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Copyright L. A. Prieto-Portar - 2007
EGN-5439 The Design of Tall Buildings
Lecture #04
ASCE 7ASCE 7--02 Solved Problem #1:02 Solved Problem #1:
Analytical Method 2 (for buildings < 60 feet high).Analytical
Method 2 (for buildings < 60 feet high).
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This lecture applies the ASCE 7-02 code requirements for wind
(Section 6.0) to a simple structure and analyzes it with,
The ASCE 7-02 Method 2, the Analytical Method for buildings
smaller than 60 feet in height.
The structure chosen is a warehouse-office building in downtown
Tampa. Its dimensions are 100 feet long by 50 feet wide by 20 feet
tall.
A drawing is shown on slide #3 depicting the location of all the
windows and doors. The location of these windows and doors are
either in the field (or internal) zones or in the end (or external)
zones.
The analysis consists of finding all pressures affecting every
part of this structure that come from all four directions.
Finally, when all the pressures have been calculated, the
engineer will choose the largest positive pressure and the largest
negative pressure for the design of the building.
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Insert here plan and elevations for the office-warehouse
building.
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The basic formula used to compute the wind design pressure p
that is applied to a structure or a portion of a structure is,
The wind velocity comes from County maps in lieu of Fig 6-1b pg
73
This formula is performed upon 10 different zones of the
structure in 4 different wind directions for both the transverse
and the buildings longitudinal directions. The analysis is also
performed for both the MWFRS and C&C. Therefore, there are a
total of 160 calculated pressures. From these, the engineer will
choose the largest positive and negative pressures for the final
design.
( ) ( ) ( )20 00256 z zt d p pip . K K K V I GC GC = A constant
/ Table 6-3 pg 75 / Figure 6-4 pg 47+48 / Table 6-4 pg 76 / Table
6-1 pg 73
A constant = 0.85 or Equation 6-4 pg 30 / Fig 6-6 to 6-8 pg
50-53 / Fig 6-5 pg 49
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( )( )20 00256= ztz dp . K K V I fK actorThe wind exposure
category coefficient Kz shall be taken from ASCE 7-02, Section 6,
page 75, Table 6-3. The Exposure Category is discussed in ASCE
6.5.6, pages 28 and 29.
6.5.6 Exposure. For each wind direction considered, an exposure
category that adequately reflects the characteristics of ground
roughness and surface irregularities shall bedetermined for the
site at which the building or structure is to be constructed.
Account shall be taken of variations in ground surface roughness
that arises from natural topography and vegetation as well as
constructed features.
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6.5.6.1 Wind Directions and Sectors. For each selected wind
direction at which the wind loads are to be evaluated, the exposure
of the building or structure shall be determinedfor the two upwind
sectors extending 45 degrees either side of the selected wind
direction. The exposures in these two sectors shall be determined
in accordance with Sections 6.5.6.2 and 6.5.6.3 and the exposure
resulting in the highest wind loads shall be used to representthe
winds from that direction.
6.5.6.2 Surface Roughness Categories. A ground surface roughness
within each 45-degree sector shall be determined for a distance
upwind of the site as defined in Section 6.5.6.3 from the
categories defined below, for the purpose of assigning an exposure
category as defined in Section 6.5.6.3.
Surface Roughness B: Urban and suburban areas, wooded areas or
other terrain with numerous closely spaced obstructions having the
size of single-family dwellings or larger.
Surface Roughness C: Open terrain with scattered obstructions
having heights generally less than 30 ft (9.1 m). This category
includes flat open country, grasslands, and all water surfaces in
hurricane-prone regions.
Surface Roughness D: Flat, unobstructed areas and water surfaces
outside hurricane-prone regions. This category includes smooth mud
flats, salt flats, and unbroken ice.
This Example
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ASCE 7ASCE 7--02 Table 602 Table 6--3, page 753, page 75This
Example
Kh=Kz=0.70
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( )( ) ( )20 00256 0 70= z dtKp . . K V I factorwhere Kzt is the
Topographic Factor, and is applied to structures sitting on hills,
ridges and escarpments (ASCE 7-02, Section 6.5.7, pages 29 and 30).
This topographic factor is required when,
1. The hill, ridge, or escarpment is isolated and unobstructed
upwind by other similar topographic features of comparable height
for 100 times the height of the topographic feature (100 H) or 2
miles (3.22 km), whichever is less. This distance shall be measured
horizontally from the point at which the height H of the hill,
ridge, or escarpmentis determined;2. The hill, ridge, or escarpment
protrudes above the height of upwind terrain features within a
2-mile (3.22-km) radius in any quadrant by a factor of two or
more;3. The structure is located as shown in Figure 6-4 in the
upper half of a hill or ridge or near the crest of an escarpment;4.
