SX017a - Single Span Truss and Post Frame for a Low Pitch Roof Using Battened Section Chords

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Document Ref: SX017a-EN-EU Sheet 1 of 23 Title Example: Single span truss and post frame for a low pitch roof using battened section chords Eurocode Ref EN 1993-1-1, EN 1993-1-8 & EN 1990 Made by Jonas Gozzi Date August 2005 CALCULATION SHEET Checked by Bernt Johansson Date August 2005 Example: Single span truss and post frame for a low pitch roof using battened section chords This example deals with the design of a low pitch roof truss. The truss is part of the roof structure in a 72 m long single storey building and spans 30 m. The spacing of the trusses is 7,2 m and the roofing is an insulated steel sheeting on purlins. The building where the truss is situated is based on that shown in worked example SX016. In the Figure below, one frame from the building is shown. SX016 30,0 [m] 6,0 7,3 The truss is symmetric about its centre. In the figure below a more detailed geometry of the truss is shown. The inclination of the upper chord of the truss is α = 5°. The roof is providing lateral restraint for the top chord, either by a wind bracing or by diaphragm action of corrugated sheeting in structural class I or II according to EN 1993-1-3. 1,5 1,5 1,5 1,5 1,5 1,5 1,5 1,5 1,5 1,5 [m] 1,3 1,0 1 14 13 10 9 8 7 6 5 2 4 3 17 16 15 12 19 18 20 21 11 22 1,51 1,51 1,51 1,51 1,51 1,51 1,51 1,51 1,51 0,84 0,57 α Example: Single span truss and post frame for a low pitch roof using battened section chords Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

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Example: Single span truss and post frame for a low pitch roof using battened section chords

CALCULATION SHEET

Document Ref: Title

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

Eurocode Ref Made by Checked by

August 2005 August 2005

Example: Single span truss and post frame for a low pitch roof using battened section chordsThis example deals with the design of a low pitch roof truss. The truss is part of the roof structure in a 72 m long single storey building and spans 30 m. The spacing of the trusses is 7,2 m and the roofing is an insulated steel sheeting on purlins. The building where the truss is situated is based on that shown in worked example SX016. In the Figure below, one frame from the building is shown.[m]

SX016

Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

6,0

7,3

30,0

The truss is symmetric about its centre. In the figure below a more detailed geometry of the truss is shown. The inclination of the upper chord of the truss is = 5. The roof is providing lateral restraint for the top chord, either by a wind bracing or by diaphragm action of corrugated sheeting in structural class I or II according to EN 1993-1-3.[m]

1,51 12

1,5

1,5

1,5

1,56

1,57

1,58

1,59

1,510

1,511

2

3

4

5

1,3 1,0

13

14

15

16

17

18

19

20

21

22

0,84 1,51

1,51

1,51

1,51

1,51

1,51

1,51

1,51

1,51 0,57

Example: Single span truss and post frame for a low pitch roof using battened section chords

CALCULATION SHEET

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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Partial safety factors G = 1,35 or 1,0 Q = 1,5 M0 = 1,0 M1 = 1,0 M2 = 1,25 Loads Permanent loads Roof and insulation PurlinsCreated on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

(permanent loads) (imposed loads)

EN 1990 EN 1993-1-1

0,35 kN/m2 0,05 kN/m2 0,12 kN/m2

Truss self weight

g = (0, 35 + 0, 05 + 0,12) 7, 2 = 3,74 kN/m

Snow load The imposed load from snow, qs, is shown in the figure below. In SX016 a detailed description of how to calculate this snow load can be found. qs = 4,45 kN/m[m] qs

7,3

30,0

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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Wind load The wind load, when wind on the side is considered is shown below. The details of how to determine this load can be found in SX016. qw1 = 9,18 kN/m qw2 = 5,25 kN/m e = min(b; 2h) = min(72,0; 14,6) = 14,6 m In this context qw1 is negligible.[m] qw1 qw2 qw2

See SX016

Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

7,3

e/10 30,0

Member forces The roof is attached to purlins fixed at every second joint of the truss, implying that all loads will be applied at the truss joints, as shown in the figure below.

