NBR 6123 Building Construction - Bases For Design of Structures - Wind Loads [PDF]

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ABNT - Brazilian Association of Technical Norms WIND LOADS ON BUILDINGS Procedure Origin: Project NB-599/1987 CB-02 – Brazilian Civil Construction Committee CE – 02:003.16 – Commission for the Study of Wind Loads on Buildings NBR 6123 – Building construction – Bases for design of structures – Wind loads - Procedure Descriptors: Wind. Edification Incorporates Errata no 1 of Dec. 1990 Reprinting of NB-599 of Dec. 1987 __________________________________________________________________ Keywords: Wind. Building  66 pages __________________________________________________________________ ABSTRACT 1.Objective 2.Letter conventions 3.Definitions 4.Procedure for the calculation of wind loads on buildings 5.Characteristic wind speed 6. Aerodynamic coefficients for current buildings 7.Force coefficients for prismatic bars and grids 8.Wind load coefficients for walls, boards and isolated roofs 9.Dynamic effects due to atmospherical turbulence ANNEX A- Normalized speed S2 and time intervals ANNEX B-S3 statistical factor for Pn probability and useful life of buildings in m years ANNEX C-Location and altitude of meteorological stations ANNEX D-Determination of the internal pressure coefficient ANNEX E- Aerodynamic coefficients for curved roofs ANNEX F-Additional data ANNEX G-Neighborhood effects ANNEX H-Aerodynamic effects on slender and flexible buildings ANNEX I-Determination of the dynamic response due to atmospherical turbulence Index

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1 Objective 1.1 This Norm establishes the conditions exigible in the consideration of the forces due to stactic and dynamic wind loads for buiding calculation purposes 1.2 This Norm is not applicable to buildings of unusual forms, dimensions or location, in which cases special sudies must be undertaken to determine wind acting loads and their effects. Experimental results obtained in wind tunnels, with the simulation of the major feature of natural wind, can be used as a replacement for the coefficients contained in this Norm. 1.3 Letter conventions For the effects of this Norm, letter conventions from 2.1 to 2.3 are adopted. 2.1 Roman capital letters A – Area of a flat surface on which wind load is calculated from form coefficients C e and Ci (surface perpendicular force) and attrition coefficient C f (surface tangential load) Reference area for calculation of load coefficients Ae – Actual frontal area: orthogonal projection area of the building, structure or structural element on a plane perpendicular to wind direction (“shadow area”); used in calculating drag coefficient Ai – Area of influence corresponding to coordinate I Ao – Area of reference Ca – Drag coefficient; Ca = Fa / qA Cai – Drag coefficient corresponding to coordinate I Ce – Outer form coefficient; Ce = Fa / qA Cf – Force coefficient; Cf = F / qA C’f – Attrition coefficient; Cf = F’a / qA Ci – Inner form coefficient; Ci = Fi / qA Cx – Load coefficient in direction x; Cx = Fx / qA Cy – Load coefficient in direction y; Cy = Fy / qA F – Load on a flat surface of area A, perpendicular to the surface 2

F’ – Force of attrition on a flat surface of area A, tangent to the surface Fa – Drag force: force component due to wind in wind direction Fe – Force external to the building acting on a flat surface of area A, perpendicular to that surface Fg – Global wind load: resultant of all forces exerted by the wind on a building or part of it Fi – Force internal to the building acting on a flat surface of area A, perpendicular to that surface Fr – Gust factor Fx – Wind load coefficient in direction x Fy – Wind load coefficient in direction y L – Height h or width l of the frontal surface of a building to determine time interval t Characteristical dimension of (L = 1,800 m) used to determine the dynamic amplification coefficient Pm – Probability of a given wind speed being exceeded at least once in a period of m years – Static (force, flector moment, tension, etc.) or geometrical variable (deformation, dislocation, turn) Re – Number of Reynolds S1 – Topographic factor S2 – A factor considering the influence of rugosity of the terrain, of the dimensions of the building or part of the building under study and of its height on the terrain S3 – A factor based on probabilistic concepts T – Fundamental period of the structure Vo – basic wind speed: speed of a 3-second gust, exceeded on the average once in 50 years, 10 m above the terrain, in open flat terrain Vk – Characteristic wind speed:

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Vk = Vo S1 S2 S3____________ – Project speed:

