Wind Load Example

Ferenc Papp Ph.D. Dr.habil

Steel Buildings DESIGN NOTES

Practice 2 LOADS AND EFFECTS

Written in the framework of the project TÁMOP 421.B JLK 29 Reviewed by Dr. Béla Verőci honorary lecturer

2012 Budapest

Ferenc Papp Steel Buildings – Loads and effects

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 1991-1-4:2007 Eurocode 1: Actions on structures - General actions - Part 1-4: Wind actions (EC1-1-4); • EN 1998-1:2008 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, FEMDesign), 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.

2

Ferenc Papp Steel Buildings – Loads and effects

2.2.2 Weight of the covering system 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 1.8 in Practice 1). The densities of the materials may be found in the appropriate tables of EC1-1-1. The weights of 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÷0,45kN/m2 dead load which is totally distributed on the roof. 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 kN - external trapizoidal sheet : LTP 85 t=0.75mm q tr.ext := 0.0804⋅ 2 m - internal trapizoidal sheet: LTP 20 t=0.4mm

kN

q tr.int := 0.0390⋅

2

m

- heat insulation (mineral rockwool) γ ins := 1.5 ⋅

density

kN 3

m

tins := 0.150 ⋅ m

thickness

q ins := tins⋅ γ ins = 0.225 ⋅ kN

q ins.other := 0.100 ⋅

- further layers for insulation

2

m

kN

q purlin := 0.0579⋅

- purlin: LINDAB Z 200 (t=2,0)

m

- main frame: automatically considered 2.1.2 Installation loads projected to the total area of the roof q light := 0.10 ⋅

- lightning

kN 2

m q equip := 0.15 ⋅

- building equipments

kN 2

m q other := 0.20 ⋅

- other loads

kN 2

m

3

kN 2

m

Ferenc Papp Steel Buildings – Loads and effects

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 = µi ⋅ Ce ⋅ Ct ⋅ sk - exceptional design situation: s = µi ⋅ Ce ⋅ Ct ⋅ s Ad where s snow load on the horizontal ground [kN/m2]; µi shape coefficient; 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: A   sk = 0 ,25 ⋅  1 +  100  

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: s Ad = Cesl ⋅ sk

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

windswept: normal: sheltered:

Ce = 0,8 Ce = 1,0 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 µi may be taken from the Table 2.1.

4

Ferenc Papp Steel Buildings – Loads and effects

Tab.2.1 Shape factor for duopitch roof (free slip of the snow) tető hajlásszöge (α α)

µ1

0°° ≤ α ≤ 30°°

30°° < α < 60°°

60°° ≤ α

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

A see := 300 ⋅ m

- charactheristic ground snow load

s k.calc := 0.25⋅ s k := 1.25 ⋅

 2 m  kN

 kN  = 1⋅ 100 ⋅ m  2 m A see

⋅ 1 +

kN 2

m

- exposure coefficient (normal)

Ce := 1.0

- thermal coefficient

Ct := 1.0

- shape coefficient (α<30 deg)

µ 1 := 0.8

- ground snow load

s := µ 1⋅ Ce⋅ Ct⋅ s k = 1 ⋅

kN 2

m

2.2.2 Snow load for the exceptional design situation - exceptional snow load coefficient

Cesl := 2.0

- exceptional snow load

s Ad := Cesl⋅ s k = 2.5 ⋅

kN 2

m s r := µ 1⋅ Ce⋅ Ct⋅ s Ad = 2 ⋅

- exceptional ground snow load

kN 2

m

2.3.2 Wind effect 2.3.2.1 Wind pressure on surfaces The effect is specified in 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; 5

Ferenc Papp Steel Buildings – Loads and effects

• • •

terrain properties; size and arrangement of the openings; dynamic properties.

The external and internal wind pressure may be calculated by the following expressions: we = q p ( ze ) ⋅ c pe wi = q p ( zi ) ⋅ c pi

where qp( z )

is the peak velocity pressure;

z e , zi c pe ,c pi

is the external and internal reference heights; is the external and internal pressure coefficients.

Figure 2.1 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.

