction openings, and (C p)e,1 and (C p)e,2 represent the average values of external pressure coefficients on windward and suction sides, respectively. (7 marks) c) Determine the internal pressure coefficient of the building shown in Fig. Q2 . The external pressures coefficients coefficients are shown in the figure in boldface. boldface. State any assumption assumption used. used. (6 marks) d) Determine the drag and lift force coefficients.
(6 marks)
30m
10m -0.3
Wind direction
0.8 -0.5
10m
30m
0.4
Fig. Q2
2
3. a) Determine the temporal autocorrelation function of the sinusoid x(t)=a cos (ωt). The compound angle formula is given by cos (A+B)= cos(A)cos(B)-sin(A)sin(B) cos(A)cos(B)-sin(A)sin(B) (5 marks) Fig. Q3. The two floors with mass m each are supported b) A two story ‘shear’ building is shown in Fig. Q3. by two massless massless columns columns with lateral stiffness stiffness EI. The damping damping ratio of the building building is ξ. A random exciting force with an ideal white noise power density function S F(ω)=S0 acts on the top floor. Determine the dynamic amplification factor and the variance of the displacement under resonant response of the top floor. (20 marks)
Fig. Q3
3
4. a) A building is of 300m height, 40m width and 30m depth. The damping ratio is 0.01 and first mode frequency is 0.15Hz. The bulk density of the building is 200 kg/m 3. To reduce vibration, a water damper with circular tank is placed at the top of the building. Determine the mass and dimensions of the damper given that the frequency tuning ratio is 1.0 and the total damping ratio required is 0.04. Assume the effective damping of the water damper is 60% of the optimum damping. Density of water = 1000kg/m3. The fundamental sloshing frequency of a liquid damper with circular container is given by
= 21 √ 1.1.84 ℎ(1.84ℎ) Where n=sloshing frequency, g=9.81m/s 2, R=radius of container, h=depth of water. (10 marks)
b) A building has a rectangular cross section, and the width of the cross section varies linearly with the height in a symmetric way. The Th e cross sections at the bottom and top (z=0 and 100m respectively) are shown in Fig. Q4. The h eight of the building is 100m. Wind tunnel tunn el test of the building has been conducted using the force balance technique. The model scale is 1:400 and the velocity scale is 1:6. The mean base moment measured is 0.4Nm. 0.4 Nm. Determine the mean base moment at prototype scale. Determine the mean shear force at prototype protot ype scale acting at the building section of depth 20m from z=60m to z=80m. Assume the wind speed profile can be represented by b y a power law of power exponent 0.25. (15marks)
30m
30m
Wind 50m
30m bottom
Fig. Q4
4
top
5 a) A concrete building of height 80m, width 50m and depth 20m is to be constructed (Fig. Q5a). Determine the force due to wind blowing perpendicular to the elevation view using the Hong Kong Wind Code. If a sky garden of size 15m 15 m x15m x 20m penetrating pe netrating through the building is designed to improve air ventilation, the dimension of the building needs to be revised to keep the frontal area unchanged (Fig. Q5b). Determine the new wind force due to wind blowing perpendicular to the elevation view using the Hong Kong Wind Code. In the presence of a sky sk y garden, will the actual wind force larger or smaller than the value that you calculated? Explain briefly in terms of the wind flow behavior around the building. (20 marks) b) Describe briefly the effect of topography on the wind speed. Under what condition will the topographic multiplier be less than 1? (5 marks)
50m
80m
Elevation
Fig. Q5a
5
50m
84.5m 15m
Sky 15m
garden
25m
Elevation
Fig. Q5b
6
THE HONG KONG POLYTECHNIC UNIVERSITY DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING ENGINEERING 2018/2019 SEMESTER I EXAMINATION
Programme:
MScin Construction and Land Use (04001) PgS
Subject :
CSE531 Wind Engineering
Semester:
1
Session:
2018/19
Date:
13 December 2018
Time:
7:00 – 7:00 – 10:00p.m. 10:00p.m.
Time Allowed : 3 hours
This question paper has 6 pages.
Instructions to Candidates : 1.
THIS IS AN OPEN BOOK EXAMINATION .
2
This paper contains
3.
Answer any
4.