Example: Single span truss and post frame for a low pitch roof using battened section chords

CALCULATION SHEET

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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The member forces are calculated under the assumption of pinned joints. This simplification is allowed when the compression chord is in cross section class 1. The calculations are performed by means of a computer, meaning that only the member forces will be shown here. Two different load cases were considered; Dead Load (DL) + Snow Load (SL) and Dead Load (DL) + Wind Load (WL). DL + SL

G g + Q qs = 1,35 g + 1,5 qsDL + WL

G g + Q qw = 1, 0 g + 1,5 qwCreated on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

All member forces under these design loads are shown in the table below. Forces are in kN and negative sign means compression.Member 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22 DL+SL -139 -344 -487 -588 -653 -695 -715 -721 -711 -693 233 418 530 622 668 708 714 720 701 684 DL+WL 52 126 179 213 238 252 260 262 260 253 -84 -151 -189 -221 -237 -250 -252 -253 -246 -239 Member 1-12 12-2 2-13 13-3 3-14 14-4 4-15 15-5 5-16 16-6 6-17 17-7 7-18 18-8 8-19 19-9 9-20 20-10 10-21 21-11 DL+SL 214, -189 183 -164 119 -108 106 -96 56 -52 51 -47 9,0 -8,4 8,3 -7,8 -29 28 -28 26 DL+WL -77 68 -66 59 -41 37 -36 33 -19 17 -17 16 -2,3 2,1 -2,1 2,0 11 -11 11 -10

Example: Single span truss and post frame for a low pitch roof using battened section chords

CALCULATION SHEET

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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Member design

Channel sections will be used for all members. The upper and lower chords each consist of two profiles and are designed as uniform built-up members when out of plane deformations are considered. Buckling resistance of member in compressionEN 1993-1-1 6.3.1

N b,Rd =

A fy M11

The reduction factor, , is calculated as

=whereCreated on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

+ 2 2

1, 0

= 0 ,5 1 + ( 0 , 2 ) + 2 andA fy N cr

=

is an imperfection factor corresponding to the appropriate buckling curve.The buckling length, Lcr, should be taken as the system length for in plane EN 1993-1-1 buckling of the chords and for out of plane buckling of the web members. For Annex BB in plane buckling, a buckling length of 90% of the system length should be used for the web members. The buckling length for out of plane buckling of the upper chord should be taken as the distance between the purlins in this case.

Example: Single span truss and post frame for a low pitch roof using battened section chords

CALCULATION SHEET

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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Resistance of uniform built-up members in compression Out of plane buckling for a built-up member

EN 1993-1-1 6.4

N cr =

2 EI effL2 cr

where Ieff for a battened strut should be calculated as I eff = 0,5 h02 Ach + 2 I ch in which Ach is the area of one chord Ich is the second moment of area of one chord Eq. (6.74)

is determined according to Table 6.8 in EN 1993-1-1 andh0 is the distance between the centroids of the chords.Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

Table 6.8

Except for this it is designed for buckling as described above. Check of the chords in a built-up section For a member with two identical chords the design force Nch,Ed should be determined as N ch,Ed = 0,5 N Ed + whereM Ed =I N Ed e0 + M Ed N N 1 Ed Ed N cr Sv

EN 1993-1-1 6.4 Eq. (6.69)

M Ed h0 Ach 2 I eff

in which

Sv =e0 =

2 2 EI ch a2L 500

(stiff battens)

Eq. (6.73)

I M Ed is the design value of the maximum moment in the middle of the chord

a is the distance between battens L is the distance between lateral supports or the buckling length, Lcr

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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The shear force that the battened strut should be designed for isVEd =

M EdL

Eq. (6.70)

This shear force causes a moment in the chords distributed according to the figure below.Nch,Ed VEd/2 Nch,Ed VEd/2

