PowerFrame Part 3 - Wind and Snow Loads.pdf

Part 3: PowerFrame Wind & snow loads generators (Eurocode 1)

© BuildSoft nv All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, electronic or manual, for any purpose, without the prior written consent of BuildSoft. The programs described in this manual are subject to copyright by BuildSoft. They may only be used by the licensee and may only be copied for the purpose of creating a security copy. It is prohibited by law to copy them for any other purpose than the licensee’s own use. Although BuildSoft has tested the programs described in this manual and has reviewed this manual, they are delivered ‘As Is’, without any warranty as to their quality, performance, merchantability or fitness for any particular purpose. The entire risk as to the results and performance of the programs, and as to the information contained in the manual, lies with the end-user.

PowerFrame Manual – Wind & snow loads generators

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© BuildSoft nv All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, electronic or manual, for any purpose, without the prior written consent of BuildSoft. The programs described in this manual are subject to copyright by BuildSoft. They may only be used by the licensee and may only be copied for the purpose of creating a security copy. It is prohibited by law to copy them for any other purpose than the licensee’s own use. Although BuildSoft has tested the programs described in this manual and has reviewed this manual, they are delivered ‘As Is’, without any warranty as to their quality, performance, merchantability or fitness for any particular purpose. The entire risk as to the results and performance of the programs, and as to the information contained in the manual, lies with the end-user.


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1 Table of contents 1

TABLE OF CONTENTS ................... ............................. ................... ................... .................... ................... ................... ...................3 .........3

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WIND LOADS GENERATOR ................... ............................ ................... .................... ................... ................... ...................4 .........4

2.1 WIND LOADS GENERATOR ( EC 1) .................. ............................ .................... ................... ................... .................... .............. ....4 4 2.1.1 Introduction .................. ............................ .................... ................... ................... .................... ................... ................... ...................4 .........4 2.1.2 General principles .................... ............................. ................... ................... ................... .................... ................... ................. ........4 4 2.1.2.1 Application limitations .................... ...................... ..................... ..................... ..................... ...................... ..............4 2.1.2.2 Wind direction. ...................... ..................... ..................... ...................... ..................... ..................... ..................... ....4 2.1.2.3 Wind load cases..................... cases ..................... ..................... ..................... ...................... ..................... ..................... ..................... ....5 2.1.2.4 Wind velocity ...........................................................................................................................................................5 2.1.2.5 Reference wind pressure q ref .....................................................................................................................................6 2.1.2.6 Wind pressure on surfaces. ..................... ...................... ..................... ..................... ...................... ..................... .......7 2.1.2.7 Exposure coefficient c e(z).........................................................................................................................................7 2.1.2.8 Roughness coefficient c r (z).......................................................................................................................................8 2.1.2.9 Topography coefficient c t(z).....................................................................................................................................9 2.1.2.10 Example ...............................................................................................................................................................9 2.1.2.11 Dynamic coefficient (C d)....................................................................................................................................10 2.1.2.12 External pressure coefficient (C pe) .....................................................................................................................10 2.1.2.12.1 External pressure coefficient C pe for vertical walls.........................................................................................10 2.1.2.12.2 External pressure coefficient C pe for roofs......................................................................................................13 2.1.2.13 Internal pressure coefficient (C pi).......................................................................................................................14

2.1.3 2.1.4

Examples......................... Examples................................... ................... ................... ................... ................... .................... ................... ............... ......15 15 Country-specific maps and values........................ values.................................. .................... ................... ............... ......21 21

2.1.4.1 Direction factor (Belgium)......................................................................................................................................21 2.1.4.2 Maps .................... ..................... ...................... ..................... ..................... ..................... ...................... ................... 22 2.1.4.2.1 The Netherlands................................................................................................................................................23 2.1.4.2.2 France ................... ..................... ...................... ..................... ..................... ..................... ...................... ............24

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SNOW LOADS GENERATOR....... GENERATOR................. .................... ................... ................... .................... ................... ..................24 .........24

3.1 S NOW LOADS ............................. .................... ................... ................... .................... ............ ..24 24 LOADS GENERATOR GENERATOR (EC1) ................... 3.1.1 Introduction .................. ............................ .................... ................... ................... .................... ................... ................... ................. .......24 24 3.1.2 General principles .................... ............................. ................... ................... ................... .................... ................... ............... ......25 25 3.1.2.1 3.1.2.2 3.1.2.3 3.1.2.4

3.1.3 3.1.3.1 3.1.3.2

3.1.4 3.1.4.1 3.1.4.2 3.1.4.3 3.1.4.4 3.1.4.5 3.1.4.6 3.1.4.7 3.1.4.8 3.1.4.9 3.1.4.10 3.1.4.11 3.1.4.12 3.1.4.13 3.1.4.14 3.1.4.15

Snow load on the ground (s k )..................................................................................................................................25 Snow load on roofs (s)............................................................................................................................................25 Snow load cases......................................................................................................................................................25 Snow loads on snowguards and obstacles...............................................................................................................25

