For PRASHIL Memo 2-Enclosures-Rev A

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Revision B :

Revision A : 11.05.12 As per Amendment - 1 LSB SHKU RGB

Date: 24.02.12 Made Checked Approved

Made : LSB Checked: SHKU Approved : RGB

MEMORANDUM

NO. 2

ENCLOSURES

CCB-CIMPOR CIMENTOS DO BRASIL LTDACAXITU CEZARINA

CALCULATION GUIDE LINEBRAZILIAN STANDARD

Project No:


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MEMORANDUM NO.2Cimpor, Caxitu/Cezarina

CALCULATION GUIDE LINE 11.05.12

EnclosuresRev:

1. Genral 1.A Structural design and erection, 749500

2. Loads 2.A Pressure and force coefficients and reference height

2.B Dynamic effects coefficients

2.C Roof shape coefficients

2.D Criteria for structural integrity

2.E Earthquake response spectra

2.F Design bearing capacities, foundation depths and inclination factors

2.G Pile sizes and design capacities

2.H Wind additional shape factors

3.Reinforced

concrete 3 Strength classes for concrete

3.A Concrete breakout strength of anchor in tension

4. Structuralsteel 4.A Classification of cross sections

4.B Global Analysis and second-order effects

4.C Load factors and combinations

4.D Guide values for deflections

4.E Available sections and plates

4.F Light weight sections

4.G Figures for deductions of holes

4.H Resistance to shear and shear buckling

4.I Tension Member Capacity Calculations

4.J Buckling resistance of member and buckling curves

4.K Effective length of frame members

4.L Interaction factors - Bending and compression

4.M Buckling resistance of bending member - Slender Webs

4.N Buckling resistance of bending member - Non Slender Webs

4.O Web bearing , buckling and stiffeners

4.P Column bases on concrete foundations

4.Q Symbols and stresses for welded connections

4.R Design resistance of fillet welds4.S Distance of bolts

4.T Bearing capacities of bolts

4.U Grating details

4.V Sliding bearings

4.W Profiled metal sheeting


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Enclosure-1A

Content: Structural Design and Erection

Nos. of sheets: 15


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Enclosure-2A

Content:Pressure and force coefficients and reference heightExtract of NBR 6123 Forces due to Wind on Structures

Pages 5-32,42-49

No of sheets: 36


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5 NBR 6123/19884.2.3 Coefficients of forceThe overall strength of the wind on a building or part (Fg, isobtained by the vector sum of wind forces that act there.

The component of the global force in wind direction,strength drag Fa- is obtained by:Fa= CaqAe

Where:

Ca= drag coefficient

A = Effective front area: area of the orthogonal projection ofbuilding, structure or structural element on a planeperpendicular to the wind direction ("Shadow area")In general, a component of any overall strength is obtainedby:

F=CfqA

C = coefficient of force, specified in each ca -only: CxCyetc.

A = reference area, specified in each case

4.3 determination of the dynamic effects of the wind

To determine the dynamic effects due to the atmosphericturbulence, see calculation in Chapter 9 and examples inAnnex 1.

5 Characteristic speed of the wind

5.1 Basic Speed of the wind, VoThe basic wind speed, V is the velocity of a burst of 3 s,exceeded on average once in 50 years, 10 m above theground in the open and flat.

Note: Figure 1 presents the graph of isopleths of the basicspeed in Brazil, with Intervals of 5 m/s (see Annex C).

5.1.1 As a general rule, it is assumed that the wind canblow from any horizontal direction.

5.1.2 In case of doubt as to the basic speed selection andworks of exceptional importance, is recognized a specificstudy to determine Vo. In this case,preferential directionscan be considered for the wind basic, if properly justified

5.2 The topographical factor S1The topographical factor S1, takes into account variationsof the topography of the land and is determined as follows:a) Flat or slightly uneven: S1= 1.0;b) slopes and hills:Slopes and hills which can be elongated in a two-dimensional air flow blowing in the direction indicated inFigure 2;

- At point A (hills) and points A and C (slope):S1= 1.0- in the point B: [S1is a function S1(z)]:3: S1 (z) = 1,06<


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6 NBR 6123/1988

Vo = in m/sVo= maximum average velocity measured over 3 s, which may be exceeded on average once in 50 years to 10 m above groundlevel in an open and plan

Figure 1 Isopleths Basic velocity Vo(m / s)


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7 NBR 6123/1988

a) Slopeb) Hill

Figure 2 Topographic factorS1 (z)


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8

NBR 6123/19885.3 Roughness of the land, size of the building and heightabove the ground: Factor S2.The factor S2considers the combined effect of roughness

of ground, the variation of wind speed with heightabove the terrain and the dimensions of the building or partthe building into consideration.In strong winds in neutral stability, the speed of windincreases with height above the ground. This increasedepends on the roughness of the terrain and the range oftime considered in determining the speed. This timeinterval is related to the dimensions of the building, forbuilding small and elements of buildings are more affectedby short bursts of duration than large buildings. For these,it is more appropriate to consider the wind with a calculatedaverage longer period of time.

5.3.1 Roughness of thelandFor purposes of this Standard, the roughness of the terrainis classified into five categories (2):Category 1: Large smooth surfaces with more than 5 km inlength, measured in the direction and sense ofwind incident. Examples:- Calm seas (3);- Lakes and rivers;- Wetlands without vegetation.Category II: Ground-level open or approximate level, withfew isolated obstacles suchas trees and low buildings. Examples:- Coastal plane areas;- Wetlands with sparse vegetation;- Airfields;- Grasslands and heaths;- Farms without fences or walls.The mean elevation of the top obstacles is considered ininferiority or equal to 1.0 m.Category III: flat or wavy with obstacles, such as hedgesand walls, few windbreakstrees, buildings, low and sparse. Examples:- Farms and cottages, with the exception of parts withweeds;- Farms with hedges and / or walls;- The suburbs at a considerable distance from the center,houses low and sparse.The mean elevation of the top obstacles is consideredequal to 3.0 m.

Category IV: Land covered by numerous obstaclesresources and spaced in the forest zone, industrial orurbanized. Examples:

- Areas of parks and woodlands with many trees;- Small towns and their surroundings;- Densely built suburbs of large activities;- Industrial areas fully or partially developed

The mean elevation of the top obstacles is consideredequal 10 m.

This category also includes areas with larger obstacles andstill can not be considered in the category V.

Category V: Land covered by numerous obstacles, big, talland spaced. Examples:- Forests with tall trees of hearts isolated;- Centers of large cities;- Well developed industrial complexes.

The mean elevation of the top obstacles is consideredequal or greater than 25 m.

5.3.2 Dimensions of the building

The wind speed varies continuously, and its value mediumcan be calculated over any interval time.It was found that the shortest interval of usual measures(3s) bursts whose size corresponds to conveniently involveobstacles up to 20m in average wind direction.

The longer the time interval used in the calculation ofaverage speed, the greater the distance covered bythe burst.

To define the parts of the building to be considered indetermining of the actions of wind, it is necessary toconsider constructive or structural features that originate ornon structural continuity to the throughout the building(construction), such as:

- Buildings together with the structure in which separate lotof two or more structurally independent;- Buildings with little stiffness in the direction perpendicularto the wind direction and, therefore, with little capacity ofredistribution of loads.

(2)At the discretion of the designer, intermediate categories, conveniently interpolating the values of p and b, can be considered

as featured in S2or 5.3.3 or in Annex A.(3)

In rough seas, the value of the exponent p for 1h can reach 0.15, in heavy winds. In general, p = 0.12.


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9

NBR 6123/1988They were chosen the following classes of buildings,parts of buildings and their elements, with intervalstime to calculate the average velocity, respectively,3 s, 5 s and 10 s:Class A:All sealing unit, its elements and fixing individualpieces of structures withoutsealing. Every building in which most the horizontal orvertical dimension does not exceed 20 m.Class B:Any building or part of building for which thelarger horizontal or vertical front surface is between 20 mand 50 m.Class C: Any building or part of building for which thelarger horizontal or vertical front surface exceeds 50 m.For every building or part of building to which the largerhorizontal or vertical front surface exceed 80 m, thecorresponding time interval can be determined according tothe indications of Annex -A.

5.3.3 Height above the groundThe S2 factor used in calculating the wind speed in aheight z above the general level of the land is obtained byexpression:

S2 = b Fr (z/10)p,

and the factor F is always burst the corresponding categoryII.The above expression is applicable to all structure, whichdefines the upper boundary atmospheric layer.

The parameters for determining S2for five categories ofthis standard are presented in Table 1.

The S2values for the various categories of roughnessLand classes and sizes of buildings defined in thisStandard are given in Table 2.

To study the sealing elements, it is recommended to use

S2 factor corresponding to the top of the building. Thisrecommendation is based on the fact that the facadewindward side and on the facades wind is deflectedlow, with consequent increase in dynamic pressure

bottom of the building. For the same reason, the factor S2is considered constant up to 10 m high in category V.

5.3.3.1Annex A indicates the determining factor for S2time intervals between 1s to 3 h and for any roughnessthe ground.

