© L. Prieto-Portar - 2008

EGNEGN--5439 The Design of Tall Buildings5439 The Design of Tall Buildings

Lecture 08Lecture 08

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).

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.

The example: a single-story warehouse building, 100 feet long, 50 feet and 20 feet tall.

The location of the windows and doors are critical: are they in the “field” or in the “end” zones; are they “debris resistant” or not, in which case, this face of the

building is breached during a hurricane.

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 building’s 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

( ) ( )� �= −� �z p piwhere p q GC GC

( )( )20 00256= ztz dp . K K V I fK actor

The 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.

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

ASCE 7ASCE 7--02 Table 602 Table 6--3, page 753, page 75This Example

Kh = Kz = 0.70

Case 1 (C&C) and Case 2 (MWFRS)

( )( ) ( )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.

Figure 6-4 describes the parameters of the Topographic Factor,

( )( )( ) ( )20 00256 0 70 1 0= dp . . . V IK factor

where 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.

The Wind Directionality Factor is obtained from ASCE Table 6-4, page 76:

This Example #1:Kd = 0.85for both MWFRSand C&C.

( )( )( )( )( ) ( )20 00256 0 70 1 0 0 85=p . . . . I faV ctor

where 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).

Basic Wind Speed ASCE-7-02, Figure 6-1b.

Within the State of Florida the wind speeds are obtained from the local county where the project is located through the county’s 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

Hillsborough County does allow interpolation, although it is not practical.This Example #1’s site.Use V = 120 mph.

( )( )( )( )( ) ( )20 00256 0 70 1 0 0 85 120= Ip . . . . factor

where 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).

The Importance Factor (from ASCE Table 6-1, page 73),

Category II

V = 120 mph

This Example:I = 1.0

( )( )( )( )( ) ( )( )( )( )

20 00256 0 70 1 0 0 85 120 1 0

21 9

=

=

p . . . . . factor

p . 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.

WIND

An unbreached house is subjected to positive and negative pressures from the external wind.

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.

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.

( ) ( )( ) ( ) ( )21 9

� �= −� �

� �= −� �

Z pi

pi

p

p

p q GC

p . psf GC

GC

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.

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.

This Example #1:

( ) ( ) ( )21 9 0 18� �= − ±� �pp .GC. psf

where 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 7-02’s 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.

The distance a of the end zones corresponds to the Components and Cladding case:

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

( ) ( ) ( )21 9 0 18� �= − ±� �pp .GC. psf

Calculating 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.

Figure 6-10, pages 55 and 56.

An expanded view of the ten (10) zones of a building under a Transverse A loading:

The calculations of GCpf for the MWFRS case involve these ten (10) zones; notice the values given in the Table for our Example #1’s 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.

-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:

Consider the first line of calculations for the building’s 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 ) 0.18

Using the positive value of yields,

(21.9 ) 0.40 0.18

Using the negative value of yields,

(2

0.40

4.82

12.701.9 ) 0.40 0.18

pf

pi

pi

p psf psf

GC

p ps

GC

f

GC

p

psf

pps sff

� �= − ± = − ±� �� �� �

= − =� �� �

= − − =� �� �

+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

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°,

-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 roof’s pitch, although zone #2E has not changed,

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 these two separate procedures (MWFRS and C&C) are united into a single procedure.

Consider now the External Pressure Coefficients for the walls in the C&C case (ASCE 7-02, Figures 6-1a and 6-1b, pages 57 and 58):

Wall coefficients

These are the C&C roof coefficients,

Consider the External Pressure Coefficients for a wall component that has an area of only 10 square feet:

The design pressures for a C&C of only 10 SF of wall effective area 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

Now what happens when the componentNow what happens when the component’’s area is increased to 100 square feet?s area is increased to 100 square feet?

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

Similarly, for a roof effective area of only 10 square feet, the coefficients are,

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 +GCpiqzzone

Design pressuresGCpfVelocity PressureBuilding

Contrast the high pressures on a roof component 10 SF with the same component that is 100 SF,

Notice the drop in design pressures for this case of a 100 SF roof 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

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.