3D Wind-Load Generator - Openings - Internal pressure determination
Since version 22, the possibilities of the 3D Wind-Load Generator have been expanded in order to consider influence of the openings on the C_pi internal pressure coefficients. The implementation has been conducted in accordance with EN 1991-1-4:2005 (E), chapter 7.2.9.
New wind data property - Openings
For wind data of type wall, a new check box "openings" has been introduced. If this is activated, it is possible to define the area of the openings (in square meters) of the corresponding wind-data and a check box "dominant face" is available to be activated.
Default value for the area of openings is 0 m2, and the input value is limited to the area of the item the wind-data is assigned to. E.g. for wind-data assigned to a wall, if value larger then the wall surface is input, the value is replaced by the wall surface.
Internal pressure coefficient (Cpi) determination
Based on the presence of openings in the structure envelope, 3 options of internal pressure coefficient determination exist.
A) There are no openings in the building envelope at all
In case there are no openings in the building envelope at all, the internal pressure coefficients are considered by the value which is input in the corresponding load case (automatically determined within the generated load cases, or possibly altered by the user).
In this case, for each load direction, there are two sets of C_pi values considered - positive and negative C_pi, and these values are used in the corresponding load cases.
While using the "add wind load cases" within the "3D wind load generator" - the default values for +/- C_pi are defined in accordance with chapter 7.2.9 (6) Note 2 of EN 1991-1-4:2005 (E), hence +0.2 and -0.3
It is possible to alter these C_pi values either before the automatic generation of the load cases (figure above), or within the load case if already generated (figure below)
Note: Since v 22, there is a change in the logic of C_pi input for a load case due to certain internal reasons and consistency with 3D wind generator. Each wind load has a defined direction, and under the direction angle input slot, there are two slots to define C_pi negative and positive. Afterwards, the option "utilized Cpi value" is defined, which determines what C_pi (either negative or positive) should be considered for that particular load case. See the figure above.
An example is provided below.
There is a simple structure with no openings in wall wind-data defined at all.
For load case "3DWind1 - 0, +CPE, +CPI" which considers the wind in x direction (0°), and positive value for C_pi (default value has been kept according to 7.2.9 (6) Note 2 of EN 1991-1-4) - hence +0.2, for all the wind data entities, this value is considered (see the figure below).
Note: In SCIA, the signs of C_pi and C_pe are exactly opposite to the EN convention. In EN documentation, positive values mean pressure, and negative suction, as defined in the figure 5.1. EN 1991-1-4 - figure below. In SCIA however, the positive load on surface is defined in the same direction as the normal of this surface. Normal is visible for the outer surface (blue arrow, which should point out of the building). For internal surface, the normal would be the opposite to the outer surface normal. See the figure from SCIA below. There, for zone E (wall), the C_pe as defined in EN has negative value (-0.42 = suction), and C_pi positive (+0.2 - hence pressure on the internal surface). For walls, there is no difference for +/- C_pe (which is applicable for roof zones only) - hence for this LC for wall zone "- sign" (EN), suction, is considered (in SCIA +0.42 due to surface normal), and the positive internal pressure C_pi is in SCIA interpreted as -0.2. The net pressure will then be determined as: w_net = q_p(z) * (C_pe - C_pi) = q_p(z) * (0.42 - (-0.2)) = q_p(z) * 0.62 ; where q_p(z) is the peak pressure dependent on the height z.
B) There are openings defined in the building envelope, but no face is set as "dominant"
In this case, the internal pressure coefficient C_pi is determined in accordance with 7.2.9 (6) of EN 1991-1-4, hence from the figure below, which defines the C_pi as a function of the opening ratio μ and the ratio of the height to the depth of the building h/d. The C_pi should be determined for each wind direction.
In this case (if there is at least one 3d-wind data entity with opening defined), the values of C_pi from load cases are ignored.
For the calculation of μ, be aware of the different convention of the +/- signs for C_pe in SCIA, which are opposite to EN convention. For the formula above, the "area where C_pe is negative" means "negative by EN convention", hence, suction (Fig. 5.1. EN 1991-1-4), hence in SCIA positive values of C_pe.
An example is provided below for wind in x direction on a simple structure.
opening ratio μ = (13 + 17) / (13 + 17 + 22) = 0.576923
h = 7 m ; d = 10 m (for x direction, depth of the structure); h / d = 0.7
By interpolation in the graph, value +0.034 is determined for the C_pi. Hence in SCIA convention, "-" sign is used for C_pi coefficients for all the load cases with this wind direction, no matter what is the setting within the load case. The C_pi values from load case influence the considered values only if there are no openings in the structure defined!
Second example for the wind direction in y axis (the same structure geometry from above):
opening ratio μ = (13 + 17 + 22) / (13 + 17 + 22) =1.0
h = 7 m ; d = 18 m (for y direction, depth of the structure); h / d = 0.38889
By interpolation in the graph, value -0.337 is determined for the C_pi. Hence in SCIA convention, "+" sign is used for C_pi coefficients for all the load cases with this wind direction, no matter what is the setting within the load case.
C) There are openings defined in the building envelope with some face set as "dominant"
If a certain 3D wind data property of wall type is considered as "dominant face", the C_pi is determined in accordance with equations 7.1 and / or 7.2 from chapter 7.2.9 (5) of EN 1991-1-4, hence:
When the area of the openings at the dominant face is twice the area of the openings in the remaining faces, C_pi = 0.75 * C_pe
When the area of the openings at the dominant face is at least three times the area of the openings in the remaining faces, C_pi = 0.90 * C_pe
For both cases, the C_pe is the value for external pressure coefficient in the dominant face. When there are more zones with different values of C_pe, an area weighted average value of C_pe is used.
When the area of the openings at the dominant face is between 2 and 3 times the area of openings in the remaining faces, linear interpolation for C_pi is used.
When the area of the openings at the dominant face is smaller then 2 times the area of openings in the remaining faces, a warning is shown (and such area is treated as no dominant, with C_pi determination conducted as for no dominant face - chapter B of this help-page):
Example: in the example below, the dominant face has openings of 5 m2 , two of the other faces each 1 m2. Are of the opening at the dominant face (5 m2) is between twice and three times the area of the openings at the remaining faces (exactly in the middle between 4 and 6). Hence, C_pi = 0.825 * C_pe, where C_pe is -0.76, therefore C_pi = -0.627 .
For the wind in y direction, weight average of the C_pe (1.2, 0.8 and 0.5) of dominant face is used (with value C_pe = 0.652), hence C_pi = 0.825 * 0.652 = 0.5379
Only one face needs to be considered as dominant. If there are more areas set as dominant by the user, only the one with the largest value for openings is considered as dominant.
In case one of several areas within one continuous plane is considered as dominant, all the areas within that plane are treated as the dominant face.
An example is provided below. The bottom wall which is in one continuous plane is divided into 4 walls, each with some defined openings (see figure). Only one of this walls is defined as the dominant (the one with only 2 m2of openings). Furthermore, there is another wall on the opposite side set as dominant with 3 m2of openings). Areas at the bottom face are merged (for the purpose of opening and dominant face evaluation), because these are in the same continuous plane. The opening areas are summed up (3*15+2). A warning is issued, that multiple dominant faces were detected, and only the one with the highest opening value is treated as dominant (the bottom wall in the example, as this is compared after any area merges within one face).
Only the areas in the continuous plane are merged for the purpose of dominant face evaluation, if not continuous, these are treated separately (example below)
Additional information
In accordance with 7.2.9(2) EN 1991-1-4, when in at least two sides of the buildings (facades) the total area of openings in each side is more than 30% of the area of that side, the actions on the structure should not be calculated from the rules given in this chapter, but the rules of chapters 7.3. and 7.4. (canopies, free standing walls, parapets, fences). There is no automatic check of this value, the user should choose himself how to proceed.
The clauses 7.2.9 (3) , (4), (7) and (8) from EN 1991-1-4 are not included in this functionality.