EN 1993-1-1 Figure 6.11

a/2 VEda/h0Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

VEda/2 VEda/4

VEda/4 VEda/2 VEda/h0 a/2

VEd/2 Nch,Ed h0

VEd/2 Nch,Ed

The individual chords should be checked for axial force, bending moment and shear force according to the figure above. Resistance of members in tension The tension resistance is determined as EN 1993-1-1 6.2.3

N b,Rd =

A fy

M0

Example: Single span truss and post frame for a low pitch roof using battened section chords

CALCULATION SHEET

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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Upper chord The member in the upper chord that carries the highest force is member 8-9. Compression force: Tension force: NEd = -721 kN (under dead load and snow load) NEd = 262 kN (under dead load and wind load)

Only this member will be checked since if this member has enough resistance then the other members in the upper chord will as well. Two UPE 160 S355 are used as upper chord. Battens of the same section as the web members are used. fy = 355 106 Pa E = 210 109 PaCreated on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

A = Ach = 2,17 103 m2 (one profile) Iy = 9,11 106 m4 (one profile) Iz = Ich = 1, 07 106 m4 (one profile) Wpl = 40, 7 106 m3 (one profile) h0 = 0,1254 m (UPE 80 in between)

z

From trade literature

y

= 0,49 (buckling curve c)

h0

EN 1993-1-1 6.3.1.2

E g

0

x

a

m

p

l

e

:

S

i

n

g

l

e

s

CALCULATION SHEETi y

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SX017a-EN-EU

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

Eurocode Ref Made by

r

August 2005 August 2005

a

y

Checked by

In-plane bucklingp

M

Lcr = L / cos(5) = 1,5 / cos(5) = 1,51 mN cr =, c

2 EI yL2 cr

=

2 210 109 2 9,111061,512

o

Ncr = 16 562 000 N = 16 562 kNy

2 2,17 103 355 106 = = 0,305 16562 103

a

= 0,5 1 + 0, 49 ( 0 ,305 0, 2 ) + 0,3052 = 0,572

d

s

=

1 0,572 + 0,5722 0,3052

= 0,947

n

i

N b,Rd =o l

0,947 2 2,17 103 355 106 1,0

Ncr = 1 459 000 N = 1459 kN > 721 kN = NEdM a C T r h e i a s t e m d a t o e n r i

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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August 2005 August 2005

Design of battened strut The upper chord is designed with battens with length 200 mm at a distance of a ~ 1,0 m, meaning that at every purlin position a batten is attached and two in between those positions. Purlins that work as lateral support are attached at every second joint, i.e. the out of plane buckling length is between two joints.

Lcr = L / cos(5) = 3, 0 / cos(5) =3,01 mI1 = 0,5 h02 Ach + 2 I ch = 0,5 0,1254 2 2,17 103 + 2 1, 07 10 6 I1 = 19, 2 106 m 4i0 =Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

I1 19, 2 106 = 0,067 m = 2 Ach 2 2,17 103

=

Lcr 3, 01 = = 44,9 i0 0, 067

= 1,0

I eff = I1 = 19, 2 106 mm 4

N cr = Sv =

2 210 109 19, 2 1063, 012

= 4 392 000 N = 4392 kN

2 2 EI ch 2 2 210 109 1, 07 106 = 4 435 00 N = 4435 kN = a2 1, 02

M Ed =

N Ed e0 + M N N 1 Ed Ed N cr Sv

I Ed

3, 01 +0 500 = = 6,6 kNm 721 721 1 4392 4435 721

N ch,Ed = 0,5 N Ed +Nch,Ed = 405,9 kN

M Ed h0 Ach 6, 4 0,1254 2,17 103 = 0,5 721 + 2 I eff 2 19, 2 106

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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The shear force that the battened strut should be designed for is

VEd =

M EdL

=

6, 63, 01

= 6,9 kN EN 1993-1-1 6.4.3 Figure 6.11

and the moment from this shear force at the position of the battens isM ch,Ed = VEd a 6,9 1, 0 = 1,7 kNm = 4 4