All questions carry equal marks.
5.
Students are allowed to bring lecture notes, tutorials and Hong Kong Wind Code 2004 into the examination venue.
4
5
questions.
questions.
DO NOT TURN OVER THE PAGE UNTIL YOU ARE TOLD TO DO SO
1
1. a) Typhoon Ellen invaded Hong Kong in 1983. The minimum central pressure p 0=950mb and the radius to maximum wind R=40km when it was closest to Hong Kong. The closest distance between the typhoon center and Hong Kong is approximately 43km. The undisturbed ambient pressure pn=1010mb and the air density ρ a=1.2kg/m3. The latitude of Hong Kong is 22.3 0 N. i) ii)
Using the Holland’s model, determine the maximum gradient wind speed at Hong Kong. Determine the maximum wind speed at the level of 100m in the urban area where the average building height was 100m. Given that the Hong Kong design wind profile is a power law profile profile with gradient height H=500m H=500m and power power exponent exponent α=0.11. (13 marks)
b) Wind tunnel tunnel test has been been carried out to study wind load and wind-structure wind-structure interaction interaction of a cylindrical building of diameter 30m, height 120m under the 50 yr extreme wind speed of 59.5m/s. For a geometric scale ratio of 1:400 (model to prototype) and a velocity 10m/s used in the wind tunnel, the vortex shedding frequency measured is 28Hz, determine the corresponding vortex shedding frequency in the prototype. The surface of the model cylinder has been roughened so that the flow phenomenon in the model matches that in the prototype. If the natural frequency of the building is 0.3Hz, what undesirable effect will happen and under what wind condition will this undesirable effect happen. Also suggest one remedial measure. (12 marks)
2
2. a) Table Q2 lists the annual maximum 3s gust wind speed recorded at Waglan Island from 1993 to 2012 regardless of wind direction. Determine the sample mean value and the standard deviation of the annual maximum 3s gust wind speed at Waglan Island. Assume that the Gumbel distribution can be used to describe the extreme wind conditions in Hong Kong, find the 50yr return period 3s gust wind speed. The measurement station at Waglan is at a level of 90m. Determine the design wind pressure at a level of 90m for a special structure of which the design life is 50 years and the accepted risk is 50%. The air density is 1.2kg/m 3. (18 marks)
Table Q2 Year U(m/s) Year U(m/s)
1993 48.5
1994 25.2
1995 37.3
1996 29.1
1997 37.6
1998 31.7
1999 64.9
2000 27.3
2001 30.4
2002 31
2003 33.8
2004 29.4
2005 29.9
2006 36.1
2007 32.6
2008 43.7
2009 38.4
2010 34.1
2011 30.3
2012 41.4
b) Referring to Table D1 of the Hong Kong Wind Code 2004, explain briefly why the height aspect factor Ch increase with the height/ breath ratio. Also, referring to Ta ble D2 of the Hong Kong Wind Code 2004, explain briefly why the shape factor Cs increases with the b/d ratio and for rectangular building. (7 marks)
3