(-) szí

(+)

Fig.2.1 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 2.2): • if the height of the building (h) is not greater than the width (b) of the windward surface of the building: ze = h and zi = ze ; • if the height of the building (h) is greater than b but it is not greater than 2b: - zone for height of b: - zone for height of (h-b):

ze = b and zi = ze ; ze = h and zi = ze .

h≤b

b < h ≤ 2b ze=h

maximum height

h h

b

ze=h b

ze=b

b

Fig.2.2 Reference heights for plane buildings 6

maximum height

Ferenc Papp Steel Buildings – Loads and effects

2.3.2.2 Peak velocity pressure The peak velocity pressure may be calculated by the following expression: q p ( z ) = ce ( z ) ⋅ qb

where ce ( z )

is the exposure factor;

qb

is the basic velocity pressure.

The basic velocity pressure may be calculated as follows: qb =

1 ρ ⋅ vb2 ( z ) 2

where the density of the air:

ρ = 1,25

kg m3

and where the basic wind velocity: vb = cdir ⋅ cseason ⋅ vb ,0

According to the Hungarian National Annex (HNA) the initial basic wind velocity and the direction and season coefficients may be taken as m vb ,0 = 23 ,6 ; cdir=0,85 ; cseason=1,0 s 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: ce ( z ) = ( 1 + 7 ⋅ I v ( z )) ⋅ cr2 ( z ) ⋅ c02 ( z )

where cr ( z ) c0 ( z ) Iv( z )

is the roughness factor; is the orography factor; is the turbulence intensity.

The roughness factor depends on the reference height: z  - if z < zmin than cr ( z ) = k r ⋅ ln min   z0 

 z if z ≥ zmin than cr ( z ) = kr ⋅ ln   z0  where the terrain factor:

-

7

Ferenc Papp Steel Buildings – Loads and effects 0 ,07

 z  kr = 0 ,19 0   z0 ,II  where z0 ,II = 0 ,05[m] , see the second category (II) in the Table 2.2. In the expression z0 is the roughness length and zmin is the minimum height. These constants are given in the Table 2.2. Tab.2.2 Roughness lengths and minimum heights terrain category 0 I II III

IV

Sea or coastal area exposed to the open sea 1

Lakes or flat and horizontal area with negligible vegetation and without obstacles Area with low vegetation such as grass and isolated obstacles (trees, buildings) with separations of at least 20 obstacle heights 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) Area in which at least 15 % of the surface is covered with buildings and their average height exceeds 15 m

z0 [m]

zmin [m]

0,003 0,01

1 1

0,05

2

0,3

5

1,0

10

When the average slope of the upwind terrain is less than 3°, the orography factor may be c0 ( z ) = 1,0 . The turbulence intensity may be calculated by the following expressions: kI - if z < zmin than I v ( z ) = z  c0 ( z ) ⋅ ln min   z0  kI - if z ≥ zmin than I v ( z ) =  z c0 ( z ) ⋅ ln   z0  where the turbulence factor may be kI=1,0. The exposure factor may be calculated using the Figure 4.2 of EC1-1-4 (see the graphics below):

8

Ferenc Papp Steel Buildings – Loads and effects

2.3.2.3 Application 2.3 Wind loads 2.3.1 Basic velocity pressure - initial parameters specified by the Hungarian NA m

initial basic velocity

v b0 := 23.6 ⋅

direction factor

cdir := 0.85

season factor

cseason := 1.0

air density

ρ := 1.25 ⋅

s

kg 3

m

m

v b := cdir⋅ cseason⋅ v b0 = 20.060⋅

- basic velocity

q b :=

- basic velocity pressure

1 2

2

⋅ ρ⋅ v b

q b := 0.252 ⋅

2.3.2 Peak velocity pressure - parameters for terrain category (Category III) z0 := 0.3 ⋅ m zmin := 5.0 ⋅ m - parameter for category II

kN 2

m

z0.II := 0.05 ⋅ m

0.07

- terrain factor

 z0  kr := 0.19⋅    z0.II 

- reference height

z := Hf = 9.019 ⋅ m

- roughness coefficient

z > zmin cr := kr⋅ ln

s

= 0.215

 = 0.733   z0  z

- orography coefficient (plane country, slope less than 3 degs)

c0 := 1.0

- turbulence coefficient (no specific rule)

kI := 1.0 Iv :=

- turbulence intensity

kI c0⋅ ln

  z  0 z

= 0.294

- exposure factor

ce := ( 1 + 7⋅ Iv) ⋅ cr ⋅ c0 = 1.643

- peak velocity pressure

q p := ce⋅ qb = 0.414 ⋅

2

2

kN 2

m

The peak velocity pressure can be determined or checked using the Figure 4.2 of the EN 1991-1-4: z = 9.019 ⋅ m

reference height terrain category

III

exposure factor by graphics

ce.graphics := 1.63

peak velocity pressure

q p.graphics := ce.graphics⋅ qb = 0.411 ⋅

kN 2

m

9

Ferenc Papp Steel Buildings – Loads and effects

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: - c pe ,1 is for area of 1.0 m2 as local coefficient; - c pe ,10 is for area of 10.0 m2 as overall coefficient. Between the two limit areas (for 1m2
cpe,10