Buckling resistance of one chord in lateral direction

Lcr = a = 1,0 m N cr =Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

2 EI chL2 cr

=

2 210 109 1, 07 1061, 02

= 2 218 000 N = 2218 kN

=

2,17 103 355 106 = 0,589 2218 103

= 0 ,5 1 + 0, 49 ( 0 ,589 0 , 2 ) + 0 ,5892 = 0,769

=

1 0, 769 + 0,7692 0,5892

= 0,792

N b,Rd =

0 ,792 2 ,17 103 355 106 1, 0

Nb,Rd = 610 000 N = 610 kN > 405,9 kN = Nch,Ed

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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Both axial force and shear force occur simultaneously. If the design shear EN 1993-1-1 force, VEd, does not exceed 50% of the plastic shear resistance no reduction of 6.2.10 (2) the resistance to axial force is needed.Vpl,Rd = Av f y / 3

M0

where Av is the shear area, in this case the flange area of the U-section Av = 2 hf tf = 2 (70 5,5 12) 9,5 106 = 9,975 104 m2

Vpl,Rd

2 9,975 104 355 106 / 3 = 1, 0

Vpl,Rd= 408 900 N = 409 kN > 6,7 kN = VEdCreated on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

0,5 Vpl,Rd = 0,5 409 = 204,5 kN > 6,7 kN = VEd No reduction of the buckling resistance of the chord needs to be made. At the batten position, the combination of moment and axial force needs to be checked. Equation (6.62) in EN 1993-1-1 can for this case be reduced to EN 1993-1-1 6.3.3 (4) N ch,Ed M ch,Ed + kzz 1, 0 N b,Rd M z,Rd

M z,Rd = M pl,Rd =

Wpl f y

M0

=

40, 7 106 355 106 1, 0 N ch,Ed Cmz 1+1, 4 N b,Rd

6.2.5

Mz,Rd = 14 450 N = 14,4 kNm

N kzz = Cmz 1+ ( 2 z 0, 6 ) ch,Ed N b,Rd Cmz = 0,9

Annex B

(sway buckling)

405,9 kzz = 0,9 1+ ( 2 0,589 0, 6 ) = 1,25 610

405,9 1, 7 + 1, 25 = 0,81 < 1,0 610 14, 4

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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The battens are made of 200 mm long UPE 80 tw = 4 mm.

Wpl =Vb,Ed

tw l 2 0, 004 0, 2002 = = 40 106 m3 4 4

From trade literature EN 1993-1-1 Figure 6.11

V a 6, 7 1, 0 = Ed = = 53,4 kN h0 0,1254

Av = l tw = 0, 20 0, 004 = 8 104 m2

Vpl,Rd

8 104 355 106 / 3 = = 164 000 N = 164 kN > 53,4 kN = Vb,Ed 1, 0VEd a 6, 7 1, 0 = 3,35 kNm = 2 2

M Ed =Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

M pl,Rd =

Wpl f y

M0

=

40 106 355 106 1, 0

Mpl,Rd = 14 200 Nm = 14,2 kNm > 3,35 kNm = MEd Tension resistance of the upper chord

N b,Rd =

A fy

M0

2 2,17 103 355 106 = = 1541 kN > 262 kN = NEd 1, 0

Web members The most utilized web members are Compression force: 12-2 NEd = -189 kN (under dead load and snow load) Tension force: 1-12 NEd = 214 kN (under dead load and snow load)

The web members are attached with their weak direction in the plane of the truss and their strong direction out of plane.