Examples......................... Examples................................... ................... ................... ................... ................... .................... ................... ............... ......26 26 Example 1...............................................................................................................................................................26 Other examples........ ..................... ..................... ..................... ...................... ..................... ..................... ................ 29

Maps ............ ..................... ................... .................... ................... ................... ................... ................... .................... ................... ............... ......31 31 Austria ..................... ..................... ..................... ..................... ...................... ..................... ..................... ................ 31 Belgium ................... ..................... ..................... ..................... ...................... ..................... ..................... ................ 32 Denmark ..................... ..................... ...................... ..................... ..................... ..................... ...................... ............32 Finland....................................................................................................................................................................32 France ...................... ..................... ..................... ..................... ...................... ..................... ..................... ................ 33 Germany ..................... ..................... ...................... ..................... ..................... ..................... ...................... ............34 Greece.....................................................................................................................................................................35 Italy.........................................................................................................................................................................36 Luxemburg .............................................................................................................................................................37 The Netherlands ................... ...................... ..................... ..................... ..................... ...................... ................... 37 Portugal ...................... ..................... ..................... ..................... ...................... ..................... ..................... .........37 Spain ..................................................................................................................................................................37 Sweden........ ...................... ..................... ..................... ...................... ..................... ..................... ..................... ..39 Switzerland.........................................................................................................................................................39 United Kingdom.................................................................................................................................................41


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2 Wind loads generator 2.1 Wind loads generator ( EC 1) 2.1.1 Introduction PowerFrame includes several wind loads generators corresponding to different Standards (EC1, NBN 1991-2-4, BS 6399, NV 65, NEN 6702). This part of the manual deals with the generation of wind loads as per Eurocode 1. This document is not a substitute to this Standard, but provides a better insight on the effective use of PowerFrame’s wind loads generator.

2.1.2 General principles 2.1.2.1 Application limitations The application of the wind loads generator has only one limitation related directly to the prescriptions of Eurocode 1. Eurocode 1 is not applicable to buildings characterized by a dynamic coefficient (Cd) exceeding the value of 1.2. The dynamic coefficient Cd takes into account the reduction effects due to the lack of correlation of pressures over large surfaces as well as the increasing effects due to the frequency content of turbulence close to the fundamental frequency of the structure. It depends on the overall dimensions and the type of structure (steel, timber, concrete,...). For instance, a reinforced concrete building not higher than 100 meter or a steel construction lower than 35 meter have a dynamic coefficient Cd lower than or equal to 1. The dynamic coefficient of a building can be obtained using the diagram given in section 9 of Eurocode 1 part 2-4, or through the application of the formula given in annex B of Eurocode 1 part 24. The wind loads generators as implemented in PowerFrame are applicable to buildings, and are not necessarily appropriate for other types of structures, as eg. bridges, …

2.1.2.2 Wind direction The Eurocode proposes a method to model the effects of wind blowing perpendicular to the vertical surfaces of a building. PowerFrame will enable to generate wind loads over planes parallel to the XY and ZY planes.


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2.1.2.3 Wind load cases PowerFrame allows to generate wind loads in case wind acts from the left to the right, or from the right to the left. In addition, EC1 specifies 2 possibilities for each case, related to the angle between the wind direction and the horizontal plane (? 15°). In other words, PowerFrame allows to handle both upward or downward winds. Normally, a building should be able to resist wind loads in all possible cases.

2.1.2.4 Wind velocity The reference wind velocity vref is defined as 10 minutes mean wind velocity, at a height of 10 meter above ground level on a terrain of category II (see further for more background information), having a mean return period of 50 years. It shall be determined from v ref

?

C DIR ? C TEM ? C ALT ? v ref , 0

where vref,0 : CDIR : CTEM :

C ALT :

basic value of reference wind velocity; direction factor (taking into account wind direction); reduction factor for temporary or provisional structures.CTEM = 1, unless otherwise specified in annex A of Eurocode 1 part 2-4 altitude factor (taking into account the altitude of the building location).

The values of above parameters are specified for each country and each region: ?

in Belgium, vref,0 is fixed at 26.2 m/s, CTEM and C ALT both equal 1. A table defines CDIR as a function of wind direction. CDIR = 1 for winds blowing from the North, West or South but varies between 1 and 0.837 for wind directions between North and East, and between East and South.

?

in the Netherlands, a distinction is made between 3 regions for which the basic reference wind velocity is 25.0, 27.5 and 30 m/s. The 3 regions are illustrated on the map included in the Country-specific maps and values. section. The parameters CDIR, CTEM and C ALT are all equal to 1.


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?

in Luxemburg, vref,0 is taken equal to 26.0 m/s. CDIR, CTEM and C ALT are all equal to 1.

?

In France, 4 zones are specified for which different basic reference wind velocities are applicable (24.0, 26.0, 28.0, 30.5 m/s). The zones are defined as shown on the map in this manual’s section Countryspecific maps and values. The parameters CDIR, CTEM and C ALT are all equal to 1.

?