H / Lh 0.2; and5. H is greater than or equal to 15 feet (4.5 m) for
Exposures C and D and 60 feet (18 m) for Exposure B.
When not required, use Kzt = 1.0.
This Example #1.
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Figure 6-4 describes the parameters of the Topographic
Factor,
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( )( )( ) ( )20 00256 0 70 1 0= dp . . . V IK factorwhere Kd is
the Wind Directionality Factor, and is only applied when used in
conjunction with load combinations specified in Sections 2.3 and
2.4 (pages 5 and 6 of ASCE 7-02, Section 6.5.4.4, page 28).
The load combinations can be, for example,
- Live load + wind, or- Dead load + wind, or- Snow + wind, etc,
etc.
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The Wind Directionality Factor is obtained from ASCE Table 6-4,
page 76:
This Example:Kd = 0.85for both MWFRSand C&C.
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( )( )( )( )( ) ( )20 00256 0 70 1 0 0 85=p . . . . I faV
ctorwhere V is the Basic Wind Speed, and is assumed to come from
any direction and can be obtained from local data (ASCE 7-02,
Section 6.5.4, page 28).
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Basic Wind Speed Figure 6-1b.
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Within the State of Florida the wind speeds are obtained from
the local county where the project is located through the countys
wind maps, through,
www.dca.state.fl.us/fbc/maps/2_maps.htm
Some counties allow interpolation between wind speed lines,
whilst others do not.
To obtain a wind map of this specific example in downtown Tampa
(Hillsborough County), use this address,
www.dca.state.fl.us/fbc/index_page/maps/county_maps/hillsborough2.pdf
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Hillsborough County does allow interpolation, although it is not
practical.This Examples site.Use V = 120 mph.
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( )( )( )( )( ) ( )20 00256 0 70 1 0 0 85 120= Ip . . . .
factorwhere I is the Importance Factor, and is based on the use of
the structure as well as the Nature of Occupancy (ASCE 7-02,
Section 6.5.5, page 28).
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The Importance Factor (from ASCE Table 6-1, page 73),
Category II
V = 120 mph
This Example:I = 1.0
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( )( )( )( )( ) ( )( )( )( )
20 00256 0 70 1 0 0 85 120 1 021 9
=
=
p . . . . . factorp . psf factor
Thus, the raw wind pressure (also known as qz, the velocity
pressure) is,
This raw wind pressure now needs to be modified by the internal
and external pressure coefficients (the factor) in order to
determine what is the actual pressure that is going to be applied
at different points of the structure.
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WIND
An unbreached house is subjected to positive and negative
pressures from the external wind.
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WIND
When the house is breached (a broken window, or a door that
loses its latch, etc) the wind entering the house will quickly
increase the loads on the remaining windows,
doors and roof until they too, fail.
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WIND
The pressure coefficients will add pressure on some walls and
roof (see the wind effect upon the right side wall and roof) and
subtract on others. The analysis searches
for the largest positive and negative pressures on the
structure.
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( ) ( )( ) ( ) ( )21 9
=
=
Z pi
pi
p
p
p q GC
p . psf GCGC
GC
Now the raw pressure (also known as qz, the velocity pressure)
must be modified by the pressure coefficients,
where GCpi is the Internal Pressure Coefficient and is based on
the Building Enclosure Classification (ASCE 07-2, Section 6.5.11.1,
page 31).
What is the wind pressure doing internally? How does the wind
affect an Enclosed Building, which is the case for this
example?
Even enclosed buildings have cracks around the doors and the
windows, so that the building breaths and feels a portion of the
raw pressure.
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A Building Enclosure is defined in ASCE 7-02, Section 6.2, page
23,Building, open: A building having each wall at least 80% open.
This condition isexpressed for each wall by the equation Ao 0.8 Ag
where: Ao = total area of openings in a wall that receives positive
external pressure, in ft2 (m2) Ag = the gross area of that wall in
which Ao is identified in ft2 (m2).
Building, partially enclosed: A building which complies with
both of the following conditions:1. the total area of openings in a
wall that receives positive external pressure exceeds the sum of
the areas of openings in the balance of the building envelope
(walls and roof) by more than 10%, and2. the total area of openings
in a wall that receives positive external pressure exceeds 4 ft2
(0.37 m2), or 1% of the area of that wall, whichever is smaller,
and the percentage of openings in the balance of the building
envelope does not exceed 20%.These conditions are expressed by the
following equations:1. Ao > 1.10 Aoi2. Ao > 4 ft2 (0.37 m2)
or > 0.01Ag, whichever is smaller, and Aoi /Agi 0.20 where: Ao,
Ag are as defined for Open Building Aoi = the sum of the areas of
openings in the building envelope (walls and roof) not including
Ao, in ft2 (m2) Agi = the sum of the gross surface areas of the
building envelope (walls and roof) not including Ag, in ft2
(m2).