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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UPE 80 is used for the web members. A = 1, 01103 m2 Iy = 1, 07 106 m4 Iz = 25 10 8 m4 From trade Literature EN 1993-1-1 6.3.1.2

= 0,49 (buckling curve c)L = 1,31 m In-plane buckling

Lcr = 0,9 L = 0,9 1,31 = 1,18 m N cr =Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

2 EIL2 cr

=

2 210 109 25 1081,182

= 372 100 N = 372,1 kN

=

1, 01103 355 106 = 0,982 372 ,1103

= 0,5 1 + 0, 49 ( 0,982 0, 2 ) + 0,9822 = 1,17

=

1 1,17 + 1,17 2 0,9822

= 0,554

N b,Rd =

0,554 1,01103 355 106 1,0

Nb,Rd = 198 600 N = 199 kN > 189 kN = NEd

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

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Out of plane buckling Lcr = L = 1,31 m

N cr =

2 EIL2 cr

=

2 210 109 1, 07 1061,312

= 1 292 000 N = 1292 kN

=

1, 01103 355 106 = 0,527 1292 103

= 0,5 1 + 0, 49 ( 0,527 0, 2 ) + 0,5272 = 0,719

=

1 0, 719 + 0,7192 0,527 2

= 0,828

N b,Rd =Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

0,828 1,01103 355 106 1,0

Nb,Rd = 297 000 = 297 kN > 189 kN = NEd Tension resistance of the web members

N b,Rd =

1010 355 = 358 600 N = 359 kN > 214 kN = NEd 1, 0

Web members of UPE 80 are enough. Lower chord The most utilized member in the lower chord is the member 19-20. Compression force: Tension force: NEd = -253 kN (under dead load and wind load) NEd = 720 kN (under dead load and snow load)

Two UPE 140 are used for the lower chord. Ach = 1,84 103 m2 (one profile) Iy = 5,99 106 m4 (one profile) Iz = Ich = 79 10 8 m4 (one profile) h0 = 0,1234 m From trade literature

= 0,49 (buckling curve c)

EN 1993-1-1 6.3.1.2

Example: Single span truss and post frame for a low pitch roof using battened section chords

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In-plane buckling Lcr = L = 1,51 m

N cr =

2 EIL2 cr

=

2 210 109 2 5,99 1061,512

= 10 890 000 N = 10890 kN

=

2 1,84 103 355 106 = 0,346 10889 103

= 0,5 1 + 0, 49 ( 0,346 0, 2 ) + 0,3462 = 0,596

=

1 0,596 + 0,5962 0,3462

= 0,925

N b,Rd =Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

0,925 2 1,84 103 355 106 1,0

Nb,Rd = 1 208 000 N = 1208 kN > 253 kN = NEd Out of plane buckling (lateral buckling) of the battened lower chord In this case the lower chord does not have any lateral supports and should be designed with a continuous elastic lateral restraint. This lateral restraint depends on the stiffness of the purlins kp, the screws between purlins kc and upper chord and the web members kw. A Z250x2,0 section is used as purlins I z = 7,33 106 m4 h = 1,9 m lp = 7,2 m Stiffness, kp, for the purlins (height of truss in the most utilized section) (distance between trusses)

SN027

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Assume a force of 1 N per unit length, yielding a moment of

M = 3 hwith purlins at every 3 m. The corresponding angel of rotation, , from this moment is

=

M lp 2 EI p

=

3 h lp 2 EI p 3 h lp 2 EI p 3 1,9 7, 2 = 2,53 105 m 9 6 2 210 10 7,33 10

The displacement of the lower chord due to this unit force is

= h = h kp =Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

= 1,9

1

=

1 = 39 500 N/m2 = 39,5 kN/m2 5 2,53 10

M,

kp

h

1

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

Eurocode Ref Made by Checked by

August 2005 August 2005

M

e = 190 mm

250

Stiffness of the connection between the purlins and the upper chordCreated on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

Four self tapping screws with diameter, d = 6,3 mm, are used for the connection. Screw force

Fs =

3 h 3 1, 9 = = 15 N 2 e 2 0,19

Design thickness of purlint = (2, 0 0, 05) 0,98 = 1,91 mm

The shear deformation, v, in the connection can be calculated according to the following equation from the Swedish handbook for cold-formed sections and sheeting. (Force in N, d and t in mm)v= Fs d t 103

