steel_buildings_design_notes.pdf

Ferenc Papp

Ph.D., Dr habil

Steel Buildings

DESIGN NOTES

Reviewed by

Dr. Béla Verőci honorary lecturer

This work is to the scientific program of the Development of quality-oriented and harmonized R+D+I strategy and functional model at BME.

This work is supported by the New Széchenyi Plan. The rroject ID is TÁMOP-4.2.1/B-09/1/KMR-2010-0002.

Practice 1

PRELIMINARY DESIGN

Written in the framework of the project TÁMOP 421.B JLK 29.

1.1 The aim of the design task

The objective of the design task is the steel structure of a simple hall. The main properties of the structure are the following:

- Symmetric form with duopitch roof; - Equal interval between main frames; - Equal interval between purlins;

- Horizontal wall girder system, with wall columns in the end walls; - Covering system with double trapezoidal plates and heat isolation.

1.2 The initial data for the design

The work starts with the preliminary design of the structure. It is based on the initial data which are determined and supplied by the architectural engineer which satisfy both the appropriate building regulations and the requirements of the owner. In the case of the present design project the initial data concerns to the outer surfaces of the flanges of the steel main frames (see Figure 1):

• Base area to be built: A [m2];

• Horizontal distance between the flanges of the main frame: b [m];

• Height of the side walls: Hw [m]

• Slope of the roof: αααα [deg]

Fig.1 Initial data for the design 1.3 The theoretical parameters of the main structure

The main theoretical parameters of the steel structure should be determined for the structural analysis (see Figure 2 which considers both the prismatic and the tapered members). The

theoretical span of the main frame is equal to the horizontal distance between the central

(reference) axes of the columns:

c h L=b−

where hc is the initial height of the column section, b is the outer distance of the columns

prescribed by the architectural engineer. The theoretical height of the columns is equal to the distance between the theoretical column base point and the intersectional point of the column and the beam central axis. This parameter may be calculated approximately by the following expression:

A [m

]

H

[m]

b [m]

_αααα

_[deg]

Fig.2 Theoretical parameters of the main frame

2 h

H b

c =Hw−

where Hw is the initial height of the side walls, hb is the initial depth of the beam section. The theoretical ridge (top) point of the frame may be calculated by the following expression:

) ( tg 2 L H H_f = _c + ⋅ α

1.4 The number of the main frames and their interval

The architectural concept has prescribed the basic area of the building (A), from which the

theoretical length of the steel structure may be calculated,

b A = 0

d

where the parameters are defined in the Section 1.2. The required number of the main frames may be determined as following:

1 c d

n 0

n = +

In the expression c denotes the interval between the main frames, where the optimal value is c=5

÷

required number of frames nn. The real theoretical length between the final frames is the

following (see Figure 3):

(

)

αααα

Fig.3 The applied number of main frames and the real theoretical length of the structure

Since the distance between the main frames is normally uniform, therefore the initial basic area (A) of the building may be kept only approximately. The real basic area can be calculated by the main parameters of the structures which were determined previously:

(

)

(

)

a L h d b 2 h

A = + ⋅ + + ⋅

where bbf [m] is the flange width of the beam section, hcsw is the depth of the column section

in the end wall system (see Figure 4). It should be noted that the previous expression is valid for the structural solution illustrated in the Figure 4.

Fig.4 Structural system of the end wall 1.5 The initial cross-sectional parameters for the main frames

As a matter of fact, the main frames at the end walls carry lower loads than the intermediate ones. This is why these two frames might be fabricated from weaker cross-sections. In order

purlin

beam of the frame

wall column

b

h

for easy enlarging the building longitudinally in the future, these frames are suggested being as strong as the intermediate ones. The parameters of the cross-sections of the main frames are related to the span L and the height Hf. Assuming that the building to be designed is

relatively low and the roof is relatively flat, i.e: o c 15 és 5 . 0 L H _{≤ α ≤} ,

and the structure is loaded only by dead load and meteorological loads, the initial types and parameters of the cross-sections may be determined as the function of the theoretical span L.

Table 1 contains the suggested initial values for the cross-sectional parameters which are

based on practical experiences. The used symbols of the geometrical parameters can be found in the Table 2.

Tab.1 The initial sizes of the cross-sections of the main frames in the function of the span L

span L [m] type of the section size* [mm]

12÷16 hot rolled (IPE/HEA) 300÷450/200÷260

16÷24 welded I flange: 200÷300 – 16÷20

web: 400÷600 – 8÷10

24÷32 tapered I flange: 300÷340 – 16÷20

web: 800÷1200 – 6÷8

* in the case of hot rolled sections the values mean depth of the section for the lower and the upper limits of the span L; in the case of welded sections the values mean the width and thickness of the plates for the lower and the upper limits of the span L

Tab. 2 The signs of the geometrical properties of the cross-sections

structural member property meaning

bcf width of the flange

tcf thickness of the flange

hcw width of the web

column

tcw thickness of the web

bbf width of the flange

tbf thickness of the flange

hbw width of the web

beam

tbw thickness of the web

1.6 The initial grade of material

The main structural elements are normally made from S235 or S355 steel. Unless there is any previous reason to use S355 steel grade, the grade of S235 is suggested using. If it is reasonable, the initial grade of steel may be changed during the analysis and design of the structure.

1.7 Application

1. PRELIMINARY DESIGN

1.1 Initial parameters

- area to be built [m2_{] A 725}

- width of the building [m] b 20.0

- heigth of the side walls [m] _{H w 7.5}

- slope of the roof [deg] _α 10

1.2 Initial data for the main structural members

- main frames (welded I section) column [mm] flange _{b cf 240 t cf 16} web _{h cw 468 t cw 8} depth _{h c h cw 2 t cf}. _{h c 500}= beam [mm] flange _{b bf 240 t bf 16} web _{h bw 368 t bw 6} depth _{h b h bw 2 t bf}. _{h b 400}=

- columns in side walls HEA160 _{h csw} 150

- purlin Lindab Z 200 _{h p 200}

- beams in walls Lindab C 200 _{h bsw} 200

1.3 Theoretical properties of the structural model

- span of the frames [m]

L b h c

1000 L=19.5

- height of the columns [m]

H c H w h b 2 1 1000 . _{H c 7.3=}

- heigth of the frame [m]

H f H c

L

2 tan α π180 .

. _{H f 9.019=}

1.4 Number of the main frames

- prescribed length of the building [m]

d 0

A

b d 0 36.25=

- interval of the frames [m] c 6.0

- required number of the frames _{n n} d 0

c 1 n n 7.042=

- applied number of the frames

n a 7

The building consists of 7 frames! 1.5 Area of the bulding

- length of the building [m]

d _{n a 1 c}. d=36

- actual area of the building [m2_]

A tény L h c 1000 d b bf 1000 2 h csw 1000 . . A tény 730.8=

The actual area of the building satisfies the official plan!

