CIDECT 1- CHS joint under static loading.PDF

8/9/2019 CIDECT 1- CHS joint under static loading.PDF

1/68

DE8OBW BUUDE

FOR CIRCULAR HOLLOW

SECTION

(CHS) JOINTS

UNDER PREDOMINANTLY STATIC LOADING

Construction with Hollow Steel Sections - Design guide for circular hollow section (CHS) joints under predominantly static loading

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CONSTRUCTION

WITH HOLLOW STEEL

SECTION

Edited by: Comite International pour le Developpement et I'Etude

Authors: Jaap Wardenier, Delft University of Technology

de laConstruction Tubulaire

Yoshiaki Kurobane, Kumamoto University

Jeffrey A. Packer, University of Toronto

Dipak Dutta, Chairman Technical Commission

of

Cidect

Noel Yeomans, Chairman Cidect Joint and Fatigue Working Group


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FOR

CIRCULAR HOLLOW

SECTION

(CHS

JOINTS

UNDER PRED MINANTLY

STATIC LOADING

Jaap Wardenier, Yoshiaki Kurobane, Jeffrey A. Packer,

Dipak Dutta, Noel Yeomans

Verlag

TUV Rheinland


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CIP-Titelaufnahme der DeutschenBibliothek

Design guidefor circular hollow sectionCHS)

joints under predominantly static loading

[ed. by: Comite Internationalpour le Developpement

et IEtude de la Construction Tubulaire]. Jaap

Wardenier .

.

- Koln :Verl. TUV Rheinland, 1991

(Construction with ollow steel sections)

ISBN 3-88585-975-0

NE: Wardenier, Jaap; Comite International pour le

Developpement et Etude de la Construction

Tubulaire; For circular hollow section (CHS) joints

ISBN 3-88585-975-0

y Verlag TUV Rheinland GmbH, Koln 1991

Entirely made by: Verlag TUVRheinland GmbH, Koln

Printed inGermany 1991


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The necessity to solve the design problems concerning the versatile applications f hollow

sections, which are somewhat supplementary o he general structural engineering with

plates and open sections and apply particularly to this youngest membern the familyof steel

sections, led to the foundation of CIDECT in

1962

as an international organization of major

hollow section manufacturers. The aim is to combine together all the resources worldwide

from ndustry,universitiesandothernationaland nternationalbodies orresearchand

application of technical data, development of simple design and calculation methods and

dissemination of the resultsof the researches by publications.

Since its inception CIDECTactivities have been focussed onirtually all aspects of the hollow

section design including buckling behaviourf empty and concrete-filled columns,tatic and

fatiguestrength of joints, aerodynamicproperties,corrosion esistanceandworkshop

fabrication. The results of the researches sponsored by CIDECT are available n extensive

reports and monographs and have been incorporated into many national and international

design recommendations e. g. DIN (Deutsche lndustrie Normung - German Standard), NF

(NormeFrancaise - FrenchStandard), BS (British Standard),ACNOWCSA Canadian

Standard),AIJ(Architectural Institute of Japan), IW(International Institute of Welding),

EUROCODE3 (draft) etc. This design guide forhe design and calculationof circular hollow

section joints n steel structures under predominantly static load is theirst of a series, which

CIDECT has planned to publish in the near future. Four further design manuals are now in

preparation:

- Design guide for circular and rectangular hollow section joints under fatigue loading

- Structural stability of hollow sections.

- Design guide for rectangular hollow section joints under predominantly static loading

-

Design guide for hollow section columns susceptible toire

The design of the connections in welded atticed structures of structural hollow sections

requires not only he knowledge about proper welding but also special nsight nto he

connection behaviour mainly dependent on the connection configuration governed by the

geometricalparameters. In order osecure hestructural ntegrity of ahollowsection

connection, it is

of

vital importance thathe dimensions of the constructional memberss well

as the configurationof the connection resultn adequate deformation and rotation capacity.t

was necessary to carry out extensive experimental investigations besides theoretical analysis

to omeoheproperunderstanding of the olution.Simpledesignormulaeand

constructional rules have been derived from these technical data obtained by the analytical

and experimental research works.

The intention f this design guides to communicate to the architects, structural engineers and

constructors these simplified design methods with worked-out examples n order to enable

them oconstructa echnicallysecureandeconomicsteelstructure in circularhollow

sections.

We wish to express our hearty thanks to threef the outstanding personalities n the field of

research of hollowsectionstructures - Professor J. Wardenier of DelftUniversity of

Technology, The Netherlands, Professor

Y.

Kurobane of Kumamoto University, Japan and

Professor J. A. Packer

of

University of Toronto, Canada, who kindly consented to participate

in writing this guide.

Further, our thanks go toll CIDECT member firms, who madehis design guide possible.

Dipak Dutta

Chairman of the Technical Commission

of CIDECT

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Contents

1

General

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2

Design of tubulartructures

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Designprocedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3

Fabrication of tubulartructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

4 Joint esign nder redominantlytaticoading . . . . . . . . . . . . . . . . . . . . . . 16

4.1

4.2

4.3

4.4

4.5

4.6

4.6.1

4.6.2

4.6.3

Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Joints in uni-planar trusses

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Joints in multi-planar structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Joints under moment loading

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Interaction between axial loading and bending moments . . . . . . . . . . . . . . . . . .