3. a) A low-rise building of flat roof is subjected to a typhoon. The maximum wind speed of the typhoon is 40m/s. There are openings at the surfaces of the building. The total area of the openings at the windward surface is 3m2, the total area of the openings at the roof is 1m 2, the total area of openings at the leeward surface is 1m 2, and the total area of openings at the internal partition is 0.5m 2. The average external pressure coefficients for the surfaces of the building are shown in Fig. Q3a. Determine the internal pressure coefficients and hence the lift force at the roof given that the area of the roof is 20mx20m. 20mx20m. The air density is 1.2kg/m 1.2kg/m3. (13 marks) Roof Cpe= -1.2
Cpe=1.0
Cpi1
u=40m/s
Cpe= -1.0 Cpi2
Fig. Q3a b) A one-story one-story building of two bays bays is subjected subjected to a horizontal random excitation excitation F(t) having an ideal white noise power density S F(n)=S0 at the girder (Fig. Q3b). The girder is rigid and the columns are assumed to be massless. The total mass of the building is m and the damping ratio is ζ. The length of each column is L and the flexural rigidity of each column is EI. Calculate the frequency response function H(n) for the displacement of the girder and the standard deviation displacement response of the girder. Given that m=40000kg, L=4m, EI=2.14x107 Nm2, =0.015, S0=107 N2/s
Fig. Q3b
4
(12 marks)
4. a) A 200 m tall building with uniform mass of 2.6x10 5 kg/m was observed to have excessive vibration under typhoon. A field measurement showed that the first natural frequency and the corresponding damping ratio of the building were 0.23Hz and 0.01 respectively. The first mode shape can be assumed linear. A tuned mass damping is proposed to be installed at 180m level in the building to reduce the excessive wind induced vibration. Determine the design parameters of the tuned mass damper such that the first mode damping ratio of the building can be increased to 0.04. Due to space limitation, the mass of the damper should not be greater than 0.02 of the first generalized mass of the building and the relative relative movement movement of the damper should should not be greater than 3.2. (15 marks)
b) Explain why why a square square building with corner corner cut or with with cross opening opening will have a drag coefficient coefficient smaller than that of the original square building without shape modification. The design wind load on a square building of 160m height and 20m width is found to be excessive. It is intended to reduce the wind load by at least 15%. Propose a revised cross-sectional shape of the building with with dimensions dimensions such that that the cross cross sectional sectional area remains unchanged and the wind wind load is reduced by at least 15%. (10 marks)
5
5. a) A concrete building of height 90m, width 50m and depth 20m is to be constructed on a flat ground. Determine the force due to wind blowing perpendicular to the face with 50m width using the Hong Kong Wind Code. (8 marks) b) If the building is constructed at a location X=100m on an escarpment with slope height H=100m and slope length Lu=1000m (Fig. Q5), determine the wind load on the building for wind blowing uphill along direction A. What is the wind load on the building if wind blowing along direction B.? (12 marks) c) Describe briefly the effect of topography on the wind speed. Under what condition will the topographic multiplier be less than 1? (5 marks)