Table 1 - Meteorological Parameters

Category zg(m)

Parameter Classes

A B C

I 250b

p

1,10

0,06

1,11

0,065

1,12

0,07

II 300

b

Fr

p

1,00

1,00

0,085

1,00

0,98

0,09

1,00

0,95

0,10

III 350

b

p

0,94

0,10

0,94

0,105

0,93

0,115

IV 420

b

p

0,86

0,12

0,85

0,125

0,84

0,135

V 500

b

p

0,74

0,15

0,73

0,16

0,71

0,175


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10 NBR 6123/1988Table 2-Factor,S2

Category

5.4 Statistical Factor S3The statistical factor S3is based on statistical concepts, andconsiders the degree of security required and the durabilityof building. According to definition 5.1, the basic speed Vois the speed of the wind that has a period averagerecurrence 50 years.The probability that V is the velocity in this period equaledor exceeded is 63%.The level of probability (0.63) and lifetime (50 years) resultsare considered suitable for normal buildings eg. homes,hotels, offices, etc.. (Group No. 2).

In the absence of a specific safety in buildings or in thecorresponding directions standard structure, the minimum

values of the factor S3 are in products listed in Table 3.

5.4.1 Annex B indicates the determining factor for S3orprobability levels and for other periods of exposition of thebuilding by the wind.

Table 3 - Minimum values of the statistical factorS3

S3

1 Buildings whose total or partial destruction may affect the safety or

ability to rescue people after a destructive storm (hospitals, barracksfire and security forces, central communication, etc.).

1,10

2 Buildings for hotels and residences. Buildings for commerce andindustry with a high load factor

1,00

3 Buildings and plants with low factor occupation (tanks, silos, farmbuildings, etc.)

0,95

4 Seals (tiles, windows, fence panels, etc.) 0,885 Temporary buildings. Structures 1 to 3 groups during construction 0,83


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11 NBR 6123/19885.5 Change of land roughness

5.5.1If the category of field change with the lengthroughness from Z01to Z02, the wind will travel to a certaindistance before they fully established a new profile ofaverage velocity with height zg.Changing the profile begins near the ground, and the newprofile increases its height Zx, as it grows the distance xmeasured from the line of change of category.

This profile of average speeds is determined according tothe following.

5.5.1.1Transition to higher roughness category (z01 < z02)

zx e ziHeights shall be determined by the expressions:

zx = A z02 (x/z02)0,8

zi = 0,36 z02 (x/z02)0,75

Where:

A = 0,63 - 0,03 in (z02/z01)

The profile of average speeds (factor S2) is well defined as(see Figure 3-a):a) The height zxup, the factors are considered S2corresponding to the field farthest from the building (z01);

b) The height zi down factors are considered S2corresponding to the land surrounding the building (z02);

c) in the transition area between zi and zx, to consider onelinear variation of the factor S2.

5.5.1.2 Transition to lowest category of roughness(z01 > z02)Determine the height zxby the expression:

zg = A z02 (x/z02)0,8Where:

A = 0,73 - 0,03 in (z01/z02)

The mean velocity profile (S2 factors) is well defined (seeFigure 3-b):

a) The height zxup, the factors are considered S2corresponding to the field farthest from the

building (z01);

b) the height zxdown factors are considered S2corresponding to the terrain surrounding the building, but

without exceeding the value of S2determined at the time zxfor the roughness land z01.

5.5.2The heights of the boundary layers, zg,speed profilesin medium-sized cities fully developed and the follow

roughness elements z0, are as follows:

Category I II III IV V

zg(m): 250 300 350 420 500

z0(m): 0,005 0,07 0,30 1,0 2,5

Perfil para- Profile for

Figure 3 - S2profile downwind of a change of roughness


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12 NBR 6123/19886. Aerodynamic coefficients for buildings currents (seealso Annex E and F)

6.1 6.1 pressure coefficients and external form,6.1.1Coefficient values of pressure and external form,for various types of buildings and directions for criticalwind directions are given in Tables 4 to 8 and Figures,Tables and Annexes E and F. Surfaces in which they occurconsiderable variations of pressure were subdividedand coefficients are given for each part.

6.1.2Areas with high suctions appear along the edges ofwalls and roofs and are depending on their location ofthe angle of incidence of the wind. Therefore, these highsuctions do not appear simultaneously in all these zones, forwhich the tables present average values of external

pressure coefficients (cpeaverage).These coefficients should be used only for calculation ofwind forces in their areas, applying to the design, verificationand anchoring of the sealing elements and secondarystructure.

6.1.3For the calculation of sealing elements and their

fixings to structural parts the factor corresponding S2to class A, should be used with the value of Ce o cpeapplicable to the area where it is their element.For the calculation of the main structural parts S2 should beused, the factor corresponding to the class A, B or C, withthe value of Ce applicable to the area where it has itsStructural parts.

6.1.4For the determination of the external pressures in acylindrical construction of circular section, the values cshould be used as given in the Table 9. These coefficientsapply only in flux above the critical region, thisis, for Reynolds number Re> 420,000, windyincident perpendicular to the axis of the cylinder,diameter- d. The Reynolds number is determined byexpression:

Re = 70000 Vk d,

Where - Vk is in meters for seconds and d in meters.

6.1.5The coefficients in Table 9 are applicable to cylindersof vertical axis (chimneys, silos, gas meters, tanks,etc..) or horizontal (tanks, pipes air, etc..), since in the lattercase, the distance clearance between the cylinder and theground is not smaller than the diameter of the cylinder.These coefficients depend on the ratio h/d between thelength of the cylinder and its diameter in case Wind ispassing freely only by one end of the cylinder. In the case ofwind passing freely, the two ends of the cylinder, considerthe value h to calculate the ratio h/d should be half thelength of the cylinder.

6.1.6The coefficients in Table 9 are also applicable tocases in which the land is replaced by surfaces of horizontalor vertical plane, sufficiently long respect to the cross

section of the cylinder, in way to originate flow conditionssimilar to caused them for the land.

6.2 Coefficients of internal pressure6.2.1 If the building is totally impervious to air,pressure inside will be time-invariant and independent onthe speed of the airflow outside. But usually walls and / orcoverage of buildings are considered as closed, undernormal service or as a result of accidents, allow air flow bymodifying the ideal conditions given in tests.While the permeability not to exceed the limits specified in6.2.3, can be taken as the external pressure is not modifiedby permeability and the internal pressure is calculated inaccordance with the specifications given below.

6.2.2 For purposes of this Standard, are consideredimpervious the following building elements and seals:curtains and slabs of reinforced concrete or prestressed;walls masonry, stone, brick, concrete block and the like,without doors, windows or any other apertures. The otherbuilding elements and seals are considered permeable.The permeability should be the presence of openings suchas joints between panels. Sealing and between tiles,cracks in doors and windows, vents and roof tiles, gapsopen doors and windows, chimneys, skylights, etc.

6.2.3 The rate of permeability of a part of the buildingis defined by the relationship between the openingsand the total area of this part. This index should bedetermined with all possible accuracy. As a generalstatement, the typical permeability index of a building forhousing or office, with all windows and doors, is between0.01% and 0.05%. for application of items 6.2, except forthe opening event of dominant the index of permeability ofany wall or Water coverage exceed 30%. Thedetermination of this index should be undertaken with carein order that changes in permeability during the life ofbuilding, can lead to values of more harmful loading.

6.2.4 For the purposes of this Standard, the opening isdominant an aperture whose area is equal to or greaterthan the total area of other openings that are consideredthe permeability over the entire outer surface of thebuilding (including coverage, if there is air permeable liner

or in the absence of lining). This ruling may openoccur by accident, such as broken windows caused fixedby wind pressure (pressure or suction),by objects thrown by wind or other causes.

6.2.5 For buildings with permeable internal walls,the internal pressure can be considered uniform. in thiscase the following values must be used for the coefficient

of internal pressure cpi.

a) two opposite faces are also permeable, theother impermeable surfaces:

- perpendicular wind to a permeable face:

cpi = + 0,2;- perpendicular wind to an impermeable face:

cpi = - 0,3;


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13 NBR 6123/1988b) four faces equally permeable: cpi = - 0,3or 0 (to consider the most harmful value);

c) dominant opening in a face; the other faces

of equal permeability:- dominant opening in windward side.

Ratio between the area of all openings inwindward side and the total area of openings inall surfaces (walls and roof, under the conditionsof 6.2.4) subject to external suctions:

1 ........................................... cpi = + 0,11,5 ........................................ cpi = + 0,32 ........................................... cpi = + 0,53 ........................................... cpi = + 0,66 or more ............................. cpi = + 0,8

- Opening in the face of dominant downwind.Adopting the value of the coefficient of external form,

Ce,, corresponding to this face (see Table 4).- Opening a dominant face parallel to the

the wind.- Dominant opening area not located in highexternal suction.

Adopting the value of the coefficient of external form, Ce,corresponding to the location of the opening on the face(see Table 4).- Opening located in an area of dominant high externalsuction.- Ratio of the dominant area of the opening (or area ofopenings located in this area) and area Total otheropenings located on all faces subjected to externalsuctions:

0,25 ............................................... cpi = - 0,40,50 ................................................... cpi = - 0,50,75 ................................................ cpi = - 0,61,0 ................................................. .cpi = - 0,7

1,5 ................................................. .cpi

= - 0,83 or more ......................................... ..cpi = - 0,9

Areas of high external suction areas are given in

Tables 4 and 5 cpeaverage).

6.2.6For buildings with windows and effectively sealed stillhaving a negligible probability to be broken by accident,consider the most harmful following values:cpi = - 0,2 or 0

6.2.7When it is not considered necessary or whencan not be determined with reasonable accuracy thepermeability ratio of 6.2.5-c) must be adoptedfor coefficient of internal pressure equal to the valueof the coefficient of external form, Ce (for incidence ofWind from 0 and 90 ), indicated in this Standard for thezone, where it is located in dominant opening, both wallas in coverage.

