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Workshop on Vertical Shelter from TsunamisCIAPR June 18-20 2012
Calculation of Wind LoadsAccording to PR Building
Code 2011Dr. Ricardo R. López Rodríguez,
Ph.D., P.E.
Professor of Civil Engineering
University of Puerto Rico at
Mayagüez, ri.lopez@upr.edu
Earthquake Commission of CIAPR
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2
Some slides taken and adapted from FEMA presentation
by Adam Reeder, PE, CFM from presentation
Wind Provisions of the 2009 International Building
Code and International Residential Code
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P646 on Wind Loading
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Agenda
• Wind effects on structures
• About the PR Building Code
• Wind Load Provisions for Buildings
Definitions and terms used in all Procedures
Alternative Procedures of Analysis
– Simplified
– Analytical (Low rise or high rise)
– Wind Tunnel
• Examples of calculation of horizontal wind pressures
• Cylindrical Structures
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Wind effects on structures
6
V I E N
T O
Rectangular BuildingsThe wind generates pressure in windward wall and
suction in leeward wall, lateral walls, and part of the roof.
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Internal Pressures
7
There is always some
internal pressure, unless
the building is completely
open. Partially enclosed
buildings have the highest
internal pressures.
It is important for doors and
windows to resist the wind
pressure and impact of flying objects.
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Effect of openings on internal pressure
Windward or leeward opening
8
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Organization of the IBC
Chapter 1: Administration
Chapter 2: Definitions
Chapter 3: Use and Occupancy Classification
Chapter 5: General Building Heights and Areas
Chapter 6: Types of Construction
Chapter 14: Exterior Walls
Chapter 15: Roof Assemblies and Rooftop Structures
Wind Loads
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Organization of the IBC
Chapter 18: Soils and Foundations
Chapter 19: Concrete
Chapter 21: Masonry
Chapter 22: Steel
Chapter 24: Glass and Glazing Chapter 25: Gypsum Board and Plaster
Chapter 34: Existing Structures
Chapter 35: Referenced Standards
Appendix H: Flood-Resistant Construction
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Main vs Components
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ASCE 7-05 – Wind Loads
Wind directionality factor, K d
22
Structure Type Directionality Factor, K d
Buildings
Main Wind Force Resisting System
Components and Cladding
0.85
0.85
Arched Roofs 0.85
Chimneys, Tanks and Similar Structures
Square
Hexagonal
Round
0.90
0.95
0.95
Solid Freestanding Walls and
Solid Freestanding and Attached Signs 0.85
Open Signs and Lattice Framework 0.85
Trussed Towers
Triangular, square, rectangular
All other cross sections
0.85
0.95
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Exposure Categories
27
Exposure Category B
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ASCE 7-05 – Wind Loads
Exposure category
• Surface Roughness Category B, C or D
• Exposure Category B, C or D
• Wind Direction and Sectors
For each direction at which the wind loads are to be
evaluated, the exposure shall be determined for the two
upwind sectors extending 45° either side of the selected
wind direction.
The exposure resulting in the highest wind loads shall be
used to represent winds from that direction.
7-05 Does not use Exp. D in Hurricane Prone Coasts, 7-10 does
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ASCE 7-05 – Wind Loads
Topographic factor, K zt Wind Speed-Up over Hills, Ridges and Escarpments
30
H Height of hill or escarpment relative to the upwind terrain, in meters.
Lh
Distance upwind of crest to where the difference in ground elevation is half the
height of hill or escarpment, in meters.
x Distance (upwind or downwind) from the crest to the building site, in meters.
z Height above ground surface at building site, in meters.
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ASCE 7-05 – Wind Loads
Topographic factor, K zt Wind Speed-Up over Hills, Ridges and Escarpments
Kzt = (1 + K1 K2 K3)2
32
K1
Factor to account for shape of
topographic feature and maximumspeed-up effect.
K2
Factor to account for reduction in
speed-up with distance upwind or
downwind of crest.
K3
Factor to account for reduction in
speed-up with height above local
terrain.
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ASCE 7-05 – Wind Loads
Topographic factor, K zt • K1 is determined using the table below
Factor to account for shape of topographic feature and
maximum speed-up effect.
33
Hill Shape
K1/(H/Lh)
Exposure
B C D
2-D Ridges
(or valleys with -H) 1.30 1.45 1.55
2-D Escarpments 0.75 0.85 0.95
3-D Axisym. Hill 0.95 1.05 1.15
H
Height of hill or
escarpment relative tothe upwind terrain, in
meters.
Lh
Distance upwind of crest
to where the difference
in ground elevation is
half the height of hill or escarpment, in meters.