– Average wind speed in t seconds at a height h above the terrain (z) – Average wind speed in t seconds at a height z above the terrain for category i (not considering the S1 and S3 parameters) Xi – Total wind load in the direction of coordinate i – Average Xi force – floating component of Xi 2.2 Roman small letters a – Longer side: the larger horizontal dimension of a building Dimension between supports of a structural part b – Smaller side: the smaller horizontal dimension of a building Dimension of a structural part according to wind direction Meteorological parameter used to determine S 2 c – Reference dimension in flat prismatic bars Distance from plate or wall edge to point of application of F cas – Surface drag coefficient cp – Pressure coefficient: cp = cpe - cpi cpi – External pressure coefficient: cpo = pe / q cpi - Internal pressure coefficient:

cpo = pe / q

ca – Width of a prismatic bar measured in a perpendicular direction with the wind d – Diameter of a circular cylinder Diameter of the circle of the base of a cupula Level difference between the base and top of a hill or slope 4

ea – Excentricity in the direction of dimension a, in relation to the vertical geometric axis of the building eb - Excentricity in the direction of dimension b, in relation to the vertical geometric axis of the building f – arc height of a cylindrical vault or cupula Natural vibration frequency h – Height of a building above the terrain, measured to the top of the cover plate or weatherboard level. Height of a wall or board Height for determination of the average speed l – length of a bar, wall or board l1 – length: horizontal dimension of a building perpendicular to wind direction Dimension of reference on the frontal surface of a building l2 – Depth: dimension of a building in the direction of the wind m – useful life of a building, in years mo – Discrete mass of reference mi – Discrete mass corresponding to coordinate i n – Number of freedom degrees p – Exponent of the potential variation law of S 2 q – Dynamic wind pressure, corresponding to the characteristic speed V? under normal pressure ( 1 atm = 1013,2 mbar = 101320 Pa) and temperature (15 o C) conditions

t – time interval for determination of the average wind speed xi – dislocation corresponding to coordinate i – Vibration mode

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z – Height above the terrain zo – Rugosity length z01 - Rugosity length of the terrain located windward of a rugosity change z02 – Rugosity length of the terrain located leeward of a rugosity change zg - Gradient height: height of the atmospheric limit layer zi – Height of the structure’s i element above terrain level Height above the terrain up to which average speed profiles are defined by the rugosity of the terrain situated at leeward of the rugosity change line, for z 01 < Z02 zx - Height above the terrain up to which average speed profiles are defined by the rugosity of the terrain situated windward of the rugosity change line, for z 01 < Z02 zr – Height of the reference: Zr = 10 m 2.3 Greek letters a -Angle of incidence of the wind, measured between wind direction and the larger side of the building b – Central angle between wind direction and the radius passing through the point considered in the periphery of a circular cylinder. Dp – Efective pressure on a point in the surface of a building: D r = Dpe - Dpi Dpe – Effective external pressure: difference between atmospheric pressure on a point in the outer surface of the building and the atmospheric pressure of the incident wind, windward of the building, in the air stream undisturbed by the presence of obstacles Dpi – Effectice internal pressure: difference between atmospheric pressure on a point in the inner surface of the building and the atmospheric pressure of the incident wind, windward of the building, in the air stream undisturbed by the presence of obstacles h – Protection factor in parallel grids q – Angle of inclination of roofs

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Angle of inclination of the average surface of slopes and hill sides, in airstream considered as bi-dimensional x – Mechanical amplification coefficient – Exposed area rate: actual frontal area of a grid divided by the frontal area of the surface limited by the grid’s contour

z – Damping rate 3. Definitions Definitions from 3.1 to 3.9 have been adopted for the purposes of this Norm. 3.1 Windward Direction from which the wind blows, in relation to the construction. 3.2 Grid - Any structure made of straight bars. 3.3 Overpressure Effective pressure above the reference atmospheric pressure (positive). 3.4 Leeward Direction opposite to that from which the wind blows, in relation to the construction. 3.5 Suction Effective pressure below atmospheric pressure of reference (negative). 3.6 Frontal surface The surface defined by the orthogonal projection of the construction, structure or structural element over a plane perpendicular to wind direction (“shadow surface”). 3.7 Basic wind Wind to which corresponds basic speed Vo. 3.8 High-turbulence wind Wind according to 6.5.3.