Special types of uni-planar joints

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Otherconfigurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Plate type jotnts

Flattened and cropped end bracing joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

19

30

32

35

36

36

38

40

5 Boltedonnections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6 Workedutesignxamples

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.1 a) Uni-planarruss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

b) Arch-formedtruss

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

c) Vierendeelruss

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

6.2Multi-planarrusstriangularirder)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

6.3Trusswith emi-flattenedendbracings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.4Effectivebucklingength of trussmembers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.5 Boltedconnections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

7

Symbols

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

8 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

CIDECT International Committee forhe Development and Study f Tubular

Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

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Lift shaft with glass hQuses upported by tubu lar latt ice frames

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1 General

Many examples n nature demonstrate the excellent propertiesf the circular hollow section

as a structural element n resisting compression, tension, bending and torsion. Further, the

circular hollow section has proved to be the best shape for elements subjected to wind-,

orwaveoading.Thecircularhollowsectioncombines hesecharacteristicswithan

architecturally attractive shape. Structures madeof hollow sections have a smaller surface

area than comparable structures of open sections. This, n combination with the absence f

sharp corners, results n a better performanceof corrosion protection.

These excellent properties should result inight open designs with a small numberf simple

joints in which gussets or stiffening plates can often be eliminated. Since theoint strength is

influenced by the geometrical properties of the members, optimum design can only be

obtained if the designer understands the joint behaviour and takes it into account in the

conceptual design. Although at present the unit material costf hollow sectionss higher than

that of open sections, this can be compensated by the ower weight of the construction,

smallerpaintingarea orcorrosionprotectionand eductionof abricationcost by the

application of simple joints without stiffening elements. Many existing constructionsn hollow

sectionsshow hat ubularstructurescaneconomicallycompetewithdesigns in open

sections.

Over the ast twenty five years CIDECT hasnitiated many research programmesn the field of

tubularstructures:e. g. in the field of stability, fire protection,wind oading,composite

construction, and the static and fatigue behaviour ofoints. The results f these investigations

areavailable in extensive eportsandhavebeen ncorporated ntomanynationaland

international design recommendations with background informationn CIDECT Monographs.

Initially many of these esearchprogrammeswereacombination of experimentaland

analytical research. Nowadays many problems can be solvedn a numerical way and the use

of the computer opens up new possibilities for developing the understanding of structural

behaviour. It is important that the designer understands this behaviour and is aware of the

influence of various parameters on structural performance.

This practical design guide shows how tubular structures under predominantly static loading

should be designedn an optimum way, taking accountf the various influencing factors. This

guide concentrates on the ultimate limit states design of lattice girders or trusses. Joint

resistance formulae are given and also presentedn a graphical format, to give the designer a

quick insight during conceptual design.

The graphical format also allowsquick check of computer calculations afterwards. The basic

design rules or uni-planar oints (Fig.

8 )

satisfy he safety procedures e.g. used in the

European Community and n Canada. The formulae for other typesof joints are in a certain

way related to those for the basic typesf joints.

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2

Design

of

tubular structures

2.1

introduction

In designing tubular structures t is important that the designer considers theoint bahaviour

right from the beginning. Designing members e. g. of a girder based on member loads only

may result in undesirable stiffening of joints afterwards. This does not mean that the joints

have to be designed n detail at the conceptual design phase. It only means that chord and

bracing members have to be chosenn such a way that the main governingoint parameters

(Fig. 7) such as diameter ratio d,/do, thickness ratio to/t,, chord diameter to thickness ratio

dolto, ap g between bracings, overlap , of bracings and angle

4,

provide an adequateoint

strength and an economical fabrication.

Since he design s always a compromise between various requirements, such as static

strength, stability, economy in fabrication and maintenance, which are sometimesn conflict

with each other, he designer should be aware f the implications of a particular choice.

The following guidance is given to arrive at optimum design:

-

Lattice structures can usually be designed assuming pin jointed members. Secondary

bending moments due to he actual joint stiffness can be neglected for static designf the

joints have sufficient rotation capacity. Thisill be the casef the joint parameters are within

the range recommended n this design guide.

-

It is common practice to design the members with the centre lines noding. However, for

ease of fabrication it is sometimes required to have

a

certain noding eccentricity. If this

eccentricity is kept within the limits

-0.55

5 e/do

.25

indicated in Fig. 1 the resulting

bending moments can be neglected for joint design and for chord members oaded in

tension.

Chord members oaded in compression, however, have always

to

be checked or he

bending effects of noding eccentricity (i.e. designed as beam-columns, with all of the

moment due to noding eccentricity distributed to the chord sections).

Full overlapping results in an eccentricity e = -0.55 do but provides a more straight

forward fabrication than artial overlap joints and better girder behaviour than gapoints.

