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Lecture 6<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> <str<strong>on</strong>g>Resistant</str<strong>on</strong>g> <str<strong>on</strong>g>Design</str<strong>on</strong>g><br />

<str<strong>on</strong>g>AIJ</str<strong>on</strong>g> <str<strong>on</strong>g>Recommendati<strong>on</strong>s</str<strong>on</strong>g> <str<strong>on</strong>g>for</str<strong>on</strong>g><br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> <str<strong>on</strong>g>Loads</str<strong>on</strong>g> <strong>on</strong> Buildings<br />

Tokyo Polytechnic University<br />

The 21st Century Center of Excellence Program<br />

Yukio Tamura<br />

Background<br />

• Building Standard Law of Japan<br />

(BSLJ) --- Minimum building design<br />

requirements<br />

- completely revised in 2000<br />

- Per<str<strong>on</strong>g>for</str<strong>on</strong>g>mance<br />

Based<br />

<str<strong>on</strong>g>Design</str<strong>on</strong>g><br />

(PBD)<br />

• <str<strong>on</strong>g>AIJ</str<strong>on</strong>g> <str<strong>on</strong>g>Recommendati<strong>on</strong>s</str<strong>on</strong>g> <str<strong>on</strong>g>for</str<strong>on</strong>g> <str<strong>on</strong>g>Loads</str<strong>on</strong>g> <strong>on</strong><br />

Buildings (<str<strong>on</strong>g>AIJ</str<strong>on</strong>g>-RLB<br />

RLB) 1993<br />

- to be revised in 2004<br />

1


Major Revisi<strong>on</strong>s<br />

• Introducti<strong>on</strong> of the wind directi<strong>on</strong>ality<br />

ity<br />

factor (8 wind directi<strong>on</strong>s);<br />

• Explicit introducti<strong>on</strong> of wind load<br />

combinati<strong>on</strong>s;<br />

• Correcti<strong>on</strong> and additi<strong>on</strong> of topographic<br />

effects;<br />

• Substantial fulfillment of aerodynamic<br />

shape factors<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Load Estimati<strong>on</strong><br />

in <str<strong>on</strong>g>AIJ</str<strong>on</strong>g>-RLB<br />

Low-rise<br />

Small Size<br />

Medium-rise<br />

Rigid<br />

Buildings and Structures<br />

High-rise<br />

Slender<br />

Flexible<br />

Particularly<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Sensitive<br />

Simplified<br />

Detailed Method<br />

- Crosswind<br />

Method<br />

- Al<strong>on</strong>g-wind<br />

- Roof<br />

- Torsi<strong>on</strong><br />

- Cladding<br />

- Quasi-steady<br />

steady- Size Reducti<strong>on</strong> Effects<br />

- Quasi-static<br />

static - Res<strong>on</strong>ance Effects<br />

- Vortex<br />

Res<strong>on</strong>ance<br />

- Aerodynamic<br />

Instability<br />

- <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Tunnel<br />

Tests, etc.<br />

2


<str<strong>on</strong>g>Design</str<strong>on</strong>g> <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U H (m/s)<br />

U<br />

H<br />

= U<br />

0<br />

K<br />

D<br />

E<br />

H<br />

k<br />

rW<br />

U 0 : Basic wind speed<br />

K D : <str<strong>on</strong>g>Wind</str<strong>on</strong>g> directi<strong>on</strong>ality factor<br />

E H : <str<strong>on</strong>g>Wind</str<strong>on</strong>g> speed profile factor<br />

rW : Return period c<strong>on</strong>versi<strong>on</strong> factor<br />

k rW<br />

Basic <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed<br />

• Meteorological Standard C<strong>on</strong>diti<strong>on</strong><br />

- 10min mean<br />

- 10m above ground<br />

- Open flat terrain<br />

- 100-year<br />

year-recurrencerecurrence<br />

• Typho<strong>on</strong> <str<strong>on</strong>g>Wind</str<strong>on</strong>g>s : M<strong>on</strong>te-Carlo<br />

Simulati<strong>on</strong><br />

• Synoptic <str<strong>on</strong>g>Wind</str<strong>on</strong>g>s : Meteorological Data<br />

Combined probability<br />

3


Basic <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U 0 (m/s)<br />

36<br />

32<br />

34<br />

34 30<br />

32<br />

36<br />

32<br />

30<br />

32<br />

32<br />

38<br />

30<br />

36<br />

34<br />

34<br />

32<br />

40<br />

34<br />

32<br />

30 34<br />

36<br />

32<br />

30<br />

36<br />

36<br />

30<br />

40<br />

32<br />

36<br />

44<br />

36<br />

34<br />

42<br />

34 30<br />

34<br />

44<br />

36<br />

40<br />

38<br />

40<br />

44<br />

36<br />

40 42<br />

44<br />

Okinawa: 50m/s<br />

Lower Limit: 30m/s<br />

Orientati<strong>on</strong> of Building and<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong><br />

• B = 20m, D = 40m, H = 40m<br />

Maximum<br />

Accelerati<strong>on</strong><br />

63%<br />

100%<br />

Maximum<br />

Displacement<br />

50% 100%<br />

4


<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong>alityity Factor<br />

• Davenport (1969)<br />

• Holmes (1981)<br />

• Cook (1983)<br />

• Melbourne (1984, 1990)<br />

→ AS 1170.2 (1989)<br />

AS/NZS 1170.2 (2002)<br />

• Simiu & Heckert (1998)<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong>alityity Factor<br />

in Major Codes<br />

• ASCE 7-987<br />

- Buildings: 0.85 <str<strong>on</strong>g>for</str<strong>on</strong>g> all directi<strong>on</strong>s<br />