0,1

1,0

10,0

log10 A[m2]

Fig.2.3 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: α=5o 1 2 3 4

F

Zones of the roof H

G

I

J

cpe,10

cpe,1

cpe,10

cpe,1

cpe,10

cpe,1

cpe,10

cpe,1

cpe,10

cpe,1

-1,7 -1,7 0 0

-2,5 -2,5 0 0

-1,2 -1,2 0 0

-2,0 -2,0 0 0

-0,6 -0,6 0 0

-1,2 -1,2 0 0

-0,6 -0,6 -0,6 -0,6

-0,6 -0,6 -0,6 -0,6

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

+0,2 -0,6 +0,2 -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.

10

Ferenc Papp Steel Buildings – Loads and effects

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 width perpendicular to the wind direction

b 0 := d a = 36 ⋅ m

width parallel to the wind direction

d 0 := b = 20 ⋅ m

height

h 0 := Hf = 9.019 ⋅ m h0

- size factor

η0 :=

- size of the zones

e0 := 2⋅ h 0 = 18.038⋅ m

d0

e0.4 := e0.10 := -slope of the roof (approximately)

= 0.451

e0 4 e0

= 4.51 ⋅ m

10

= 1.804 ⋅ m

10 deg

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 (1m 2 or 10 m2)

Wind pressure on the walls According to Annex 1: - interpolation factor (between h/d=1 and h/d=0,25)

β 0 :=

(η0 − 0.25)

- pressure coefficients cpe.A.0.10 := −1.2

cpe.B.0.10 := −0.8

cpe.D.0.10 := 0.7 + 0.1⋅ β 0 = 0.727

0.75

= 0.268

cpe.C.0.10 := −0.5

cpe.E.0.10 := −( 0.3 + 0.2⋅ β 0) = −0.354

- wind pressures wA.0.10 := cpe.A.0.10⋅ q p = −0.497 ⋅

kN 2

wB.0.10 := cpe.B.0.10 ⋅ q p = −0.331 ⋅

m wC.0.10 := cpe.C.0.10 ⋅ q p = −0.207 ⋅

kN 2

2

m wD.0.10 := cpe.D.0.10⋅ q p = 0.301 ⋅

m wE.0.10 := cpe.E.0.10 ⋅ qp = −0.146 ⋅

kN

kN 2

m

kN 2

m 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 cpe.F.0.1 := −2.25 wF.0.1 := cpe.F.0.1 ⋅ q p = −0.931 ⋅

cpe.F.0.10 := −1.30 kN 2

m

11

wF.0.10 := cpe.F.0.10 ⋅ qp = −0.538 ⋅

kN 2

m

Ferenc Papp Steel Buildings – Loads and effects cpe.G.0.1 := −1.75

cpe.G.0.10 := −1.0

wG.0.1 := cpe.G.0.1 ⋅ q p = −0.724⋅

kN

wG.0.10 := cpe.G.0.10 ⋅ q p = −0.414⋅

2

m

2

m

cpe.H.0.1 := −0.75 wH.0.1 := cpe.H.0.1 ⋅ q p = −0.31 ⋅

kN

cpe.H.0.10 := −0.45 kN

wH.0.10 := cpe.H.0.10 ⋅ q p = −0.186⋅

2

m

kN 2

m

- wind pressure cpe.FGH.0 := 0.1

cpe.I.0.1 := −0.50

wFGH.0 := cpe.FGH.0 ⋅ q p = 0.041⋅

kN

wI.0.1 := cpe.I.0.1 ⋅ q p = −0.207⋅

2

m

kN 2

m

cpe.I.0.10 := −0.50

cpe.J.0.1 := −0.65

wI.0.10 := cpe.I.0.10 ⋅ q p = −0.207⋅

kN

wJ.0.1 := cpe.J.0.1 ⋅ q p = −0.269⋅

2

m

kN 2

m

cpe.J.0.10 := −0.4 wJ.0.10 := cpe.J.0.10 ⋅ q p = −0.166 ⋅

kN 2

m 2.3.3.2 Longitudinal wind direction (90 degrees) Initial parameters - size of the building width perpendicular to the wind direction