C

D

cl

partsal overlap jwnt wl th negatlve eccentrlclty dl

total

overlap

joint

wt th negatlve eccentrlclty

T e l l w e t r e Uberlappung mlt negatlver

Exrentrlritdr

V o l l e Uberlappung ml t negatlver Exr ent rlz ~ta l

e / O

e O

Fig. 1

-

Noding eccentricity

- Secondary bending moments due to the end fixities of the members can be generally

omittedwith espect odesign of bothmembersandconnections,provided here is

adequate deformation and rotation capacityn both members and connections. Thisan be

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achieved by limiting the wall slendernessf certain members, particularly the compression

bracing members, which is the basis for somef the geometric limits of validity shown in

Fig. 8 .

-

Gap joints are preferred to partial overlap joints (Figs. 1C and

2)

since the fabrication is

easier with regard o end cutting, fitting and welding. However, fully overlapped oints

(Fig. 1D) provide better oint strength with similar fabrication than gapoints.

The gap g is defined as the distance measured along the length

f

the connecting facef the

chord, between the toesf the adjacent bracing member (ignoring welds). The percentage

overlap

O

efined in Fig. 2, s such that the dimension p pertains to the

overlapping

bracing.

In good designs a minimum gap should be provided such that g,

+

t

so

that the welds

do not overlap each other; on the other hand,n overlap joints the overlap should be at least

0 2 25%.

9 0 = over lap = x

100~

Fig.

2

-

Gap and overlap

-

In common lattice structures, (e.g. trusses), about 50%f the material weight is used for the

chords in compression, roughly 30% for the chordn tension and about

20%

for the web

members or bracings. This means hat with respect o material weight, he chords in

compression should likely be optimised o result in thin walled sections. However, or

corrosion protection (painting) the outer surface area should be minimized. Furthermore

joint strength ncreaseswithdecreasingchorddiameter o hickness ratio dolto and

increasing chord thickness to bracing thicknessatio to/t, .As a result the inal diameter to

thickness ratio dolto or the chord in compression will be a compromise between joint

strength and buckling strengthf the member and relatively stocky sectionsill usually be

chosen. For the chord n tension the diameter to thicknessatio dolto hould be chosen to

be as small as possible.

-

Since theoint strength efficiency i. e. joint strength divided by the bracing yield load

,

.

fyl)

increases with increasing chord to bracing thicknesso/t,, his ratio should be chosen to be

as high as possible.

Furthermore the weld

volume

required for a thin walled bracing is smaller than that f a

thick walled bracing with the same cross section.

- Since the joint strength also depends on the yield stress of the chord, the use of higher

strength steel for chords (when available and practical) may offer economicalossibilities.

2.2 Designprocedure

The design of tubular structures should be approached in the following way to obtain an

efficient and economical structure:

- Determine structure or truss geometry keeping the numberf joints to a minimum.

- Determine member forces assuming pinned joints and noding centreines.

- Determine chord member sizes considering axial loading, corrosion protection and joint

geometry (usual dolt, ratios are 20 to 30). Usually an effective buckling lengthf 0.9 times

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the system length is assumed if supports in-plane and out-of-plane are available athe joints

- The use of high strength steel (fy=

355

Nlmm) for the chords should be considered.The

delivery time of he required sections has to be checked.

-

Determine bracing member sizes, (based on axial oading), preferably with thicknesses

smaller than the chord thickness.

-

The effective length for the bracings can be assumed conservatively to be .75 times the

system tength 116,

32, 3 .

A

more precise calculation method for the effective length i s

given in chapter 6.4.

- Standardize the bracing members to a few selected dimensions (or even two) to minimize

the number of the section sizes or the structure. Due to aesthetic reason one outer

diameter with differentiated wall thicknesses may be preferred.

Il61.

-

Check joint geometry with regard to eccentricity limits and fabrication.

- Check joint efficiency with the diagrams given in chapter 4. From a abrication point of view

gap joints are preferred to overlap joints.

-

If the joint strengths are not adequate, changehe bracing or chord dimensions. Only a few

joints will normally require to be checked.

- Check the effects of eccentricity noding moments (if any) on the chord members, by

checking the moment-axial force interaction.

- If required, check russ deflections, at the unfactored oad level, by analyzing the truss as a

pin-connected rame if

it

hasnodingnon-overlapped oints. f joints areoverlapped

throughout, check the truss deflection by assuming continuous chord members and pin-

ended bracing members taking account of the eccentricity.

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3

Fabrication

of

Tubular Structures

In designing tubular structures he designer should keep in mind that the costs of the structure

are significantly influenced by the fabrication costs. This means that utting, end preparation

and welding costs should be minimized.

-

Taking account of the standard mill lengths in design may reduce theend oend

connections of chords.For large projects it maybeagreed that special lengths are

delivered.

- The end profile cutting of tubular members which have to fit other tubular members, as

shown in Fig. 5 , is normally done by automatic flame cutting (see Fig.3).However, if such

equipment is not available especially for small sized tubular members, other methods do

exist, such assingle, double or triple plane cuttings as shown n Fig.

4

[ l ,4, 241.

Fig. 3 Automatic flame cutting

In a tubular joint, fillet welds, full penetration butt welds or filletlbutt welds are applied

depending on the geometry as shown in Fig.

5 .

When welds are used, these have to be

designed on the basis of the strength of the member to be connected. They have o be

considered as automatically prequalified for any member load.

The weld at he toe of the bracing is most important. If the bracing angle is less than

60,

the toeshould always be bevelled and a butt weld usedas shown in Fig. 5-C2.