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3.9 Low-turbulence wind All the remaining types of wind. 4 Procedure for calculation of forces due to wind loads on buildings Wind loads on buildings must be calculated separately for: a) Covering elements and their fastenings (tiles, glass panes, frames, panels, etc.); b) Structural parts (roofs, walls, etc.); c) The structure as a whole. 4.1 Wind loads on partially-erected structures Wind loads on a partially-erected structure depend on the method and sequence of construction. It is reasonable to admit that the wind’s maximum characteristic speed will not occur over a short time period. Thus, verification of the safety of a partially-erected structure may be done with a lower characteristic speed (see 5.4 and Group 5 of Table 3). 4.2 Determination of the static forces due to the wind The static forces due to the wind are determined as follows: a) the basic wind speed, Vo suitable to the location where the structure will be built is determined in accordance with the disposed in 5.1; b) the basic wind speed is multiplied by the factors S 1, S2 and S3 to obtain the wind characteristic speed Vk for the part of the construction considered, in accordance with 5.2 to 5.5:

c) wind characteristic speed allows for the calculation of the dynamic pressure through the expression:

, Where (SI units): q in N/m2 and Vk in m/s 4.2.1 Pressure coefficients As the wind load depends on the pressure differential between the opposite faces of the part of the building under study, the pressure coefficients are given for external and internal surfaces. For the objectives of this Norm, it is understood that

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the effective pressure Dp on a point on the surface of a construction is the value defined as:

Where: Dpe = effective external pressure Dpi = effective internal pressure Thus:

Where: Positive values of external or internal pressure coefficients correspond to overpressures, and negative values to suctions. A positive value for Dp indicates an effective pressure with the direction of an external overpressure, and a negative value for Dp indicates an effective pressure towards an external suction. 4.2.2 Form coefficients The wind force exerted over a flat element of a building of area A acts in a perpendicular direction, and is given by:

Where: Fe = force external to the building, acting on the flat surface of area A Fi = force internal to the building, acting on the flat surface of area A Thus:

Where: Ce = external form coefficient: Ce = Fe / qA Ci = external form coefficient: Ci = Fi / qA 9

Positive values of the external and internal form coefficients correspond to overpressures, and negative values correspond to suctions. A positive value for F indicates that this force acts inward, and a negative value indicates that it acts outward from the building. For the cases foreseen in this Norm, internal pressure is considered as evenly distributed inside the building. Thus, in flat internal surfaces, c pi = Ci . 4.2.3 Load coefficients The global wind force on a building or part of it, F g, is obtained by the vectorial addition of the wind forces acting on it. The global force component in the direction of the wind, drag force F a, is obtained by:

Where: Ca = drag coefficient Ae = effective frontal area: area of the orthogonal projection of the building, structure or structural element over a plane perpendicular to wind direction (“shadow area”) In general, any component of the global force is given by:

Where: Cf = force coefficient, specifying each case: Cx, Cy, etc. A = area of reference, specified in each case 4.3 Determination of the wind’s dynamic effects For the determination of the dynamic effects due to atmospheric turbulence, see the calculation guide in Chapter 9 and examples in Annex 1. 5 Characteristic speed of the wind 5.1 Basic wind speed, Vo

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The basic wind speed, V o, is the speed of a gust of 3 s, exceeded on average once in 50 years, 10 m above the terrain, in open, level terrain. Note: Figure 1 presents a graph of the basic speed isoplets in Brazil, with 5 m/s intervals (see Annex C).

5.1.1 As a general rule, it is accepted that basic wind can blow from any horizontal direction. 5.1.2 When in doubt in selecting basic speed and in buildings of exceptional importance, a specific survey is recommended to determine V o. In such a case, preferential directions may be considered for the basic wind, if properly justified. 5.2 Topographic factor, S1 The topographic factor, S1, takes into consideration the terrain relief variations, and is determined as follows: a) level or slightly rough terrain: S1 = 1.0 b) slopes and hills: -

elongated slopes and hills where a bi-dimensional air flow can be admitted blowing in the direction indicated in Figure 2; at point A (hills) and at points A and C (slopes): S 1 = 1.0; at point B: [S1 is a function of S1 (z)]:

[make linear interpolation for 3o < q < 6º < 17 < q < 45º ] Where: z = height measured from the surface of the terrain at the point considered

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d = level difference between the base and the top of the slope or hill q = average incline of the slope or hillside Note: Between A and B and between B and C, the S 1 factor is obteained by linear interpolation.