=

15 = 1, 72 103 mm 3 6,3 1,91 10

=

v 1, 72 103 = = 1,81105 e/2 190 / 2

= h = 1,9 1,81105 = 3, 44 105 mkc = 1 = 29 070 N/m2 = 29,1 kN/m2 5 3, 44 10

Example: Single span truss and post frame for a low pitch roof using battened section chords

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SX017a-EN-EU

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

Eurocode Ref Made by Checked by

August 2005 August 2005

Stiffness, kw, of the web members Only the web members that are connected to the joints with purlins are used in the calculations of the stiffness, i.e. two web members are used. I w = 1, 07 106 m4 l1 = 3,0 m (distance between purlins) lw = 2,2 m (length of web member)

SN027

kw = 2

3 EI w 3 210 109 1, 07 106 = 2 3 l1 lw 3, 0 2, 23

kw = 42 200 N/m2 = 42,2 kN/m2 The total stiffnessCreated on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

ks =

1 1 = 12,0 kN/m2 = 1 1 1 1 1 1 + + + + kp kc k w 39,5 29,1 42, 2

Effective second moment of area for the lower chordI1 = 0,5 h02 Ach + 2 I ch = 0,5 0,12342 1,84 103 + 2 79 108 I1 = 15,59 106 m 4i0 = I1 15,59 106 = 0,065 m = 2 Ach 2 1,84 103

EN 1993-1-1 6.4 Table 6.8 SN027

The wave length, l0, is calculated according tolc = 4 EI1 210 109 15,59 106 = 12,8 m = 4 ks 12 103

=

lc 12,8 = = 187 i0 0, 065

=0

I eff = 0,5 0,12342 1,84 10 3 = 14, 0 106 m 4

The effective second moment of area will give a new value of the wave length, lc

lc = 4

210 109 14, 0 106 = 12,4 m 12 103

Example: Single span truss and post frame for a low pitch roof using battened section chords

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SX017a-EN-EU

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20

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

Eurocode Ref Made by Checked by

August 2005 August 2005

Battens are placed at a spacing of a 1,0 m.2 2 EI ch 2 2 210 109 79 108 = 3 275 000 N = 3275 kN Sv = = a2 1, 02

N cr = ks EI eff

ks EI eff 2 if S v / ks EI eff > 1 Sv

SN027

ks EI eff = 12 103 210 109 14, 0 106 = 187 800 N = 187,8 kN

S v / ks EI eff = 17,4 > 11 N cr = 187,8 2 = 365 kN 17, 4 Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

=

2 1,84 103 355 106 = 1,89 365 103

= 0 ,5 1 + 0, 49 (1,89 0, 2 ) + 1,892 = 2,70

=

1 2,70 + 2,702 1,892

= 0,216

N b,Rd

0, 216 2 1,84 103 355 106 = 1,0

Nb,Rd = 282 000 N = 282 kN > 253 kN = NEd Check of battened strut in the lower chord for compression and bending Sv = 3275 kNI N e + M Ed = Ed 0 = N Ed 1 N cr

253

M Ed

12, 4 +0 500 = 20,4 kNm 253 1 365

SN027

N ch,Ed

M Ed h0 Ach 20, 4 0,1234 1,84 103 = 0,5 N Ed + = 0,5 253 + 2 I eff 2 14, 0 106

Nch,Ed = 292 kN

Example: Single span truss and post frame for a low pitch roof using battened section chords

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SX017a-EN-EU

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21

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

Eurocode Ref Made by Checked by

August 2005 August 2005

The shear force that the battened strut should be designed for is VEd =

M Edlc

=

20, 412, 4

= 5,2 kN

and the moment from this shear force at the position of the battens isM ch,Ed = VEd a 5, 2 1, 0 = 1,3 kNm = 4 4

Buckling resistance of one chord in lateral direction

Lcr = a = 1,0 m

N cr =Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

2 EI chL2 cr

=

2 210 109 79 1081, 02

= 1 637 000 N = 1637 kN

1,84 103 355 106 = = 0,632 1637 103

= 0 ,5 1 + 0, 49 ( 0 ,632 0, 2 ) + 0 ,6322 = 0,806

=

1 0,806 + 0,8062 0, 6322

= 0,766

N b,Rd =

0, 766 1,84 103 355 106 1,0

Nb,Rd = 500 000 N = 500 kN > 293 kN = Nch,Ed From the upper chord it could be concluded that the shear force in the chord is not important for this case. At the batten position, the combination of moment and axial force needs to be checked.