To allow proper weldingt the heel of the bracing the bracing angle should not beess than

300.

Since the welding volume is proportional o t2 thinalled bracings can generallly be welded

more economically than hick walled bracings.

A

minimum gap limit oft ,

+

t is recommended for and N joints to ensure that adequate

space is available to enable welding at the bracing toes to be performed satisfactorily.

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Sizes of CHS bracings which can e fitted toCHS main members with a single cut; do must be

equal to or greater than .08 d + 3 with d, in mm)

diameter

of

main

do

(mm)

33,7

42,4

48.3

60.3

76.1

88.9

114.3

139.7

168.3

193.7

219.1

323.9

355.6

406.4

457.0

508.0

size of bracing (d,)

up toand including:

straight cut

CHS

dia. dl

(mm)

-

-

-

26.9

26.9

26.9

33.7

33.7

42.4

48.3

48.3

60.3

60.3

60.3

60.3

76.1

wenn

(all dimensions are in mm)

Fig.

4 -

Single, double

or

triple plane cuttings

Detall A Delal l

E

n

Detall C l Detal l C 2 Detall D

Fig.

5 -

Weld details

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-

From a fabrication point of view gap joints are preferred o overlap joints not only because

the cutting and endpreparation are easierbut also becauseof tolerances and nspection.

- In partially overlapped oints the toe of he overlapped memberhidden part) is usually not

welded.

If the bracing load componentsperpendicular

to

the chord wall are rather unbalanced (e. g.

exceed a factor of

1.5)

it is ecommended thathe most heavily oaded member is the through

bracing with its full ircumference being welded to the chord, that means alsohe hidden part

has to be welded.

cropp ing A)

full f la t tening

(B.

angedruckt IAI

vol l

abgeflacht (B,

Cl

part ia l f la t tening

ID1

te i lwei re abgeflacht D)

Fig. 6

-

Various typesof f lat tening

Especially or small sized tubular structures, or in those cases wherehe fabricator does not

have proper equipment for endrofile cuttingpartial), flattening of the ends of members can

be used as shown in Fig. 6.More detailed information regarding fabrication is given in refs.

[ l ,

4,

261.

Transp arent roof with tubular trusses and colum ns for a Tropic Bush Garden

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4 Joint design under predominantly static oading

4.1

introduction

All

joint design strength formulae given in this guide are developed in ultimate limit state

terms. This means thathe effect of the characteristic loadsQ, multiplied by appropriate load

factors

ys

should not exceed he joint design strengthN*, .e.

effect

yS

Q, N* where N' =-

If the allowable load

or

allowable stress) methods used, the oint design strengths should be

divided by the load factor

S

applicable, i. e.

Nk

Ym

N* Nk

effect Q,

Ys

Ys

Ym

In this case

yS =

1.5

is

recommended.

The chord, bracing andoint symbols generally used are indicatedn Fig. 7 for uni-planar joints

and are defined n chapter

7.

chord

rymboir

GurtBezelchnungen

bracing

a n d jolnt symbols

Fullstab und Knoten-Berefchnung

T ~ K n o t e n

T- ty pe p n t

X-type

olnt (91 = 90. c r o s s ~ o ~ n t )

X-Kno ten 191 =

90

Kreuzknotenl

K-type jo ln t

K-Knoten

N type oint

N-Knoten

K T - p n t

KT- Knatrn

Fig. 7 - Chord, bracing andoint symbols

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i

L

Roof structure for an automobi le exhibi t ion hal l

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The joint design strength formulae incorporating the effect of the value of Y,,, are given in

tables as well as in diagrams [l l]. The formulae given in Fig.

8

an be used for computer

calculations whereas the diagrams of Figs. 9 to 12 are very helpful in design and for a quick

check of computer calculations.

In the diagrams the joint strength is expressed in terms of the efficiency of the connected

bracings, i.e. the joint strength for axially loaded oints

N*

is divided by the yield load

Ai

fyi of

the connected bracing.

This results in efficiency formulae of the following type:

(4.1 l

The efficiency parameter

C

is given for each type of joint in diagrams as a function of the

diameter ratiop and the chord diameterlthickness ratio dolto.

The value of the parameter C in the ormula above gives the efficiency for the bracing of a

joint with a tensile prestress oading in the chord

f

(n') = 1 O a bracing angle g i =

90

and the

same wall thickness and design yield stress for chord and bracing.

From the efficiency equation

it

can be easily observed that yield stress and thickness ratio

between chord and bracing are extremely important for an efficient material use of the

bracing. Decreasing he angle

li

ncreases he efficiency. The function f (n') depends n the

chord loading (f (n') S 1 O for compression prestressing). The efficiency formula shows

- higher strength steel for chords than for the bracings (fyo

>

fyi)

- bracing wall thickness as small as possible (ti < to) but such that the limits for local buckling

- angle

ai

> 90; hence, prefer K-joints to N-joints.

For moment oading the design formulae are shown in Fig. 19. The respective design charts

are given in the Figs.

20

and

21.

n these charts the joint fficiency is based onhe plastic yield

moment capacity MP,, of he bracings. Here the same rules apply for an efficient design as

those mentioned for axially loaded joints.