Chimneys: 0.9 or 0.95 <str<strong>on</strong>g>for</str<strong>on</strong>g> all directi<strong>on</strong>s<br />

Except <str<strong>on</strong>g>for</str<strong>on</strong>g> hurricane-pr<strong>on</strong>e regi<strong>on</strong>s<br />

• AS/NZS1170.2(2002)<br />

- Tropical-cycl<strong>on</strong>e<br />

cycl<strong>on</strong>e-pr<strong>on</strong>e regi<strong>on</strong>s:<br />

0.95 or 1.0 <str<strong>on</strong>g>for</str<strong>on</strong>g> all directi<strong>on</strong>s<br />

- N<strong>on</strong>-tropical<br />

tropical-cycl<strong>on</strong>e-pr<strong>on</strong>e regi<strong>on</strong>s:<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong> Multiplier <str<strong>on</strong>g>for</str<strong>on</strong>g> 8 sectors<br />

5


<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong>alityity Factor<br />

• Difficulty in tropical-cycl<strong>on</strong>e<br />

cycl<strong>on</strong>e-pr<strong>on</strong>e<br />

regi<strong>on</strong>s<br />

Meteorological records in Japan:<br />

- 75 years of reliable records at most<br />

- Approx. 3 landfalls/year of typho<strong>on</strong>s<br />

- Very few typho<strong>on</strong> data in each sector<br />

divided into 8 or 16 sectors of azimuth<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> a given site<br />

Large sampling error<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Distributi<strong>on</strong> in Typho<strong>on</strong><br />

Directi<strong>on</strong> of<br />

Movement<br />

10m/s 20m/s 30m/s<br />

40m/s<br />

50m/s<br />

Northern Hemisphere<br />

Dangerous<br />

Semicircle<br />

6


<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong>ality Factor<br />

in Japan<br />

• Hybrid use of meteorological data<br />

during typho<strong>on</strong> passage and Typho<strong>on</strong><br />

Simulati<strong>on</strong> technique<br />

→ Reflecting effects of large-scale<br />

topography and terrain roughness<br />

- Correlati<strong>on</strong>s between observed wind<br />

speed and simulated fricti<strong>on</strong> free<br />

wind speed<br />

- Correlati<strong>on</strong>s between observed wind<br />

directi<strong>on</strong> and simulated fricti<strong>on</strong> free<br />

wind directi<strong>on</strong><br />

p 1<br />

Generati<strong>on</strong> of Virtual<br />

Meteorological Data in Tropical<br />

Cycl<strong>on</strong>e Pr<strong>on</strong>e Regi<strong>on</strong><br />

Simulated Fricti<strong>on</strong> Free <str<strong>on</strong>g>Wind</str<strong>on</strong>g><br />

(FFW)<br />

- <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U FF<br />

Correlati<strong>on</strong>s<br />

- <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong> D FF<br />

Typho<strong>on</strong> Path<br />

p 3<br />

Meteorological Records<br />

p p - <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U<br />

p 2 i<br />

p ME<br />

4 - <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong> D ME Pressure Records at<br />

Meteorological Stati<strong>on</strong>s<br />

Typho<strong>on</strong> Simulati<strong>on</strong><br />

Virtual<br />

(FFW)<br />

Meteorological Data<br />

5000 years 5000 years<br />

7


Generati<strong>on</strong> of Virtual<br />

Meteorological Data in Tropical<br />

Cycl<strong>on</strong>e Pr<strong>on</strong>e Regi<strong>on</strong><br />

Calculati<strong>on</strong> of Correlati<strong>on</strong>s<br />

Correlati<strong>on</strong>s Between Evaluated FFW (U FF , D FF ) and Observed<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Records (U(<br />

ME , D ME ) Using All Available Typho<strong>on</strong> Records<br />

Typho<strong>on</strong> Simulati<strong>on</strong>s<br />

(5,000 years)<br />

M<strong>on</strong>te-Carlo Simulati<strong>on</strong><br />

at Meteorological Stati<strong>on</strong>s<br />

- <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U SFF<br />

- <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong> D SFF<br />

(FFW)<br />

Virtual Meteorological <str<strong>on</strong>g>Wind</str<strong>on</strong>g><br />

Data (5,000 years)<br />

Probabilistic C<strong>on</strong>versi<strong>on</strong><br />

of<br />

Simulated FFW W (U(<br />

SFF , D SFF )<br />

to<br />

Virtual Meteorological <str<strong>on</strong>g>Wind</str<strong>on</strong>g><br />

Data (U(<br />

vir , D vir )<br />

Evaluati<strong>on</strong> of Directi<strong>on</strong>al<br />

R-year Recurrence <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed<br />

in Tropical Cycl<strong>on</strong>e Pr<strong>on</strong>e Regi<strong>on</strong><br />

Virtual L<strong>on</strong>g-term<br />

Meteorological Data<br />

Sufficient <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Records<br />

in Each Sector<br />

R-year Recurrence <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> Each <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong><br />

8


<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong>ality<br />

(Tokyo, 100-year Recurrence<br />

Hybrid Use of Typho<strong>on</strong> Simulati<strong>on</strong> and<br />

Meteorological Records<br />

Equivalent Annual<br />

Exceedence Probability of<br />

Directi<strong>on</strong>al <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed<br />

• Corresp<strong>on</strong>ding to an annual<br />

exceedence probability of load effects<br />

(base shear, base moment, etc.)<br />

corresp<strong>on</strong>ding to 100-year recurrence<br />

• Under different c<strong>on</strong>diti<strong>on</strong>s:<br />

- load effects<br />

- building shape<br />

- orientati<strong>on</strong><br />

- geographic locati<strong>on</strong><br />

- design target (structural(<br />

frames,<br />

comp<strong>on</strong>ents and cladding)<br />

9


Equivalent Directi<strong>on</strong>al<br />

<str<strong>on</strong>g>Design</str<strong>on</strong>g> <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U D<br />