1.8 Arrangement of the purlin system

In our case (the building is under static loading) the purlin system and the wind bracing system may be independent ones, but they also may form a unified system. In the present phase of the design it should be determined which concept is followed:

• Concept A: Purlin system is independent to the wind bracing system

• Concept B: Purlin and wind bracing members form a unified static system

In case of Concept A it is assumed that the purlin system carry the loads and effects which act directly to the roof, and it does not take part in the bracing of the building. In this case the wind bracing system is a trussed structure, which consist of two neighboring main frames, the diagonals and the longitudinal bars are placed under the purlins independently to them. In the case of Concept B the longitudinal bracing bars are replaced by the purlin system (besides the primary rule the purlins are part of the wind bracing system). Which concept to be followed in the design may be supported by the following rules and suggestions:

• Application of the Concept A may be suggested in the case of L≥18m, since the solution is not economical for relatively small spans with relatively low design loads and effects.

• The application of the Concept B may not be suggested for structures loaded by other considerable loads (e.g. crane load) besides the dead load and the meteorological loads.

In the framework of this design project the Lindab Z purlin is suggested for the roof system. It is a practical experience that the optimal distance between two neighboring purlins is e=1,5

÷

Fig.5 Optimal arrangement of purlin system in term of the distance Ls

Ls

≈

÷

≈

≈

Ls - distance between the ridge point of the roof and the outer point of the edge purlin in

The practical purlin arrangement shown in Figure 6 may differ from the theoretical arrangement shown in Figure 5:

(i) at the ridge double purlins are used (Figure 6a);

(ii) at the edge of the roof special edge shape is used (Figure 6b).

The distances denoted in Figure 6 may be calculated by the following expressions:

α

α

α

where hbsw is the depth of the wall beams and g=150

÷

Fig. 6 The scheme of the practical purlin arrangement: (a) double purlins at the ridge; (b) special shaped edge purlin 1.9 Wind bracing system

The wind bracing system is shown in Figure 7. According to the Concept A (see Section 1.8) the purlin system is independent to the wind bracing system, therefore the main frames should be connected to each other by bracing bars (see the dashed lines).

Fig. 7 The wind bracing system which is independent to the purlin system (dashed lines denote the bracing bars)

e e g (b) (a) f Ls _e

These bars may be connected to the beams under every second purlin, close to the upper flange of them. It is noted that according to the Concept B the longitudinal bracing bars could be replaced by the purlins (see the continuous lines).

1.10 Application

1.6 Arrangement of the purlin system

- distance between the edge purlin and the theoretical point of the frame corner [mm] f h c 2 h bsw cos α π 180 . f=456.942

- distance between the edge beam and the ridge of the frame [mm]

L s 1000 L. 2 cos α π 180 . . h b sin α π 180 . . 2 f L s 1.03910 4 . = - interval of purlins [mm] four spans _{e 4} L s 4 e 4 2.598 10 3 . = six spans _{e 6} L s 6 e 6 1.732 10 3 . = applied spans e _{e 4} e=2.598 10. 3

The e=2598 mm distance is choosen for the arrangement of the purlin system (except the last distance at the ridge) ! 1.11 Covering system

Two different constructions of the covering system are shown in Figure 8. In any case the external loads and effects are carried by the external trapezoidal sheet.

Fig. 8 Covering system with heat isolation and double trapezoid sheets: (a) isolation is placed between the purlins

(b) isolation is placed on the purlins external trapezoid sheet

vapour permeable leaf heat isolation (150 mm) vapour proof leaf internal trapezoid sheet

external trapezoid sheet vapour permeable leaf heat isolation (150 mm) vapour proof leaf internal trapezoid sheet

spacer members

1.12 Preliminary drawings

The aim of the preliminary drawing is to establish the initial parameters of the design in drawings. The preliminary drawings are the basic documents for the structural analysis and design. Therefore, these drawings should contain all the initial parameters of the building used in the procedure of the analysis and design. These drawings should not be confused with the architectural plans and the scenario of the building. In this design project the following three drawings should be prepared (the format of the drawings is A4 or A3):

• top view of the foundation and the roof structure

• side views of the building

• side views of the main frame.

1.12.1 Foundation and roof view (M 1:200)

The building is symmetric, therefore the one half of the drawing may show the top view of the foundation, while the other half of it may show the top view of the roof. If the wind bracing system follows the Concept A (the bracing system is independent to the purlin system), the top view side of the drawing may be divided into two symmetrical parts: the upper quarter of the drawing shows the arrangement of the purlin system, while the lower quarter of the drawing shows the bars of the bracing system. The view of the foundation and the roof system is projected to the horizontal plane. The drawing gives exact answer to the following parameters:

• top view of the foundation (right side of the drawing): - theoretical span (L)

- number of the frames (n) - distance between the frames (c)

- arrangement and initial parameters of the columns in the side walls - scheme of the foundation

• top view of the roof structure (left side of the drawing): - arrangement and initial parameters of the purlins

- arrangement and parameters of the wind bracing system.

The drawing of the top view of the foundation and the roof structure which satisfies the Sections 1.7 and 1.10 (Applications) is shown in the Figure 9. It can be seen that the bracing system follows the Concept A. Furthermore, it can be seen that the column foundations are tied up by beams, and this system works together with the concrete slab of the industrial floor. 1.12.2 Side views of the building (M 1:200)

The aim of the side view drawings of the building is to give direct information about the arrangement of the wall beams and about the area and place of the openings as well. The building is symmetrical, therefore the right hand side of the drawing may show the arrangement of the openings, while the left hand side may show the arrangement of the wall beams and the bracing system. The drawing should give exact answer for the following parameters:

- places and initial section of the wall beams

- arrangement and initial sections of the bracing system - place and area of the openings.

The drawing of the side view does not contain architectural sceneries, it concentrates to the above parameters. The drawing which satisfies the Sections 1.7 and 1.10 (Applications) is shown in the Figure 10.