The values indicated in 5.2-b) and 5.2-c) are an initial approximation and should be used with caution. If a more in-depth knowledge of the topographic relief influence is needed, or if the application of these indications is made difficult due to the complexity of the relief, assays with topographic models in wind tunnels or anemometric measurements on the terrain itself are recommended.

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Figure 1 – Isoplets of basic speed Vo (m/s)

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Figure 2 – Topographic factor S1 (z) 5.3 Rugosity of the terrain, building dimensions and height above the terrain: Factor S2 Factor S2 takes into account the combined effect of the rugosity of the terrain, of the variation in wind speed with the height above the terrain and of the dimensions of the building considered or part of it.

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In strong winds in neutral stability, wind speed increases with the height above the terrain. This increase depends on the rugosity of the terrain and the time interval considered in determining speed. This time interval is related with the building’s dimensions, since small buildings and building elements are more affected by short-duration gusts than large constructions. For the latter, it is more suitable to consider the average wind calculated within a greater time interval. 5.3.1 Rugosity of the terrain For the purposes of this Norm, the rugosity of the terrain is classified into five categories(2): Category I: Smooth surfaces of large dimensions, with over 5 km, measured in the course and direction of the incident wind. Examples: -

calm sea(3): lakes and rivers; swamp with no vegetation.

Category II: Open terrain, level or nearly level, with few isolated obstacles, such as trees and low constructions. Examples: -

level coast zones; swamps with scattered vegetation; air fields;

-

prairies and barren lands; farms without fences or walls.

The average height of obstacle tops is considered inferior or equal to 1.0 m. Category III: Level or undulated terrain with obstacles, such as fences and walls, few wind-breaking trees, low and scattered constructions. Examples: -

ranches and country cottages, except the parts with dense vegetation/forests; farms with fences and/or walls; suburbia far away from city center, with low, scattered housing.

Notes: (2) Depending on the project designer, intermediate categories may be considered, interpolating conveniently p and b values or S2 values indicated under 5.3.3 or in Annex A. (3) For battered seas, the value of exponent p for 1 h can reach 0.15 in violent gusts. Generally, p = 0.12

The average height of obstacle tops is considered as 3.0 m.

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Category IV: Terrain covered with numerous, tightly spaced obstacles, in forest, industrial or urbanized zones. Examples: -

park zones and woods with many trees; small towns and their vicinity and outskirts; densely developed suburbia of large cities; industrial areas totally or partially developed.

The average height of obstacle tops is considered as equal to 10 m. This category also includes zones with larger obstacles that still cannot fit under category V. Category V: Terrain covered with multiple large, high and tightly packed obstacles. Examples: -

forest with high trees, with isolated tops; large city downtown centers; highly-developed industrial centers.

The average height of obstacle tops is considered equal or greater to 25 m. 5.3.2 Dimensions of the construction Wind speed varies continually, and its average value can be calculated over any time interval. It has been verified that the shortest interval of usual measurements (3 s) corresponds to gusts which dimensions conveniently involve obstacles of up to 20 m in the direction of the average wind. The greater the time interval used in the calculation of the average speed, the larger the distance covered by the gust of wind. To define those parts of the construction to consider in determining wind actions, it is necessary to take into account constructive or structural characteristics originating little or no structural continuity along the building, such as: -

buildings with joints separating the structure in two or more structurally independent parts; buildings with little rigidity in the direction perpendicular to that of the wind and, thus, with little load-redistribution capacity.

The following classes of buildings, building parts and their elements were chosen with time intervals for the calculation of the 3-s, 5-s and 10-s average speed respectively:

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Class A: All coverings, their fixation elements and individual parts of structures without cover. Every building in which the larger horizontal or vertical dimension does not exceed 20 m. Class B: Every building or building part in which the larger horizontal or vertical dimension of the frontal surface is between 20 m and 50 m. Class C: Every building or building part in which the larger horizontal or vertical dimension of the frontal surface exceeds 50 m. For every building or building part in which the larger horizontal or vertical dimension of the frontal surface exceeds 80 m, the corresponding time interval can be determined in accordance with the indications of Annex A. 5.3.3 Height above the terrain The S2 factor used in the calculation of wind speed at a height z above the general terrain level is obtained by the expression:

, and the gust factor Fr always corresponds to category II. The expression above is applicable up to height zg, which defines the upper contour of the atmospheric layer. The parameters that allow determination of S 2 for the five categories in this Norm are presented in Table 1. The values of S2 for the different categories of terrain rugosity and classes of building dimensions defined in this Norm are displayed in Table 2. To study the covering elements, it is recommended to use the S 2 factor corresponding to the top of the building. This recommendation is based on the fact that in the windward façade and lateral façades the wind is deflected downwards, with the consequent increase in aerodynamic pressure on the lower part of the building. For the same reason, the S 2 factor is considered as constant up to a height of 10 m in category V. 5.3.3.1 Annex A indicates the determination of the S 2 factor for time intervals between 3 s and 1 h for any terrain rugosity.