Germany is divided in 4 zones in which the basic reference wind velocity varies between 24.3 and 31.5 m/s. In zones 1 and 2, for which the average wind velocity is relatively low, the C ALT coefficient is to be used for all constructions located at an altitude of more than 800 meter. o In zone 1, C ALT = 0.65 + altitude /2270 for an altitude ranging from 800 to 1100 meter. Above an altitude of 1100 meter, measurements are required to determine the appropriate value for C ALT. o In zone 2, measurements are required for altitudes from 800 meter onwards. For buildings designed for a life time of max. 4 years, a reduction of the design wind pressures is allowed and can be introduced through the factor CTEM.

Should parameters referring to other countries be required, please check Eurocode Part 2-4 Annex A.

2.1.2.5 Reference wind pressure qref The reference wind pressure qref , expressed in N/m2, is calculated as: ? ?

q ref

?

2 v ref

2

where vref : reference wind velocity in m/s ? : air density in kg/m3. Air density is affected by the altitude and depends on the temperature and pressure to be expected in the considered region during wind storms. Unless otherwise specified in annex A of Eurocode 1 part 2-4, the value of ? shall be taken equal to 1.25 kg/m3. For instance: in Belgium, the reference wind pressure is equal to 429 N/m2 in case C ALT = CTEM = CDIR = 1. PowerFrame Manual – Wind & snow loads generators

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2.1.2.6 Wind pressure on surfaces The net value of the wind pressure on a surface corresponds to the difference between the « external » and « internal» pressure on this surface. The wind pressure acting on the external surfaces of a structure (we) is given by: we

?

q ref ? ce ( z e ) ? C pe

where qref : reference wind pressure; ce(ze): exposure coefficient; cpe: external pressure coefficient. The wind pressure acting on the internal surfaces of a structure (wi) is given by: wi

?

q ref ? c e ( z i ) ? C pi

where qref : reference wind pressure; ce(zi): exposure coefficient; cpi: internal pressure coefficient.

2.1.2.7 Exposure coefficient ce(z) The exposure factor ce(z) takes into account the impact of several parameters on the average wind velocity. For example : terrain characteristics, presence or absence of obstacles, topography and height above ground level. This factor can be derived from the following formula: ?

c e ( z ) ? c r 2 ( z ) ? ct 2 ( z ) ? ?1 ? ?

where

? ? c r ( z ) ? c t ( z ) ?

7 ? k T

kT: terrain factor (see table below) ; cr (z) roughness coefficient (see section Roughness coefficient cr (z) of this manual) ; ct(z) topography coefficient (see section Topography coefficient ct(z) of this manual).

Following terrain categories are considered : I

rough open sea, lakes with at least 5 km fetch upwind and smooth flat country without obstacles.


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II

farmland with boundary hedges, occasional small farm structures, houses or trees.

III

suburban or industrial areas and permanent forests.

IV

urban areas in which at least 15% of the surface is covered by buildings having a height exceeding 15 meter.

The parameters kT, z0 and zmin are defined as a function of the following terrain categories : Terrain category

kT

I II III IV

0.17 0.19 0.22 0.24

z0 [m] 0.01 0.05 0.3 1

zmin [m] 2 4 8 16

The parameters z0 and zmin (minimum height) allow to determine the roughness coefficient cr (z).

2.1.2.8 Roughness coefficient cr (z) cr (z) , as a function of height z, is given by: ? z ? cr ( z ) ? k T ? ln?? ?? ? z 0 ?

( z min ? z ? 200m)

? z ? cr ( z ) ? cr ( z min ) ? k T ? ln?? min ?? ? z 0 ?

( z ? z min )

Calculation example cr (z): Consider a terrain of category III on which a 4 meter high building will be erected. Based on the previous table, it is derived that: kT = 0.22 z0 = 0.3m zmin = 8m The height z is equal to 4m and is thus lower than the minimum height. Thus: PowerFrame Manual – Wind & snow loads generators

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cr (z) = cr (zmin) = cr (8) = 0.22 * ln(8/0.3) = 0.722

2.1.2.9 Topography coefficient ct(z) The topography coefficient ct(z) accounts for the increase of the mean wind speed over isolated hills and escarpments (not undulating and mountainous regions). It is related to the wind velocity at the base of the hill or escarpment. It shall be considered for locations closer than half the length of the hill slope from the crest or 1,5 times the height of the cliff. It is defined by: ct = 1 ct = 1 + 2 . s . ? ct = 1 + 0.6 . s where s: ? :

in case ? < 0.05 in case 0.05 < ? < 0.3 in case ? > 0.3

a factor derived from diagrams 8.1 & 8.2 of EC1, part 2-4 upwind slope of terrain in wind direction [%].

2.1.2.10 Example Hypotheses:

Terrain of category III, situated in Belgium. Construction height and length: 1 meter.

Suppose the construction is situated on top of a hill which is 30 m high, and has a slope of 30% in all directions.

Calculation of wind pressure:

?

the roughness coefficient cr (z) has the same value as in the previous example : KT = 0.22 cr (z) = 0.722


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?

topography coefficient ct(z): ? =

0.3 Le = Lu = 100m Z/Le = 0.3 Diagram 8.2 of the Eurocode shows s = 0.5, which finally yields to ct(z) = 1.3 ?

exposure coefficient ce(z) ce(z) = 2.328

Hence, the wind pressure on the vertical surface at the left hand side in the above picture is equal to: 2.328 x 429 = 999N/m2.