• Annual probability of exceedence of a<br />

wind load effect = 1/1001<br />

100 (100-year<br />

Recurrence)<br />

1. Calculati<strong>on</strong> of 100-year recurrence<br />

wind load effect (e.g. internal <str<strong>on</strong>g>for</str<strong>on</strong>g>ce,<br />

peak pressure) based <strong>on</strong> the actual<br />

wind climate at a given site<br />

Q X,100<br />

← Site, Building Shape,<br />

Orientati<strong>on</strong>, Load Effect, etc.<br />

Equivalent Directi<strong>on</strong>al<br />

<str<strong>on</strong>g>Design</str<strong>on</strong>g> <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U D<br />

2. Calculati<strong>on</strong> of equivalent return<br />

period causing the same 100-year<br />

recurrence wind load effect in the<br />

most unfavorable case<br />

≈ 150 – 200 years<br />

Q X,100<br />

10


Equivalent Directi<strong>on</strong>al<br />

<str<strong>on</strong>g>Design</str<strong>on</strong>g> <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U D<br />

2. Calculati<strong>on</strong> of equivalent return<br />

period causing the same 100-year<br />

recurrence wind load effect in the<br />

most unfavorable case<br />

3. Calculati<strong>on</strong> of average directi<strong>on</strong>al<br />

wind speeds U D based <strong>on</strong> the<br />

equivalent return period <str<strong>on</strong>g>for</str<strong>on</strong>g> various<br />

cases at each meteorological site<br />

Equivalent Directi<strong>on</strong>al<br />

<str<strong>on</strong>g>Design</str<strong>on</strong>g> <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U D<br />

Ave. ± σ<br />

(m/s)<br />

11


Equivalent Directi<strong>on</strong>al<br />

<str<strong>on</strong>g>Design</str<strong>on</strong>g> <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speeds<br />

Chiba<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Directi<strong>on</strong>ality Factor K D<br />

(8 azimuths)<br />

Equivalent Directi<strong>on</strong>al <str<strong>on</strong>g>Design</str<strong>on</strong>g> <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed<br />

K D = <br />

<br />

Basic <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed U 0<br />

• If you have aerodynamic shape factors<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> all wind directi<strong>on</strong>s, K D can be used<br />

directly.<br />

• If you use aerodynamic shape factors<br />

C f specified in the <str<strong>on</strong>g>AIJ</str<strong>on</strong>g>-RLB, there is a<br />

limitati<strong>on</strong>.<br />

Structural Frames : Specified<br />

method<br />

Cladding/Comp<strong>on</strong>ents : K D = 1<br />

12


<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Speed Profile Factor E<br />

E r<br />

E g<br />

E = E r E g<br />

: Exposure factor <str<strong>on</strong>g>for</str<strong>on</strong>g> flat terrains<br />

: Topography factor <str<strong>on</strong>g>for</str<strong>on</strong>g> mean<br />

wind speed<br />

E<br />

r<br />

Z G<br />

Z b<br />

Exposure Factor<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> Flat Terrains E r<br />

α<br />

⎧ ⎛ Z ⎞<br />

⎪1.7<br />

< ≤<br />

⎪<br />

⎜<br />

⎟ Z<br />

b<br />

Z Z<br />

=<br />

⎝ Z<br />

G ⎠<br />

⎨<br />

α<br />

⎪ ⎛ Z<br />

b<br />

⎞<br />

⎪<br />

1.7<br />

⎜<br />

⎟ Z ≤ Z<br />

b<br />

⎩ ⎝ Z<br />

G ⎠<br />

: Gradient height<br />

: Interfacial layer height<br />

G<br />

13


Z<br />

700 m<br />

600<br />

500<br />

400<br />

300<br />

200<br />

100<br />

Exposure Factor<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> Flat Terrains E r<br />

<br />

<br />

<br />

<br />

<br />

Category V<br />

IV<br />

III<br />

II I<br />

V<br />

III<br />

I<br />

IV<br />

II<br />

0 0 0.5 1 1.5 2<br />

E r<br />

Topography Factor E g<br />

H S<br />

Escarpments<br />

θ S<br />

X S<br />

Ridges<br />

θ S<br />

X S<br />

H S<br />

14


Topography Factor E g<br />

• A series of wind tunnel tests and<br />

numerical simulati<strong>on</strong>s<br />

<br />

<br />

<br />

<br />

E<br />

g<br />

C<br />

=<br />

1<br />

Topography Factor E g<br />

( C −1)<br />

⎧<br />

× exp⎨−<br />

C<br />

⎩<br />

, C and C<br />

2<br />

1<br />

⎧<br />

⎨C<br />

⎩<br />

3<br />

2<br />

⎛<br />

⎜<br />

⎝<br />

Z<br />

H<br />

S<br />

2<br />

− C<br />

⎛<br />

⎜<br />

⎝<br />

3<br />

Z<br />

H<br />

S<br />

⎞ ⎫<br />

⎟ + 1⎬<br />

⎠ ⎭<br />

− C<br />

⎞⎫<br />

⎟⎬<br />

+ 1<br />

⎠⎭<br />

: C<strong>on</strong>stants depending<br />

<strong>on</strong> slope angle and<br />

distance from upper<br />

edge<br />

3<br />

≥ 1<br />

15


Topography Factor E g<br />

0 Eg 1<br />

Proposed Formula<br />

E g<br />

-3 -2 -1 0 1 2 3 4 5 6<br />

X<br />

H<br />

<br />

S<br />

<br />

S<br />

1 1<br />

Return Period C<strong>on</strong>versi<strong>on</strong><br />

Factor k rW<br />

k<br />

rW<br />

0 .62( λ −1)ln<br />

r − 2.9λ<br />

+ 3.9<br />

=<br />

U<br />

U<br />

λ U<br />

= U 500<br />

U 0<br />

U 500<br />

U 0<br />

: 500-year<br />

year-recurrence recurrence wind speed<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> the meteorological standard<br />

c<strong>on</strong>diti<strong>on</strong>s<br />

: Basic wind speed<br />

(100-year<br />

year-recurrence)<br />

recurrence)<br />

16


500-year<br />

year-recurrence recurrence <str<strong>on</strong>g>Wind</str<strong>on</strong>g><br />