,

directly that the folowing measures are favourable for the joint efficiency:

or interaction are satisfied, see chapter

4.2.

Tubular t r iangular russes for a highway tax paying stat ion

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4.2

Joints in uni-planar trusses

Typical uni-planar joints arellustrated in Fig.

7.

The most recent design recommendations for

uni-planar T-,X- and K-joints are givenn Fig. 8. These formulae habe also been adopted by

the International Institute of Welding [2] and by the Eurocode Drafting Committee [S]. Most

of

these formulae are based on the basic formulaeriginally developed by Kurobane (9,

o].

Thedesign ormulae or T-, Y- andX-jointshavebeenbasedon hestrengthunder

compression loading but can also be used for tensile loading. The ultimate resistance under

tensile loading is usually higher than under compressive loading, however, t is not always

possible to take advantage of this strength due to large deformations or due to premature

cracking. The strengthof other types of joint configurations not givenn Fig. 8 can be related

to these basic typesas will be shown n section 4.6.

The design strengths generally governed by two criteria,.e. plastification of the chord cross

section and chord punching shear. In order to designjoint, both criteria have to be checked

according to the formulaen Fig.

8.

These design strengths are presented graphicallyn terms

of bracingefficiency in Figs.

9

to 12. These figures show thatunchingshear (horizontal ut off

of the curves) only becomesritical for joints with thick chords (low dolt, ratio), and generaly

in combination with low p ratio. The horizontal cut off for punching shear n Figs. 9 to 12 is

conservative i f the bracing angle 0 < 90.

The most common types of T- and X-joints are those with 90 angle between bracing and

chord axes. The graphs and the examples show that T- and X-joints are less efficient than

joints, especially for high dol to atios. However, these types of joints are less important in

common tubular structures.

K- and N-joints arehe common typesf joints used in tubular structures. Figs. 11 and 12 show

four design diagrams i.e. with gapsf 2t0, 6t0, lot, respectively and with overlap. The effect

of the gap or overlap is also shown in Fig. 13. It can be observed that overlapping of the

bracings is especially efficient for hin walled chords.

As

shown in fig. 11, for the design of gap K-joints an nitial value C = 0.3 can be usedas a

design basis for ratios of 0.4 to 1 O, dolto atios of 20 to 30 and relative gap glt,of 4 to

10.

To minimize the numberof joints and to allow good welding, bracing angle

0

of about 40'

will be efficient. For tension loaded chords with (n') = 1 O, and with 0 = 40, the bracing

can be fully effective if toltl is larger than about 2.0. If the chords are made of steel with a

higher yield stress than thatf the bracings the thicknessatio may need to be even lower,.e.

(4.2.7)

The design charts 1, 2 and 4 (Figs. 9, 10 and12) show the function f (n'). It should be noted

here that only the prestressf the chord has to be considered; thushe horizontal bracing load

components have to be extracted,s shown in fig. 14.

For lattice girders which are simply supportedt the ends f the span, the prestressings small

at the girder ends where the bracing loads are highest and the prestressing isigh where the

bracing oads are low in the centre).

For continuous attice girders the effect f f (n ) needs special attention t the supports.

K-, N- and KT-joints with external cross chord oading (e.g. through purlin loads), can be

calculated using the criteria for K-joints by checking the arger normal component of the

bracing orce. If, however, all the bracing loads act eithern tension or in compression (in the

same sense) or f only one bracing is load bearing, theoint should be checkedas an X-joint

(see also Fig. 24c).

The KT-type and other types are dealt withn chapter 4.6.

To avoid interactionbetween bracing ocal buckling and joint strength its recommended[25]

to limit the joint strength efficiencies by the compression bracing for high bracing diameter to

wall thickness ratiosd,lt,.

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Type of joint

I

Design strength i

= 1

2)

I T-

and-joints

I

chord plastification

X-joints

N;

= (2.8 14.2p2). o.2. (n')

f '

t

sln el

(eq. 4.2.1)


(eq. 4.2.2)

I K

and

N

gap or overlapoints

I


(eq. 4.2.3)

N.- N'

sin B

2 - W

(eq. 4.2.4)

I

general

I

punching shear

punching chear checkor T, Y,

X

and

K,

N,

KT joints with gap

(eq. 4.2.5)

functions

I

f(n')

=

1 + 0.3n'

-

0.3n"or n'

1.0

Fig. 11

-

contd.

-

Design chart for

K-

and N-joints with gap

of

circular hollow sections

Design chart 4 Tubular ioints

K- and N-overlap oints of circular hollow sections

symbols

da

fop = chord stress as a result of additional axial

force or bending moment

calculation example

chord 0): 219.1 x

10.0

(compr.) do/to= 21.9

bracing (1): 39.7x 6.3 (compr.) d,/t,

=

22.2

bracing (2):

0

114.5 x 5.0 (tension) d,/t, = 22.9

fyo

= f = f e = e =

40; 50

1.O

ranges of validity

d,

d0

0 .25- 51 .0

f 55 N/mm2

OV

>

25%

-

0.55I .25 300

I, _C

goo

d0

welds are to be dimensioned on the yield

strength of the bracing

definition gap

ov

=

-

100%

P

Fig. 12 - Design chart for K- and N-overlap joints of circular hollow sections (see next page for

C,-

and

f (n') diagrams)

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Efficiency K- and N-overlap joints

1

.o

Y

0.9

t

0.4

0.3

0.2

0.1

0

10

15

20

30

40

50

I I

1

1 1

0

0.2

0.4

0.6

0.8 1

.o

dl /d

Function

f

(n )

-1.0 -0.80.6 -0.4 -0.2 0

n

Fig.