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Table 1 – Meteorological parameters Classes Category

I

II

Zg (m)

Parameter A

B

C

b

1.10

1.11

1.12

p

0.06

0.065

0.07

b

1.00

1.00

1.00

300

F1 P b

1.00 0.085 0.94

0.98 0.09 0.94

0.95 0.10 0.93

350

p

0.10

0.105

0.115

b

0.86

0.85

0.84

p b

0.12 0.74

0.125 0.73

0.135 0.71

p

0.15

0.16

0.175

250

III

IV

420

V

500

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Table 2 – S2 factor Category

z

I

II

Class

Class

Ill

IV

Class

V

Class

Class

(m) A

B

C

A

B

z02) The height zx is determined by the expression:

The profile of average speeds (S2 factors) is defined as follows (see Figure 3-b): a) from the zx height upwards, the S2 factors corresponding to the terrain farthest from the building (z01) are considered; b)from the zx height downwards, the S2 factors corresponding to the terrain around the building are considered, but without exceeding the value of S2 determined at the height zx for the terrain of rugosity z01. 5.5.2 The heights of the limit layers, z g, in the average speed profiles fully developed and the lengths with rugosity zo are the following: Category zg (m) zo (m)

I 250 0.005

II 300 0.07

III 350 0.30

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IV 420 1.0

V 500 2.5

Figure 3 – Profile of S2 leeward of a rugosity change 6. Aerodynamic coefficients for current buildings (see also Annexes E and F) 6.1 Pressure and form coefficients, external 6.1.1 Values of the pressure and form coefficients, external, for several types of buildings and for critical wind directions are given in Tables from 4 to 8 and in Figures and Tables of Annexes E and F. Surfaces where considerable variations of pressure take place were subdivided, and coefficients are given for each of the parts. 6.1.2 Zones with high suctions appear next to the edges of walls and roofs, and their location depends on the angle of incidence of the wind. Thus, these high suctions do not appear simultaneously in all these zones, for which the tables show average values of external pressure coefficients (average c pe). These coefficients must be used only to calculate wind forces in the respective zones, and are applied to the dimensioning, verification and anchoring of covering elements and of the secondary structure. 6.1.3 For the calculation of enclosing elements and their fastenings unto structural parts, the factor S2 corresponding to class A should be used, with the average value of Ce or cpe applicable to the zone where the respective element is located. For the calculation of the main structural parts the S 2 factor corresponding to class A, B or C should be used, with the value of C e applicable to the zone where the respective structural part is located. 6.1.4 To determine external pressures on a cylindrical building with circular section, the values of cpe given in Table 9 must be used. These coefficients are applicable only for the flow above the critical region, that is, for a number of Reynolds Re > 420000 and wind inciding perpendicularly to the axis of the cylinder, of diameter d. The number of Reynolds is determined by the expression:

with Vk given in meters per second and d in meters. 6.1.5 The coefficients of Table 9 are applicable to cylinders with a vertical axis (chimneys, silos, gasometers, reservoirs, etc.), or with horizontal axis (reservoirs, aerial pipings, etc.), provided that, in the latter case, the free distance between the cylinder and the terrain is not shorter than the diameter of the cylinder. These coefficients depend on the h/d ratio between the length of the cylinder and its diameter, for the case of wind flowing freely by only one of the cylinder’s extremities. In the case of wind flowing freely by both extremities of the cylinder, the value of h to consider for the calculation of the h/d ratio must be half of the cylinder’s length.