Speed U 500 (m/s)<br />

38 36<br />

36<br />

40<br />

34<br />

36<br />

36<br />

38<br />

42<br />

34<br />

40<br />

42<br />

38<br />

38<br />

36<br />

38<br />

46<br />

44<br />

36<br />

34<br />

34 38<br />

36<br />

36<br />

40<br />

34<br />

40<br />

42 40<br />

34<br />

34<br />

36<br />

36<br />

44<br />

40<br />

48<br />

40<br />

44<br />

36<br />

48<br />

36<br />

34<br />

44<br />

48<br />

40<br />

38<br />

42<br />

40<br />

42<br />

44 48 40<br />

44 46<br />

48<br />

36<br />

38<br />

36 34<br />

36<br />

Okinawa: 58m/s<br />

Lower Limit: 34m/s<br />

Turbulence Intensity I Z<br />

at Height Z<br />

I =<br />

Z<br />

I<br />

rZ<br />

E<br />

gI<br />

I rZ<br />

E<br />

gI<br />

=<br />

E<br />

E<br />

I<br />

g<br />

: Turbulence Intensity <str<strong>on</strong>g>for</str<strong>on</strong>g><br />

flat terrains<br />

Topography factor <str<strong>on</strong>g>for</str<strong>on</strong>g><br />

fluctuati<strong>on</strong> wind speed σ u<br />

: Topography factor <str<strong>on</strong>g>for</str<strong>on</strong>g><br />

turbulence intensity<br />

Topography factor <str<strong>on</strong>g>for</str<strong>on</strong>g><br />

mean wind speed U<br />

17


Turbulence Intensity <str<strong>on</strong>g>for</str<strong>on</strong>g> Flat<br />

Terrains I rZ at Height Z<br />

⎧ ⎛ Z<br />

⎪0.1<br />

⎪<br />

⎜<br />

⎝ Z<br />

⎨<br />

⎪ ⎛ Z<br />

⎪<br />

0.1<br />

⎜<br />

⎩ ⎝ Z<br />

⎞<br />

⎟<br />

⎠<br />

⎞<br />

⎟<br />

⎠<br />

−α<br />

−0.05<br />

G<br />

I<br />

rZ<br />

=<br />

−α<br />

−0.<br />

05<br />

b<br />

G<br />

Z<br />

b<br />

< Z ≤ Z<br />

Z ≤ Z<br />

b<br />

G<br />

Turbulence Scale L Z (m)<br />

at Height Z<br />

L<br />

Z<br />

=<br />

⎧<br />

⎪<br />

⎛<br />

100⎜<br />

⎨ ⎝<br />

⎪<br />

⎩<br />

Z<br />

30<br />

100<br />

⎞<br />

⎟<br />

⎠<br />

0.5<br />

30m<br />

Z<br />

<<br />

≤<br />

Z ≤ Z<br />

30m<br />

G<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> every terrain category<br />

18


<str<strong>on</strong>g>Wind</str<strong>on</strong>g> <str<strong>on</strong>g>Loads</str<strong>on</strong>g> Specified<br />

in <str<strong>on</strong>g>AIJ</str<strong>on</strong>g>-RLB<br />

• For Main Frames<br />

- Horiz<strong>on</strong>tal Al<strong>on</strong>g-wind Load<br />

Ccrosswind Load<br />

Torsi<strong>on</strong>al Load<br />

- Roof <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Load<br />

• For Cladding / Comp<strong>on</strong>ents<br />

- Peak Cladding Load<br />

Al<strong>on</strong>g-wind <str<strong>on</strong>g>Loads</str<strong>on</strong>g> <strong>on</strong><br />

Ordinary Buildings W D (N)<br />

at Height Z<br />

W<br />

q H<br />

D =<br />

q<br />

H<br />

C<br />

G<br />

A<br />

: Velocity pressure at reference<br />

height H<br />

C D<br />

: Aerodynamic shape factor<br />

G D<br />

: Gust loading factor<br />

A : Projected area<br />

• GLF based <strong>on</strong> Base Bending Moment<br />

(Zhou & Kareem, 2001)<br />

D<br />

D<br />

19


C ′<br />

φ D<br />

R D<br />

GLF <str<strong>on</strong>g>for</str<strong>on</strong>g> Al<strong>on</strong>g-wind <str<strong>on</strong>g>Loads</str<strong>on</strong>g><br />

<strong>on</strong> Ordinary Buildings<br />

'<br />

g<br />

2<br />

GD = 1+ gD 1+φD RD<br />

Cg<br />

g D<br />

and<br />

g<br />

C g<br />

C<br />

: Peak factor<br />

: Fluctuating and mean<br />

coefficients <str<strong>on</strong>g>for</str<strong>on</strong>g> al<strong>on</strong>g-<br />

wind OTM<br />

: Correcti<strong>on</strong> factor depending<br />

<strong>on</strong> mode shape<br />

: Res<strong>on</strong>ance factor<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> <str<strong>on</strong>g>Loads</str<strong>on</strong>g> <strong>on</strong> Roof<br />