1.12.3 Side view of the frame (cross section of the building) (M 1:100)

The aim of the side view drawing of the frame is to give direct information to take the structural and load model for analysis and design. The frame is symmetrical, therefore the right hand side of the drawing may contain the general parameters, while the left hand side of it may show the theoretical parameters and the arrangement of the structural members:

• general parameters (right hand side)

- distance between the outer flanges of the columns (b) - height of the facade (Hw);

- slope of the roof (αααα); - height of the structure (Ht);

- parameters of the column section (bcf;tcf.hcw;tcw);

- parameters of the beam section (bbf;tbf.hbw;tbw);

- parameters of the haunching (bhf;thf.hhw;thw);

- type of the joints; - type of the column base; - layers of the covering system;

• arrangement of members and theoretical parameters (left hand side)

- theoretical height of the columns (Hc);

- theoretical height of the frame (Hf);

- arrangement and initial section of the purlins; - arrangement and initial section of the wall beams; - length of the haunch.

The drawing which satisfies the Sections 1.7 and 1.10 (Applications) is shown in the Figure

11. It can be seen that the column foundation, the beams between the concrete blocks and the

Department of Structural Engineering BUTE Steel Buildings

Draw No. 1: Preliminary drawing/Top view M 1:200

Designer Clever Student (XYZVW) Supervisor Clever Teacher assistant professor 6000 6000 6000 19500 4632 4632 10126 Purlin system Bracing system 10236 2559 2559 2559 2559 9750 5118 4632 Bracing bars (CHS) Bracing cross bars (L or rod section)

Lindab purlin (Z section)

Wall columns (HEA or IPE)

Department of Structural Engineering BUTE Steel Buildings

Draw No. 002: Preliminary drawing/Side view M 1:200

Designer Clever Student (XYZVW) Supervisor Clever Teacher assistant professor

0,0 3,600

4,600

6000 6000 6000 length of the window: 11600 18 400 3000 1200 2900 600 18 000 3000 1200 2900 600 0,0 7,900 3,600 4,600 9,650 4632 5118 5000 (door) 3600 (window) 7700 7700 Bracing bars (CHS) Bracing diagonals (L or rod section)

Lindab wall beam (C200)

Department of Structural Engineering BUTE Steel Buildings

Draw No. 003: Preliminary drawing /Side view of the frame M 1:200

Designer Clever Student (XYZVW)

Supervisor Clever Teacher assistant professor

19 500/2 20 000/2

Rigid column base Welded I section: - flanges: 240-16 - web: 468-8 - flanges: 240-16 - web: 368-6 Moment resistant end-plated bolted connections 9019 2597 2598 3500

- vapour permeable leaf - heat insulation (150 mm) - vapour proof leaf - internal trapezoidal sheet

3000 2900 600 1200 7300 7500 9219 Purlins (Lindab Z200)

Wall beams (Lindab C200)

Haunch:

- flanges: 240-20 - web: 330-6

CHS bracing members

Slope of roof: 100

Practice 2

LOADS AND EFFECTS ON THE

BUILDING

Written in the framework of the project TÁMOP 421.B JLK 29.

2.1 General

The loads and effects in general are the subject of the course of Basis of the design (BMEEOHSAT16) in the framework of the BSc education. Here the application of the general knowledge to the design of simple halls is presented. The loads and effects should be determined using the following design standards:

• EN 1991-1-1:2005 Eurocode 1: Actions on structures Part 1-1: General actions. Densities, self-weight, imposed loads for buildings (EC1-1-1);

• EN 1991-1-2:2005 Eurocode 1: Actions on structures. Part 1-2: General actions. Actions on structures exposed to fire (EC1-1-2);

• EN 1991-1-3:2005 Eurocode 1: Actions on structures. Part 1-3: General actions. Snow loads (EC1-1-3);

• EN 1991-1-4:2005 Eurocode 1: Actions on structures - General actions - Part 1-4: Wind actions (EC1-1-4);

• EN 1998-1:2005 Eurocode 8: Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings (EC8-1).

In the present phase of the design procedure we are dealing with the basic loads and effects which act on the building. The applied load cases and load combinations are discussed in the sections which are denoted to the design of the structural members. In general the following loads and effects should be taken into consideration in the case of a symmetric and duopitch building:

• dead loads;

o weight of the structural members; o weight of the covering system; o other dead load type loads;

• meteorological loads and effects; o snow load; o wind effect; • imposed loads; • seismic effect; • fire effect. 2.2 Dead loads

2.2.1 Weight of the structural members

The self weight of the structural members should be taken on the base of the initial structural parameters. The evaluation should follow the specifications of EC1-1-1. The density of the steel material is 78,5 kN/m3. The dead loads which are based on the initial design parameters should not be changed unless these initial design parameters have changed considerably. The change is considerable if the effect of the change of any parameter on the design forces exceeds by 3%. If the effect of the change is at the safe side, the modification of the initial loads may be neglected. The theoretical self weight of the structural members of the frame is automatically taken into consideration by the analysis software (Axis, ConSteel, FEM-Design), but the self weight of the purlins and trapezoidal sheets or panels should be given by the designer (DimRoof). The self weights of the additional elements (stiffeners, bolts, ect.) are usually taken into consideration by 5÷10% of the theoretical self weight.

The weight of the covering system of the roof and the walls should be evaluated according to the layers specified in the preliminary drawing (see Figure 8 in Practice 1). The densities of the materials may be found in the appropriate tables of EC1-1-1. The weights structural sections (purlin, wall beam, etc.) may be found in the product information of the producers. 2.2.3 Other dead load type loads

This type of loads refers to the loads which are acting regularly. Such loads are the weights of the electrical and mechanical equipments, for example the weights of lighting, climate technology. Such dead load is the weight of the earth layer of the special ‘greenroof’. These type of loads should be specified by the mechanical engineer and the architectural engineer, respectively. The applied intensity and the distribution of this type of loads should satisfy the specifications of EC1-1-1. In present design project – in lack of precise information – we can apply approximately 0,25kN/m2

÷

2.2.4 Application

2. LOADS AND EFFECTS

2.1 Dead loads

2.1.1 Weights of the structural members and the layers of the covering system

- external trapizoidal sheet : LTP 85 t=0.75mm [kN/m2_]

q tr.ext 0.0804

- internal trapizoidal sheet: LPT 20 t=0.4mm [kN/m2_]

q tr.int 0.0390

- heat insulation (mineral rockwool) [kN/m2_]

density [kN/m3_{] and thickness [m] γ}

iso 1.5

thickness [m] _{t iso 0.150}

q iso t iso.γ iso q iso 0.225=

- further layers for insulation [kN/m2_]

q iso.other 0.100

- purlin: LINDAB Z 200 (t=2,0) [kN/m] _{q purlin 0.0579}

- main frame: automatically considered 2.1.2 Installation loads

Installation load projected to the total area of the roof

- lightning [kN/m2_] q light 0.10 - building equipments [kN/m2_] q equip 0.15 - other loads [kN/m2_] q other 0.20

2.3 Meteorological loads and effects

2.3.1 Snow load

2.3.1.1 Surface snow load

The snow loads on the building are determined by the specifications of EC1-1-4. In Hungary the additional specifications of the Hungarian National Annex (HNA) should be considered. The surface snow load may be calculated as follows:

- persistent and transient design situations: s=

µ

µ

s snow load on the horizontal ground [kN/m2];

µ

Ce exposure coefficient;

Ct thermal coefficient;

sk characteristic value of the ground snow load [kN/m2]-ben;

sAd exceptional value of the ground snow load [kN/m2]-ben.