1 2

- contd.

-

Design chart for

K-

and N-overlap joints of circular hollow sections

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4.0

3.5

3.0

-

m

2.5 i

-

2.0

t

1.5

Fig. 13

-

Gap , over lap nf luence unc t ion

Uberlappung Spal t

overlap gap

chord preload = No,

n =- No,

Fig. 14

-

Prestressin g of thehord N o = N I c 0 5 e 1 + N z c o s B z +O P A0 . yo

NO

d, / t l l imits for which the joint

ef f ic iencies der ived

from Figs. 8 to 12

can always be used

eff iciency l imit '

for compression bracing

N

A,

.

y ,

* - S values given in the tab le.

As a formula these efficiency limits can be expressed by:

(4.2.8)

Considering member buckling the above mentioned limitations will not frequently be critical.

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c

Braced tubular column

support

4.3 Joints in multi-planar struc tures

Multi-planar joints are frequently used in tubular structures e. g. in towers, offshore jacket

structures, triangular or quadrangular girders, etc.

Design rules covering the multi-planar effects are given onlyn

[l

However, the multi-planar

effects in 117) have been on lastic considerations and have notet been checked ufficiently

against the actual plastic behaviour of joints. For design, however, some guidelines can be

given.

One can imagine that the multi-planar effects are most substantial for double X-joints as

shown in Fig. 15. Finite element calculations [l81 have shown thatmulti-planar loading hasa

substantial influence on the strength and stiffness as compared to a uni-planar X-joint. n the

case where the loadscting in one plane have the same magnitude as thosen the other plane,

but with anpposite sense (e. g. comression vs. tension), theoint strength may drop by about

1/3 compared to the uni-planar joint (see Fig. 17).

On the other hand, for loadings with the same sensehe joint strength increases considerably.

However, this increase in strength may be accompanied by a reduction in deformation and

rotation capacity.

A

conservative assumption for the time being will be to adopt the same

percentage increase n strength for loads in the same senseas the percentage eduction for

opposite loads.

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bracing 399-10

chord 006-25

P = d lD = 0.4

l

I

F1

3

1

F1

bracing 599-10

chord 006-25

2

I

F 1

7

F 2 =

R es u lt s o r p

= 0.4

Erg e bn i rs e u r p = 0 .4

7000

6000

-

5000

-

4 0 0 0

3 0 0 0

-

-

r__o 1 n t 5

K n o t e n l

(Re

Kn o te n 3

Knoten B

0 10

20

30 40 50

Verrchiebung

(mm\

de f lec t i on (mm)

o , , , , , ,

R e r u l t s f o r p =

0.6

E rg eb n m e f u r b =

0.6

- oint

6

K n o t e n 6

Knoten 7

0

1

3 W O b

Knoten 4

J o i n t 4

J o i n t 2 ( r e f . )

2030 '

,'

K n o t e n 2Ref . l /

1000 ,

/

I----

o l n t 9

Kno ten 9

0

0 10 20

30

40 50 M)

Verschlebung (mm)

de f lec t l on (mm)

Fig . 15

-

Mult i-planar X-joints

For K- joints n t r iangular g irders as shown in Fig. 16, var ious tests h ave been carr ied

out

by

Makino [20]. l though an interact ion equat ions establ ished in [20],his funct ion can easi ly e

replaced by a constant of

0.9,

to b e appl ied to the st rength of un i-planar joints.

deflec ted shape at fa i lure

For m nach Versagen

Fig . 16 - Mult i -planar K- joints

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For T-joints, tests have been arried out only on double -joints (V-joints) witha 90' included

angle betweenbracings and both bracingsoaded in compression (Fig. 17). Compared tohe

strength of uni-planar jointshe multi-planar oint strength did ot varysubstantially,although

the stiffness increasedonsiderably [

19).

Based on the available evidence it is recommended to design multi-planar joints using the

formulae for uni-planar oints with the correction factors as given n Fig. 17.

Type of joint

KK

____ ~

correction factor to uni-planar

joint (limits according to Fig. 8)

60

4 0'

1.o

1

+

0.33-

Z

NI

Note:

take account of the sign of

NZand N,

N,

NZ)

0.9

Fig. 17 - Correction factors for multi-planar joints

4.4

Joints under moment

loading

One should distinguish between primary bending moments due o noding eccentricities

(Fig. 1) needed forhe equilibrium withhe external oading and secondary bending moments

due to end fixities of the joint members as a result of induced deformations in the structural

system. The secondary moments are in principle not needed for the equilibrium with the

external oading e.g. the secondary moments in members of lattice girders.