Structures W R (N)<br />

W = q<br />

q H<br />

C<br />

R<br />

G R<br />

A R<br />

R<br />

H<br />

C<br />

R<br />

G<br />

: Velocity pressure at reference<br />

height H<br />

C :<br />

pe<br />

− C<br />

pi<br />

Aerodynamic shape factor<br />

: Gust loading factor<br />

: Subjected area <str<strong>on</strong>g>for</str<strong>on</strong>g> roof beam<br />

=<br />

R<br />

A<br />

R<br />

20


GLF <str<strong>on</strong>g>for</str<strong>on</strong>g> <str<strong>on</strong>g>Wind</str<strong>on</strong>g> <str<strong>on</strong>g>Loads</str<strong>on</strong>g><br />

<strong>on</strong> Roof Structures<br />

G<br />

C<br />

R<br />

= 1±<br />

G<br />

R<br />

12.3r<br />

2<br />

Re<br />

( 1+<br />

R )<br />

1−<br />

r<br />

Re<br />

c<br />

+ 0.3r<br />

2<br />

c<br />

( 1+<br />

R ) 0. 3<br />

2<br />

= ± 0.25 12.3r<br />

Re<br />

Re<br />

+<br />

C pi<br />

−0.4,<br />

C ≠ 0<br />

=<br />

R<br />

C pi<br />

−0 .4, C = 0<br />

=<br />

R<br />

R<br />

( )<br />

2<br />

G +<br />

r<br />

2<br />

R<br />

= 1±<br />

12.3rRe 1+<br />

RRe<br />

0. 3rc<br />

R<br />

Re,<br />

Re<br />

, and<br />

r c<br />

C pi<br />

= 0<br />

: Parameters depending <strong>on</strong> roof<br />

beam directi<strong>on</strong>, dynamic<br />

characteristics of roof structure,<br />

and wind characteristics<br />

Al<strong>on</strong>g-wind <str<strong>on</strong>g>Loads</str<strong>on</strong>g> <strong>on</strong><br />

Lattice Towers W D (N)<br />

at Height Z<br />

W = q<br />

q Z<br />

C D<br />

G D<br />

A<br />

D<br />

Z<br />

C<br />

D<br />

G<br />

D<br />

A<br />

F<br />

: Velocity pressure at height Z<br />

: Aerodynamic shape factor<br />

: Gust loading factor<br />

: Projected area<br />

21


g D<br />

C ′<br />

φ D<br />

R D<br />

GLF <str<strong>on</strong>g>for</str<strong>on</strong>g> Al<strong>on</strong>g-wind <str<strong>on</strong>g>Loads</str<strong>on</strong>g><br />

<strong>on</strong> Lattice Towers<br />

C′<br />

G = 1+<br />

φ 1+<br />

D<br />

and<br />

g<br />

C g<br />

g<br />

g D D RD<br />

Cg<br />

: Peak factor<br />

: Fluctuating and mean<br />

coefficients <str<strong>on</strong>g>for</str<strong>on</strong>g> al<strong>on</strong>g-<br />

wind OTM<br />

: Correcti<strong>on</strong> factor depending<br />

<strong>on</strong> mode shape<br />

: Res<strong>on</strong>ance factor<br />

Crosswind <str<strong>on</strong>g>Loads</str<strong>on</strong>g> and<br />

Torsi<strong>on</strong>al <str<strong>on</strong>g>Loads</str<strong>on</strong>g><br />

Slender and flexible buildings<br />

to satisfy following c<strong>on</strong>diti<strong>on</strong>:<br />

H<br />

BD<br />

≥ 3<br />

U H<br />

D<br />

H<br />

B<br />

22


W<br />

Crosswind <str<strong>on</strong>g>Loads</str<strong>on</strong>g> <strong>on</strong><br />

Buildings W L (N) at Height Z<br />

g L<br />

L<br />

Z<br />

2<br />

= 3q<br />

H<br />

C′<br />

L<br />

A g<br />

L<br />

1 + φL<br />

R<br />

H<br />

3<br />

2<br />

( D B) − 0.071( D B) + 0. ( D B)<br />

C L<br />

′ = 0.0082<br />

22<br />

φ L<br />

R L<br />

: Peak factor<br />

: Correcti<strong>on</strong> factor <str<strong>on</strong>g>for</str<strong>on</strong>g> mode shape<br />

: Res<strong>on</strong>ance factor<br />

L<br />

Torsi<strong>on</strong>al <str<strong>on</strong>g>Wind</str<strong>on</strong>g> <str<strong>on</strong>g>Loads</str<strong>on</strong>g> <strong>on</strong><br />

Buildings W T (Nm) at Height Z<br />

W = 1.8q C′<br />

AB Z g 1+<br />

φ R<br />

H<br />

2<br />

T H T T T T<br />

C T<br />

′ = 0.0066 +<br />

g T<br />

φ T<br />

R T<br />

{ 0.015( D / B)<br />

2 } 0.78<br />

: Peak factor<br />

: Correcti<strong>on</strong> factor <str<strong>on</strong>g>for</str<strong>on</strong>g> mode shape<br />