The characteristic value of the ground snow load according to the specification HNA 1.5 is the following:       ₊ ⋅ = 100 A 1 25 , 0 sk but sk ≥1,25

where A is the height of the ground above the sea level in [m]. The exceptional value of the ground snow load according to the specifications HNA 1.2 and 1.7 is the following:

k esl

Ad C s

s = ⋅

where Cesl is the exceptional snow load factor which is 2,0. The exposure factor Ce depends on

the topography:

- windswept: Ce = 0,8

- normal: Ce = 1,0

- sheltered: Ce = 1,2

Windswept topography: flat unobstructed areas exposed on all sides without, or little shelter

afforded by terrain, higher construction works or trees.

Normal topography: areas where there is no significant removal of snow by wind on construction

work, because of terrain, other construction works or trees.

Sheltered topography: areas in which the construction work being considered is considerably

lower than the surrounding terrain or surrounded by high trees and/or surrounded by higher construction works.

In the present design project it is assumed that the snow is not prevented from sliding off the roof, and the shape factor

µ

Tab.3 Shape factor for duopitch roof (free slip of the snow) tető hajlásszöge (αααα) 0°°°° ≤ αααα ≤ 30°°°° 30°°°° < αααα < 60°°°° 60°°°° ≤ αααα

µ1 0,8 0,8(60-α)/30 0,0

The thermal coefficient Ct should be used to account for the reduction of snow loads on roofs

with high thermal transmittance (> 1 W/m2K), in particular for some glass covered roofs, because of melting caused by heat loss. In the present design Ct=1,0 may be applied.

In regions with possible rainfalls on the snow and consecutive melting and freezing, snow loads on roofs should be increased, especially in cases where snow and ice can block the drainage system of the roof. In the present design this effect may be neglected.

2.3.1.2 Application

2.2 Snow load

2.2.1 Snow load for the persistent design situation

- height of the building ground [m] _{A see} 300

- charactheristic ground snow load [kN/m2_]

s k 0.25 1. A see₁₀₀ s k 1= s k 1.25

- exposure coefficient (normal) _{C e 1.0}

- thermal coefficient _{C t 1.0}

- shape coefficient (α<30 deg) µ ₁ 0.8

- ground snow load [kN/m2_{] s µ}

1 C e. .C t.s k s= 1

2.2.2 Snow load for the exceptional design situation

- exceptional snow load coefficient _{C esl 2.0}

- exceptional snow load [kN/m2_]

s Ad C esl s k. s Ad 2.5=

- exceptional ground snow load [kN/m2_]

s r µ 1 C e. .C t.s Ad s r 2=

2.3.2 Wind effect

2.3.2.1 Wind pressure on surfaces

The effect is specified by the EC1-1-4. The wind load is the compressive or the sucking load which is caused by the wind effect. The wind load is perpendicular to the surface. The load may affect on the external and the internal surfaces as well. Besides the normal wind load the friction load of the wind effect may be considered. Any wind effect may be considered by a simplified set of loads which is equivalent to the effect of the turbulent peak velocity. The wind load belongs to the group of imposed loads. The wind effect depends on the following parameters of the building:

• dimensions;

• shape;

The external and internal wind pressure may be calculated by the following expressions: pe e p e q (z ) c w = ⋅ pi i p i q (z ) c w = ⋅ where ) z (

q_p is the peak velocity pressure;

i e,z

z is the external and internal reference heights;

pi pe,c

c is the external and internal pressure coefficients.

Figure 12 shows the physical direction of the wind loads in the cases of wind sucking (-) and

wind pressure (+). It is noted that the summation of the wind loads should be done by these physical directions.

Fig.12 Physical direction of the wind loads in the cases of wind sucking (-) and wind pressure (+)

The reference heights may be determined using the following rules (see Figure 13):

• if the height of the building (h) is not greater than the width (b) of the windward surface of the building:

h

z_e= and z_i =z_e;

• if the height of the building (h) is greater than b but it is not greater than 2b: - zone for height of b: ze=b and zi = ze;

- zone for height of (h-b): ze=h and zi =ze.

Fig.13 Reference heights for plane buildings

(-)

szí

(+)

2.3.2.2 Peak velocity pressure

The peak velocity pressure may be calculated by the following expression:

b e p(z) c(z) q q = ⋅ where ) z (

ce is the exposure factor; b

q is the basic velocity pressure.

The basic velocity pressure may be calculated as follows:

) z ( v 2 1 q_b = ρ⋅ _b2

where the density of the air:

3 m kg 25 , 1 = ρ

and where the basic wind velocity:

0 , b season dir b c c v v = ⋅ ⋅

According to the Hungarian National Annex (HNA) the initial basic wind velocity and the direction and season coefficients may be taken as

s m 6 , 23 vb,0 = ; cdir=0,85 ; cseason=1,0

The exposure factor is the ratio of the peak velocity pressure to the basic velocity pressure, and it may be calculated by the following expression:

) z ( c ) z ( c )) z ( I 7 1 ( ) z ( c 02 2 r v e = + ⋅ ⋅ ⋅ where ) z (

c_r is the roughness factor; )

z (

c0 is the orography factor; )

z (

I_v is the turbulence intensity.

The roughness factor depends on the reference height: - if z<z_min than _      ⋅ = 0 min r r z z ln k ) z ( c - if z≥z_min than _      ⋅ = 0 r r z z ln k ) z ( c where the terrain factor:

07 , 0 II , 0 0 r z z 19 , 0 k _       =

where z_0,II =0,05

[ ]

Tab.4 Roughness lengths and minimum heights terrain category

0

z [m] z_min[m]

0 Sea or coastal area exposed to the open sea 1 _{0,003 1}

I Lakes or flat and horizontal area with negligible vegetation and without obstacles

0,01 1

II Area with low vegetation such as grass and isolated obstacles (trees, buildings) with separations of at least 20 obstacle heights

0,05 2

III Area with regular cover of vegetation or buildings or with isolated obstacles with separations of maximum 20 obstacle heights (such as villages, suburban terrain, permanent forest)

0,3 5

IV Area in which at least 15 % of the surface is covered with buildings and their average height exceeds 15 m

1,0 10

When the average slope of the upwind terrain is less than 3°, the orography factor may be 0 , 1 ) z ( c₀ = .