b 90 := b = 20 ⋅ m

width parallel to the wind direction

d 90 := d a = 36 ⋅ m

height

h 90 := Hf = 9.019⋅ m η90 :=

- size factor - size of the zones e90 := 2⋅ h 90 = 18.038⋅ m e90.5 :=

e90

= 3.608⋅ m 5 Wind pressure on the walls

e90.2 :=

e90 2 e90

e90.10 :=

10

= 9.019⋅ m

h 90 d 90

e90.4 :=

e90 4

= 0.251 = 4.51 ⋅ m

= 1.804 ⋅ m

According to Annex 1 - size factor

β 90 :=

h 90 d 90

- wind pressures cpe.A.90.10 := −1.2

= 0.251 cpe.B.90.10 := −0.8

wA.90.10 := cpe.A.90.10 ⋅ q p = −0.497⋅

kN 2

m

cpe.C.90.10 := −0.5 wC.90.10 := cpe.C.90.10 ⋅ q p = −0.207⋅

kN 2

m

cpe.E.90.10 := −0.3 wE.90.10 := cpe.E.90.10 ⋅ q p = −0.124⋅

kN 2

m

12

kN

wB.90.10 := cpe.B.90.10 ⋅ q p = −0.331⋅

2

m

cpe.D.90.10 := 0.7 wD.90.10 := cpe.D.90.10 ⋅ q p = 0.29 ⋅

kN 2

m

Ferenc Papp Steel Buildings – Loads and effects

Wind pressure on the roof According to Annex 3 cpe.F.90.1 := −2.1

cpe.F.90.10 := −1.45

wF.90.1 := cpe.F.90.1 ⋅ qp = −0.869 ⋅

kN

wF.90.10 := cpe.F.90.10 ⋅ q p = −0.6 ⋅

2

m

cpe.G.90.1 := −2.0 wG.90.1 := cpe.G.90.1⋅ q p = −0.828 ⋅

cpe.G.90.10 := −1.30

kN

kN 2

m

wG.90.10 := cpe.G.90.10⋅ qp = −0.538 ⋅

2

m

2

m

cpe.H.90.1 := −1.2

cpe.H.90.10 := −0.65

wH.90.1 := cpe.H.90.1⋅ q p = −0.497 ⋅

kN

wH.90.10 := cpe.H.90.10⋅ qp = −0.269 ⋅

2

m

kN 2

m

cpe.I.90.1 := −0.55 wI.90.1 := cpe.I.90.1⋅ q p = −0.228 ⋅

kN

cpe.I.90.10 := −0.55 kN

wI.90.10 := cpe.I.90.10⋅ qp = −0.228 ⋅

2

m

kN 2

m

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, c pi = 0 ,75 ⋅ c pe When the area of the openings at the dominant face is at least 3 times the area of the openings in the remaining faces, c pi = 0 ,90 ⋅ c pe 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:

13

Ferenc Papp Steel Buildings – Loads and effects

•

•

if h / d ≤ 0 ,25 - if µ ≤ 0 ,33

than

c pi = 0 ,35

- if µ rel="nofollow"> 0 ,9

than

c pi = −0 ,3

- if 0 ,33 < µ ≤ 0 ,9

than

c pi = 0 ,726 − 1,14 µ

if h / d ≥ 1,0 - if µ ≤ 0 ,33

than

c pi = 0 ,35

- if µ > 0 ,95

than

c pi = −0 ,5

- if 0 ,33 < µ ≤ 0 ,95

than

c pi = 0 ,802 − 1,37 µ

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

∑A ∑A

µ= where areas.

neg

∑A

neg

is the area of openings where cpe is negative or zero and ∑ A is the area of all

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 width of the area of windows

Lw.s := 23.2 ⋅ m

height of the area of windows

h w.s := 1.2 ⋅ m 2

A s := Lw.s ⋅ h w.s = 27.84 ⋅ m - area of openings in the end walls windows width of the area of windows height of the area of windows