A s

already

mentioned n chapter 4.2, these secondary moments do not influence the oad bearing

capacity of lattice girders i f the joints have sufficient deformation capacity, i.e. within the

parameter limits of the formulae given inFig. 8.

The momentsdue to noding eccentricity inattice girders may be assumed to be taken by the

chord members.

Joints predominantly oaded by in-plane bending moments are generally of the T-type and

called Vierendeel joints (Fig. 18). These oints also exist n framed structures.

Fig. 18 - Uni-planar Vierendeel joints

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Out-of-plane bending moments are not very common in uni-planar structures. This type of

loading generally appears more frequentlyn multi-planar structures.

The joint design strength or oints oaded by bending can also be used or other joint

configurations such as K-, N- and KT-joints[5].

I

Type

of

joint

I

T.Y.X.K.N.

MOD

General

punching shear check

for dl

5

do

-

2

.

,

Same range

of

validity as for

axially loaded joints, see Fig. 8

Design strength


fJnJ

Ml p = 4.85 f . g .

P

' d l .


f(n')

=

1 + 0.3n' -

0.3

n'*

for n' S 1.0

f(n')

=

1 for n'

2

1.O

n ' = foplfyo

(4.4.1)

(4.4.2)

(4.4.3)

(4.4.4)

(4.4.5)

(4.4.6)

Fig. 19- Design recommendations for joints loaded by primary bending moments

For punching shear the plastic shear moment capacitys given, however, the angle functions

based on an elastic approach.

In a similar manner to axially loadedoints, these formulae are presented as efficiency design

charts (Figs. 20 and 21). The joint efficiency

Cipb

or Cop, gives the joint moment design

strength divided by the plastic moment capacity,, . fy, of the bracing. The horizontal cut

of f line gives he imitationbasedonpunchingshear(plasticpunchingshearmoment

capacity).

Thesediagramsshow hat in mostcases he n-planebendingmoment esistance s

considerably better than that for out-of-plane bending.

It should benoted that the joint rotational stiffnessC (moment per radian) may considerably

influence the moment distribution in statically indeterminate structural systems, e.g . portal

frames and Vierendeel trusses. Ifigid connections are requiredt is recommended to choose

a p

ratio near 1

.O

or low dolto atios in combination with high to/tl atios.

Figs. 22 and3 give a graphical presentationf the rotational oint stiffness of T-joints21] for

in-plane and out-of-plane bending moments.

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dollo

Fig. 20 - Design diagram for joints loaded by in-plane bend ing mom ents

i

~

-+

t

15

d o l t 0

20

25

30

40

50

0.1 -

. - i

L

l

0 -

~ 1 1 1 , ) 1 /

0 011 0.2.3

0. 4

0,'s

0'6 017 Ole 0

1.0

P

Fig. 21

-

Design diagram for joints loaded by ou t-of-plnae bend ing mom ents

-+

0 0.2

0.4

0.6 0.8 l 0

P P

Fig.

22

-Jo int st i f fness for in-plane bend ing Fig. 23

-

Jointtiffness for ou t-of-plane

of T-jointsending of T-joints

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4.5 Interaction between axial loading and bending moments

Especially n three dimensional structures the joints may be loaded bycombinations of axial

loading and bending moments.

Several investigations have been carried out to study this problem and as a result many

interaction'formulae exist.

All

investigations have shown that in-plane bending is less

severe than out-of-plane bending nd a reasonable simplified lower bound interaction

function is given by [16]:

(4.5.1)

in which:

Ni, Mi, and

M

are the loads acting, and

N

M; and

M,

are the design strengths.

It should be noted that the joint stiffnesses given in Figs.22and23 can be affected

considerably by the presence of axial loading [22]; however not sufficient test evidence is

available for a more precise recommendation.

Triangular girder

85 m

length) for the

support

of a roof.

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4.6

Special types of uni-planar oints

4.6.1

Other onfigurations

In tubular structures various otheroint configurations exist which have not been dealt withn

the previous chapters. However,he strength

of

several typesof joints can be directly related

to the basic types dealt withn chapter 4.2.

Fig. 24 shows some special types

of

joints with tubular bracings directly welded to the tubular

chord.

~

Type of joint

a

b

Relationship with the formulae in Fig. 8

N,

N;

N; from X-joint

(eq. 4.6.1

. l )

N,

. sine, +

N,.

sin0, 5 N;. sine,

NZ.

sin

0 5

N;

.

sin

0

(eq. 4.6.1.2)

(N; from K-joint)

(eq. 4.6.1.3)

replace y

strength formula

d ld l

+

d2 + d3

d0

3

do

In K-joint

N, . sine, + NZ. ine, 5 N? sine, (eq. 4.6.1.4)

(N,

from X-joint)

where N sin0, is the larger of N

.

sine, and N sine,

N, 5

N

(K-joint)

NZ

N (K-joint)

check cross section 1-1 for plastic shear capacity

(gap joints only)

Fig. 24 -Other configurationsof uni-planar tubular joints

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Arch-formed t russes for sport hall

Fish-shaped t russes or an ice-skat ing hal l

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4.6.2

Plate type

joints

Various joint configurations arepossible or joints with gusset plates. The designtrength of

these joints is mainly based on testsarried out in Japan [5,9]. n the originalesearch reports

a distinction s made between TP-joints (plateo

CHS

T-joints) and XP-joints (plateo CHSX-

joints), with the ormer having aplate on one side of theube and the latter having plates on

both sides of the tube.