N ch,Ed N b,Rd

+ kzz

M ch,Ed M z,Rd

1, 0

M z,Rd = M pl,Rd =

Wpl f y

M0

32, 6 106 355 106 = = 11 600 N = 11,6 kNm 1, 0 N ch,Ed Cmz 1+1, 4 N b,Rd

N kzz = Cmz 1+ ( 2 z 0, 6 ) ch,Ed N b,Rd

Example: Single span truss and post frame for a low pitch roof using battened section chords

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Document Ref: Title

SX017a-EN-EU

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

Eurocode Ref Made by Checked by

August 2005 August 2005

Cmz = 0,9

(sway buckling)

293 kzz = 0,9 1+ ( 2 0, 632 0, 6 ) = 1,25 500

293 1,3 + 1, 25 = 0,73 < 1,0 500 11, 6TensionN b,Rd = 2 1,84 103 355 106 1, 0

Nb,Rd = 1 306 000 N = 1306 kN > 720 kN = NEd

OK

The battens are of the same type as for the upper chord and they can carry the forces without any problems.Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

Two battened UPE 140 as lower chord is sufficient. Joints The web members are welded to the upper and lower chords. Only one joint will be designed here but the procedure is the same for all joints. Joint 1[mm]

85 31

NEd

Example: Single span truss and post frame for a low pitch roof using battened section chords

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SX017a-EN-EU

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Example: Single span truss and post frame for a low pitch roof using battened section chords EN 1993-1-1, EN 1993-1-8 & EN 1990 Jonas Gozzi Bernt JohanssonDate Date

Eurocode Ref Made by Checked by

August 2005 August 2005

The force in the web member is NEd = 214 kN This force needs to be transferred through the weld into the upper chord. The weld will be a fillet weld with a = 4 mm fu = 510 106 Pa The resistance of the weld is determined according to Fw,Rd = f vw.d a where EN 1993-1-8 4.5.3.3

f vw.d =Created on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

fu / 3 w M2Table 4.1

w is a correlation factor, w = 0,9 M2 = 1,25Fw,Rd

510 106 / 3 = 0, 004 = 1 047 000 N = 1047 kN/m 0,9 1, 25

Design criterion Fw,Rd l N Ed where l is the required length of the weldl 214 = 204 mm 1047

With the design according to the figure above the weld length on one side of the web member is l = 85 + 31 = 116 mm As the upper chord consists of two sections, the web member will be welded to both yielding a symmetric joint. The total length of the weld is

l = 2 116 =232 mmwhich is sufficient. The truss has two UPE 160 as upper chord, UPE 80 as the web members and two UPE 140 as lower chord.

Example: Single span truss and post frame for a low pitch roof using battened section chords

Example: Single span truss and post frame for a low pitch roof using battened section chords SX017a-EN-EU

Quality RecordRESOURCE TITLE Example: Single span truss and post frame for a low pitch roof using battened section chords

Reference(s) ORIGINAL DOCUMENT Name Created by Technical content checked by Editorial content checked by Technical content endorsed by the following STEEL Partners: 1. UK 2. FranceCreated on Monday, May 05, 2008 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement

Company SBI SBI

Date 28/07/2005 16/08/2005

Jonas Gozzi Bernt Johansson

G W Owens A Bureau A Olsson C Mller J Chica G W Owens

SCI CTICM SBI RWTH Labein SCI

27/1/06 27/1/06 27/1/06 27/1/06 27/1/06 27/07/06

3. Sweden 4. Germany 5. Spain Resource approved by Technical Coordinator TRANSLATED DOCUMENT This Translation made and checked by: Translated resource approved by: