The option for automatically generating Wind and Snow 2D/3D loads according to Eurocode 1 in Robot is based on the European standard: EN 1991-1-4:2005 for wind and EN 1991-1-3:2003 for snow. In addition, this option generates wind and snow loads according to the National Application Documents (NAD) of many European countries.
Wind load
The load is generated for typical workshop structures with repeating frames along the length of a structure. Wind loads are generated as uniform or trapezoidal loads on bars in the local direction Z with respect to the bar length. The load sign depends on the direction the wind is acting on an element.
For a 2D structure, a linear load on a bar is calculated as a product of wind pressure q and the distance between frames, that is, spacing e. For the outermost frame, one-half of the spacing is considered. A wind load according to the EC1 code, is generated separately for each of the repeating frames, because the code designates successive zones (A, ... , J) of different wind pressure. If a given frame and its spacing belongs to more than one zone, the value of pressure q is calculated in proportion to the frame participation in each zone (as shown in following image).
The pressure acting on a given area is calculated as the difference of external and internal pressures according to the formula:
q = q b * c s c d * Ce (ze) * (Cpe - Cpi),
Where:
- q b - Reference mean velocity pressure
- c s c d - Structure coefficient as a product of the size coefficient and the dynamic coefficient
- Ce - Exposure coefficient for the reference height ze
- Cpe - External pressure coefficient
- Cpi - Internal pressure coefficient
The following shows the calculation methods for the components in the previous formula.
qb
The reference mean velocity pressure can be specified directly by a user or can be calculated based on the wind velocity value from the formula (4.10):
qb = (1.25/2) * Vb * Vb
In some of the codes (EC1-PL and EC1-FR), the pressure value is determined by default based on the region.
The reference wind velocity in the formula above is computed using formula (4.1):
Vb= Cdir * Cseason * Vb,0
Where:
- Cdir - Direction factor a user specifies globally for all wind directions (except for EC1-PL, where the Cdir value depends on the wind direction).
- Cseason - Temporary (seasonal) factor a user specifies globally for all wind directions.
- Vb,0 - The basic value of the reference wind velocity as given in annexes for individual countries.
The reference wind velocity is most often specified as the velocity having the annual probability of exceedence p = 0,02, that is, having a mean return period of 50 years. If a different return period is needed, the wind velocity is calculated using formula (Cprob - 4.2):
Vb,0 = Vb * Cprob(K, p, n)
Where:
- K - Shape parameter (default value K = 0.2) specified by a user.
- p - The annual probability of exceedence (default value p = 0.02) specified directly by a user or specified as an inverse of the structure life time in years
- n - A representative value of n = 0,5 is assumed.
CsCd
The value of the structure coefficient that is defined directly by a user. By default, value 1 is used.
Ce (ze)
The exposure coefficient considers the influence of roughness of the terrain Cr and topography Co on the mean wind velocity depending on the height above ground level z. The roughness coefficient is determined by the formula 4.4 EN 1991-1-4. The variables in this formula are defined by selecting a terrain type from the drop-down list prepared according to table 4.1 EN 1991-1-4.
The topography coefficient accounts for the growth of wind speed over isolated hills or escarpments. It is assumed as constant, specified by a user. Its value is used in compliance with the annex to EN 1991-1-4.
Cpe
The external pressure coefficient is used automatically based on the recognized shape of a roof. The following surface types and their pressure coefficients are assumed according to EN 1991-1-4:
- Vertical walls of buildings, Cpe according to table 7.1 (fig. 7.5)
- Flat roofs, Cpe according to table 7.2 (fig. 7.6)
- Monopitch roofs, Cpe according to table 7.3a and 7.3b (fig. 7.7)
- Duopitch roofs, Cpe according to table 7.4a and 7.4b (fig. 7.8)
- Multispan roofs, Cpe according to figure 7.10
Vaulted roofs and domes are not supported by the general EC1 algorithm for generating loads. They are available in Robot for the EC1-SERRES code.
Cpi
The internal pressure coefficient is used, by default, according to point 7.2.9 (6) as extreme values (fig. 7.13):
- Cpi = 0,8 pressure (+) case
- Cpi =-0,5 pressure (-) case.
When the Tight structure option is selected, the coefficient Cpi = 0,0 is used.
Snow load
Snow loads are generated as uniform or trapezoidal loads on bars in the vertical global direction Z minus, referred to the length projected onto the horizontal direction X. Loads are applied to elements that are not vertical (that is, not parallel to Z axis). For a 2D structure, a linear load applied to a bar is calculated as a product of snow pressure S and spacing between frames spacing e.
The value of a snow load is calculated from the formula (depending on the conditions):
- Normal conditions (5.1)
S = μi * Ce * Ct * sk
- Accidental conditions - accidental precipitation (5.2)
S = μi * Ce * Ct * Cesl * sk
- Accidental conditions - accidental snowstorms (5.3)
S = μi * sk
Where:
- μi - Snow load shape coefficient, as indicated in the following relationships
- Ce - Exposure coefficient is 1.0
- Ct - Thermal coefficient is 1.0
- Cesl - Accidental snow load coefficient is 2.0
- sk - Characteristic value of the snow load on the ground, specified by a user or dependent on a selected zone.
The following load arrangements according to point 5.3 are considered:
Monopitch roofs
Value of the μi coefficient according to table 5.2
Load arrangements: uniform load arrangement μ 1 (α) (fig. 5.2).
Duopitch roofs
Value of the μi coefficient according to table 5.2
Load arrangements:
- Uniform load arrangement μ 1 (α 1 ) and μ 1 (α 2 ) (fig. 5.3(i))
- Load arrangement consisting of one-half of the load intensity 0.5*μ 1 (α 1 ), acting on one roof pitch and non-uniform load arrangement equal to μ 1 (α 2 ), acting on the other roof pitch (fig.7.3 (ii))
- Non-uniform load arrangement equal to μ 1 (α 1 ), acting on one roof pitch and load arrangement consisting of half of the load intensity 0.5*μ 1 (α 2 ), acting on the other roof pitch (fig. 7.3(iii)).
Multipitch roofs
Value of the μi coefficient according to table 5.2
Load arrangements:
- Uniform load arrangement, as above (fig. 5.4(i))
- For cases not fulfilling the conditions as in fig. B1 - non-uniform load arrangement, μ 1 (α i ) on the extreme roof pitches, linearly-varying load arrangement with the extreme μ 2 (α m ), where α m =( α 1 + α 2 )/2 on internal roof pitches (fig. 5.4(ii))
- For cases fulfilling the conditions as in fig. B1 - non-uniform snow drift loading, coefficient μ 1 (fig.B.1), where μ 1 according to B2(2).
Cylindrical roofs
This type of roof is not supported by the general EC1 algorithm for generating loads. They are available in Robot for the EC1-SERRES code.
Roofs with abrupt changes of roof height
The snow drift loading is not supported correctly.