The turbulence intensity may be calculated by the following expressions: - if z<z_min than       ⋅ = 0 min 0 I v z z ln ) z ( c k ) z ( I - if z≥z_min than       ⋅ = 0 0 I v z z ln ) z ( c k ) z ( I

where the turbulence factor may be kI=1,0.

The exposure factor can be calculated using the Figure 4.2 of EC1-1-4 (see the graphics below).

2.3.2.3 Application

2.3 Wind loads

2.3.1 Basic velocity pressure

- initial parameters specified by the Hungarian NA

initial basic velocity [m/s] _{v b.0 23.6}

direction factor _{c dir 0.85}

season factor _{c season} 1.0

air density [kg/m3_{] ρ 1.25}

- basic velocity [m/s] _{v b c dir c season}. ._{v b.0 v b 20.06}=

- basic velocity pressure [kN/m 2_]

q b 1 2 ρ . _{.v b}2 1 1000 . _{q b 0.252=}

2.3.2 Peak velocity pressure

- parameters for terrain category (Category III) _{z 0 0.3}

z min 5.0

- parameter for category II [m] _{z 0.II 0.05}

- terrain factor _{k r 0.19} z 0

z 0.II

0.07

. _{k r 0.215=}

- reference height z _{H f} z= 9.019

- roughness coefficient _{z z min}>

c r k r ln z z 0

. _{c r 0.733=}

- orography coefficient (plane country, slope less than 3 degs) _{c 0 1.0}

- turbulence coefficient (no specific rule) _{k I 1.0}

- turbulence intensity _{I v} k I c 0 ln z z 0 . I v 0.294= - exposure factor _{c e} 1 _{7 I v}. ._{c r}2._{c 0}2 _{c e 1.643}= q p c e q b. q p 0.413=

- peak velocity pressure [kN/m2_]

The peak velocity pressure can be determined or checked using the Figure 4.2 of the EN 1991-1-4:

reference height z= 9.019

terrain category: III

exposure factor by the graphics _{c e.graphics} 1.63

peak velocity pressure [kN/m2_]

q p.graphics c e.graphics q b. q p.graphics 0.41=

2.3.2.4 External pressure coefficient

The external pressure coefficients depend on the reference height and the size of the loaded area A, which is the area of the structure that produces the wind action in the section to be calculated. The external pressure coefficients are given for two loaded areas:

- cpe,1 is for area of 1.0 m

2

as local coefficient; - c_pe,10 is for area of 10.0 m2 as overall coefficient.

Between the two limit areas (for 1m2<A<10m2) the following interpolation may be used (see

Figure 14): A lg ) c c ( c c_pe,A = _pe,1− _pe,1− _pe,10 ⋅ ₁₀

Fig.14 Interpolation of the external pressure coefficient

In the present design project the interpolation may be neglected. For the design of the trapezoidal sheet the cpe.1 may be used, while for the design of the purlins and the main frames

the cpe.10 may be used. The external pressure coefficients are given in tables. The tables for

symmetric buildings with duopitch roofs are contained in the following Annexes: - Annex 1: Wind effect on vertical walls of the building

- Annex 2: Cross wind effect on the roof (θ=0°)

- Annex 3: Longitudinal wind effect on the roof (θ=90°)

Notes for application of the tables

The tables of the external pressure coefficients have more rows (one row belongs to one slope) where there are two sub-rows (for example one “+” and one “-“ values). It is an important rule that for one roof plane (actually for the half roof) the sub-rows should not be changed. For example in the Annex 2 for roof slope of 5o there are two sub-rows which define four combinations:

Zones of the roof

F G H I J

α αα α=5o

_{cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1}

1 _{-1,7 -2,5 -1,2 -2,0 -0,6 -1,2 -0,6 -0,6 +0,2 +0,2}

2 -1,7 -2,5 -1,2 -2,0 -0,6 -1,2 -0,6 -0,6 -0,6 -0,6

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

4 _{0 0 0 0 0 0 -0,6 -0,6 -0,6 -0,6}

The automatic use of the tables may lead to a large number of wind load cases. At the design of simple buildings the designer may select the most dangerous case by a decision based on his experience and intuition.

cpe,1

cpe,10

2.3.2.5 Application

2.3.3 External wind pressure 2.3.3.1 Cross wind (0 degree)

Initial parameters

- size of the building [m]

width perpendicular to the wind direction _{b 0 d b 0 36}=

width parallel to the wind direction _{d 0 b d 0 20}=

height _{h 0 H f h 0 9.019}= η ₀ h 0 d 0 η 0 0.451 = - size factor

- size of the zones [m] _{e 0 2 h 0}. _{e 0 18.038}=

e 0.4 e 0

4 e 0.4 4.51=

e 0.10 e 0

10 e 0.10 1.804=

-slope of the roof (approximately) [deg] 10

Indeces used below

A,B,... mark of the wall and the roof zone 0; 90 mark of the wind direction in degree 1;10 mark of the loaded area (1m2 _{or 10 m}2₎ Wind pressure on the walls

According to Annex 1:

- interpolation factor for the case of 0,25<h/d<1,0 β ₀ η 0 0.25

0.75 β 0 0.268 = - pressure coefficients c pe.A.0.10 1.2 c pe.B.0.10 0.8 c pe.C.0.10 0.5 c pe.D.0.10 0.7 0.1.β 0 c pe.D.0.10 0.727= c pe.E.0.10 0.3 0.2.β _{0 c pe.E.0.10}= 0.354 - wind pressures [kN/m2_] w A.0.10 c pe.A.0.10 q p . _{w A.0.10}= 0.496 w B.0.10 c pe.B.0.10 q p. w B.0.10= 0.33 w C.0.10 c pe.C.0.10 q p. w C.0.10= 0.207 w D.0.10 c pe.D.0.10 q p. w D.0.10 0.3= w E.0.10 c pe.E.0.10q p. w E.0.10= 0.146

Wind pressure on the roof

Annex 2 contains the pressure coefficients for roof slope of 10 deg which were interpolated linearly between 5 and 15 degrees given by the EN 1991-1-4.