: Res<strong>on</strong>ance factor<br />

23


Correcti<strong>on</strong> Factors<br />

Depending <strong>on</strong> Mode Shape φ<br />

• Ordinary buildings<br />

1−<br />

0.4ln β M<br />

φD<br />

=<br />

2 + β M<br />

2<br />

( )<br />

2<br />

M B + D<br />

φT<br />

=<br />

36I<br />

T<br />

M ⎛ Z ⎞<br />

φL<br />

= ⎜ ⎟<br />

3M<br />

⎝ H ⎠<br />

L<br />

β −1<br />

• Lattice Towers<br />

φ<br />

D<br />

=<br />

M<br />

M<br />

D<br />

⎛<br />

⎜<br />

⎝<br />

⎧⎛<br />

B<br />

⎨<br />

⎜0.5<br />

⎩⎝<br />

B<br />

5<br />

D<br />

0<br />

Z<br />

H<br />

⎞<br />

⎟<br />

⎠<br />

β −1<br />

( 1−<br />

0.4ln β )<br />

H<br />

Al<strong>on</strong>g-wind loads<br />

(1 − 0.4 ln β )<br />

Crosswind loads<br />

Torsi<strong>on</strong>al wind loads<br />

⎞ ⎫<br />

− 0.3<br />

⎟(<br />

β − 2) + 1.4⎬( 1−<br />

0.4ln<br />

β )<br />

⎠ ⎭Al<strong>on</strong>g-wind loads<br />

β<br />

⎛ Z ⎞<br />

µ = ⎜ ⎟<br />

⎝ H ⎠<br />

Mode shape<br />

Vortex Res<strong>on</strong>ance and<br />

Aerodynamic Instabilities<br />

• Particularly wind-sensitive<br />

buildings to satisfy following<br />

c<strong>on</strong>diti<strong>on</strong>s:<br />

H<br />

N<strong>on</strong><br />

≥ 4<br />

BD<br />

and<br />

f<br />

,<br />

⎛<br />

⎜<br />

⎝<br />

L<br />

f T<br />

U H<br />

N<strong>on</strong>-dimensi<strong>on</strong>al<br />

<strong>on</strong>set velocity<br />

H<br />

D<br />

B<br />

U<br />

⎞<br />

H<br />

* U<br />

H<br />

*<br />

≥ 0.83U<br />

⎟<br />

Lcr<br />

or ≥ 0.83U<br />

Tcr<br />

f<br />

L<br />

BD<br />

fT<br />

BD ⎠<br />

: Fundamental natural<br />

frequencies of crosswind<br />

vibrati<strong>on</strong> and torsi<strong>on</strong>al vibrati<strong>on</strong><br />

24


N<strong>on</strong>-dimensi<strong>on</strong>al<br />

Onset Velocity (Crosswind)<br />

Terrain<br />

Category<br />

I & II<br />

III, IV<br />

& V<br />

Side Ratio<br />

D/B<br />

D/B≤ 0.8<br />

0.8 0.7<br />

All<br />

δ L ≤ 0.2<br />

0.2 0.8<br />

δ L ≤ 0.4<br />

δ L > 0.4<br />

All<br />

Onset Velocity<br />

U* Lcr<br />

16δ L<br />

11<br />

1.2δ L +7.3<br />

2.3<br />

12<br />

15 δ L<br />

3.7<br />

Not occur<br />

4.5δ L +6.7<br />

0.7δ L +8.8<br />

11<br />

D<br />

B<br />

N<strong>on</strong>-dimensi<strong>on</strong>al<br />

Onset Velocity (Torsi<strong>on</strong>al)<br />

Side Ratio<br />

D/B<br />

D/B≤1.5<br />

1.5


Vortex Res<strong>on</strong>ance of<br />

Circular Cylinders<br />

• Buildings with a circular plan<br />

to satisfy following c<strong>on</strong>diti<strong>on</strong>s:<br />

H<br />

D<br />

m<br />

U<br />

H<br />

≥ 7 and ≥<br />

f D<br />

L<br />

m<br />

4.2<br />

U H<br />

D m<br />

H<br />

f L<br />

: Fundamental natural frequency<br />

of crosswind vibrati<strong>on</strong><br />

W<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> <str<strong>on</strong>g>Loads</str<strong>on</strong>g> <strong>on</strong> Circular<br />

Cylinders W r (N) <str<strong>on</strong>g>for</str<strong>on</strong>g> Vortex<br />

Res<strong>on</strong>ance at Height Z<br />

U = 5 f<br />

r<br />

C r<br />

r<br />

f L<br />

= 0.8ρU<br />

D<br />

2<br />

r<br />

C<br />

r<br />

Z<br />

H<br />

A<br />

U H<br />

: Res<strong>on</strong>ance wind speed<br />

L m<br />

(m/s)<br />

: Equivalent aerodynamic shape<br />

factor <str<strong>on</strong>g>for</str<strong>on</strong>g> vortex res<strong>on</strong>ance<br />

- tabulated in <str<strong>on</strong>g>AIJ</str<strong>on</strong>g>-RLB<br />

: Fundamental natural frequency<br />

of crosswind vibrati<strong>on</strong><br />

Z<br />

D m<br />

H<br />

26


Phase-plane Expressi<strong>on</strong>s of<br />

Column Tip Displacements<br />

and Base Bending Moments<br />

Displacement<br />

Bending Moment<br />

Peak Normal Stresses in<br />

Column C1<br />

Load C<strong>on</strong>diti<strong>on</strong>s<br />

ALL :<br />

F D F L F T M D M L M T<br />

Al<strong>on</strong>g-wind<br />

F D <strong>on</strong>ly<br />

Crosswind<br />

F L <strong>on</strong>ly<br />

Torsi<strong>on</strong>al Moment M T<br />

<strong>on</strong>ly<br />

ALL<br />

Al<strong>on</strong>g-wind F D <strong>on</strong>ly<br />

(Low-rise Sq. Model, α =1/4)<br />

Tensile Compressive<br />

Stress kN/cm 2 Stress kN/cm 2<br />

Peak Value (P.F.) Peak Value (P.F.)<br />

5.4 (4.56)<br />

4.2 (4.42)<br />

1.7 (3.95)<br />

0.9 (4.36)<br />

130%<br />

• Ensemble averaged values of 12 samples<br />

• The worst case was a 75% increase in tensile stress.<br />

− 4.7 (− 4.50)<br />

− 4.1 (− 4.42)<br />

− 1.8 (− 3.95)<br />

− 0.9 (− 4.36)<br />

115%<br />

27


Combinati<strong>on</strong>s of <str<strong>on</strong>g>Wind</str<strong>on</strong>g><br />