Lw.e := 12.6 ⋅ m h w.e := 1.2 ⋅ m 2

A e.w := Lw.e⋅ h w.e = 15.12 ⋅ m

industrial door width of the door

b w.d := 5.0 ⋅ m h w.d := 4.6 ⋅ m

height of the door

2

A e.d := bw.d⋅ h w.d = 23 ⋅ m

2

A f := A e.w + A e.d = 38.12 ⋅ m 2.3.4.2 Cross wind effect (0 degree) - initial parameters

A sum := 2⋅ ( A s + A f) = 131.92⋅ m

2

area of all openings

area of openings with negative or zero external pressure 2

A neg.0 := A s + 2⋅ A f = 104.08⋅ m

14

Ferenc Papp Steel Buildings – Loads and effects

opening ratio

µ 0 :=

A neg.0 A sum

= 0.789

- pressure coefficients for h/d=0.25

cpi.0.0.25 := 0.726 − 1.14⋅ µ 0 = −0.173

for h/d=1.00

cpi.0.1 := 0.802 − 1.37⋅ µ 0 = −0.279

cpi.0 := cpi.0.0.25 + β 0⋅ ( cpi.0.1 − cpi.0.0.25 ) = −0.202

- wind pressure

wi.0 := cpi.0 ⋅ q p = −0.083 ⋅

kN 2

m

2.3.4.3 Longitudinal wind effect (90 degrees) - initial parameters

area of openings with negative and zero external wind pressure coefficient 2

A neg.90 := A f + 2⋅ A s = 93.8 ⋅ m opening ratio

µ 90 :=

A neg.90 A sum

= 0.711

- internal pressure coefficient for h/d<0.25 - wind pressure

cpi.90 := 0.726 − 1.14⋅ µ 90 = −0.085 wi.90 := cpi.90⋅ q p = −0.035 ⋅

kN 2

m

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 2.3 shows the design imposed loads for the category H. Tab.2.3 Imposed loads for roof of category H slope of roof distributed load concentrated load α Qk [kN ] kN   qk  2  m  o 0,4 1,0 ≤ 10 o 0 0 ≥ 20 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 sheet and the purlins, but it is considered by the design software (DimRoof).

15

Ferenc Papp Steel Buildings – Loads and effects

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: a g = γ I ⋅ a gR

where agR is the reference peak ground acceleration of type A ground (see Figure 2.4), γI is the importance factor given in Table 2.4. The building in the present design project may belong to importance category I or II. Tab.2.4 Importance categories of buildings importance category

I. II. III.

IV.

importance factor γI

Buildings of minor importance for public safety, e.g. agricultural buildings, etc. Ordinary buildings, not belonging in the other categories. Buildings whose seismic resistance is of importance in view of the consequences associated with a collapse, e.g. schools, assembly halls, cultural institutions etc. Buildings whose integrity during earthquakes is of vital importance for civil protection, e.g. hospitals, fire stations, power plants, etc.

0,8 1,0 1,2

1,4

Fig.2.4 The reference peak ground acceleration of type A ground in Hungary The effect of ground acceleration to the building structure depends on the type of the response spectra. In Hungary the Type 1 should be applied, which assumes a heavy earthquake with an epicentre relatively far from the building. For the elastic design method (modal analysis) the following response spectra may be used:

16

Ferenc Papp Steel Buildings – Loads and effects

0 ≤ T ≤ TB TB ≤ T ≤ TC TC ≤ T ≤ TD

 2 T 2 ,5 2  Sd ( T ) = ag ⋅ S ⋅  + ⋅ −   3 TB q 3  2 ,5 S d ( T ) = ag ⋅ S ⋅ q   2 ,5 TC S d ( T ) = max a g ⋅ S ⋅ ⋅ ; β ⋅ ag  q T  

  2 ,5 TC ⋅ TD S d ( T ) = max a g ⋅ S ⋅ ⋅ ; β ⋅ ag  2 q T   where q is the behaviour factor, T [sec] is the period time of the structure, β=0.2 is the limit factor, and S and TB, TC and TD are given in the Table 2.5. Tíd ≤ T

Tab.2.5 Parameters for Type 1 response spectra ground type

A B C D E

description of stratigraphic profile Rock or other rock-like geological formation, including at most 5 m of weaker material at the surface. Deposits of very dense sand, gravel, or very stiff clay, at least several tens of metres in thickness, characterised by a gradual increase of mechanical properties with depth. Deep deposits of dense or medium-dense sand, gravel or stiff clay with thickness from several tens to many hundreds of metres. Deposits of loose-to-medium cohesion less soil (with or without some soft cohesive layers), or of predominantly soft-to-firm cohesive soil. A soil profile consisting of a surface alluvium layer with vs values of type C or D and thickness varying between about 5 m and 20 m

S

TB

TC

TD

1,0

0,15

0,4

2,0

1,2

0,15

0,5

2,0

1,15

0,20

0,6

2,0

1,35

0,20

0,8

2,0

1,4

0,15

0,5

2,0

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.