For roof zones of F-G-H there are two cases: wind sucking and wind pressure. zones of F-G-H

- wind sucking [kN/m2_]

c pe.F.0.1 2.25 _{w F.0.1 c pe.F.0.1 q p}. _{w F.0.1}= 0.929 c pe.F.0.10 1.30 _{w F.0.10 c pe.F.0.10 q p}. _{w F.0.10}= 0.537

c pe.G.0.1 1.75 _{w G.0.1 c pe.G.0.1 q p}. _{w G.0.1}= 0.723 c pe.G.0.10 1.0 _{w G.0.10 c pe.G.0.10q p}. _{w G.0.10}= 0.413 c pe.H.0.1 0.75 _{w H.0.1 c pe.H.0.1 q p}. _{w H.0.1}= 0.31 c pe.H.0.10 0.45 _{w H.0.10 c pe.H.0.10 q p}. _{w H.0.10}= 0.186 - wind pressure [kN/m2_] c pe.FGH.0 0.1 w FGH.0 c pe.FGH.0 q p. w FGH.0 0.041=

c pe.I.0.1 0.50 _{w I.0.1 c pe.I.0.1 q p}. _{w I.0.1}= 0.207 c pe.I.0.10 0.50 _{w I.0.10 c pe.I.0.10 q p}. _{w I.0.10}= 0.207 c pe.J.0.1 0.65 _{w J.0.1 c pe.J.0.1 q p}. _{w J.0.1}= 0.269 c pe.J.0.10 0.4 _{w J.0.10 c pe.J.0.10 q p}. _{w J.0.10}= 0.165

2.3.3.2 Longitudinal wind direction (90 degrees) Initial parameters

- size of the building [m]

width perpendicular to the wind direction _{b 90 b b 90 20}=

width parallel to the wind direction _{d 90 d d 90 36}=

height _{h 90 H f h 90 9.019}=

- size factor η₉₀ h 90

d 90 η90=0.251

- size of the zones [m]

e 90 2 h 90. e 90 18.038=

e 90.2 e 90₂ e 90.2 9.019=

e 90.4 e 90₄ e 90.4 4.51=

e 90.5 e 90₅ e 90.5 3.608=

e 90.10 e 90₁₀ e 90.10 1.804=

- slope of the roof (approximately) [deg] 10

Wind pressure on the walls According to Annex 1 - size factor β ₉₀ h 90 d 90 β 90=0.251 - pressure coefficients c pe.A.90.10 1.2 c pe.B.90.10 0.8 c pe.C.90.10 0.5 c pe.D.90.10 0.7 c pe.E.90.10 0.3

- wind pressures [kN/m2_]

w A.90.10 c pe.A.90.10 q p. w A.90.10= 0.496 w B.90.10 c pe.B.90.10q p. w B.90.10= 0.33 w C.90.10 c pe.C.90.10q p. w C.90.10= 0.207 w D.90.10 c pe.D.90.10q p. w D.90.10 0.289= w E.90.10 c pe.E.90.10q p. w E.90.10= 0.124

Wind pressure on the roof According to Annex 3 c pe.F.90.1 2.1 _{w F.90.1 c pe.F.90.1 q p}. _{w F.90.1}= 0.868 c pe.F.90.10 1.45 _{w F.90.10 c pe.F.90.10q p}. _{w F.90.10}= 0.599 c pe.G.90.1 2.0 _{w G.90.1 c pe.G.90.1q p}. _{w G.90.1}= 0.826 c pe.G.90.10 1.30 _{w G.90.10 c pe.G.90.10q p}. _{w G.90.10 0.537}= c pe.H.90.1 1.2 _{w H.90.1 c pe.H.90.1 q p}. _{w H.90.1}= 0.496 c pe.H.90.10 0.65 _{w H.90.10 c pe.H.90.10q p}. _{w H.90.10}= 0.269 c pe.I.90.1 0.55 _{w I.90.1 c pe.I.90.1 q p}. _{w I.90.1}= 0.227 c pe.I.90.10 0.55 _{w I.90.10 c pe.I.90.10q p}. _{w I.90.10}= 0.227

2.3.2.6 Internal pressure coefficient

Internal and external pressures shall be considered to act at the same time (but external pressure may act without internal pressure). The internal pressure coefficient (cpi) depends on

the size and distribution of the openings (windows and doors). When in at least two sides of the buildings (walls or roof) 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 here.

For a building with a dominant face the internal pressure should be taken as a fraction of the external pressure at the openings of the dominant face. A face of a building should be regarded as dominant when the area of openings at that face is at least twice the area of openings and leakages in the remaining faces of the building considered. When the area of the openings at the dominant face is twice the area of the openings in the remaining

faces,

pe pi 0,75 c

c = ⋅

When the area of the openings at the dominant face is at least 3 times the area of the openings in the remaining faces,

pe pi 0,90 c

c = ⋅

where cpe is the value for the external pressure coefficient at the openings in the dominant

face. When these openings are located in zones with different values of external pressures an area weighted average value of cpe should be used.

In the present design project we may assume that there is no dominant face and the distribution of the openings is uniform. In this case the internal pressure coefficient may be calculated as follows:

• if h/d ≤0,25 - if µ ≤0,33 than c_pi =0,35 - if µ >0,9 than cpi =−0,3 - if 0,33<µ ≤0,9 than c_pi =0,726−1,14µ • if h/d ≥1,0 - if µ ≤0,33 than cpi =0,35 - if µ >0,95 than c_pi =−0,5 - if 0,33<µ ≤0,95 than cpi =0,802−1,37µ

The opening ratio in the expressions may be calculated with the following term:

∑

∑

µ

where

∑

∑

2.3.2.7 Application

2.3.4 Internal wind pressure 2.3.4.1 Parameters of the openings

- area of openings in the side walls [m2_]

width of the area of windows [m] _{L w.s 23.2}

height of the area of windows [m] _{h w.s 1.2}

A s L w.s h w.s. A s 27.84=

- area of openings in the end walls [m2_]

windows

width of the area of windows [m] _{L w.e 12.6}

height of the area of windows [m] _{h w.e 1.2}

A e.w L w.e h w.e. A e.w 15.12=

industrial door

width of the door [m] _{b w.d 5.0}

height of the door [m] _{h w.d 4.6}

A e.d b w.d h w.d. A e.d 23= A f A e.w A e.d A f 38.12=

2.3.4.2 Cross wind effect (0 degree) - initial parameters

area of all openings [m2_]

A sum 2 A s A f. A sum 131.92=

area of openings with negative or zero external pressure [m2_]

opening ratio µ ₀ A neg.0

A sum µ 0=0.789

- pressure coefficients

for h/d=0.25 _{c pi.0.0.25 0.726 1.14}.µ _{0 c pi.0.0.25}= 0.173

for h/d=1.00 _{c pi.0.1 0.802 1.37}.µ _{0 c pi.0.1}= 0.279

c pi.0 c pi.0.0.25 β 0 c pi.0.1. c pi.0.0.25 c pi.0= 0.202

- wind pressure [kN/m2_]

w i.0 c pi.0 q p

. _{w i.0}= 0.083

2.3.4.3 Longitudinal wind effect (90 degrees)

- initial parameters

area of openings with negative and zero external wind pressure coefficient [m2_]