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ASCE 7-05 – Wind Loads
Topographic factor, K zt • K2 = (1 - )
Factor to account for
reduction in speed-up with
distance upwind or downwind of crest.
• K3 = e-γz/Lh
Factor to account for
reduction in speed-up with
height above local terrain.
34
hL
|x|
Lh
Distance upwind of crest to where the difference
in ground elevation is half the height of hill or
escarpment, in meters.
xDistance (upwind or downwind) from the crest to
the building site, in meters.
zHeight above ground surface at building site, in
meters.
μ Horizontal attenuation factor.
γ Height attenuation factor.
Hill Shape γ
μ
Upwind of
Crest
Downwind
of Crest
2-D Ridges
(or valleys with -
H) 3 1.5 1.5
2-D Escarpments 2.5 1.5 4
3-D Axisym. Hill4
1.5 1.5
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ASCE 7-05 – Wind Loads
Topographic factor,
Kzt = (1 + K1 K2 K3)2
35
Notes:
1.Linear interpolation
between values ispermitted.
2.For H/Lh > 0.5,
assume H/Lh = 0.5 for
finding K1 and
substitute 2H for Lh for
finding K2 and K3. 3.Multipliers assumewind approaches along
the direction of
maximum slope.
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ASCE 7-05 – Wind Loads
Gust Effect Factor, G
• G = 0.85 for rigid buildings and other structures
• G is determined by formula for flexible or dynamically
sensitive buildings or other structures
Flexible: natural frequency < 1
36
Note:
Where combined gust-effect factors and pressure
coefficients (GCp), (GCpi) and (GCpf ) are given in figuresand tables, the gust-effect factor shall not be determined
separately.
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ASCE 7-05 – Wind Loads
Enclosure classification
37
Open
Ao ≥ 0.8Ag
Ao = total area of openings in a wall that receives positive
external pressure, in m2
Ag = gross area of that wall in which Ao is identified, in m2
Partially
Enclosed
• Ao > 1.10Aoi AND
• Ao > 0.37 m2 OR Ao > 0.01Ag (whichever is smaller) AND
• Aoi / Agi ≤ 0.20
Aoi = sum of the areas of openings in the building envelope
(walls and roof) not including Ao, in m2
Agi = sum of the gross surface areas of the building envelope(walls and roof) not including Ag, in m2
Enclosed Not open or partially enclosed.
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Velocity pressure qz
Velocity pressure
Factor Kz includes the effect of height
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ASCE 7-05 and 7-10 – Wind Loads
Internal Pressure Coefficient, (GCpi)
39
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ASCE 7-05 – Wind Loads
Internal Pressure Coefficient, (GCpi)
40
Enclosure
Classification(GCpi)
Open 0.00
Partially Enclosed+0.55
-0.55
Enclosed+0.18
-0.18
Note:
Plus and minus signssignify pressures acting
toward and away from
the internal surfaces,
respectively.
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ASCE 7-05 – Wind Loads
Procedures for determining wind loads for Main Wind-Force Resisting System (MWFRS)
41
Procedure Application Location
Simplified Procedure Low-rise buildings Section 6.4
Analytical Procedure
Buildings of all heights
Distinguish low rise and
High-rise
Section 6.5
Wind Tunnel Procedure All buildings and other structures
Section 6.6
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ASCE 7-05 – Simplified Procedure
MWFRS and C&C Simplified Procedure (Sec 6.4)
for Enclosed Low-Rise Bu i ld ings
• Applicability
Building has simple diaphragm and low-rise (h<60’)
Enclosed and meets WBD requirements
Building not classified as flexible Building is not subject to the following:
– Across-wind loading
– Vortex shedding
– Instability due to galloping or flutter
– Channeling effects – Buffeting in the wake of upwind obstructions
Building has a symmetrical cross section
Building exempted from torsional load cases
42
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MWFRS and C&C Simple Procedure (Sec 6.4)
Enclosed Low-Rise Bu i ld ings
ASCE 7-05 – Wind Loads
Step 1 Basic wind speed, V Sec 6.5.4
Step 2 Importance Factor, I Sec 6.5.5
Step 3 Exposure Category Sec 6.5.6
Step 4 Height and Exposure Adjustment, λ Fig 6-2
Step 5Design pressure at 30 ft ps30 shall be
determined
Fig 6-2
Step 6 Topographic amplification factor calculated. Sec 6.5.7
Step 7
Wall and roof pressures calculated. Check
Minimum
Sec 6.4.2.1.1 or
Sec 6.4.2.2.1
43
Fi 6 2 Si lifi d P d
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Fig 6-2 Simplified Procedure
44
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Fi 6 2
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Simplified Method
Fig 6-2
Fig 6-2 Simplified Design Wind
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Fig 6 2 Simplified Design Windpressure ps30
47
p
D i Si lifi d P d
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=
Design pressure, Simplified Procedure
ASCE 7-05 – Wind Loads
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ASCE 7 05 Wind LoadsAnalytical Procedure
MWFRS and C&C Analytical Procedure (Sec 6.5)Enclos ed, Part ia lly Enclos ed and Open Bu i ld ings of A l l Heights
• Applicability
Building is regular-shaped
Building is not subject to the following:
– Across-wind loading
– Vortex shedding
– Instability due to galloping or flutter
– Channeling effects
– Buffeting in the wake of upwind obstructions
49
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1. V and Kd (directionality)2. Importance, I
3. Exposure and height, Kz, Kh