2.1.2.11 Dynamic coefficient (Cd) The pressure calculated in accordance with the principles outlined above, still needs to be multiplied by a factor cd, to take into account the possible risk of a dynamic excitation of the structure. The dynamic coefficient of a building can be obtained using the diagram given in section 9 of Eurocode 1 part 2-4, or through the application of the formula given in annex B of Eurocode 1 part 2-4.

2.1.2.12 External pressure coefficient (Cpe) 2.1.2.12.1 External pressure coefficient Cpe for vertical walls Cpe for buildings and individual parts of buildings depends on the size of the loaded area A: Cpe,1

in case the loaded area A is smaller than or equal to 1m2

Cpe,10

in case the loaded area A is larger than or equal to 10 m2

Cpe = Cpe,1 + (Cpe,10 – Cpe,1) . log10 A, in case the loaded area A is larger than 1 m2 but smaller than 10 m2.


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The value of Cpe also depends on the ratio d/h, where d corresponds to the depth of the building (in the wind direction) and h corresponds to the height of the building.

The table below shows the values that correspond to the front and rear vertical walls of a rectangular building: Zone

D

E

d/h

Cpe,10

Cpe,1

? 1

0.8 0.6

1 1

? 4

Cpe,10

Cpe,1

-0.3 -0.3

In case the ratio d/h is between 1 and 4, the values of Cpe are obtained by interpolation. In the previously presented example, the wind pressure on the vertical walls can now be calculated. ?

wind pressure on front wall (windward side): 429 x 1.634 X 1.0 = 701 N/m2

?

wind pressure on rear wall (leeward side): 429 x 1.634 x (-0.3) = -210 N/m2.

Using the same hypotheses as in the previous example, assume a construction of 4 meter high. The surface exposed to the wind is thus 4m2. Cpe

= Cpe,1 + (Cpe,10 – Cpe,1) . log10 A = 1.0 + (0.8 – 1.0) . log104 = 0.880

?

wind pressure on front wall (windward side):


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429 x 1.634 X 0.880 = 616 N/m2 ?


Again using the same hypotheses, considering a building with a depth of 2 meter in the direction of the wind:

d/h = 2 The value of Cpe,10 is obtained through interpolation: Cpe,10 = 0.8 – 0.2/3 = 0.733 Cpe

?

= Cpe,1 + (Cpe,10 – Cpe,1) . log10 A = 1.0 + (0.733 – 1.0) . log104 = 0.840

wind pressure on front wall (windward side): 429 x 1.634 X 0.840 = 589 N/m2

?


Note: the reference heigt z e for walls of rectangular buildings depends on the aspect ratio h/b (height over width): ? buildings whose height h is less than b shall be considered to be one part ? buildings whose height h is larger than b but less than 2b, shall be considered to be of 2 parts, comprising: a lower part extending upwards from the ground to a height equal to b and an upper part ? buildings whose height h is larger than 2b shall be considered to be in multiple parts, comprising: a lower part extending upwards from the ground to a height equal to b; an upper part extending downwards from the top by a height equal to b and a middle region, between the upper and lower parts, divided into as many horizontal strips as desired,each one with a maximum height of b. PowerFrame Manual – Wind & snow loads generators

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2.1.2.12.2 External pressure coefficient Cpe for roofs The Eurocode considers two different types of roof. Hereafter, the calculation of the external wind pressure will be discussed and presented in detail for 2 specific roof types. It should be outlined that PowerFrame can handle other types of roof than those discussed hereafter, in order to meet the Eurocode requirements as closely as possible.

2.1.2.12.2.1

Flat roof

All roofs with a slope smaller than 4% are qualified as flat roofs. A flat roof can be divided in different zones, as outlined in the plan view given below :

The parameter « e » is the minimum of 2h and b, h being the height of the flat roof above ground level. The factors given in the following table apply to the different zones indicated in the above diagram : Zone

f

g

h

i

Cpe,10

Cpe,1

Cpe,10

Cpe,1

Cpe,10

Cpe,1

Cpe,10

Sharp eaves

-1.8

-2.5

-1.2

-2.0

-0.7

-1.2

? 0.2

With Hp/h = 0.025 parapets Hp/h = 0.05 Hp/h = 0.1

-1.6 -1.4 -1.2

-2.2 -2.0 -1.8

-1.1 -0.9 -0.8

-1.8 -1.6 -1.4

-0.7 -0.7 -0.7

-1.2 -1.2 -1.2

? 0.2

Cpe,1

? 0.2 ? 0.2

The values of Cpe in zone i can be positive or negative. Therefore, 2 cases need to be considered (corresponding to positive pressure and suction). An example will be presented further in this manual.