Standard fire curve Required resistance: 15 min Unprotected

Fig.2.5 Unified fire compartment of the isolated main frame structure

17

Ferenc Papp Steel Buildings – Loads and effects

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 2.5). 2.7 Application 2.4 Imposed load - service class of the roof: H - slope of the roof: α=10o - imposed load surface distributed load

q k := 0.4 ⋅

kN 2

m

Qk := 1.0 ⋅ kN

concentrated load 2.5 Seismic effect - importance category of the building: II. - importance factor

γ I := 1.0

-seismic zone

Esztergom region

- horizontal component of the reference peak ground acceleration

agR := 0.15⋅ g = 1.471 ⋅

- ground type

m s

2

C

ground factor

S := 1.15

parameters of the response spectra

TB := 0.2

TC := 0.6

TD := 2.0

2.6 Fire effect - applied temperature-time curve: standard (ISO) - category of fire resistance: IV (simple building) - required limit for fire resistance (R15)

tfi := 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"

18

Ferenc Papp Steel Buildings – Loads and effects

Annex 1 External pressure coefficient for vertical walls (for case of h
A

cpe,10 -1,2 -1,2

zones C

B

cpe,1 -1,4 -1,4

cpe,10 -0,8 -0,8

cpe,1 -1,1 -1,1

D

cpe,10 cpe,1 -0,5 -0,5

cpe,10 0,8 0,7

E

cpe,1 1,0 1,0

cpe,10

cpe,1 -0,5 -0,3

e = min( b;2 h )

Top view

Side zones for e
h w

D

E

A

B

C

B

C

b e/5 e

d

A

h

side Side zones for e>d:

A

B

e/5

A

B

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=00) and to the front side (θ=900), respectively. 0

19

Ferenc Papp Steel Buildings – Loads and effects

Annex 2 External pressure coefficients of roof due to cross wind (θ θ=00) (for case of h
F

cpe,10 -1,8

zones H

G

cpe,1 -2,5

cpe,10 -1,2

cpe,1 -2,0

cpe,10 -0,7

I

cpe,1 -1,2

cpe,10 +0,2 -0,2 -0,6

J

cpe,1 +0,2 -0,2 -0,6

-1,7 -2,5 -1,2 -2,0 -0,6 -1,2 +0,0 +0,0 +0,0 +0,0 +0,0 +0,0 -1,3 -2,25 -1,0 -1,75 -0,45 -0,75 -0,5 -0,5 10** +0,1 +0,1 +0,1 +0,1 +0,1 +0,1 -0,9 -2,0 -0,8 -1,5 -0,3 -0,3 -0,4 -0,4 15 +0,2 +0,2 +0,2 +0,2 +0,2 +0,2 +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=50 and α=150 5

θ=00

w α h

Ridge

e/4

F

w G

e/4

H

J

b

I

F

e/10

e/10

20

cpe,10 +0,2 -0,2 +0,2 -0,6 -0,4 -0,3 -1,0 +0,0

cpe,1 +0,2 -0,2 +0,2 -0,6 -0,65 -0,3 -1,5 +0,0

Ferenc Papp Steel Buildings – Loads and effects

Annex 3 External pressure coefficients of roof due to longitudinal wind (θ θ=900) (for case of h
F

cpe,10 -1,8

0*

G

cpe,1 -2,5

cpe,10 -1,2

H

cpe,1 -2,0

cpe,10 -0,7

I

cpe,1 -1,2

cpe,10 +0,2

cpe,1 +0,2

-0,2

-0,2

5 10** 15

-1,6 -2,2 -1,3 -2,0 -0,7 -1,2 -0,6 -0,6 -1,45 -2,1 -1,3 -2,0 -0,65 -1,2 -0,55 -0,55 -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=50 and α=150 θ=900 w h

Ridge e/4 w

F G

H

I

H

I

G e/4

F e/10

e/2

21