Building, enclosed: A building that does not comply with the
requirements for open or partially enclosed buildings.
This Example.
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This Example:
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( ) ( ) ( )21 9 0 18 = pp .GC. psfwhere GCp is the External
Pressure Coefficient and is computed separately for the MWFRS cases
and the C&C cases (ASCE 7-02, Section 6.5.11.2, page 31).
These external pressures are also determined and applied based
on which zone of the building is being evaluated (that is, in the
field or in the end zones).
Up to this point, ASCE 7-02s procedure is identical for both
the,
- Method 2, Analytical Procedure for any height, and- Method 2,
Analytical Procedure for the roof at < 60 feet in height.
From now on, the method of finding GCp is different for these
two.
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The distance a of the end zones corresponds to the Components
and Cladding case:
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In summary, a = 0.10L= 0.10B the least of these= 0.40h
a = 0.04L= 0.04B but not less than these= 3 feet
This Example: a = (0.10)(50 ft) = 5 feet= (0.40)(20 ft) = 8
feet
= (0.04)(50 ft) = 2 feet= 3 feet therefore a = 5 feet
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( ) ( ) ( )21 9 0 18 = pp .GC. psfCalculating GCp for the MWFRS
case is represented by GCpf,
The values of GCpf are found in ASCE 7-02, Section 6.5.11.2,
page 31, Figure 6-10, pages 55 and 56.
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Figure 6Figure 6--10, pages 55 and 56.10, pages 55 and 56.
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An expanded view of the ten (10) zones of a building under a
Transverse A loading:
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The calculations of GCpf for the MWFRS case involve these ten
(10) zones; notice the values given in the Table for our Example
#1s flat roof ( = 0):This Example: a flat roof.
This line of coefficients are now used to calculate the
pressures shown on the spread-sheet shown on the next slide.
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-5.50-13.40-0.4321.9 psf4E
-7.70-15.50-0.5321.9 psf3E
-19.50-27.40-1.0721.9 psf2E
17.309.400.6121.9 psf1E
-5.90-13.80-0.4521.9 psf6
-5.90-13.80-0.4521.9 psf5
-2.40-10.30-0.2921.9 psf4
-4.20-12.00-0.3721.9 psf3
-11.20-19.10-0.6921.9 psf2
12.704.820.4021.9 psf1
Using -GCpiUsing +GCpiqzzone
Design pressuresGCpfVelocity pressureBuilding
The design pressures for the MWFRS at all ten zones for a
Transverse A are:
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Consider the first line of calculations for the buildings zone
#1,
Thus, for zone #1, the pressures range from +4.82 psf to +12.70
psf; therefore, we would choose +12.70 psf for our design
pressure.
This procedure now continues for all ten zones in four (4)
directions for the transverse wind loading and the four (4)
directions for the longitudinal wind loading, or a total 80
calculated pressures for the MWFRS case.
Choose the largest positive and the largest negative
pressures.
( ) ( ) ( ) ( )
( ) ( )
( ) ( )
(21.9 ) 0.18 (21.9 ) 0.18Using the positive value of yields,
(21.9 ) 0.40 0.18Using the negative value of yields,
(2
0.40
4.82
12.701.9 ) 0.40 0.18
pf
pi
pi
p psf psfGC
p ps
GC
fGC
p
psf
pps sff
= =
= =
= =
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+12.70 psf
-19.10 psf
-12.00 psf-10.30 psf
-13.80 psf
-13.80 psf
+17.30 psf
-27.40 psf
-15.50 psf
-13.40 psf
The ten zones for the Transverse A can now be shown with their
calculated design pressures:
Wind direction
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Consider now, what would happen to the design pressures if the
roof had a small pitch of = 20 (which corresponds roughly to a
pitch of 5:12),
This new variant of Example #1 with = 20,
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-10.10-18.00-0.6421.9 psf4E
-11.20-19.10-0.6921.9 psf3E
-19.50-27.40-1.0721.9 psf2E
21.5013.600.8021.9 psf1E
-5.90-13.80-0.4521.9 psf6
-5.90-13.80-0.4521.9 psf5
-5.50-13.40-0.4321.9 psf4
-6.60-14.50-0.4821.9 psf3
-11.20-19.10-0.6921.9 psf2
15.507.700.5321.9 psf1
negativepositiveqzzone
Design pressuresGCpfVelocity PressureBuilding
Notice the slight increase in pressure due to the increase in
the roofs pitch, although zone #2E has not changed,
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The main wind force resisting system (MWFRS) design pressures
just found are used as the lateral forces upon the structural
skeleton frame of the building, such as the steel frame, the
reinforced concrete columns, beams and slabs, shear walls, etc.