2.1.2.12.2.2

Duopitch roof


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A duopitch roof can be divided in different zones, as presented in the diagram below:

The height ze = h is the height above ground level of the highest point of the roof (roof crest). The parameter « e » is the minimum of 2h and b. For a wind blowing in the direction of the roof slope, the values of Cpe can be derived from the table below: Zone

f

g

h

i

Slope

Cpe,10

Cpe,1

Cpe,10

Cpe,1

Cpe,10

Cpe,1

5° 15°

-1.7 -0.9

-2.5 -2.0

-1.2 -0.8

-2.0 -1.5

-0.6

-1.2

0.2 30° 45° 60° 75°

-0.5

0.2 -1.5

0.7 0.7 0.7 0.7

-0.5

-1.5 0.7 0.7 0.7 0.8

-0.3 0.2 -0.2 0.4 0.6 0.7 0.8

Cpe,10 -0.3 -0.4

j Cpe,1

Cpe,10

Cpe,1

-0.3 -1.0

-1.5

-0.4

-0.5

-0.2 -0.2 -0.2

-0.3 -0.3 -0.3

An example will be presented further in this manual.

2.1.2.13 Internal pressure coefficient (C pi) The theoretical background given below can easily be understood by using PowerFrame’s dialogue window related to the internal pressure coefficient.The user is to select the corresponding case in the dialogue window to directly view the value of Cpi . Eurocode 1 part 2-4 considers several cases. ?

The first case relates to nearly square buildings, characterized by a homogeneous distribution of openings. In this case, Cpi is equal to – 0.25.

?

The second case corresponds to closed buildings with internal partitions, and opening windows. In this case, Cpi is to be taken equal to 0.8 or –0.5. Both possibilities have to be considered.


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?

The third case includes all situations not covered by the first and second case described above. First, the opening ratio µ needs to be determined as follows: Taking into account the area of temporary openings, 2 values for µ need to be determined (a maximum value and a minimum value). Once both limit values have been determined, the graph below should be used to derive the related value of Cpi :

Consequently, 2 values are obtained for Cpi. Both of them must be considered during the calculation of wind pressure.

2.1.3 Examples The use of PowerFrame’s wind loads generator will now be explained through a number of practical examples. First, the user defines the model geometry and boundary conditions as he usually does in PowerFrame. Then, the user selects the contour of the frame on which the wind load is to be defined, and should keep in mind that the selected frame must always be in one plane, either parallel to the XY- or the XZ-plane. The user will then focus on the 2D frame contour as shown below :

Column height : 4m Total height : 8m Frame width: 16m


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This frame is part of a larger model, representing a structure with a total length of 18 meter and a distance of 6 meter between the frames. In the ‘Loads’-window, the user first selects the appropriate load group in the icon toolbox before starting the definition of the wind loads. He should check that the frame shown above has been properly selected, and will then notice that the

icon has become active.

Using the icon, the following dialogue window will appear on the screen :

At this point, PowerFrame offers the user a choice between different Standards. In the context of this manual, the Eurocode 1 will be used. Confirming the selection of Eurocode 1, the following dialogue will appear on the screen:


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The user first starts to specify whether the wind blows from left to right or from right to left. He will notice that a possible choice exists between an upward or downward wind. The external pressure coefficients can effectively change depending on this condition. The structure needs to be analyzed for both conditions. The external pressure coefficients do depend on the position of the selected frame within the whole building. The Eurocode makes a difference between the frames that can be considered as located in the middle of the building, at the front side or at the rear side. For example, a frame with a duopitch roof is considered to be at the edge of the building, if its distance D from the edge meets the following condition : D < 0.25 * min (2H , B), where ? B: width of the building (in the direction of the wind) ? H: height of the building In the case of a canopy roof, a frame is considered to be at the edge if the distance D between the edge and the frame meets the following condition: D < 0.1 L, where ? L: length of the building exposed to the wind PowerFrame Manual – Wind & snow loads generators

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The next entry in the dialogue window allows to specify the width of the building or that part of the building to be analyzed. When the building consists of 2 blocks with different dimensions, it is recommended that both blocks be considered separately when using the wind loads generator, defining the width to be equal to the width of the part the user is currently working on. The distance between frames needs to be indicated in the line below. This distance is actually used to define the roof surface that will transmit wind loads to the frame. The user should therefore remember to divide the actual distance by a factor 2 for both end frames. The dynamic coefficient is filled in in the next editor field. The user is to refer to section 9 of Eurocode 1 part 2-4, or to annex B of Eurocode 1 part 2-4 for more information. In the open dialogue window, two buttons allow to open secondary dialogue boxes. First, the user has to click on below:

to open the dialogue box

The user should now enter the terrain parameters as specified in the first part of this manual. ce(z), ct(z) and cr (z) will be calculated automatically using the values the user has entered in the dialogue window. At this stage, to have a good understanding of the considered example, the user should fill in the dialogue tab as shown in the above figure. Using the

button, the user has to go back to the main dialogue

window and then click on the button window shown below:


to open the dialogue

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This dialogue window helps to choose the most appropriate internal pressure coefficient depending on the effective frontal area of the structure. The user will continuously see in this dialogue window the value of Cpi depending on the selection that has been made and on the values that have been defined. Indeed, the current value is always shown in the field at the bottom of the dialogue window, corresponding to the option ‘User-defined value’. For this example, the user fills in the dialogue tab as shown above. Using the button, he then returns to the main dialogue window and checks that all parameters have been defined as shown previously. The following results will then be displayed:

Should the internal pressure coefficient Cpi have not been considered, the pressure distribution would be: PowerFrame Manual – Wind & snow loads generators

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A second example looks into the calculation of Cpe in case of a building with a flat roof. The global procedure being the same as the one outlined in the previous example, the user now considers Cpi to be equal to zero (by selecting the option : ‘Do not take internal pressures into account’).