4. Topographic Effect
5. Gust effect G6. Enclosure
7. Internal pressure GCpi
8. External Pressure Cp
9. Velocity pressure qz10. Design wind load p
Analytical Method - Procedure
Exposure Coefficient Kh and Kz
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p
Internal press re coefficients
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Internal pressure coefficients
53
Fig 6-6 Monoslope roof
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g pExternal wall pressures
54
Fig 6 6 Cp for Analytical Method
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Fig 6-6 Cp for Analytical Method
55
Fig 6 10 Low Rise Analytical Procedure
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Fig 6-10 Low-Rise Analytical Procedure
56
Wall pressures
Windward: 1, 1E
Leeward: 4, 4E
Low Rise Force coefficients GCpf
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Low Rise Force coefficients GCpf
57
Velocity pressure and wall pressures
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CIAPR June 18-20 2012
Velocity pressure and wall pressures
Velocity pressure
Wall pressure, analytical method
Pressures for Analytical Procedure
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CIAPR June 18-20 2012
Pressures for Analytical Procedure
ASCE 7 05 Wind Loads
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ASCE 7-05 – Wind Loads
Wind Tunnel Procedure (Section 6.6)
• Permitted for any building or structure
• Tests shall meet the following conditions:
Atmospheric boundary layer modeled for wind speed variation
Atmospheric turbulence modeled to match the same scale as
the building model Modeled building, surrounding building and topography scaled
properly
Modeled building and surrounding area is less than 8 percent
of the test section
Longitudinal pressure gradient accounted for
Reynolds number effects on pressure minimized
Response characteristics consistent with model
60
Cylindrical Structures
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Cylindrical Structures
61
ASCE 7-05 does not consider buildings with shapes
different from rectangular or combinations of rectangular.
The only guidance for cylindrical structures is in thesection on Other Structures (Sec 6.5.15).
The total lateral load is calculated from equation 6-28
Other Structures
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Other Structures
62
Fig 6-21 – Other Structures Coeff Cf
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Fig 6-21 – Other Structures Coeff. Cf
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CIAPR June 18-20 2012 64
Example
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Example
65
Rectangular building
Plan dimensions 70’ x 70’
Height = 60’
Plan View
70’
70’
Elevation
24’
12’
12’
12’
Story
Heights
Solution using simplified procedure
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Solution using simplified procedure
66
V = 145 mph from Fig 6-1
I = 1.15 from table 6-1 and occupation Cat IV (or III)
Exposure Category = C
λ = 1.62 from Fig 6-2 with h=60’ and Exp C
Width of special zone A = 2a
• a < 0.10 (B) = 0.10 (70) = 7’
• a < 0.4 (h) = 0.4 (60) = 24’
• Select the smallest = 7’ but not less than
• a > .04 (B) = .04 (70) = 2.8’• a > 3’,
•Select a = 3’, 2a = 6’
Solution using simplified procedure
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Solution using simplified procedure
67
Width of zone A = 6
Width of zone C = 70 – 2(6) = 58’ assuming zone A on both corners simultaneously
Horizontal pressures from Fig and roof angle ϴ = 0
Ps30 = 33.4 psf in zone A
Ps30 = 22.1 psf in zone C
Topographic factor Kzt =1 for flat terrain
Pressures =
• psA = 1.62(1)(1.15)(33.4) = 62.2 psf • psC = 1.62(1)(1.15)(22.1) = 41.2 psf
Fig 6-2 Simplified Design Wind
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CIAPR June 18-20 2012
pressure ps30
68
p
PA = 33.4 psf PC = 22.1 psf
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A l ti l M th d P d
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Workshop on Vertical Shelter from Tsunamis
CIAPR June 18-20 2012
1. V and Kd (directionality)2. Importance, I
3. Exposure and height, Kz, Kh
4. Topographic Effect
5. Gust effect G6. Enclosure
7. Internal pressure GCpi
8. External Pressure Cp
9. Velocity pressure qz10. Design wind load p
Analytical Method - Procedure
Solution using analytical procedure
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Solution using analytical procedure
71
V = 145 mph from Fig 6-1
Kd = 0.85 from Table 6-4
I = 1.15 from table 6-1 and occupation Cat IV (or III)
Exposure Category = C
For Low-rise buildings use Fig 6-10 and q = qh
• Select a = 3’, 2a = 6’
• Select values of GCpf for zones 1, 1E, 4, 4E
• GCpf1 = 0.40, GCpf1E = 0.61
• GCpf4 = -0.29, GCpf4E = -0.43
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Solution using analytical procedureL i b ildi
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Low-rise buildings
73
Design pressures
Use q = qh
Windward
p1 = 59.5(0.40 + 0.18) = 34.5 psf
p1E = 59.5(0.61 + 0.18) = 47.0 psf
Leeward
p4 = 59.5(-0.29 + 0.18) = -6.5 psf
p4E = 59.5(-0.43 + 0.18) = -14.9 psf
Solution using analytical procedureL i b ildi
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Workshop on Vertical Shelter from Tsunamis
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Low-rise buildings
74
Forces per level, calculated adding the windward and
leeward pressures because they act in the samedirection.