6.2.8Gaps in coverage will affect the efforts where thewalls lining are permeable (natural porosity, trap doors,light boxes, non-sealed units, etc.) or non-existent.Otherwise, these openings will interest only to study thestructure of the roof, its supports and coverage, as well asto the study of the own lining.

6.2.9The value of cpi, can advantageously be limited or

controlled to deliberate distribution of permeabilitywalls and roof, or the aerator that acts as a dominant inopen position with appropriate value of external pressure.examples of such devices are:- Vented roof gables subjected to suction for all thedirections of the wind, causing reduction of buoyancy onthe roof;- Permanent openings in the walls parallel to wind directionand located near the edges of windward (areas of highexternal suction), causing considerable reduction of thebuoyancy on the roof.

6.2.10In the scope of Table 9, for the calculation forcesdue to wind on the wall of a cylindrical building when it istop (s) open (s) the following values should be adopted forcpi:

h/d 0,3 ......................................... cpi = - 0,8h/d < 0,3 .......................................... cpi = - 0,5

6.2.11For cases not considered in 6.2.5 to 6.2.7, thecoefficient of internal pressure can be determinedaccording to the wording of Annex D.


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14 NBR 6123/1988Table 4 - Coefficients of pressure and form, external walls for buildings of rectangular plan

Altura relative relative height,Valores de Ce para - Values forCe, mdio average, porem however, (o menor dos dois)-(the lesser of two),

Notes: a) For a / b between 3 / 2 and 2, interpolate linearly.b) To wind at 0 , parts A3 and B3, the coefficient of form Ce has the following values:- For a / b = 1: same value of lots A2 and B2;- For a / b 2: Ce = - 0.2;- For 1


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15 NBR 6123/1988Table 5 - Pressure coefficients and external form, with two roof slopes, symmetrical, in buildings ofrectangular plan

Altura relative relative height,Valores de Ce para - Values forCe, mdio average, porem however, (o menor dos dois)-(the lesser of two),

Details 1

Notes: a) The coefficient of Ce form on the underside of theeaves is equal to the corresponding wall.b) In the areas around the protruding parts of buildings roof(chimneys, tanks, towers, etc..) should be considered as acoefficient of Ce = 1.2, to a distance equal to half the size of thediagonal. Projection in plan view.c) On the roof of skylights, cpemean = - 2.0.d) To wind at 0 , in Parts I and J as the coefficient of Cehas the following values:a / b = 1: share the same value of F and H, a / b 2: Ce = - 0.2.Linearly interpolated for intermediate values of a / b.

(o menor dos dois)- (the lesser of two),porem however


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16 NBR 6123/1988Table 6 - pressure coefficients and form for external roof with water, in buildings of rectangular plan, withh/b < 2

Vento wind Corte - Section

y = h or 0.15b (taking the smaller of the two values)The surfaces H and L refer to its entire quadrant.

e Values

Ce

angle of incidence of the wind:

90(C) 45 0o

-45 -90

H L H H e L He L H L H L(A) (B)

5o

-1,0 -0,5 -1,0 -0,9 -1,0 -0,5 -0,9 -1,0 -0,5 -1,010 -1,0 -0,5 -1,0 -0,8 -1,0 -0,5 -0,8 -1,0 -0,4 -1,015 -0,9 -0,5 -1,0 -0,7 -1,0 -0,5 -0,6 -1,0 -0,3 -1,020 -0,8 -0,5 -1,0 -0,6 -0,9 -0,5 -0,5 -1,0 -0,2 -1,025 -0,7 -0,5 -1,0 -0,6 -0,8 -0.5 -0,3 -0,9 -0,1 -0,930 -0,5 -0,5 -1,0 -0,6 -0,8 -0,5 -0,1 -0,6 0 -0,6

Cpe Average

H1 H2 L1 L2 H e L e

5o

-2.0 -1,5 -2,0 -1,5 -2.0 -2.010 -2.0 -1,5 -2,0 -1,5 -2.0 -2.015 -1.8 -0,9 -1,8 -1,4 -2.0 -2.020 -1.8 -0,8 -1,8 -1,4 -2.0 -2.025 -1.8 -0,7 -0.9 -0,9 -2.0 -2.030 -1.8 -0,5 -0,5 -0,5 -2.0 -2.0

(A)to a depth equal to b/2.

(B)of b/2 to a/2.

(C)Consider symmetric values across the axis of symmetry parallel to the wind.

Note: For wind at 0, in Parts I and J, which refer to their respective quarters, the coefficient of the form Ce has the following values:a / b = 1, shares the same value of H and L a / b = 2 - Ce = - 0.2. Linearly interpolated for intermediate values of a/b.


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17 NBR 6123/1988Table 7 - Pressure coefficients and external form, multiple roof, symmetrical in equal spans, with h a'

tomar o menor dos dois valores - take the smaller of the two valuestomar o menor dos tres valores - take the smaller of the three values

Inclination of

the roof

Angle of

incidence of

the wind

c

First scheme

(stretch)

First

intermediate

scheme

Other

intermediate

scheme

Last

scheme

Cpe Average

e a* b* c* d* m* n* X* z*

5o

10

20

30

45

0o

-0,9-1,1

-0.7,

-0,2

+0,3

-0,6

-0,6

-0,6

- 0,6

-0,6

-0,4

-0,4

-0,4

-0,4

-0,4

-0,3

-0,3

-0,3

-0,3

-0,4

-0,3

-0,3

-0,3

-0,2

-0,2

-0,3

-0,3

-0,3

-0,3

-0,4

-0,3

-0,3

-0,3

-0,2

-0,2

-0,3

-0,4

-0,5

-0,5

-0,5

-2,0 -1,5

Inclination of the

roof, Angle ofincidenceof the wind

Ce at the distance

b1 b2 b3


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y = h or 0.1 b (taking the smaller of the two values) y '= hor b or 0.26 to 0.1' (take the smallest of three values)

18 NBR 6123/1988Table 8 - Pressure coefficients and external form for multiple roofing, asymmetrical, in equal spans, withwater slope less than 60 and h a '

Angle of

incidence of

the wind

First scheme

(stretch)

First intermediate

scheme

Other intermediate

scheme

Last scheme Cpe Average

a* b* c* d* m* n* X* z*

0o

+0,6 -0,7 -0,7 -0,4 -0,3 -0,2 -0,1 -0,3 -2,0 -1,5180 -0,5 -0,3 -0,3 -0,3 -0,4 -0,6 -0,6 -0,1

Inclination of the

roof,

Ce at the distance

b1 b2 b3

90 -0,8 -0,6 -0,2

Notes: a) Friction forces:- For = 0 , the horizontal forces of friction values are already considered in the Table;- For = 90 , the horizontal forces of fr iction shall be determined according to section 6.4.b) Information on multiple roofs is still incomplete. Cases other than those considered in Tables 7 and 8 and Annex F should bespecifically studied.


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19 NBR 6123/1988

Table 9 - Distribution of external pressures on buildings of cylindrical circular section External pressure coefficientCpe

Rough surface or protrusions Smooth surface

h / d = 10 h / d


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20

NBR 6123/1988

Vento windFigure- 4:Coefficient of drag, Caparallel piped for buildings in low-turbulence wind

6.4 Coefficient of friction6.4.1In certain buildings, a strength friction should beconsidered (the force and direction of the wind, causedby roughness and ribs), as well as the calculatedas per 6.1 and 6.2.6.4.2For buildings current rectangular plan, thisfriction force should be considered only whenratio I2/ h or I2/I1, is greater than 4. For these buildings,the friction force F is given by:

F' = Cf, q I1 (I2 - 4 h) + Cf, q 2 h (I2 - 4 h), se h I1and for:

F' = Cf, q I1 (I2 - 4 I1) + Cf, q 2 h (I2 - 4 I1), se h I1

In each formula, the first term of the second membercorresponds to the friction force on the roof, and thesecond term, the friction force on the walls.The terms are given separately to allow the usedifferent values of Cf and q in the various surfaces..6.4.3The values of Cf, are as follows:a) Cf = 0,01 for surfaces without transverse ribs to the winddirection;

b) Cf, = 0,02 for surfaces with round ribs (undulations)traverse to the direction of the wind;

c) Cf, = 0,04 for rectangular ribbed surfaces homes crossto the direction of the wind.

6.4.4For single coverage, the friction force is determinedaccording to the instructions of 8.2.


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21 NBR 6123/1988

6.5 Reductions in form and coefficients of drag

6.5.1In general, the aerodynamic coefficient data, in thisstandard were obtained from tests in which the flow of airwas moderately smooth, about the type of wind thatappears in the open and flat (wind low turbulence). In highwind turbulence that appears in large cities, there is adecrease in suction network parallel piped of buildings withconsequent reduction of the corresponding coefficients,except for buildings with a relative depth / width of 1 / 3 orless.

6.5.2For buildings parallel piped exposed to winds of highturbulence, the following reductions are allowed:a) coefficient of leeward wall of form:consider 2 / 3 the value given in Table 4 (Wall B = 90 and wall D for = 0 );b) drag coefficient: Use the graph of the figure 5.