A neg.90 A f 2 A s. A neg.90 93.8=

opening ratio

µ ₉₀ A neg.90

A sum µ 90=0.711

- internal pressure coefficient

for h/d<0.25 _{c pi.90 0.726 1.14}.µ _{90 c pi.90}= 0.085

- wind pressure [kN/m2_]

w i.90 c pi.90 q p

. _{w i.90}= 0.035

2.4 Imposed loads

The imposed loads are specified by the EC1-1-1. The determination of the imposed loads should be based on careful examination of the design situation and extended consultations with the design partners (mechanical designer, electrical designer, etc.). The roof structures are classified into categories. The standard orders a distributed and a concentrated fictive load to every category. In the present design situation the walking on the roof is not allowed, except maintenance and repairing work, therefore the roof belongs to the category H. Table 5 shows the design imposed loads for the category H.

Tab.5 Imposed loads for roof of category H slope of roof α distributed load     2 k m kN q concentrated load

[ ]

Notes: between the two limits linear interpolation may be used

The imposed load and the snow load shall not be considered to act at the same time. Since the effect of the snow load is greater, the imposed load may be neglected in the present design. It is noted that the concentrated imposed load (Qk) may be relevant at the design of the trapezoid

2.5 Seismic effect

The seismic effect is specified by the EC8-1. Due to the earthquake the displacement and the acceleration of the ground is changing in time. The seismic design of the buildings is based on the consideration of the ground acceleration. The acceleration has vertical and horizontal components, but in Hungary the vertical component may be neglected. The horizontal component of the ground acceleration depends on the reference peak ground acceleration of type A ground:

gR I

g a

a =γ ⋅

where agR is the reference peak ground acceleration of type A ground (see Figure 15),

γ

importance factor given in Table 6. The building in the present design project may belong to importance category I or II.

Tab.6 Importance categories of buildings

importance category importance factor

γγγγI

I. Buildings of minor importance for public safety, e.g. agricultural buildings, etc.

0,8 II. Ordinary buildings, not belonging in the other categories. 1,0 III. Buildings whose seismic resistance is of importance in view of

the consequences associated with a collapse, e.g. schools, assembly halls, cultural institutions etc.

1,2

IV. Buildings whose integrity during earthquakes is of vital importance for civil protection, e.g. hospitals, fire stations, power plants, etc.

1,4

Fig.15 The reference peak ground acceleration of type A ground in Hungary

2.6 Fire effect

The fire effect on the building is specified by the EC1-1-2. In the present design project the

standard (ISO) fire curve should be considered at the design of the main frame. The

required fire resistance is 15 minutes, R15, which means of fire resistance class IV and one floor building. All the steel structural members (I sections) of the main frame are unprotected,

and they are imposed to fire effect at four sides. The main frame is examined for fire effect as an isolated structure, and the room which is specified by the frame is a unified fire compartment (see the Figure 16).

Fig.16 Unified fire compartment of the isolated main frame structure

2.7 Application

2.4 Imposed load

- service class of the roof: H - slope of the roof: α=10o - imposed load

surface distributed load [kN/m2_]

q k 0.4

concentrated load [kN] _{Q k 1.0}

2.5 Seismic effect

- importance category of the building: II.

γ _I 1.0

- importance factor

-seismic zone: region of Esztergom, Hungary

- horizontal component of the reference peak ground acceleration [m/s2_]

a gR 1.5 [m/s2_]

2.6 Fire effect

- applied temperature-time curve: standard (ISO) - category of fire resistance: IV (simple building)

- required limit for fire resistance (R15) _{t fi 15} [min]

- type of the passive fire protection: "unprotected I section exposed to fire at four sides" - fire compartment: "internal room determined by the main frame structure"

Standard fire curve Required resistance: 15 min

Annex 1

External pressure coefficient for vertical walls

(it is valid for case of h<b)

zones

A B C D E

h/d

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1

1 _{-1,2 -1,4 -0,8 -1,1 -0,5 0,8 1,0 -0,5} ≤0,25 _{-1,2 -1,4 -0,8 -1,1 -0,5 0,7 1,0 -0,3} w _b d

D

E

A

B

C

A

B

A

B

C

A

B

Side zones for e<d: ) h 2 ; b min( e=

Side zones for e>d:

Note

In the case of rectangular building b is the width of the side which is affected by the wind, and d is the width of the perpendicular side. The wind may affect to the longitudinal side (

θ

θ

Annex 2

External pressure coefficients of the roof due to cross wind (

θθθθ

=0

)

(it is valid for case of h<b)

zones

F G H I J

α αα α

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1

+0,2 +0,2 +0,2 +0,2 0* _{-1,8 -2,5 -1,2 -2,0 -0,7 -1,2} -0,2 -0,2 -0,2 -0,2 -1,7 -2,5 -1,2 -2,0 -0,6 -1,2 +0,2 +0,2 5 _{+0,0 +0,0 +0,0 +0,0 +0,0 +0,0} -0,6 -0,6 -0,6 -0,6 -1,3 -2,25 -1,0 -1,75 -0,45 -0,75 -0,4 -0,65 10** _{+0,1 +0,1 +0,1 +0,1 +0,1 +0,1} -0,5 -0,5 -0,3 -0,3 -0,9 -2,0 -0,8 -1,5 -0,3 -0,3 -0,4 -0,4 -1,0 -1,5 15 _{+0,2 +0,2 +0,2 +0,2 +0,2 +0,2 +0,0 +0,0 +0,0 +0,0} * given for the case of sharp eaves of flat roof (no parapet or curved eaves)

** given by linear interpolation between slopes of

α

α

e/10 e/10 h α w θθθθ=00 w G H J I F F e/4 e/4 Ridge b

Annex 3

External pressure coefficients of the roof due to longitudinal

wind (

θθθθ

=90

)

(it is valid for case of h<b)

F G H I

α αα α

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1

+0,2 +0,2 0* _{-1,8 -2,5 -1,2 -2,0 -0,7 -1,2} -0,2 -0,2 5 _{-1,6 -2,2 -1,3 -2,0 -0,7 -1,2 -0,6 -0,6} 10** _{-1,45 -2,1 -1,3 -2,0 -0,65 -1,2 -0,55 -0,55} 15 _{-1,3 -2,0 -1,3 -2,0 -0,6 -1,2 -0,5 -0,5} * given for the case of sharp eaves of flat roof (no parapet or curved eaves) ** given by linear interpolation between slopes of

α

α

h θθθθ=900 w w G H I F H e/2 e/10 Ridge G F e/4 I e/4

Practice 4

DESIGN OF THE SECONDARY

ELEMENTS

Written in the framework of the project TÁMOP 421.B JLK 29.