Height: 5m Width : 8m

The frame is 5 meter high and 8 meter wide. It is part of a construction with a total length of 18 meter, and frames every 6 meter. In this case, the results are:

These results can easily be verified manually using the information that was previously given in the Eurocode. In the last example, a canopy roof will be handled. In this particular case, the user will have only to select the roof girders to define the wind loads, as the open walls will of course take no wind load. User’s selection will thus look as follows:


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As a result, two important changes in the dialogues will be noticed. The first change will be observed in the main dialogue window of the wind loads generator. An extra editor field will request to define the height above ground level of the lower roof edge. The second change is related to the internal pressure coefficient, as this coefficient no longer needs to be defined (Eurocode 1 part 2-4 directly specifies the net pressure coefficients). Indeed, if the user presses the button ‘Internal pressure ‘, he will get the following message:

If the user proceeds to the calculation of wind pressure, having defined all parameters as in the previous example and specified a total height of 6 meter, the following results will be displayed:

2.1.4 Country-specific maps and values 2.1.4.1 Direction factor (Belgium) Direction 0° (North) 22.5°

Direction factor 1.0 1.0


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37.75° 0.949 45° 0.894 56.25° 0.837 90° (East) 0.894 120° 0.894 150° 0.949 180° (South) 1.0 270° (West) 1.0 For intermediate interpolate between values.

directions, the given

2.1.4.2 Maps


22

2.1.4.2.1

The Netherlands


23

2.1.4.2.2

France

3 Snow loads generator 3.1 Snow loads generator (EC1) 3.1.1 Introduction PowerFrame includes several snow loads generators corresponding to different Standards (EC1, NBN ENV 1991-2-3, BS 6399 Part 3, N 84, NV 65, NEN 6702). This part of the manual is dedicated to the generation of snow loads based on Eurocode 1 part 2-3. This document is not a substitute to this Standard, but is aimed at providing a better insight on the effective use of PowerFrame’s snow loads generator. PowerFrame Manual – Wind & snow loads generators

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3.1.2 General principles 3.1.2.1 Snow load on the ground (sk) The snow load on the ground is the reference value to be taken into account for the calculation of the snow load on roofs. This reference snow load depends on the geographical position and the altitude of the building. Eurocode 1 part 2-3 annex A gives characteristic values for the snow load on the ground for most of the European countries.

3.1.2.2 Snow load on roofs (s) The snow load on a roof shall be determined using the following formula: s

? ?i ?

C e ? C t ? s k

where ? i:

snow load shape coefficient, function of the type of roof Ce : exposure coefficient (generally taken equal to 1) ; Ct : thermal coefficient (for normal standards of thermal insulation, taken equal to 1. A reduction in the snow load on the roof may be permitted by the introduction of values of the thermal coefficient smaller than 1, to take account of the effect of heat loss through the roof). The snow load is assumed to act vertically and shall refer to the horizontal projection of the area of the roof. ? i is determined automatically by PowerFrame, using section 7 of Eurocode 1 part 2-3 concerning snow on buildings.

3.1.2.3 Snow load cases The Eurocode specifies different snow load situations depending on the type of roof. PowerFrame schematizes those situations by means of sketches. As a result, the user can easily see all possible load situations by going through the example that is presented further in this manual.

3.1.2.4 Snow loads on snowguards and obstacles The Eurocode does not specify any change in snow loads depending on the presence or absence of snowguards. Nevertheless, a formula is given to PowerFrame Manual – Wind & snow loads generators

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determine the force exerted by a sliding mass of snow in the direction of the slope, per unit width . F ? s ? b ? sin ?

where : ? ? ?

s: snow load on the roof ? : roof pitch measured from the horizontal b: distance on plan from the guard or obstacle to the ridge.

This force is not considered or calculated by PowerFrame. If the user wants to account for those forces in the PowerFrame model, they need to be introduced manually in the model. Note : PowerFrame’s snow loads generator has not been designed for cylindrical roofs. Therefore, it will not always produce snow loads which comply completely with the Eurocode standard for those types of roof. Nevertheless, by selecting the most frequent load cases, the user will be able to obtain appropriate snow load models.

3.1.3 Examples 3.1.3.1 Example 1 In this section, the snow loads generator will be further explained through a practical example. The snow loads generator only becomes available in the icon toolbox of the ‘Loads’-window after a frame contour has been selected. This frame contour should be in a (vertical) plane parallel to the XY- or XZplane. The following frame contour will be considered.