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6.1.6 The coefficients of Table 9 are also applicable in the cases where the terrain is replaced by level horizontal or vertical surfaces sufficiently large in relation to the cylinder’s transversal section, in such a way as to originate wind flow conditions similar to those caused by the terrain. 6.2 Internal pressure coefficients 6.2.1 If the building is totally airtight, the pressure inside will be invariable over time and independent from the speed of the outside air flow. However, the walls and/or roofs of buildings considered as closed allow, in service conditions or by accident, the passage of air, changing the ideal conditions supposed in the assays. As long as permeability does not exceed the limits indicated in 6.2.3, it may be admissible that the external pressure is not modified by permeability, and the internal pressure must be calculated in accordance with the specifications given below. 6.2.2 For the purposes of this Norm, the following constructive elements and coverings are considered impermeable: reinforced or prestressed concrete slabs and curtains; mortar, stone, brick, concrete block or similar material walls, without doors, windows or any other openings. The remaining constructive elements and coverings are considered permeable. Permeability is due to the presence of openings, such as joints between enclosure panels and between tiles, apertures on doors and windows, ventilation openings in tiles and roofs, open door and window gaps, chimneys, lanterns, etc. 6.2.3 The permeability index of a part of a building is defined by the relation between the area of apertures and the total area of this part. This index must be determined with the greatest precision possible. As a general indication, the typical permeability index of a building for housing or office use, with all windows and doors closed, is between 0.01% and 0.05%. For the application of the items in 6.2, with the exception of the case of a dominant aperture, no wall or roof pitch permeability index can exceed 30%. The determination of this index must be made with caution, in view of the fact that changes in permeability during the useful life of the building may lead to more unfavourable loading values. 6.2.4 For the purposes of this Norm, the dominant aperture is one which area is equal to or greater than the total area of the other apertures that constitute the permeability considered over the whole external surface of the building (including the roof, if there is a ceiling permeable to air or in the absence of ceiling). This dominant opening may occur by accident, such as the rupture of fixed glass panes caused by wind pressure (overpressure or suction), objects thrown by the wind or other causes. 6.2.5 For buildings with permeable internal walls, the internal pressure can be considered as uniform. In such a case, the following values must be adopted for the internal pressure coefficient cpi:

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a) two opposite faces equally permeable; the other faces impermeable: -

wind perpendicular to one permeable face: cpi = + 0.2

-

wind perpendicular to one impermeable face: cpi = - 0.3

b) four faces equally permeable: cpi = - 0.3 or 0 (consider the most noxious value); c) dominant aperdure on one face; the others have equal permeability: -

dominant aperdure on the windward face.

Proportion between the area of all openings in the windward face and the total area of openings in all faces (walls and covering, in the conditions of 6.2.4) submitted to external suctions:

-

dominant aperture in the leeward face.

Adopt the value of the external form coefficient, C e, corresponding to this face (see Table 4). - dominant aperture in one face parallel to the wind - dominant aperture not located in a zone with high external suction Adopt the value of the external form coefficient, C e, corresponding to the location of the opening in this face (see Table 4). -

dominant aperture located in a zone with high external suction

Proportion between the area of the dominant aperture (or area of the apertures located in this zone) and the total area of openings in all faces submitted to external suctions:

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Zones with high external suction are those marked in Tables 4 and 5 (average C pe). 6.2.6 For effectively wind tight buildings and having fixed windows with negligible prospects of being broken by accident, consider the most noxious of the following values: cpi = - 0.2 or 0 6.2.7 When it is not considered necessary or when it is not possible to determine with reasonable exactitude the permeability ratio in 6.2.5-c), the same value of the external form coefficient C e (for 0o and 90o wind incidence) indicated in this Norm for the zone where the dominant aperture is located should be adopted for the value of the internal pressure coefficient, in walls as well as roofs. 6.2.8 Openings in the roof will influence the stresses on the walls in the cases with permeable ceiling (natural porosity, trap-doors, non-windtight light/power boxes, etc.) or no ceiling. In the opposite case, these openings are of interest only for the study of the roof structure, its supports and covering, as well as for the study of the ceiling itself. 6.2.9 The value of cpi may be limited or controlled advantageously by the purposeful distribution of permeability in the walls and cover, or by a ventilation device acting as dominant aperture in a position with suitable external pressure value. Examples of such devices are the following: -

ventilated ridges in roofs submitted to suctions for all wind orientations, causing a reduction of the ascensional force on the roof; permanent apertures in the walls parallel to wind direction and situated near the windward edges (high external suction zones), causing an important reduction of the ascensional force on the roof;

6.2.10 In the scope of application of Table 9, for the calculation of the forces due to wind on the wall of a cylindrical building having an open top, the following values should be adopted for cpi:

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6.2.11 For cases not considered from 6.2.5 to 6.2.7, the internal pressure coefficient can be determined in accordance with the indications contained in Annex D.