4.1 General

In this project the external trapezoidal sheet and the purlins as secondary elements are designed. The design of the elements of the façade is based on the same methods, therefore it is neglected. The design methods are specified by the EN 1993-1-3 Eurocode 3: Design of Steel structures Part 1-3: Cold-formed thin gauge members and sheeting (EC3-1-3). The theoretical background of this code is the objective of the MSc courses. The most important expressions used in the design are summarized in the Table 7. In the practice the direct use of the theory and methods given by the code may be neglected since the producers of the products (purlins, sheeting) supply design tables and design software. Design of the Lindab elements is supported by the DimRoof software which is suggested using in this project. The software may be safely used without any deep knowledge of theoretical background on the design of cold-formed thin gauge elements.

Tab.7: Most important expressions used in design theory of cold-formed thin gauge elements (informative)

special structural properties special structural behaviors specialties in design

Large plate slenderness (b/t) Plate buckling „Shear lag” effect Flange induced buckling

Class 4 cross-sections

Partially stiffened plates Distorsional instability Class 4 cross-sections Buckling of the stiffeners

One symmetric or no symmetric cross sections

Lateral torsional buckling Flexural-torsional buckling

Class 4 cross-sections Global instability Relatively thin plates Relatively large initial

geometrical imperfections

Plate thickness as the parameter of the design Special connections Special structural failing modes New design methods based

on tests

The loads for design of the purlins and sheeting should be calculated taking the effects of the slope of roof, the directions of the loads and the constructions into consideration by the following rules:

dead load and snow load are gravity loads with vertical direction;

wind pressure is perpendicular to the structural plane;

design load consists of transverse loads only (the loads which are parallel with the axis of elements may be neglected).

These rules lead to the reduction of the loads (see Figure 17). It is noted that in case of relatively small (5o÷10o)slope of roof the approximation of cos

α≅

α≅

Fig. 17 Reduction of loads

4.2 Design of the external trapezoidal sheet

Figure 8 shows the alternative constructions for covering system. Both systems have external

trapezoidal sheet which should be designed. 4.2.1 Structural model

The structural model of the external trapezoidal sheet may be approximated by a multispan continuous beam (see Figure 18), which is perpendicular to the purlins supporting it rigidly. The reference axis of the model lies in the plane of the roof. The length c1 depends on the

covering system, the length c2 is the distance between the last purlin and the ridge point (150÷200 mm).

Fig. 18 Structural model for external trapezoidal sheet

Figure 19 shows the cross-section of the beam (as 1000 mm wide part of sheet). In the case

of Lindab products the cross-section is defined by the nominal depth (eg. LTP45) and the thickness of the plate (eg. t=0,5 mm).

Slope of roof: α [deg]

Ridge point Edge point Basic load [kN/m2] ps Design load [kN/m2]

α

Edge of building Purlins as rigid supports

Fig. 19 Cross-section for the beam model

4.2.2 Load model

The sizes of the trapezoidal sheets (external and internal) normally uniform on the whole roof. For the load model the adequate loading area (the load band with 1000 mm width) along the longitudinal direction of the roof should be found (see Figure 20). The dead load and the snow load are uniformly distributed, therefore the position of the load band does not matter. The intensity of the wind load is changing from zone to zone of the roof, therefore the maximum wind pressure (Wind Load Case 1) and the maximum wind sucking (Wind Load Case 2) should be found. The wind pressure, the dead load and the snow load may be the components of Load Combination 1, while the wind sucking and the dead load may be the components of Load Combination 2. For example, in case of 50 slope of and assuming cross wind, both of wind pressure and wind sucking occur on zone J but wind sucking occurs only on zones F and G (see Annex 2) which are greater than that on zone J. Assuming longitudinal wind there are no zones where wind pressure occurs and the maximum wind sucking may occur on zones F and G (see Annex 3). Consequently, the adequate place of the load band may be considered as it is shown in Figure 20. We have to take the conclusion that the determination of the load model needs an enthusiastic work.

Fig. 20 Adequate positions of load bands in case of wind effect (for 50 slope of roof)

1000 mm Depth Plate thickness (t) Ridge line H G F F

Wind direction: 0 degree

H G

F

I

Wind direction: 90 degrees

Ridge line

J I

wind load case 2 wind load case 1

In the practice we may use approximations at the load model but it should be noted that the engineer is responsible for the consequences: approximation at side of safe may lead to extra costs, while approximation at side of unsafe may be against the law. The following two load combinations may be adequate for the examination of the external trapezoidal sheet in persistent and transient design situations:

Load Combination 1 („pressure load”)

- ultimate limit state (ULS):

γ

γ

ψ

γ

ψ

Load Combination 2 („sucking load”)

- ultimate limit state (ULS):

γ

γ

g

p characteristic value of the uniformly distributed dead load in [kN/m];

s

p characteristic value of the uniformly distributed snow load in [kN/m]; k

. w

p characteristic value of the non uniformly (but uniformly within a zone) distributed wind load in [kN/m] due to cross or longitudinal wind direction, which is the relevant, and “p” denotes wind pressure, “s” denotes wind sucking.

These loads can be calculated directly from the basic loads which were defined for the building (see Practice 2). The accidental snow load is neglected in this project.

The following partial factors should be used: γG,sup =1,35 , γG,inf =1,0 , γs =1,5 , γw =1,5 The following combination factor should be used:

ψ

The ULS load combination is relevant for checking the resistances, while the SLS load combination is relevant for checking the deflections, where the suggested limit is L/150 (L is the span of sheet).

4.2.3 Design and Documentation

Design of thin gauged Lindab trapezoidal sheet may be carried out using the DimRoof design

software. The application of the software is described in Annex 4. Before starting design the

following General Settings (design parameters) should be defined:
Function

Trapezoidal sheet belongs to “Roof” category.

Country

By option of “Hungary” we specify the Hungarian National Annex to be used.

Standard

The design is governed by the „Eurocode” standard system.

Profile

The depth of the Lindab trapezoidal sheet (LTP) may be 20 mm

÷

Extra Sidelap

The type of the sidelap (“no”; “1 trough”; 2 trough” or “double”) is determined by the architectural engineer. In this project “1 trough” is suggested using.

Default statical model

Lap of sheeting should be avoided in longitudinal direction. The length of the sheets is limited by the transportability. In this project “continuous” model is suggested.