Column height: 5m Total height: 8m Frame width: 10m

To apply the snow loads generator, it is not necessary that the boundary conditions or cross-section properties have been designed already. The user should go to the ‘Loads’-window and be certain to select a load group with the PowerFrame Manual – Wind & snow loads generators

26

appropriate load factors. He should then select the frame contour, and the icon becomes active, and then click on the icon to make the following dialogue window appear:

Eurocode 1 is then to be selected by the user to launch the actual snow loads generator.

It should be noted that in the dialogue tab which comes up, PowerFrame will present the frame contour that is considered, as a confirmation of then user’s selection.


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The first line allows to define the width of the building on which snow loads are applied and transferred to the selected frame. The snow load on the ground (sk) is to be defined manually to allow the use of the snow loads generator in as many countries as possible. Please refer to annex 1 of this manual or to annex A of Eurocode 1 to get more information on the most appropriate value of sk . Eurocode specifies the concentrated loads to take into account the effect of snow overhanging the edge of a roof. By selecting or unselecting the option in the dialogue tab, this can be taken into account. The thermal coefficient and the exposure coefficient can be taken equal to 1 as a default. However, in particular situations, different values can be used. Please refer to Eurocode 1. Finally, at the bottom of the dialogue window, a button is available for the selection of the most appropriate load situation. This button gives access to the following scheme, from which the most relevant situation can be selected:

In general, the design standard requires the building to be able to support all possible cases. Once the load case has been selected, the user is to return to the main dialogue, and confirm to get results as shown in the figure below (distributed loads are shown in Newton/meter).


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3.1.3.2 Other examples Finally, additional examples are presented, which can be set up very similarly to the first example.


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A final example relates to the situation in which snow overhangs the edge of a cantilever roof. The load due to the overhang will be assumed to act along the edge of the roof and will be introduced as a concentrated load on the frame, as clearly shown in the figure below


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3.1.4 Maps 3.1.4.1 Austria

Zone A Altitude(m) < 200 300 400 500 600 700 800 900 1000 1100 1200 sk (kN/m2) 0.75 0.85 1.00 1.20 1.45 1.75 2.10 2.55 3.00 3.50 4.05

Zone B Altitude(m) < 200 300 400 500 600 700 800 900 1000 1100 1200 sk (kN/m2) 1.55 1.55 1.60 1.75 2.00 2.30 2.65 3.10 3.65 4.25 4.95

Zone C Altitude(m) < 200 sk (kN/m2) -

300 400 500 600 700 800 900 1000 1100 1200 2.15 2.35 2.70 3.10 3.60 4.20 4.95 5.75 6.65

Zone D Altitude(m) < 200 2

sk (kN/m )

-

-

-

300 -

400

500

600

1.00 1.20 1.45 1.75 2.10

700 2.50

800

900 1000 1100 1200

3.00


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3.1.4.2 Belgium The characteristic snow load on the ground is to be calculated using the formulae below: sk = 0.50 (kN/m2) sk = 0.50 + 0.007(A – 100)/6 (kN/m2)

altitude (m) altitude (m)

A ? 100 100 < A ? 700

3.1.4.3 Denmark The characteristic snow load on the ground is sk = 1.0 kN/m2.

3.1.4.4 Finland


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3.1.4.5 France

2

sk (kN/m ) s A (kN/m2)

1A 0.45 -

1B 0.45 1.00

Zones 2A 2B 0.55 0.55 1.00 1.35

3 0.65 1.35

4 0.90 1.80

Zone 1A: Aisne, Ardennes, Aube, Calvados, Charente-Maritime, Cher, Côte d’Or, Côtes d’Amor, Eure, Eure-et-Loire, Finistère, Ile et Viliane, Indre, Indreet-Loire, Loi-et-Cher, Loire-Atlantique, Loiret, Maine-et-Loire, Manche, Marne, Haute-Marne, Mayenne, Meurthe-et-Moselle*, Meuse, Morbihan, Moselle*, Nièvre, Nord, Oise, Orne, Pas-de-Calais, Sarthe, Seine-Maritime, DeuxSèvres, Somme, Vendée, Vienne, Vosges*, Yonne. Région Ile-de-France: Ville de Paris, Seine-et-Marne, Yvelines, Essonne, Hauts-de-Seine, Seine-Saint-Denis, Val-de-Marne, Val d’Oise. Zone 1B: Allier, Alpes-Maritimes, Bouches-du-Rhône, Cantal, Corrèze, Haute-Corse, Corse-Sud, Creuse, Dordogne, Haute-Garonne, Gers, Gironde, Landes, Lot, Lot-et-Garonne, Puy-de-Dôme, Pyrénées-Atlantiques, HautesPyrénées, Saône-et-Loire*, Tarn-et-Garonne, Var*, Haute-Vienne. Zone 2A: Ain, Alpes-Hautes-Provence, Hautes-Alpes, Ariège, Aveyron, Doubs, Jura, Loire, Haute-Loire, Lozère, Meurthe-et-Moselle*, Moselle*, BasPowerFrame Manual – Wind & snow loads generators

33

Rhin, Haut-Rhin, Rhône, Haute-Saône, Saône-et-Loise*, Tarn*, Var*, Vosges*. Zone 2B: Gard, Hérault*, Vaucluse. Zone 3: Ain*, Ardèche, Ariège*, Aude*, Drôme, Hérault*, Isère, PyrénéesOrientales*, Savoie, Haute-Savoie, Tarn*, Var*, Belfort (Territoire). Zone 4:

Aude*, Pyrénées-Orientales.