Fig. Q5
End
6
Examination Answers (CSE531 Wind Wind Engineering) Year 1998-1999 Q1. (a) V 18.96 m/s , V 2.43 m/s
(Tutorial No. 1 Question 2 (a))
(b) 0.528 s/m , U 17.87 m/s (c) V = = 30.25 m/s, P = 0.56 kPa
(Tutorial No. 1 Question 2 (b)) (Tutorial No. 1 Question 2 (c))
Q2. (a) Q x = 19.31 MN M y = 2856.28 MN-m (b) Q y = 20.71 MN M x = 3230.87 MN-m (c) M T = – 12 12 MN-m T =
(Tutorial No. 3 Question 1 (a)) (Tutorial No. 3 Question 1 (b)) (Tutorial No. 3 Question 1 (c))
2
2 2 T (b) (i) y 1.5811y 1000 y x t
Q3. (a) R x
A
cos
H
1
1000 1.5811i 2
(ii) y 0.031 m if define R y y 0.078 m if define R y
1
2
S y e
i
S y e
i
d
d
Q4. (a) G = 2.1895 (b) M G = 1.414109 N-m
(Tutorial (Tutorial No. 5 Question 1 (a)) (Tutorial No. 5 Question 1 (b))
Q5. (b) (i) My My1 Cy1 Ky1 cT z kT z f t mT y1 mT z cT z kT z 0
2 2 2 2 2 2 2 2 2 g g g i g g g g 4 2 1 1 1 2 2 2 g 1 H z K 1 g 2 2 g 2 2 g 2 41 2 g 2 2ig 2 1 g 2 g 2 1 2 g 2
1 (ii) H y1 K 1 g 2
in which 1
K M
, 1
C
2 M 1
, 2
k T mT
2
g 2 2i 2 g
,
mT M
, g
1
,
2 1
, 2
cT
2m 1
2 2 2 2 g 2 2 g 2 412 g 2 2 g 2 1 g 2 g 2 1 2 g 2 4 S 0 g S z 2 2 2 2 K 1 g 2 2 g 2 2 g 2 4 g 2 2 g 1 g 2 g 2 2 g 2 1 1 2 2
S (iii) S y1 02 K 1 g 2
2
2
g 2 2 2 g
2
Year 2000-2001 Q1. (a) Max. hourly wind speed: U = = 24.195 m/s, = = 0.1859 s/m 3-second gust wind speed: U = = 33.926 m/s, = = 0.1469 s/m (b) V m = 53.33 m/s V g = 70.795 m/s = 1.33 GV = Q2. (a) Q = 16.41 MN = 2047.5 MN-m M = (b) Q A = 48.86 MN M A = 5344.56 MN-m
1 of 9
Examination Answers (CSE531 Wind Wind Engineering) A
Q3. (a) x x (b) H
2
1
T0
2 T 0
2
, R x
2 A for
, x2 x 2
2
if define R x
96 EIc
L3S 0
if define R x
48 EIc
1
2
i
Sx e i
S x e
d
2
2
, x2
A
4
, x
A
2
(Tutorial No. 4 Question 1 (2))
d
Q4. (b) V = 12 m/s ymax = 0.0673 m Q5. (c)
A
(Tutorial No. 4 Question 1 (1))
48 EI 2 L3 m ic 3
x
2
T 0
1
L S 0
x
(Tutorial No. 6 Question 1 (b))
ns =
0.15 Hz = 0.27 =
Q6. (b) Mass of first storey, storey, m1 = 1.875 kg Mass of second store y, m2 = 0.9375 kg Breadth of building model, b = 0.25 m Depth of building model, d = = 0.3 m Height of first storey, h1 = 0.18 m Height of second storey, storey, h2 = 0.15 m Flexural rigidity of each column, ( EI )m = 1.1215 N-m2 0 1.875 M (kg) 0.9375 0
12.59 7.975 (kN/m) 7.975 7.975
K
Year 2002-2003 Q1. (1) V = = 70.87 m/s (2) (V ) = 10.32 m/s 50.64 m/s V 91.10 m/s for 95% confidence Q2. (3) (ii) C pi = – 0.1195 0.1195 (iii) Drag force coefficient of windward wall, C D1 = 0.7195 Drag force coefficient of leeward wall, C D3 = 0.3805 Lift force coefficient of sidewall No. 2, C L2 = – 0.4805 0.4805 Lift force coefficient of sidewall No. 4, C L4 = – 0.4805 0.4805
1 Q3. (1) p r 4 r 0 (2) (i) H (ii) x x
1 r 1 r 1; r 1
1
3k 2m 2i 2
S 0
12 k 6mk
S 0 6 k 6mk
6mk 1
2
if define R x
if define R x
S x e
i
i
Sx e
d
d
Q4. (1) G = 2.6033 (2) M G = 5.33109 N-m
2 of 9