6.5.3 A building may be considered in wind high turbulence

when its height does not exceed two times the averageheight of buildings in the vicinity, these extending in thedirection and wind direction incident, a minimum distanceof:- 500 m, for a building of up to 40 m height;- 1000 m, for a building of up to 55 m of height;- 2000 m, for a building of up to 70m of height;- 3000 m, for a building of up to 80 m height ..6.6 Eccentricity of drag forces6.6.1The effects of the eccentricity of the drag force,should be considered, where necessary

6.6.2 In the case of buildings parallelpiped thedesign should take into account the following:- Due to wind forces acting perpendicular each one of thefacades, according to the specifications of this Standard;- The eccentricities caused by wind acting obliquely orneighborhood effects. The effort vices torsion then arecalculated from these forces acting, respectively, with thefollowing eccentricities, in relation to the vertical axisgeometry;- Buildings without neighborhood effects:and a = 0.075 to 0.075 and b = b- Buildings with neighborhood effects:and a = 0.15 to 0.15 and b = b,and being measured in the direction of the next largest,and b measured toward the smaller side, b.The effects of proximity will be considered only to theheight of the top (s) of building (s) located (s) in closewithin a circle of diameter equal to height of the buildingunder study, or equal to six times the side smaller building,b, whichever is the lesser of two values.

7 Coefficients of forces for prismatic bars lattices

7.1 Prismatic bars

7.1.1The force coefficients refer to light barscharacteristics of infinite length (two-dimensional flow). Toprismatic bars of finite length, the coefficients of force must

be multiplied by a factor K that depends on the ratio I/c, as follows:I = length of the prismatic barca = width of the prism as the direction perpendicular to thewind (the orthogonal projection section of the bar on a lineperpendicular to wind direction - see Note b) of Table 12)Note: Values of reduction factor K are given in Table 11.

7.1.2When a prismatic bar is connected to a plate orwall to prevent the free flow of air around this end of the

bar, the ratio I/cshould be doubled to determination ofK. When both ends of the bar prism are so clogged, the

ratio I/cshould be considered infinite.

7.1.3Bars which, by its size and speed characteristic of thewind, are in the flow mode above the critic may requireadditional calculations to verify to become greater forcesdo not occur at speeds below the maximum of the wind,with the subcritical flow mode.

7.2 Flat faces of prismatic barsThe force coefficients Cx and Cy given in Table 12 refer totwo mutually perpendicular directions, x and y, as shown inFig. The force coefficients refer to wind actingperpendicular to the longitudinal axis of the bar. Forcesrespondents are calculated by:

- Force in the x direction: Fx = Cx q K I c;- Force in the y direction: Fy = Cy q K I c.

7.3 Prismatic bars of circular sectionFor prismatic bars of circular section, the coefficientsdrag Ca depends on the value of Reynolds number,Re, and are provided in Table 13. The values of Ca datain this table apply to all surfaces roughness uniformlydistributed to height less than 1/100 the diameter d of thebar, ie. They are valid for all the finishings of normalsurface.

7.3.1 The drag force is calculated by:

Fa = Ca q K I d


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22 NBR 6123/1988

Table 10 - Coefficient of drag, Ca, for bodies of constant section

Wind perpendicular to plane of the figure

Continued

Planta- Plan , liso (metal, concreto, alvenaria rebocada) - smooth (metal, concrete, masonry plastered), com rugosidade ousalincias -with roughness or projections, Todos valores- All values, ELIPSE ELLIPSE


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23 NBR 6123/1988Continuation.

ContinuedTodos valores- All values


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24 NBR 6123/1988Continuation.

OCTOGONO OCTOGONAL, Todos valores- All values(A) Interpolate linearly for intermediate values of Re:Re = 70000 Vk I1 (Vk in m/s; I1 in m)

Figure 5 - Drag coefficient, Ca, parallelpiped for buildings in high wind turbulence


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25 NBR 6123/1988Table 11- Values of reduction factor, K, for bars of finite length

I/caor I/d 2 5 10 20 40 50 100 oo

Section of prismatic bars circular under

sub critics (Re < 4,2 . 105)

0,58 0,62 0,68 0,74 0,82 0,87 0,98 1,0

Section of prismatic bars

circular under the above critics

(Re > 4,2 . 105)

0,80 0,80 0,82 0,90 0,98 0,99 1,0 1,0

Faces of prismatic flat bars 0,62 0,66 0,69 0,81 0,87 0,90 0,95 1,0

Table 12- Coefficients of strength, Cx and Cy, for prismatic bars of flat faces of infinite length

Vento windNotes: a) In this table, the force coefficients Cx e Cyare given in relation to the size C and not as in other tables in relation to theeffective front area.b) The size cis used to determine the reduction factor K (See Table 11).


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26 NBR 6123/1988

Table 13 - Coefficient of drag, Ca, for prismatic bars circular cross section and infinite length

Flow mode (Re = 70000 Vk d)

[Vk in m/s; d in m ]

Ca

Sub critical Re < 4,2 . 105 1,2

Above 4,2 . 105Re < 8,4 . 10

50,6

of 8,4 . 105 Re < 2,3 . 10

60,7

critical Re 2,3 . 10

0,8

7.4 Wires and cablesFor wires and cable, the drag coefficients depend on Ca,the value of the Reynolds number Re and are given inTable 14, as follows:r = radius of wire or cable side of the layerexternal cabled = diameter of the circular section of the wire or cableI= length of wire or cable

7.4.1For wire and cable perpendicular to the direction ofwind, the drag force is calculated by:

Fa = Ca q I dIf the wind direction (supposed is horizontal) form anangle with the wire rope or cable, the force F,perpendicular to the rope, is calculated by:

Fy = Fa sen2 The force Fx in the direction of the rope, can beneglected.

7.5 Lattices of individual plansFor the purpose of this Standard is considered to bereticulated the whole structure consisting of straight bars.

7.5.1The drag force is calculated by:

Fa = Ca q Ae

Where:Ae = effective front area of the lattice: the projection areaof orthogonal grid of bars on a plane perpendicular to thewind direction. The graph in Figure 6 gives values of thecoefficient. Ca to drag a plane formed by lattice barsprismatic plane faces, and the graph in Figure 7 is thevalues of Ca to a lattice plane formed for bars of circularsection. The exposed area index is equal to the effectivefront area divided by the lattice of front area of the surfacebounded by the contour of the lattice.In lattices composed of rods of circular section, theReynolds number is given by:

Re = 70000 Vkd (Vk in m/s; d in m)

Where:d = diameter of the bars of the truss.In the case of lattices consisting of prismatic bars the flatfaces and / or bars of circular section of or more differentdiameters, the respective coefficients are applied inproportion to the frontal areas of respective bars (areas ofthe orthogonal bars on a plane perpendicular to the winddirection - "Shadow area"). The index refers to the exposedarea whenever the set of all lattice bars.

Table 14 - Coefficient of drag, Ca, for wires and cables with I/d = 60

Flow regime(Re = 70000 Vk d)[Vk in m / s, d in m]

Drag coefficient for CaFlat wire Wire moderately

smooth (Galvanized) orpainted)

Twistedcables finewire

Twisted cablesthick wire

Re 2.5. 104Re 4.2. 104Re 2.5. 105Re 4.2. 105

--1.20.5

--1.20.7

1.20.9--

1.31.1--

For Re and r / d intermediate Ca values are obtained by interpolation


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27 NBR 6123/1988

Figure 6 - Drag coefficient, Ca, for lattices plane formed by prismatic or slightly rounded corners bars

7.6 Lattices multiple planesThis section applies to a structure consisting of two or morelattice planes parallel and equidistant parallel banks, wherethe lattice the windward may have a protective effect onother lattices. The lattice windward and all other parts of

lattices are protected by the first and should be calculatedas indicated in 7.5. The wind forces in protected parts ofthe lattices should be multiplied by a factor of protection n(see Figure 8), which is depend on exposed area index ofthe grid located immediately upwind of the lattice understudy, and for their removal e/h.

7.6.1In the case of n lattices and also equal apart, the dragcoefficient of all the n lattices, Can, is given by:

Can=Ca1 [1 + (n-1) ]Where:C = drag coefficient of a lattice isolated hand, determined inaccordance with 7.5

7.6.2The drag force of the set of lattices is calculated by:

Fan = Can q Ae

7.7 Cross linked towers7.7.1Towers cross linked to triangular portion can becalculated in accordance with 7.6, focusing for windperpendicular to each pair of parallel faces.The force of the wind on their faces parallel to the directionof wind is considered null.

7.7.2Towers cross linked to square or triangularequilateral, with the same lattices in all faces, are specialcases for which can be convenient to determine the overallstrength of the wind directly.For these cases, the drag force is calculated by:

Fa = Ca q Ae

Where:A = effective front area of one side of the tower and crosslinked: the area of the orthogonal projection of on one sideof the cross linked tower of a plane parallel to this face.

7.7.2.1Cross link towers consist of prismatic flat faces barswith sharp corners or slightly rounded the coefficient ofdrag, Ca, focusing perpendicular windward side, areprovided in the graph of figure 9.

For crosslinked towers of square section, the coefficient ofwind drag with a focusing angle in relation to theperpendicular to the windward side, the Ca, is given by:

Ca= K CaWhere:

K = 1 + /125 ............... 0< 20K = 1.16 ....................... 20 < 45For towers cross linked in equilateral triangular section,the wind may be allowed for constant any angle ofincidence of the wind.

7.7.2.2Cross link towers consist of prismatic circular bars

section, the values of the coefficients of drag, Ca, areprovided in the graphs of Figures 10 to12.

7.7.2.3In the case of towers made of cross linkedprismatic bars of flat faces and / or circular section bars ofone or more different diameters, the respective coefficientsare applied proportionally to the front areas of therespective bars. The index of exposed area always refersto the group of all the bars on one side of the tower.

7.7.2.4 The components of drag force, F, in faces of thetower, are obtained by multiplying F by the values given inTable 15.