The design pressures from the MWFRS portion are applied to the
columns and beams through the use of the tributary areas. For
example, if the columns are spaced at 30-foot intervals, and the
floor-to-floor height is 10-feet, the tributary area is 10 x 30 =
300 SF multiplied by the largest positive or negative design
pressures found in the two previous tables.
Now we will calculate the design pressures for the Components
and Claddings (C&C). The components and cladding are, for
example, the roof coverings, wall coverings, awnings, canopies,
etc, anything that is not affected by the internal pressure GCpi =
0. These C&C external pressures are applied to single
components, a stand-alone (one canopy, one door, etc) and are a
function of the surface effective area of that component. The
smaller the effective area, the more intense the pressure, versus,
the larger the effective area, the pressure becomes smaller,
etc.
In the ASCE Method 1: The Simplified Method (Lecture 05) these
two separate procedures (MWFRS and C&C) are united into a
single procedure.
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Consider now the External Pressure Coefficients for C&C
(ASCE 7Consider now the External Pressure Coefficients for C&C
(ASCE 7--02, Figures 602, Figures 6--1a 1a and 6and 6--1b, pages 57
and 58):1b, pages 57 and 58):
Wall coefficients
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These are the C&C roof coefficients,These are the C&C
roof coefficients,
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Consider the External Pressure Coefficients for a wall component
that has an area of only 10 square feet:
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The design pressures for a C&C of only 10 SF of wall
effective aThe design pressures for a C&C of only 10 SF of wall
effective area are,rea are,
23.3016.201.0021.9 psf5(-)-24.00-31.10-1.4021.9 psf5(+)
23.2016.201.0021.9 psf4(-)-18.10-25.20-1.1021.9 psf4(+)
Using -GCpiUsing +GCpiqzzone
Design pressuresGCpfVelocity PressureBuilding
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Now what happens when the componentNow what happens when the
components area is increased to 100 square feet?s area is increased
to 100 square feet?
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The design pressures for the 100 SF wall are smaller,The design
pressures for the 100 SF wall are smaller,
19.3012.20-0.8021.9 psf5(-)
-17.10-24.20-1.0521.9 psf5(+)
19.3012.200.8021.9 psf4(-)
-15.20-22.30-0.9521.9 psf4(+)
Using -GCpiUsing +GCpiqzzone
Design pressuresGCpfVelocity PressureBuilding
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Similarly, for a roof effective area of only 10 square feet,
theSimilarly, for a roof effective area of only 10 square feet, the
coefficients are,coefficients are,
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Therefore, the design pressures for a roof component 10 SF
is,Therefore, the design pressures for a roof component 10 SF
is,
-57.40-65.30-2.8021.9 psf3(-)10.502.600.3021.9
psf3(+)-35.50-43.40-1.8021.9 psf2(-)10.502.600.3021.9
psf2(+)-18.00-25.80-1.0021.9 psf1(-)10.502.600.3021.9 psf1(+)
Using -GCpiUsing +GCpiqzzoneDesign pressuresGCpfVelocity
PressureBuilding
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Contrast the high pressures on a roof component 10 SF with the
same component that is 100 SF,
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Notice the drop in design pressures for this case of a 100 SF
roNotice the drop in design pressures for this case of a 100 SF
roof component,of component,
-20.10-28.00-1.1021.9 psf3(-)8.300.400.2021.9 psf3(+)
-20.10-28.00-1.1021.9 psf2(-)8.300.400.2021.9 psf2(+)
-15.8023.70-0.9021.9 psf1(-)8.300.400.2021.9 psf1(+)
Using -GCpiUsing +GCpiqzzone
Design pressuresGCpfVelocity PressureBuilding
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References.References.
1. American Society of Civil Engineers, Publication ASCE 7-02,
Minimum Design Loads for Buildings and Other Structures, Washington
DC, 2002;
2. W. C. Bracken PE, Wind Load Design, Florida Engineering
Society, Tallahassee, 2007;
3. K.C. Mehta, J.M Delahey, Guide to the Use of the Wind Load
Provisions of ASCE 7-02 ASCE Press, Washington DC, 2003.