Examination Answers (CSE531 Wind Wind Engineering) (3) a = 0.897% Q5. (2) L = 2.7915 m B = 2.15 m number of TLCDs, n = 296
Year 2004-2005 Q1. (2) V g = 69.7 m/s V g = 11.7 m/s (3) With consideration of wind direction, qmax = 1960 Pa Without consideration of wind direction, qmax = 3062.5 Pa Q2. (2) (a) F R = – 31.85 31.85 kN (b) F R = – 4.9 4.9 kN (c) F R = – 26.46 26.46 kN Q3. (2) (a) R x
S 0 cos1
, x2 x2
S 0
1
2
if define R x
2 2 R x 2S 0 cos 1 , x x 2S 0 if define R x
(b) R x R x
S 0 sin 1
, x 2 x2
2S 0 sin 1
S 0 1
if define R x
1
2
, x2 x2 2S 0 1 if define R x
i
S x e
i
Sx e i
S x e
i
S x e
d
d
d
d
Q4. (a) G = 2.1012 9 (b) Resonant component of peak bending moment M GR GR = 0.585 10 N-m Q5. (1) md = = 61.0103 kg k d d = = 61.63 kN/m d = 0.22 d = x1 x2 2.2 x1
Year 2006-2007 Q1. (b) Rank
Gust Gust wind spe speed ed V (m ( m/s)
Redu educed ced variate y
1
34.0
3.0202
2
30.9
2.3018
3
30.8
1.8698
4
30.4
1.5544
5
30.3
1.3022
6
30.2
1.0892
7
29.3
0.9027
8
28.9
0.7349
9
28.8
0.5805
10
28.4
0.4360
11
28.3
0.2985
12
28.2
0.1657
13
27.9
0.0355
14
27.8
-0.0940
15
27.7
-0.2254
16
27.3
-0.3612
17
26.7
-0.5057
18
26.2
-0.6657
19
25.7
-0.8550
20
24.7
-1.1133
3 of 9
Examination Answers (CSE531 Wind Wind Engineering) Q2. (b) (i)
Height
Mean wind speed
Coefficient
Speed-up ratio
z (m)
V (m/s) (m/s)
c = exp(-2.5 z / L1)
10
18.00
0.8825
0.8825
33.88
50
29.17
0.7863
0.7863
52.11
100
35.91
0.6183
0.6183
58.12
150
40.56
0.4862
0.4862
60.28
200
44.22
0.3823
0.3823
61.12
= b0 sc
(ii) Q = 19.33 MN = 2098.62 MN-m M = 2 p a p1 (c) pi 2 1 a2 in which area for the windward opening = A1 area for the leeward opening = A2 A area ratio, a 1 A2
Amplified wind speed V ' = (1 +
Wind
) V (m/s) (m/s)
p1
p2
A1
A2
C p1
C p2
external mean pressure above ambient (wind pressure) at the windward opening = p1 external mean pressure above ambient (wind pressure) at the leeward opening = p2 internal mean pressure above ambient inside the building = pi
2
Q3. (b) R x 2 2 4 7 2 2 e (c) i)
H
1
3 EI 2 L3 k m c i 3
ii)
x
x
S0 L
2c 3EI kL
3
S0 L3
c 3EI kL
3
1
2
if define R x
if define R x
Sx e
S x e
i
i
d
d
Q4. (b) i) M G = 2792.87 MN-m ii) a = 0.386% Q5. (a) md = = 596.94 103 kg k d d = = 461.9 kN/m d = 0.125 d =
4 of 9
Examination Answers (CSE531 Wind Wind Engineering) Year 2008-2009 Q1. (1) V G 28.773 m/s
V G 2.2534 m/s V G = 38.49 m/s P = 907.5 Pa = 0.91 kPa
Q2. (1) Wind direction A
Height above ground z (m)
z Le
Wind direction B
s
S a = (1+1.2 es)2
z Le
s
S a = (1+1.2 es)2
5
0.015
0.17
1.0123
0.0169
0.44
1.3054
30
0.09
0.17
1.0123
0.1013
0.44
1.3054
50
0.15
0.16
1.0116
0.1688
0.55
1.3882
75
0.225
0.15
1.0108
0.2531
0.63
1.4499
100
0.3
0.14
1.0101
0.3375
0.55
1.3882
150
0.45
0.115
1.0083
0.5063
0.35
1.2397
200
0.6
0.095
1.0069
0.675
0.25
1.1686
250
0.75
0.085
1.0061
0.8438
0.18
1.1200
300
0.9
0.075
1.0054
1.0125
0.15
1.0996
400
1.2
0.06
1.0043
1.35
0.1
1.0658
500
1.5
0.049
1.0035
1.6875
0.07
1.0459
Q3. (1) (i)
C
1 6 3
(ii) p x
1 2 2
x2 8
exp
y2 exp p y 3 2 18 1
(2) (i) H
1
EI 2 L3 m ic 3
(ii) x x
S0 L
2 EIc
S0 L3 EIc
if define R x
1
2
if define R x
i
S x e
Sx e
i
d
d