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28 NBR 6123/1988

Figure 8 - Drag Factor Ca, for for cross linked plane formed by bars of circular section


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29 NBR 6123/1988

Vento wind, trelica isolada- isolated latticesFigure 8 - Protection Factor t, for two or more equally spaced lattice planes parallel

Vento de qualquer direcao- Wind of any direction, Vento wind

Figure 9 - Coefficient of drag, Ca, for towers cross linked equilateral triangular and square section, bars formed by

prismatic or slightly rounded corners


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30 NBR 6123/1988

Figure 10 - Coefficient of drag, Ca, cross linked for towers of square section, made up of circular section bars - focusingWind perpendicular to two parallel faces

Figure 11 - Coefficient of drag, Ca, cross linked for towers of square section, , made up of circular section bars - Windfocusing a second diagonal.


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31 NBR 6123/1988

Figure 12 - Coefficient of drag, Ca, for towers crosslinked equilateral triangular section made up by circular section bars -Wind from any direction

Table 15 - Components of drag force on the faces of towers crosslinked equilateral triangular or square section

- Wind direction,n: component perpendicular to the face (side)t: a component parallel to the face.

Note: The components of drag force, Fa, are obtained by multiplying Fa, the values in this table, where n is the protection factordefined in 7.6.


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32 NBR 6123/19888 Coefficients of forces to walls, slabs and insulatedroofs8.1.1 The force F, acts perpendicular to the plane of thewall or plate.8.1 Walls and rectangular platesWind forces on a wall or rectangular plate is calculated by:F = CfqA

Where:C = coefficient of strength, as shown in Table 16q = dynamic pressure of the wind on top of the wall or plateA = face area:A = I hI = length of the wall or plateh = height of the wall or plate

8.1.1 The force F perpendicular to the plane of the wall orplate.

8.1.2Table 16 classifies the wall or plate according to flowconditions at its edges. Except for wall board or two-dimensional flow, the incidence of worst wind isoblique. This incidence and the point of application of F aregiven in this table.8.1.3The wall or plate is considered in two-dimensionalflow when l / h> 60, in the absence of plates or walls- Placed parallel to the flow at their ends or when l / h 10,where the presence of plates or walls or under theconditions indicated above.8.1.4For intermediate values of l / h - no plates orwalls at the ends - and for removal of the soil between 0and 0.25 h, values Cf. is obtained by inter linear polation.

Table 16 - Coefficients of strength, Cf, for walls and rectangular plates

without side plates


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42 NBR 6123/1988

ANNEX - A - Standard Speed S2 and time interval

A.1 Fator S,

The factor S2 can be considered as a dimension lessspeed, normalized in Vo:

Where:i = Category of roughness of the terrain (land)

Vt,i (z)= medium speed, at the time z above the ground tothe category I (Without considering the factors S1 and S3

The characteristic speed V are defined by:

Vk,i= VoS1 S2 S3

Regardless of the categories defined roughness of thisStandard, the factor S can be obtained by the expression:

S2 = b Fr,II(z/10)p

Values of parameters b, Fr,IIand p, for various intervalstime and for the five categories are presented in thisstandard as givens in Table 21. The corresponding valuesof S are given in Table 22.

Table 21 - Parameters b, p, Fr,II

Cat. t(s) 3 5 10 15 20 30 45 60 120 300 600 3600

1 b 1,10 1,11 1,12 1,13 1,14 1,15 1,16 1,17 1,19 1,21 1,23 1,25

P 0,06 0,065 0,07 0,075 0,075 0,08 0,085 0,085 0,09 0,095 0,095 0,10II b 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

P 0,085 0,09 0,10 0,105 0,11 0,115 0,12 0,125 0,135 0,145 0,15 0,16

1,00 0,98 0,95 0,93 0,90 0,87 0,84 0,82 0,77 0,72 0,69 0,65

III b 0,94 0,94 0,93 0,92 0,92 0,91 0,90 0,90 0,89 0,87 0,86 0,85

P 0,10 0,105 0,115 0,125 0,13 0,14 0,145 0,15 0,16 0,175 0,185 0,20IV b 0,86 0,85 0,84 0,83 0,83 0,82 0,80 0,79 0,76 0,73 0,71 0,68

P 0,12 0,125 0,135 0,145 0,15 0,16 0.17 0,175 0,195 0,215 0,23 0,25

V b 0,74 0,73 0,71 0,70 0,69 0,67 0,64 0,62 0,58 0,53 0,50 0,44P 0,15 0,16 0,175 0,185 0,19 0,205 0,22 0,23 0,255 0,285 0,31 0,35

A.2 Time IntervalTo determine the time interval t, use in obtaining theaverage wind speed which in a building or part of thebuilding with larger horizontal or vertical front surfaceexceeding 80 m, the expression can be used:

t = 7,5 L/Vt (h)

Where:L = Height or width of the front surface of the building orconstruction part of study, adopting the larger of the twovalues

Vt(h)= medium speed of the wind on t seconds,at the top of the building or part of the building

study - Vt(h) = S1 S2(h) VoThe calculation of Vt(h) can be done by successiveapproximations


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44 NBR 6123/1988Continuation


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45 NBR 6123/1988

ANNEX B S3 statistical factor for the probability Pm and lifetime of building m years

Let V+ o -wind speed which has a probability Pm to beexceeded at the site into account, at least once in a periodof m years.This speed corresponds to bursts of 3 s duration under theconditions of roughness category II (see 5.3.1), the height

of 10 m above the ground. The relationship between V+ oand the base speed is set in 5.1 andTherefore:

V+ o = S3 Vo

In the absence of specific regulations on safety inbuildings, or related information in the standard structuraluse, it is likely the designer to fix the P m and life accordingto the characterictics of building.

Table 23 shows typical values of the factor S3,whosemathematical expression is:S3 = 0.54 (In (1- Pm/m)

-0.157

Table 23 - Statistical Factor S3

S3 values for Pm,

m 0,10 0,20 0,50 0,63 0,75 0,90

2 0,66 0,76 0,64 0,60 0,57 0,5310 1,10 0,98 0,82 0,78 0,74 0,6825 1,27 1,13 0,95 0.90 0,85 0,7950 1,42 1,26 1,06 1,00 0,95 0,88

100 1,56 1,41 1.16 1,11 1,06 0,98200 1,77 1,57^ 1,31 1,24 1,18 1,09

In any case a factor can be adopted S, smaller than the suitable in the Table 3 (see 5.4).


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46 NBR 6123/1988ANNEX C - - Location and elevation of meteorological stations

Numbers next to circles that appear in fullFigure 1 identifies the meteorological stations of ServiceFlight Protection, the Ministry of Aeronautics,

Whose records were the basis for the preparation ofisopletas of this figure. The following table contains thealphabetical relationship of these stations and theirgeographical coordinates.

Sl. No. Station Latitude Longitude Height [m)


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47 NBR 6123/1988

ANNEX D - Determination of the coefficient of internal pressure

The flow of air through a small opening of area A is given

by:

Q = K ApV (D1)Where:K = flow coefficientV = air velocity at the opening:

p = density of air, assumed to be constant (ie. the air isconsidered incompressible)For n number of openings as established the balance, themass of air entering the building will be equal to what comesout. That is:

Q = 0According to (D.1) and (D.2):(D.3)As (D.1) and (D.2):

With good approximation, K can be considered constant.Recalling that:

(D.3) it is:

Experience shows that the expression above can beapplied to larger openings (windows, doors, gates,ventilation, permeability, disseminated, etc..), fromcoefficients that are considered medium pressurethe peripheries of the openings. These average rates,

to be designated by (Ce * and Ci*), can be bothcoefficients of form ((Ce and Ci)as the averages ofpressure coefficients, supplied or obtained in this Standardother sources.With this generalization (D.4) is:

The root is considered positive for all terms match with airinlet openings (and C *> C * i) and negative output gapswith air (and C *


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48 NBR 6123/1988

Local/Place

OpenArea (m

2)

Ce C,

+ 0,4 + 0,7 + 0,75

Ce - C i A.. Ce - C i A.. Ce - C i A..

A

B

C1e D1C2e D2

6,000.60

0,23

0,23

+0,8 .

-0,6

-1,0

-0,6

+0,4

-1,0

-1,4

-1,0

+3,79

-0,60

-0,27

-0,23

+0,1

-1,3

-1,7

-1,3

+1,90

-0,68

-0,30

-0,26

+0,05

-1,35

-1,75

-1,35

+1,34

-0,70

-0,30

-0,27

= - +2,69 - +0,66 - +0,07

By the sign of the last sum and considering a home

decimal cpi = + 0.8.2) Determination of cpiin an industrial building, with thegeometric and aerodynamic characteristics indicated inFigure 20. Coverage is considered impervious.

By the sign of the last sum and considering a home

decimal cpi = + 0.1.It is valid to apply the expression (D5) when the dynamicpressure only for reference or so can be consideredat all openings. Otherwise, it will be necessary river work

with the effective pressurepi, The constant being inside the building.

Vento wind Corte- sectionActual heirght of ventilation:- The lantern (I): 0.20 m- Fixed Venetians (blinds) (2): 1.00m

Figure 20 - Internal pressure in industrial building


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49 NBR 6123/19883 ) The second example of the same pavilion, but with only the gateway to windward.

Local/Place

OpenArea (m

2)

Ce C,

-0,4 -0,6 -0,5 -0,45

Ce - C i A.. Ce - C i A.. Ce - C i A.. Ce - C i A..