Load<br />

Comp<strong>on</strong>ents<br />

• Low- and medium-rise buildings<br />

- Y. Tamura, H. Kikuchi and K. Hibi (2002)<br />

- H. Kikuchi, Y. Tamura and K. Hibi (2002)<br />

Peak normal stresses in columns<br />

• High-rise buildings<br />

- Asami (2000, 2002)<br />

Combinati<strong>on</strong> methods c<strong>on</strong>sidering<br />

correlati<strong>on</strong>s of al<strong>on</strong>g-wind, crosswind<br />

and torsi<strong>on</strong>al resp<strong>on</strong>ses<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Load Combinati<strong>on</strong> <str<strong>on</strong>g>for</str<strong>on</strong>g><br />

Low- and Medium-rise<br />

Buildings<br />

W D<br />

W LC = γ W D<br />

Combinati<strong>on</strong> Factor<br />

28


Combinati<strong>on</strong> Factor γ <str<strong>on</strong>g>for</str<strong>on</strong>g> Low-<br />

and Medium-rise Buildings<br />

Combinati<strong>on</strong> Factor γ<br />

=<br />

Column Normal Stress by All <str<strong>on</strong>g>Wind</str<strong>on</strong>g> Force Comp<strong>on</strong>ents<br />

Column Normal Stress by Al<strong>on</strong>g-wind Force <strong>on</strong>ly<br />

− 1<br />

Combinati<strong>on</strong> Factor γ <str<strong>on</strong>g>for</str<strong>on</strong>g> Low-<br />

and Medium-rise Buildings<br />

(Kikuchi, Tamura & Hibi, , 2002)<br />

Combinati<strong>on</strong> Factor γ<br />

Building Height<br />

Only Quasi-static<br />

static<br />

Comp<strong>on</strong>ent<br />

With Res<strong>on</strong>ant<br />

Comp<strong>on</strong>ent<br />

29


Combinati<strong>on</strong> Factor γ<br />

Combinati<strong>on</strong> Factor γ <str<strong>on</strong>g>for</str<strong>on</strong>g> Low-<br />

and Medium-rise Buildings<br />

Combinati<strong>on</strong> Factor γ<br />

1.5<br />

1<br />

0.5<br />

0<br />

0 1 2 3<br />

Side Ratio D/B<br />

(Kikuchi, Tamura & Hibi, , 2002)<br />

B<br />

W L = γ W D<br />

D<br />

W D<br />

(H = 40m)<br />

Combinati<strong>on</strong> Factor γ <str<strong>on</strong>g>for</str<strong>on</strong>g> Low-<br />

and Medium-rise Buildings<br />

Combinati<strong>on</strong> Factor γ<br />

1.5<br />

1<br />

0.5<br />

B<br />

W L = γ W D<br />

D<br />

W D<br />

γ = 0.35 (D/B(<br />

D/B)<br />

0<br />

0 1 2 3<br />

Side Ratio D/B<br />

(Kikuchi, Tamura & Hibi, , 2002)<br />

With Res<strong>on</strong>ant<br />

Comp<strong>on</strong>ent<br />

Quasi-static<br />

static<br />

Comp<strong>on</strong>ent <strong>on</strong>ly<br />

(H = 80m)<br />

30


<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Load Combinati<strong>on</strong>s s <str<strong>on</strong>g>for</str<strong>on</strong>g><br />

High-rise Buildings<br />

m<br />

my,max<br />

1<br />

2 + 2ρ<br />

−1<br />

ρ<br />

0 ( M x<br />

, M<br />

y<br />

) 1<br />

1−<br />

2 − 2ρ<br />

y<br />

<str<strong>on</strong>g>Design</str<strong>on</strong>g><br />

Points<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> M x,max<br />

= M +<br />

m<br />

m<br />

x<br />

x,max<br />

x<br />

m x,max<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> Load Combinati<strong>on</strong>s s <str<strong>on</strong>g>for</str<strong>on</strong>g><br />

High-rise Buildings<br />

Combinati<strong>on</strong><br />

Al<strong>on</strong>g-wind<br />

Load<br />

Crosswind<br />

Load<br />

Torsi<strong>on</strong>al Load<br />

1<br />

2<br />

3<br />

W D<br />

⎛ 0.6 ⎞<br />

⎜0.4<br />

+<br />

⎟<br />

⎝ G D ⎠<br />

⎛ 0.6 ⎞<br />

⎜0.4<br />

+<br />

⎟<br />

⎝ G D ⎠<br />

W D<br />

W D<br />

0.4<br />

W L<br />

W L<br />

( 2 2ρ<br />

−1)<br />

+ LT<br />

W L<br />

0.4<br />

( )<br />

W T<br />

2+ 2ρ<br />

LT<br />

−1<br />

W T<br />

W T<br />

31


Correlati<strong>on</strong> Coefficient ρ LT<br />

between Crosswind Resp<strong>on</strong>se<br />

and Torsi<strong>on</strong>al Resp<strong>on</strong>se<br />

- tabulated in <str<strong>on</strong>g>AIJ</str<strong>on</strong>g>-RLB<br />

- depends up<strong>on</strong> D/B<br />

f θ / f L<br />

f 1 B/U H<br />

The smaller of f θ and f L<br />

Combinati<strong>on</strong>s of Horiz<strong>on</strong>tal<br />

<str<strong>on</strong>g>Wind</str<strong>on</strong>g> LoadL<br />

and Roof wind<br />

Load<br />

• It t is recommended to simply<br />

superimpose the horiz<strong>on</strong>tal wind load<br />

and roof wind load.<br />

- Y. Tamura, H. Kikuchi and K. Hibi (2003)<br />

The vertical comp<strong>on</strong>ent of the wind<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g>ce acting <strong>on</strong> medium-rise buildings<br />