Q4. (i) M G = 2944.544 MN-m (ii) a = 0.681% Q5. (2)
ns =
0 Hz = 0.274 =
5 of 9
Examination Answers (CSE531 Wind Wind Engineering) Year 2010-2011 Q1. (a) V 26.68 m/s V 6.4785 m/s (b) Mode, U = = 23.7644 m/s Dispersion, 0.19797 s/m (c) V = = 51.12 m/s
C pi 0.4
Q2. (a) (i)
(ii) F H = = 44.10 kN = 26.46 kN F V V = = 330.75 kNm M = (b) Qs 11.72 MN M 1416.55 MNm
x 0 y 0
Q3. (a) (i)
(ii) x2 4 y 2
9
(iii) x2 4 y2 9 (iv) cov[X, Y] = 3
2
(b) S f s f s S 0 1.3708G1 0.2 G1*G2 G1G2* 0.02918G2 G1
G2
2
2
2
1 2
2 2 2 2.618 618 m 10.4721 m 1 k k
1 2
2 2 2 0.382 382 m 1.5279 m 1 k k
2 2 2 2 2.618 618 m 0.382 382 m 4m 1 21 k k k * * G1 G2 G1G2 2 2 2 2 2 2 2 2 2.618 618 m 10.4721 m 0.382 382 m 1.5279 m 1 1 k k k k
Q4. (a) G = 2.09 (b) M 1416 .546 MNm MNm (c) a = 0.454% ˆ
Year 2012-2013 Q1. (a) Mode, U = = 23.7644 m/s Dispersion, 0.20982 s/m (b) V 57.83 m/s (c) V z = 98.22 m/s
6 of 9
Examination Answers (CSE531 Wind Wind Engineering) Q3. (a) (i) c = 8 (ii) p x
1
7
12
1
7
16
p y
(b) H y1
1.8944 k
7 2 x 144 144
exp exp
7 2 y 256 256
exp exp
G1
S y1
3.5889 G k
where
k
S 0
1
2
12 EI h
3
G1
G1
2
2
0.1056 k
G2
0.2G1*G2 G1G2* 0.01115 G2
; 12
4.5836 EI mh
3
1
2i 1 2 1 1 2
2 4 2 2 1 2 2 1 1
; G2
2
31.4164 EI
; G2
1 2
; 22
2
mh
3
1
2i 1 2 2 2 2
1 2
2 4 2 2 1 2 2 2 2
2 2 4 2 2 21 2 1 2 1 2 1 2 * * G1 G2 G1G2 2 2 4 2 2 2 2 4 2 2 1 2 1 2 12 2 22 1
Q4. (a) G = 2.0619 (b) M 2643.40 MNm MNm M 5450 .47 MNm (c) a = 1.844% ˆ
Q5. (b)
Δns =
= Δξ =
0.17 Hz 0.3097
Year 2014-2015 Q3. (a) V 32.187 m/s V 3.4755 m/s (b) Mode, U = = 30.623 m/s Dispersion, 0.3690 s/m (c) V = = 47.33 m/s
Q4. (a) Same answer answer as Year 2008-09 Question 2(1).
Q5. (b) Same answer as Year Year 2004-05 Question Question 3(2).
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Examination Answers (CSE531 Wind Wind Engineering) Year 2016-2017 Q1. (a) U = 23.7644 m/s U = 6.0468 m/s = 55.38 m/s U = P = 1.886 kPa
2
Q3. (a) R x
a cos
2
(b) If define R x
1
2
S x e
i
d
2
H 3.5899 G1 0.01115 G2 S 0
x 0.7477 1
where
k
2
k mk 24 EI 3
L
; 12
mL
; 22
62 .8328 EI 3
mL
2
2 4 2 2 1 2 2 1 1 1
2
G2
3
1
2
G1
9.1672 EI
2
2 4 2 2 1 2 2 2 2
Q4. (a) Assume first mode shape is approximately approximately as a linear mode shape mw 96010 kg 3
R = 10.1017 m h = 2.995 m
(b) M b, prototype prototype 921.6 MNm Q 5864.8 kN
Year 2018-2019 Q1. (a) (i) V g = 54.34 m/s (ii) V z = 45.5 m/s (b) ns = 0.4165 Hz
Q2. (a) U = 35.635 m/s U = 8.7616 m/s U G = 58.43 m/s when return period T R = 50 years P = 2.231 kPa
Q3. (a) C pi1 = 0.5946 0.6811 C pi2 = – 0.6811 = 687.4 kN F =
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Examination Answers (CSE531 Wind Wind Engineering) (b) H
1
40000 300 300 .9375 0.5204 i
x = 4.47 mm
2
if define R x
1
2
S x e
i
d
Q4. (a) Ridiculous question. question. No solution can be found under the given constraints in this question. Possible answers: = = 0.02 (Mass ratio of tuned mass damper to the “equivalent” modal modal mass of the building first mode shape) shape)
4.28×105 kg
md k d d
893.8 kN/m
867.7 kN/m
d d
0.1226
0.1271
3.5
3.46
x2 x1 x1
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