A

B

EF

GH

20

80

16

16

+0,7

-0,5

-1,2

-0,4

+1,1

-0,1

-0,8

0

+21,0

-25,3

-14,3

0

+1,3

+0,1

-0,6

+0,2

+22,8

+25,3

-12,4

+7,2

+1,2

0

-0,7

+0,1

+21,9o

-13,4

+5.1

+1.15

-0,05

-0,75

+0,05

+21,4

-17,9

-13,9

+3,6

= - -18,6 - +42,9 +13.6 - -0,8

For the sign of the last sum and considering a decimalplace, C = - 0.5.

4 ) The second example of the same pavilion, but thefacade with fixed louvers doors, located at windward.

To get the greatest value of internal pressure, the gates areconsidered closed.

Local/ Place Open Area(m

2)

Ce C,+0,4 +0,5

Ce - C i A.. Ce - C i A..

A 80 +0,7 +0,3 +43,8 +0,2 +35,8EF 16 -1,2 -1,6 -20.2 -1,7 -20,9GH 16 -0,4 -0,8 -14,3 -0,9 -15,2

= - +9,3 - -0,3

For the sign of the last sum and considering a decimal

place, Cpi = - 0,5.Notes: a) Improved accuracy is obtained if it is possible todetermine the average coefficient of pressureoutline of each opening (gates, doors, windows, fixedshutters, louvers, special tiles of ventilation, etc.).

b) The fourth example shows the beneficial effect of lantern(Open), which reduces the coefficient of 0.2 in internalpressure, which would no ridge vent, equal to coefficient ofexternal shape in the region of the opening:

+ 0.7. 6.2.5 The value indicated is slightly larger (+ 0.8), asopening provided therein may be dominant in a region ofhigher pressure than the average (+ 0.7).

c) Tests have shown that in both halls rectangular plan asin domes, the existence lantern in open because of adecrease in the coefficient aware of support, which isbetween 0.2 and 0.3.


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MEMORANDUM NO.Cimpor, Caxitu/Cezarina


Enclosure-2B

Content: Dynamic effects coefficients

Extract of NBR 6123 Forces due to Wind on Structures

Page 33-36, 4, 60-62

No of sheets: 8


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33 NBR 6123/1988

8.2 Isolated coverings of plane water8.2.1In isolated coverage, that is, on the small scale roofsupports and for this reason are not significant obstacle to

the flow of air, wind action is exerted directly on the facestop and bottom coverage.

8.2.2For the coverage to one or two isolated waterplane where the clear height between the floor and thelevel of the edge lower horizontal coverage satisfies theconditions of 8.2.3 and focusing perpendicular to the windgeneratrix of the cover, apply the coefficients indicated inTables of 17 and 18. These tables provide the value andthe senses of pressure coefficients, which include theactions that are exerted perpendicular, the two sides of thecover. In cases that are suitable products listed forshipments, the two situations of forces respectively shouldbe considered considered independently

8.2.3The coefficients of Tables 17 and 18 apply onlyapplied when the following conditions are met:

- coverings to a water (Table 17): 0 tg 0,7, h 0,5 I2;- coverings to two waters (Table 18): 0,07 tg0,6, h 0,5 I2;

Where:h = clearance between the floor and the level of thehorizontal edge drop of the covering.

I2= depth of the covering8.2.4For cases where the height h is below the set limit in8.23, or where obstructions may be placed under cover orclose to it, it must resist the action. Wind in the area ofobstruction, and closed the same coverage, with Cpi= + 0.8obstructions on the leeward edge, and Cpi= - 0.3 forobstructions on the windward edge.

8.2.5 For parallel wind to the generatrix of the coverage,must be considered horizontal forces of friction calculatedby the expression:

Fat = 0,05 q a b

a and b are the dimensions in plane coverage. Theseforces include the action of wind on two sides of thecoverage.

8.2.6Horizontal forces due to the action of wind onplates placed above or below the roof are calculatedaccording to 8.1 (walls and rectangular plates)being the face of the cover plate closer to the consideredas the land.

8.2.7In the case of lattices directly exposed to wind,should be adopted as outlined in 7.5 (Isolated latticeplanes) and 7.6 (multiple lattice planes).

8.2.8 In tabs, flat or nearly flat, existing along the edges ofthe coverage must be considered a pressure evenlydistributed, with the resultant force calculated by theexpression:

F = 1,3 q Ae- the tab for the windward;F = 0,8 q Ae, the tab to the leeward,

Aeis the effective front area of the plates and relatedelements forming the flap in the study. The previousexpressions are valid for flaps that form the vertical onemaximum angle of 30 . The forces thus calculatedinclude the pressures acting on both sides oftabs perpendicular to the direction of the wind.

8.2.9In tabs parallel to the wind direction horizontal forcesof friction should be considered and calculated byexpression:

Fat = 0,05 q Ae

and applied at mid-height of the tabs. These forces includethe action of wind on the two faces of the tabs.8.2.10Each sealing element shall be calculated

Cp = 2,0.

9 Dynamic effects due to atmospheric turbulence

9.1 General considerationsIn the natural wind, the magnitude and direction of thevelocity have instantaneous air velocity fluctuations aroundaverage V, called bursts. It is assumed that the averagespeed remains constant during the time of intervals of 10less or more, producing purely static effects, designatedbelow average response. Since the fluctuations of thevelocity are induce very flexible structures, especiallyin buildings tall and slender, major fluctuations indirection of average speed, designated as floatings.In buildings with fundamental period equal to or T1 lessthan 1s, the influence of fluctuating response is small,Its effects are already being considered in determining thetime interval adopted for the factor S2. However, buildingswith fundamental period greater than 1s, in particular thoseweakly damped, may have important response floating inthe medium wind. The total dynamic response equal to thesuperposition of the responses average and fluctuating,can be calculated according to the specifications of thischapter. Examples of calculations are given in Appendix I.


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34 NBR 6123/1988Table 17 - Coefficient of pressure in isolated coverings to plane water

Table 18 - Coefficient of pressure covers for two isolated symmetric to plane water

9.2 Input data for the determination of the responsemomentum in the direction of the wind

9.2.1 Speed design VpThe speed design corresponding to speed averaged over10 min to 10 meters above the ground, having Category IIis obtained by the product:

Vp = 0,69 VoS1S2

9.2.2 Dynamic characteristics of the structure9.2.2.1 Simplified continuous modelA simplified continuous model can be adopted when theconstruction has constant section and distribution at leastapproximately uniform mass. The simplified method isapplicable to you structure supported exclusively in thebase and less than 150 m, being considered in thedynamic response of these only the contribution in thefundamental way. In general, the alone retention in the firstway in the solution leads to less errors than 10%.It is admitted that the first vibration way can be representedaccurately by the equation:

x = (z/h)Table 19 presents approximate values of j and equation,too close together, allowing the calculation straight from thefundamental frequency f1 (Hz) for various types of unusual

buildings. Alternatively, f1 and j can be obtained employingmethods of the theory of vibrations of structures.The damping ratio is also critical as indicated in Table 19,depending on the type of structure.

9.2.2.2 Discreet modelIn the general case of a building with properties variableswith height, it must be represented by a discrete model, inaccordance with the scheme of figure 13, in which:

xi- coordinate displacement corresponding to the i;Ai - influence area corresponding to the coordinate i;mi- mass corresponding to the discrete coordinate i;Cai- - drag coefficient corresponding to coordinate izi- height of the element i on the ground level;zr- reference height: zr = 10 m;n - Number of degrees of freedom (i = 1, 2,... n).

In the case of vertical structures with symmetry plan, n isalso equal to the number of elements in which the structureis divided (see Figure 13).

In general, a model with n = 10 is sufficient to be obtainedan adequate accuracy in the results. Larger numberelements may be required to submit building along itsimportant variations in their characteristics. Once the modelstructure, should be determined using methods of the

theory vibration of structures, the natural frequency fj (Hz)and modally Xj,corresponding to the mode forj = 1,2, .... r, where r < the number of modes that will beretained in the solution. As stated in 9.2.21, the retention ofsingle mode (r = 1) is usually sufficient, except very slenderbuildings and / or stiffness strongly variable. In thesecases, should be computed successive mind thecontributions of modes 1, 2, etc. Until the associated withthe latter mode equivalent calculated (J = r) are negligible.

The critical damping ratio is shown in Table 19,depending on the type of building. Other values maybe adopted, if properly justified.


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35 NBR 6123/1988

Table 19 - Parameters for the determination of dynamic effects

Construction type T1= 1 / f1Buildings with concrete structure, without curtains 1,2 0,020 0,05h + 0,015h (h in

meters)

Buildings with concrete structure, with curtains for the absorptionof horizontal forces

1,6 0,015 0,05h + 0,012h

Concrete towers and chimneys, variable section 2,7 0,015 0,02hTowers, masts and chimneys concrete section uniform 1,7 0,010 0.01 h

Buildings with structural welded steel 1,2 0,010 0.29h-0.4Towers and steel chimneys, uniform section 1,7 0,008

Wood structures -- 0,030

Figure 13 - Schematic model for dynamical discrete

9.3Calculation of dynamic response in the direction ofwind9.3.1 Simplified method

The variation of the dynamic pressure with the height isexpressed by the equation:

In which the first term within the brackets correspond of theaverage response and the second represents themaximum amplitude response of floating, being:

q0= 0,613Vp2(qp in N/m2, Vp in m/s)

The exponent p and the coefficient b depend on thecategory of roughness of the ground, as indicated in Table20. The coefficient of dynamic amplification functiondimensions of the building, the damping ratio critical, thefrequency f (through the dimension less ratio Vp/ f L),isshown in the graphs of Figures 14 to 18,for the five categories of terrain roughness considered inthis Standard. The pressure q (z) is a continuous functionof height z on the the ground. The equivalent static force,which includes the static and dynamic actions of wind, per

unit time results equal to q(z) I1 Ca,being the width ordiameter of the building. The internal forces are calculatedin the structure of the usual form.