* only partially.

3.1.4.6 Germany

Zone I Altitude (m) sk (kN/m2)

> 200 1.13

300 1.13

400 1.13

500 1.13

600 1.28

700 1.58


800 1.88

900 2.25

1000 2.70

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Zone II Altitude (m) sk (kN/m2)

> 200 1.13

300 1.13

400 1.13

500 1.35

600 1.73

700 2.25

800 2.78

900 3.45

1000 4.20

Altitude (m) sk (kN/m2)

> 200 1.13

300 1.13

400 1.50

500 1.88

600 2.40

700 3.00

800 3.83

900 4.65

1000 5.70


1100 6.95

800 5.85

900 6.98

1000 8.25

Zone III

1200 8.20

1300 9.60

1400 11.10

1500 12.70

Zone VI Altitude (m) sk (kN/m2)

> 200 1.50

300 1.73


1100 9.40

1200 10.60

400 2.33 1300 11.75

500 3.15

600 3.90

1400 12.90

700 4.88

1500 14.10

3.1.4.7 Greece Zone I :

Zone II :


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3.1.4.8 Italy Zone I sk = 1.60 sk = 1.60 + 3 (A-200)/1000 sk = 3.25 + 8.5 (A-750)/1000

kN/m2 kN/m2 kN/m2

A ? 200 m 200? A ? 750 m A > 750 m

Zone II sk = 1.15 sk = 1.15 + 2.6 (A-200)/1000 sk = 2.58 + 8.5 (A-750)/1000

kN/m2 kN/m2 kN/m2

A ? 200 m 200? A ? 750 m A > 750 m

Zone III sk = 0.75 sk = 0.75 + 2.2 (A-200)/1000 sk = 1.96 + 8.5 (A-750)/1000

kN/m2 kN/m2 kN/m2

A ? 200 m 200? A ? 750 m A > 750 m


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3.1.4.9 Luxemburg The characteristic snow load on the ground should be determined based on following formulae: sk = 0.50 (kN/m2) sk = 0.50 + 0.007 (A – 100)/6 (kN/m2)

altitude (m) A ? 100 altitude (m) 100 < A ? 700

3.1.4.10 The Netherlands sk = 0.70 kN/m2.

3.1.4.11 Portugal For the following regions: Viana do Castelo, Braga, VilaReal, Braganda, Porto, Aveiro, Viseu, Guarda, Coimbra, Leiria, Castelo Branca, Portalegre , and at altitudes above 200m: sk = (A – 50)/400 kN/m2. Elsewhere, snow loads do not have to be considered.

3.1.4.12 Spain Zone I Altitude (m) : 200 sk en kN/m2 : 0.2

400 0.2

500 0.3

600 0.3

700 800 900 1000 0.5 0.6 0.7 1.1


1100 1.6

1200 1.8

1300 1.9

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Altitude (m) : 1400 sk en kN/m2 : 2.2 ZoneII Altitude (m) : sk en kN/m2 : Altitude (m) : sk en kN/m2 :

1500 3.2

1600 3.8

1700 4.5

1800 5.3

1900 6.3

2000 7.4

200 400 500 600 700 800 900 1000 1100 0.4 0.5 0.6 0.6 0.7 1.0 1.1 1.7 1.9 1400 1500 1600 1700 1800 1900 2000 2.6 3.6 4.0 4.5 5.0 5.6 6.2

Zone III Altitude (m) : 200 sk en kN/m2 : 0.2 Altitude (m) : 1400 sk en kN/m2 : 1.6

400 0.2

500 0.2

1500 2.2

600 0.3

1600 2.6

700 800 900 1000 0.3 0.5 0.6 0.9 1700 3.0

1800 3.5

1900 4.1

1100 1.0

1300 2.4

1200 1.2

1300 1.4

1200 1.2

1300 1.4

2000 4.8

Zone IV Altitude (m) : 200 400 500 600 700 800 900 1000 1100 sk en kN/m2 : 0 0 0 0 0 0 0 0.9 1.0 Altitude (m) : 1400 1500 1600 1700 1800 1900 2000 sk en kN/m2 : 1.6 2.2 2.6 3.0 3.5 4.1 4.8


1200 2.1

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3.1.4.13 Sweden Snow zone : sk (kN/m2) :

4 4.0

3 3.0

2.5 2.5

2 2.0

1.5 1.5

1 1.0

3.1.4.14 Switzerland At altitudes below 1500 m : s k

? ? 0.4 ??1.0 ? ? ?

? Aref ? ? ? 350

? ? ? ?

2

? ? ? ?

kN / m 2

where ?

sk is the snow load on the ground, with a minimum value of 0.9 kN/m2.

?

Aref is the reference altitude from the map below.


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PowerFrame Part 3 - Wind and Snow Loads.pdf

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