Level Height
, ft
Ps1E+
4E, psf
Width
E, ft
Ps1+4,
psf
Width ,
ft
Force
Kips
1 30 61.9 12 41.0 58 93.6
2 12 61.9 12 41.0 58 37.5
3 12 61.9 12 41.0 58 37.5
4 6 61.9 12 41.0 58 18.7
Total 187.3
Solution using analytical procedure
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Solution using analytical procedure
75
For comparison the solution was obtained neglecting the
low-rise classification
V = 145 mph from Fig 6-1
Kd = 0.85 from Table 6-4
I = 1.15 from table 6-1 and occupation Cat IV (or III) Exposure Category = C
Kzt = 1
G = 0.85 for rigid structures, T< 1sec
Enclosure classification = enclosed Internal pressure coefficients Fig 6-5, GCpi = ± 0.18
Solution using analytical procedure
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Solution using analytical procedure
76
Obtain Kz from from Table 6-3 and z = level height
Velocity pressure coefficient,
Height, z, ft Kz qz, psf
24 0.94 45.5
36 1.01 53.1
48 1.08 56.8
60 1.13 59.5
Solution using analytical procedure
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Workshop on Vertical Shelter from Tsunamis
CIAPR June 18-20 2012
Solution using analytical procedure
77
Design pressures. No special regions, but pressure varieswith height
Use q = qz for windward pressures
Use q = qh for leeward pressures
Use qi = qh
Shape factors Cp = 0.8 windward, Cp = -0.5 leeward,
obtained from Fig 6-6
Solution using analytical procedure
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Workshop on Vertical Shelter from Tsunamis
CIAPR June 18-20 2012
S s g y c p c
78
Forces per level
Level Z qz,
psf
Windw
qzGCp
Internal
qhGCpi
Leew
qhGCp
Windw
pLeew
p
Total
p
Area,
sqft
Force
kips
1 24 45.5 30.9 -10.7 -25.3 41.6 14.6 56.2 70x30 118.0
2 36 53.1 36.1 -10.7 -25.3 46.8 14.6 61.4 70x12 51.63 48 56.8 38.6 -10.7 -25.3 49.3 14.6 63.9 70x12 53.7
4 60 59.5 40.5 -10.7 -25.3 51.2 14.6 65.8 70x6 27.6
Total 250.9
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Solution for Cylindrical Plan Building
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y g
80
Or assuming rough surface Cf = 0.8
F = 51.6(0.85)(0.8)(70x60) = 147 kips
Summary of examples
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y p
81
Calculated Base Shear ForcesProcedure Calculated Base
Shear Force, kips
% Difference
from Simplified
Procedure
Simplified 188.1 0
Analytical, Low-
rise
187.3 -0.4
Analytical 250.9 33.4
Cylindrical, other
structures, noteplan area is not the
same
92 for smooth
surface,147 for rough
surface
-51.1
-21.9
ASCE 7-10 – Wind Loads
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Basic wind speed, V, mph (m/s)
82
Figure 26.5-1A: Basic Wind Speeds for
Occupancy Category II Buildings andOther Structures
Figure 26.5-1B: Basic Wind Speeds for
Occupancy Category III and IV Buildingsand Other Structures
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Questions?
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Impacts of Wind Provisions onBuilding Components
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Building Components
Load Paths and Connectors
Roof Systems
Windows, Doors and Openings
Wall Systems
Foundations