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9.3.2 Discreet model9.3.2.1 Determination of the modal contributions

For each vibration mode j, with components (xi)i = xi,Xi isthe total force due to wind direction in the coordinate i isgiven by:

Xi = Xi +Xi

in which the average force is equal to Xi (symbols: see9.2.2.2):

being: qo = 0,613 V" (q0 in N/m2, Vp in m/s)3 - b, p - - shown in Table 20.The floating component Xi is given by:

In the equations above, mo and Aodenote the mass of anarbitrary reference area is the coefficient of dynamicamplification, shown in Figures 14 to 18 for the fivecategories of land of this Standard. For situations nomeditated in these figures, it can be certain for interpolationor extrapolation.

9.3.2.2 Combination of the modal contributionsWhen r modes are retained in solution (r >1), the effect ofcombination can be computed by the root criteria of

squared sum of squares. After obtaining the responsefor each mode j (j = 1 ,.... r) must be determinedall variables of interest associated with each way.Indicating a static variable to any Qj(strength, bendingmoment, stress, etc..) or geometric (deformation,displacement, rotation), corresponding to the mode j, thesuperposition effect is calculated by:

The precedent equation is applicable when the naturalfrequencies fj (j = 1, r) are reasonably spaced, or whenthere are not very close frequencies.

9.4 Calculation of cross-wind dynamic responseThe random fluctuations of the orientation of the velocityinstanstaneous with respect to the average wind speed isresponsible for vibrations of the structure in the directionperpendicular to the direction of medium flow. Resultingrespeonse Y in the direction perpendicular to the wind

directioncan be calculated from the effective forces in thedirection of the wind through the expression:

Where appropriate, the response must be in the lateraldirection added to the response due to vortex shedding.

9.5 Calculation of maximum accelerations forverification comfortIn the case of buildings intended for human occupation,oscillations induced by fluctuating forces can cause

discomfort to occupants. If ujdenotes the level zdisplacements due to the fluctuating response modej, the maximum amplitude of acceleration at this level canbe calculated by the expression:

As a general indication of the maximum amplitude shouldnot exceeds 0.1 m/s2. The verification must be done fromthe comfort should be made for wind speeds for the most

likely to occurrence than the speed of structural design, tobe defined by the designer. It is conceivable that themaximum amplitude of acceleration is exceeded, onaverage days, once every ten years.

Table 20 - Exponent p and parameter b

Roughnesscategory

I II III IV V

p 0.095 0.15 0.185 0.23 0.31b 1.23 1.00 0.86 0.71 0.50


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40 NBR 6123/1988

Figure 17 Coeficient of dynamic amplification , for category of land IV (L = 1800m, h in meters)


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60 NBR 6123/1988ANNEXI- Determination of dynamic response due to atmospheric turbulence

I.1 Simplified Method

It will be the action of the wind speed in the direction ofaverage speed of a square section of building 120.00 mhigh and 24.00 m on a side, located in land category IV,with the speed Vo = 45 m / s and the parametersS1 = 1,0 and S3 = 1,0.

The following alternatives will be analyzed:- If: building with concrete structure, in which the horizontalforces are resisted only by porticoes.- Case b: same, with sturdy of steel structure (weldedjoints).

i.1.1It is estimated first (see 9.2.1):Vp = 0.69 x 45 x 1 x 1 = 31.05 m/s

I.1.2The fundamental periods, for both cases, were basedon measurements made in similar buildings. The modalform (parameter y) and damping ratio of criticism were

obtained from Table 19:- Case a: T1 = 1, 85 s, = 1, = 0,02;- Case b: T1 = 2,8 s, = 1, 0,01.

1.1.3Determination of the coefficient of dynamicamplification :- Case a: V /f L 31,05 x 1,85 x 1800 0,032

From Figure 17, we obtain, for I1/h = 24/120 = 0.2and = 0.02:h (m): 25,100,300 1.69,1.16, 0.62- Case b: V /f L 31,05 x 2,8/1800 0,048

FromFigure 17, we obtain for I1/h= = 24/120 = 0,2and = 0.01:h (m): 25,100,300 1.50,0.88The corresponding values h = 120 m can be determined by

interpolation, as illustrated in Figure 25, resulting in:- If a: = 1.07 (concrete);- Case b: = 1.40 (steel).Calculate the following (see 9.3.1):

The dynamic pressure variation with height is given byexpression (q in N/m2, z in m):

Case a:

At the top of the building (z = 120 m), the dynamic pressureresults equal to 1693 N/m2 in the case of building with concretestructure and 1925 N/m2 in the case of building with steelstructure. The static method leads to a single value of 1557N/m2 (category IV, class C, low wind turbulence):

I.1.4The equivalent static force per unit of time is obtained bythe expression (see 9.3.1):q (z) I1 CaI1 is the width of the building, equal to 24.00 m. The coefficienttrawling, Ca, is obtained from the graph in Figure 4, or, forrare cases of high wind turbulence, the graph of Figure 5, itsvalue being considered vary with Z.I.2 Discrete modelIt will be the action of the wind speed in the direction of averagespeed of a reinforced concrete chimney with characteristicsshown in Table 34. The properties the model adopted in thedynamic analysis are indicated in Table 35. The properties ofthe model adopted in the dynamic analysis are given in theTable 35, adopting a damping ratio critical = 0.01. The dragcoefficient is Ca = 0.6, and in view of the Reynolds number androughness surface water of the chimney.As V0 = 39.4 m / s, S1 = S3 = 1, the design speedresults equal to:

The land has roughness Category III. Figure 16, up toV / f L = 0.58, values of for h = 25, 100 and 300 m andrelationships I / h = 0 and 0.2. By interpolation, come to= 1.43. From Table 20, we obtainp = 0.185 and b = 0.86.

Next, it is estimated (see 9.3.2):

The interpolation is it possible to determine as given in Figure

26, while Table 36 shows work of calculation for determiningthe forces in chimney to the fundamental mode of vibration (j =1).


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61 NBR 6123/1988Formulas (see 9.3.2.1) and the auxiliary values:

Concrete structure Steel Structure Category IVFigure 25 - Determination of graphical dynamic amplification coefficient of

Linear interpolationFigure 26 - Graphical Determination of the coefficient of dynamic amplification


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Enclosure-2C

Content: Roof shape coefficients

Extract of NBR 6123 Forces due to Wind on Structures

Page 50-58

No of sheets: 9


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51 NBR 6123/1988

E.1.3The pressure coefficients shown in Tables 27 to 29are based on tests on flow turbulent air, with the outersurface roughness coverage of the model defining points of

separation flow corresponding to Reynolds numbers abovethe critical region. These values should be consideredwith caution, since the distribution of pressures curvedsurfaces depends on several factors, such asindicated in E.1.1.The models were tested in a smallerplant, b, equal to 20 m (S1 series) and 50 m (S2 series).The characteristics of the simulated winds are as follows:

- Series S1 - I1, = 11 % and L1/b = 1,5(constant withheight)Where:l1 = the longitudinal component of turbulenceL1 = macroscale of this component

The value of these tests I1 corresponds to wind on groundcategory between l and ll.

- Series S2 - l1 = 15,5% e l1/b = 1,6(top cover)

The simulated wind is between the categories lll and IV(P = 0.23).The pressure coefficients in Table 27 correspond to windblowing perpendicular to the generatrix of the coverage.The arch is divided into six equal parts, with the pressurecoefficient assumed constant in each one of six parts (seeFigure 22-a).The pressure coefficients in Table 28 corresponds the windblowing parallel to the generatrix of the coverage. TheCoverage is divided into the wind, in four parts, as shownin Figure 22-b, and the coefficient considered constantpressure in each of the four parts.

The pressure coefficients of Table 29 correspond to suctiontips that can occur with oblique wind.These coefficients are assumed constant in respectivetracks (see Figure 22-c).

Table 24 - External pressure coefficients,Cpe,for wind blowing perpendicular to the generatrix of the covering

f/i2 h/l2

Cpefor a part

1 2 3 4 5 6

0 +0,3 -0,3 -0,6 -0,7 -0,6 -0,2

1/8 -0,5 -0,5 -0,7 -0,7 -0,5 -0,2

1/5 1/4 -0,9 -0,6 -0,8 -0,8 -0,4 -0,2

1/2 -1,2 | -0,7 -0,9 -0,8 -0,3 -0,2

1 -1,4 -0,8 -0,9 -0,9 -0,4 -0,4

5 -1,8 ! -1,0 -1,1 -1,2 -0,8 -0,7

1/8 -1,0 -0,4 -0,4 -0,4 -0,4 -0,3

1/10 1/4 -1,2 -0,5 -0,4 -0,4 -0,4 -0,3

1/2 -1,5 -1.0 -0,7 -0,5 -0,4 -0,3

1 -1,6 -1,0 -0,8 -0,6 -0,4 -0,3

Table 25 - Coefficients of external pressure, C pefor windblowing parallel to the generatrix of covering Table 26 - Coefficients of external pressure, Cpeobliquely tothe wind blowing generatrix of coveringPart of the covering Part of the covering

Table 27 - Coefficient of external pressure, Cpeand for wind blowing perpendicular to the generatrix coveringfor a part

For a Series S2: hb/b.