Table 4

-

Pressure and form coefficients, external, for walls of buildings with rectangular plan Values of Ce for

Relative height

v =0°

average cpe

v = 90°

A1 e B1

A2eB2

C

D

A

B

C1 e D1

C2 e D2

-0.8

-0.5

+ 0.7

-0.4

+ 0.7

-0.4

-0.8

-0.4

-0.9

-0.8

-0.4

+ 0.7

-0.3

+ 0.7

-0.5

-0.9

-0.5

- 1.0

-0.9

-0.5

+ 0.7

-0.5

+ 0.7

-0.5

-0.9

-0.5

- 1.1

-0.9

-0.4

+ 0.7

-0.3

+ 0.7

-0.6

-0.9

-0.5

- 1.1

-1.0

-0.6

+ 0.8

-0.6

+ 0.8

-0.6

-1.0

-0.6

- 1.2

- 1.0

-0.5

+ 0.8

-0.3

+ 0.8

-0.6

- 1.0

-0.6

- 1.2

Notes: a) For a/b between 3/2 and 2, make linear interpolation. b) For wind at 0o in parts A3 and B3 the form coefficient Ce has the following values: -

for a/b = 1: same value of parts A2 and B2; for a/b ≥ 2: Ce = - 0.2; for 1< a/b < 2: linear interpolation.

c) For each wind incidence angle (0o or 90o) the average external pressure coefficient c? is applied to the windward part of the walls parallel to the wind, within a distance equal to 0.2 b or h, considering the lesser of these two values. d) To determine the drag coefficient Ca the graph of Figure 4 (lowturbulence wind) should be used, or that of Figure 5 (high-turbulence wind – see 6.5.3).

Table 5 – Pressure and form coefficients, external, for two-pitch roofs, symmetrical, in rectangular buildings.

Values of Ce for

q v = 90°

Relative height

(A)

Average cpe

v = 0°

EF

GH

EG

FH

0°

-0.8

-0.4

-0.8

-0.4

-2.0

-2.0

-2.0

5o

-0.9

-0.4

-0.8

-0.4

-1.4

-1.2

-1.2

10° 15° 20° 30°

-1.2 -1.0 -0.4 0

-0.4 -0.4 -0.4 -0.4

-0.8 -0.8 -0.7 -0.7

-0.6 -0.6 -0.6 -0.6

-1.4 -1.4 -1.0 -0.8

-1.4 -1.2

45°

+0.3

-0.5

-0.7

-0.6

-1.1

60°

+0.7

-0.6

-0.7

-0.6

-1.1

0o

-0.8

-0.6

-1.0

-0.6

-2.0

-2.0

-2.0

__

o

5 10°

-0.9 -1.1

-0.6 -0.6

-0.9 -0.8

-0.6 -0.6

-2.0 -2.0

-2.0 -2.0

-1.5 -1.5

-1.0 -1.2

15°

-1.0

-0.6

-0.8

-0.6

-1.8

-1.5

-1.5

-1.2

20° 30° 45°

-0.7 -0.2 +0.2

-0.5 -0.5 -0.5

-0.8 -0.8 -0.8

-0.6 -0.8 -0.8

-1.5 -1.0

-1.5

-1.5

-1.0 -1.0

60°

+0.6

-0.5

-0.8

-0.8

0o

-0.8

-0.6

-0.9

-0.7

-2.0

-2.0

-2.0

o

5 10°

-0.8 -0.8

-0.6 -0.6

-0.8 -0.8

-0.8 -0.8

-2.0 -2.0

-2.0 -2.0

-1.5 -1.5

-1.0 -1.2

15°

-0.8

-0.6

-0.8

-0.8

-1.8

-1.8

-1.5

-1.2

20° 30°

-0.8 -1.0

-0.6 -0.5

-0.8 -0.8

-0.8 -0.7

-1.5 -1.5

-1.5

-1.5

-1.2

40°

-0.2

-0.5

-0.8

-0.7

-1.0

50° 60°

+0.2 +0.5

-0.5 -0.5

-0.8 -0.8

-0.7 -0.7

-1.0 -1.2 -1.2 -1.2 -1.1

DETAIL 1

TABLE 6 – Form and pressure coefficients, external, for single-pitch roofs, in rectangularplan buildings, with h/b