tended to become largest when <strong>on</strong>e of<br />

the horiz<strong>on</strong>tal wind <str<strong>on</strong>g>for</str<strong>on</strong>g>ce comp<strong>on</strong>ents<br />

reached its maximum value .<br />

32


<str<strong>on</strong>g>Wind</str<strong>on</strong>g> <str<strong>on</strong>g>Loads</str<strong>on</strong>g> <str<strong>on</strong>g>for</str<strong>on</strong>g> Comp<strong>on</strong>ents<br />

and Cladding<br />

W R (N)<br />

Cˆ<br />

W<br />

C<br />

Ĉ pe<br />

*<br />

C<br />

pi<br />

A<br />

C<br />

= Cˆ<br />

pe<br />

=<br />

− C<br />

q<br />

*<br />

pi<br />

H<br />

Cˆ<br />

C<br />

A<br />

C<br />

: Peak external pressure coefficient<br />

: Coefficient accounting <str<strong>on</strong>g>for</str<strong>on</strong>g> the<br />

effect of the internal pressure<br />

fluctuati<strong>on</strong><br />

: Tributary area<br />

Equivalent internal<br />

pressure coefficient<br />

Aerodynamic Shape Factors<br />

• External wind pressure coefficients<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> structural frames:<br />

- Buildings with rectangular secti<strong>on</strong>s (H>45m)(<br />

- Buildings with rectangular secti<strong>on</strong>s with flat,<br />

shed, or gable roofs (H≤45m)<br />

- Circular arc roofs (H≤45m)(<br />

- Dome roofs<br />

Internal wind pressure coefficients C pi<br />

• Internal wind pressure coefficients<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> structural frames<br />

- Buildings without dominant openings<br />

C pe<br />

33


Aerodynamic Shape Factors<br />

• External wind <str<strong>on</strong>g>for</str<strong>on</strong>g>ce coefficients<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> structural frames:<br />

, C<br />

D X<br />

- Buildings with circular secti<strong>on</strong>s<br />

- Pitched free roofs with a rectangular plan<br />

- Lattice structures<br />

- Fences<br />

- Members with various secti<strong>on</strong>s<br />

- Nettings<br />

C<br />

, C<br />

Y<br />

Aerodynamic Shape Factors<br />

• External peak pressure coefficients<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> cladding and comp<strong>on</strong>ents:<br />

- Buildings with rectangular secti<strong>on</strong>s (H>45m)(<br />

- Buildings with rectangular secti<strong>on</strong>s with flat,<br />

shed, or gable roofs (H≤45m)<br />

- Buildings with circular secti<strong>on</strong>s<br />

- Circular arc roofs (H≤45m)(<br />

- Dome roofs<br />

• Coefficients accounting <str<strong>on</strong>g>for</str<strong>on</strong>g> the effect of<br />

the internal pressure fluctuati<strong>on</strong> <str<strong>on</strong>g>for</str<strong>on</strong>g><br />

*<br />

C<br />

cladding and comp<strong>on</strong>ents<br />

pi<br />

- Buildings without dominant openings<br />

Ĉ pe<br />

34


Aerodynamic Shape Factors<br />

• External peak wind <str<strong>on</strong>g>for</str<strong>on</strong>g>ce coefficients<br />

<str<strong>on</strong>g>for</str<strong>on</strong>g> cladding and comp<strong>on</strong>ents:<br />

Ĉ<br />

- Pitched free roofs with a rectangular plan C<br />

1-year-recurrence recurrence <str<strong>on</strong>g>Wind</str<strong>on</strong>g><br />

Speed U 1 (m/s)<br />

• <str<strong>on</strong>g>AIJ</str<strong>on</strong>g> Guidelines <str<strong>on</strong>g>for</str<strong>on</strong>g> the Evaluati<strong>on</strong> of<br />

Habitability to Building Vibrati<strong>on</strong> (1991)<br />

(Its revised versi<strong>on</strong> will be published in 2004)<br />

- 1-year-recurrence recurrence peak accelerati<strong>on</strong> has<br />

been applied <str<strong>on</strong>g>for</str<strong>on</strong>g> the evaluati<strong>on</strong><br />

35


1-year-recurrence recurrence <str<strong>on</strong>g>Wind</str<strong>on</strong>g><br />

Speed U 1 (m/s)<br />

20<br />

• 10min mean<br />

• Flat open category<br />

• 10m above the ground<br />

20<br />

20<br />

20<br />

15<br />

15<br />

20<br />

20<br />

15<br />

20<br />

20<br />

20<br />

Miscellaneous<br />

• Evaluati<strong>on</strong> <str<strong>on</strong>g>for</str<strong>on</strong>g>mulae <str<strong>on</strong>g>for</str<strong>on</strong>g> al<strong>on</strong>g-wind,<br />

crosswind and torsi<strong>on</strong>al accelerati<strong>on</strong><br />

resp<strong>on</strong>ses<br />

• Interference effects of neighboring<br />

buildings<br />

• Uncertainty and dispersi<strong>on</strong> of<br />

parameters included in <str<strong>on</strong>g>AIJ</str<strong>on</strong>g>-RLB<br />

RLB-2004<br />

- to achieve reliability based design<br />

36

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