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Table 29 - Coefficient of external pressure, Cpefor wind blowing obliquely to the generatrix of coveringSerial for a srip (band)

For a Series S2: hb/b.

E.2 DomesIn the same way that as for the cylindrical vaults of circular

section, only approximate values of Cpe can be given tothe domes, due to the variation of distribution of pressurewith the characteristics of the wind, the relationshipbetween the dimensions of the building and outer surfaceof the dome. Special studies should be made in the case oflarge domes.

E.2.1 Domes on the groundTypical distributions of isobars (lines of equal Cpe) domebased directly on the ground are given in Figure 23, for f/d= 1 / 2 and 1 / 4.

E.2.1.1 Limit values of the coefficients of external pressurethe positive (over-pressure) and negative (suction) aregiven in Table 30 for various relationships arrow / diameter(f / d).For intermediate relations, the coefficients are obtainedby interpolation. The same table shows the values the lift

coefficient, Cs, being the sustentation force madecalculations by the expression:

Where:

q = dynamic pressure of the wind on top of the dome

d = diameter of the circle of the base of the domeE.2.1.2The lift (sustentation) force acts in the verticaldirection of bottom up.

E.2.2- Cylindrical dome wallsA dome on a cylindrical wall has a wider range of values ofthe pressure coefficient outside than when based directlyon the land. Typical distributions of isobars are given inFigure 24. No pressure area in the domes with f / d lessthan 1 / 5 and the wall height from d / 4.

E-2.2.1Limit values of the coefficients of external pressurepositive (overpressure) and negative (suction) are given inTable 31. For intermediate relations f /d and h/d, thecoefficients are obtained by interpolation


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54 NBR 6123/1988

a)Elevation

Wind

b) Top view: isobars of the coefficientsexternal pressure for f/d = 1 / 2

c) Top view: isobars of the coefficientsexternal pressure for f /d = 1 / 4

Figure 23 - Dome on the ground (land), isobars

Table 30 - Limit values of the coefficients of external pressure, C pe, and lift coefficients, Cs - Domes on the groundOverlay Suction


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56 NBR 6123/1988ANNEX-F - Additional Information

Results of recent trials are presented in this Annex, whichare applicable to buildings with relations between thedimensions indicated in the respective tablaes.Extrapolations can be made for proportions next to them.The tests were conducted with simulation of the maincharacteristics of natural winds and can be applied to anycategory of land, with tolerable error.Surfaces in considerable variations that occur pressurewere subdivided and coefficients C are given to each part.

For areas with high suctions, figures are average pressurecoefficients (C average), which should only be used for thecalculation of forces.Wind in the respective areas, applying the scalingverification and anchoring elements suction and secondarystructure.

Valid observations are given in 6.1.3.

Table 32 - Pressure coefficients and form, external, with gable roof, symmetrical, central trough, in buildings of rectangularplan (use S2 corresponding to the height h)


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58 NBR 6123/1988ANNEX- G - Effects of neighborhood

There are certain situations where it is necessary toconsider the influence of buildings located in the vicinity ofthat in study. These buildings can cause increased

wind forces in three different ways:

G.1 For the VenturiNeighboring buildings for their size, shape and guidance,may cause a "bottleneck" of the wind, acceleratingair flow, with consequent change in pressures. This effectappears mainly in buildings of very close, if they have beenobserved coefficients of negative pressure (suction)exceeding, in module, the value 2.0. These suction tipswere verified in bordering on the walls of two buildings,near the windward edge.

G.2 For wind deflection in the vertical directionTall buildings deflects downward part of the wind focuseson the windward facade, increasing the speed in closeareas close to the ground. Building more low, located inthese areas, may have loads of Wind increased by thiseffect, with the coefficients form reaching values between -1.5 and - 2.0,

G.3 For the wake turbulenceA building located in the lee of another can be significantlyaffected by the turbulence generated in this area of thewindward building, may cause Dynamic (effects "blow"),and considerable changes in the pressures. These areparticularly important in buildings with roofs and fencepanels made of lightweight materials

G.4 Determination of the effects of neighborhoodIt is not possible to specify numerical values for theneighborhood of a generic way and normative.These effects can be determined by tests of wind tunnel,which reproduce the conditions of neighborhood and thecharacteristics of natural wind can influence theoutcome. The problem is compounded the possibility ofunfavorable changes of conditions neighborhood during thelife of the building in the study.

A rough indication of increases which may suffer theeffects of aerodynamic coefficients for neighborhood will begiven below.it is:S= distance between the planes of the faces borderingtwo high neighboring buildings,axb, being in plandimensions of buildings (ax b between 1 x 1 and 4 x 1)

d * = the smaller of the two dimensions:- smaller side b;- semi diagonal a

2+b

2

FV = factor of effect of neighborhood, defined byrelationship:FV: C in the building with the neighborhood /C in the isolated building

C = drag coefficient under study ((Ce, cpe medium, Ca)

The representative values of VF are:- For drag coefficient, Ca (see Figures 4 and 5); for formcoefficient, Ce and average value of and pressurecoefficient, c average wall Standing confrontational (facesparallel to the wind as given in Table 4):s/d* 1,0 .......... FV = 1,3s/d* 3,0 .......... FV = 1,0

- To form coefficient, Ce - the average value of pressurecoefficient, Cpe - secondary covering (See Table 5):

s/d*0,5 .......... FV = 1,3s/d* 3,0 .......... FV = 1,0

Linearly interpolated for intermediate values of s / d *.

The effects of neighborhood factors are considered toheight of the top of the surrounding buildings.The tests are based on the recommendations beforeowners were made with two or a few models approximatelyequal heights. For the case of many neighboring buildingsin these conditions, the factors of neighbouring willgenerally be smaller and may be below 1.0. However,there may be effects of wind FV cause values close tothose indicated above mind, especially when there are"gaps" in the vicinity of the building under study.

Neighborhood effects in torsion coefficient, Ct, wereconsidered in 6.6.


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Enclosure-2D

Content: Criteria for structural integrity

Extract of NBR 8800 Design of steel and composite Steel-concrete structures

Page 34 & 35

No of sheets: 2


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ABNT NBR 8800:2008

If Ssecis less than ST, STbwill be negative, indicating that the torsional restraints of the beam are not effective due toinadequate stiffness to the distortion of the web.

When the stiffeners are required, they should be extended to the full height of the restrained bar and it should berestrained and fixed to the flange if the torsional restraints is also fixed to the flange. Alternatively, it is allowed to placethe stiffeners at intervals by distance equal to 4tw to any flange of the beam that is not directly attached to the torsionalrestraints. When the spacing of the restraints points is less than Lqb,then Lbbcan be taken equal Lqt.

4.11.3.8 For the continuous torsional restraints, the same expressions should be used as given in 4.11.3.7, taking L/nequal to 1,00, the moment and the stiffness per unit of length and the stiffness to the distortion of the web, Ssec, is givenby:

4.12 Structural integrity

4.12.1The structural design, provide a structure capable to meet the ultimate and service limit states for the period ofintended useful life for the construction, it should allow the fabrication, transportation,handling and assembly of thestructure in an appropriate way and in good conditions of safety. It should still take into account the need of futuremaintenance, demolition, recycling and reutilization of materials

.4.12.2 The basic anatomy of the structure for the which the actions are transmitted to the foundations should be clearlydefined. Any characteristics of the structure with influence of its global stability should be identified and properlyconsidered in the design. For effective use of this subsection, each part of a building between expansion joints should betreated as single building.

4.12.3 The structure should be designed as a three-dimensional entity and should be robust and stable under normalloading conditions and in the event of occurence of accident or used inadequately should not suffer this disproportionatedamages to their causes. To meet these strict requirements, in the absence specific studies, one can follow therequirements given in 4.12.4 to 4.12.8.

4.12.4 Each columns of a building shall be effectively supported by means of horizontal braces (restraints) at least in twodirections, preferably orthogonal, at each level supported by that columns including roofs, according to the Figure-3.

4.12.5 Continuous Lines of braces should be placed closest to edges of the floors or roofs and in each columns line, andthe reentrant corners must be appropriately connected to the structure, in accordance with the Figure-3.

34 ABNT 2008 - All rights reserved


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ABNT NBR 8800:2008

Figure-3 - Example of bracing of the columns of a building4.12.6 The horizontal braces can be made of steel profiles, including those used for other puposes such as floor beamsand roofing or the slabs connected to the columns and the remaining steel structure..4.12.7 The horizontal braces and their respective connections should be compatible with the other elements of thestructure of the which they are part of and designed for the calculated actions and also to withstand tension, which shouldnot be added to other actions, least of 1% of the calculated force on the columns or 75 kN, which ever is greater. In thecase of roofs or f loors without concrete slabs, the bracing should be designed to withstand the calcualted compressive ortensile force, which should not be added to the other action, at least 75 kN. In addition the braces should also meet theapplicable requirements as given in 4.11.

4.12.8 In the buildings of multiple floors, when the rules require that the accidental faliure of the columns doesn't causeprogressive collapse, the beams and their connections to the columns should be designed to withstand the the isolatedaction of the tensile force corresponding to vertical reaction of calculation obtained from ultimate combination ofpermanent actions and the direct results of use and occupancy of the construction. It is permitted, in that case, a morerigorous analysis, considering large displacements and large deformations. Additionally the amendments of columnsshould be able to withstand tensile force corresponding to the highest reactions calculated, obtained fro

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