The design strength formulaen Fig. 25 have beenimplified in conservative wayo that they

cover both types for various oad conditions. However for TP-joints with p)=

4 +

20 p* fits

the test results betterhan f(p) =

5

1

- 0.81

p

Furthermore, all joints have to be checked for unching shear:

-

for other oints: (fa

+

fb)

.

, .16

fp

to,

where f a and fb are the axial and bendingtress in theconnected plate, or RHS section.

The design recommendationsn the irst row coverXP-l/TP-1 and XP-3/TP-3 joints.

The XP-l/TP-l joints only have a plate perpendicular to the main chord axis whereas the

XP-3/TP-3 oints also have a late parallel to the chordxis.

Since the stiffnessf aongitudinal plate parallel to the chordxis is considerably smallerhan

that perpendicular o the chord axis,he strengths f both oint types are about similar.

-

for TP-5/XP-5: (fa

-l-

b)

.

1.I 0.58

f '

to;

Details

of

a tubular

oof

support structure

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1

oints

P-]

l

Design strength for XP- andl

axial loading N' = f p) . (7) . (n') . yo tz

(eq. 4.6.2.1)

type of joint

t N' = f(p)

bending out of planeending inplane

f

(7)

XP-1 TP-1 XP-31TP-3 I

1

.0

1 - 0.81 p

XP-2lTP-2

(1

+

0.25s)

7 5 4

M = h, . N XP-2)

(eq. 4.6.2.2)

XP-4lTP-4

I

5.0

1

-

0.81 p

(1 + 0.25~)

M = h, .N XP-l)

(eq. 4.6.2.3)

MgP= 0.5 b, .

N(Xp4)

(eq. 4.6.2.6)

XP-5lTP-5 1

5.0

1 - 0.81 p

(1 + 0.25~)

7 1 2

1152

(eq. 4.6.2.4)

1

W

General remarks: for symbols, parameters and limitations: see axially loaded joints. p

=

blldo 1= hlldo

(D Fig. 25 - Gusset plated connections


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4.6.3 Flattened and cropped end bracing oints

Jointswith lattenedendbracingsaresometimesused,especially orsmallsizedand

temporary tubular structures. As shownn Fig. 6, various types f flattening can be provided.

In the case of full or partial flattening, the maximum taper from the tube to the flat should

remain within 25% (or 1:4), as shown in Fig. 6B and C. For dol to atios exceeding 25 the

flattening will reduce the compressive strength

[ l ] .

For welded connections the length of the flat part should be minimized for compression

members to avoid local buckling. Recommended design strength formulae for cropped-web

N-joints with overlap [23] are givenn Fig. 26. Compared to the ultimateoint strength given n

[23] for the vertical bracing oaded in compression a factor of 1.25 has been adopted to

account for the transformation from ultimate strength to design strength.

Since the behaviourf this type f joint may be influenced by size effects, care should be take

in using these empirical formulae, and thats why the validity s restricted to the dimensional

range tested:

dimensions tested (mm)parametersested

114 5 do 169

d0

t0

1 4 5 -

5 5 0

42 dl 5 90

dl

d0

0.35 5-

0.8

3 5 t , 5 8

3

5

, 4.6

dl

d2

-

1.0

-

= 1.0

l

t2

f 5 400/mm2 e, = g o o ; 8 450

For chords prestressedn compression up to

0%

of the yield loadhe joint strength should be

multiplied by f (n) = 1 +

0.2

n

02

- 0.8). Higher chord prestress loads should not be

accepted since sufficient test evidences not available. For trusses with flattened and cropped

end bracings an effectivebuckling length

le

of 1

.O

imes the system lengths recommended.

Partial-flattened end bracing joints, as shown in Fig. 27, have recently been investigated n

CIDECT programme 5AP 26].

These joints can be designed with the sameoint strength formulaeas given in Fig. 8 provided

that the following modifications are adopted:

T- and X-joints in compression: replace in the formula for NI:

d l by dlmn;

K-joints with gap: replace in the formula for N,:

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30

15

10

5

0

1 1

w t h f In ') = 1.0 for n r 0

f I n ' ) = 1 + 0 . 2 n ' f o r O r n ' r - 0 . 8

14

/

I I I

0

2 0.3

0

4 0.5

0.6 0

7

0.8 0.9

- l id

(4.6.3.1)

(4.6.3.2)

(4.6.3.3)

Fig. 26

-

Design diagram for cropped end bracing connections

Fig. 27

-

K-joint with partial-flattened end bracings

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5 Bolted connections

The calculation methods used for many types of bolted connections between or to hollow

sections are not basically different from hose used or any other type of connection in

conventional steel construction.

(Some calculation examples will be given in chapter

6.5.)

Bolted connections are especially

desirable for site joints between prefabricated sub-assemblies. Various examples of bolted

connections are iven in Figs.28 to 30 and 33.

plate

Blech

I -sectton

ICHS- stub also

possible)

I

P r o f l l

(Rohrstuck auch

rnoglich)

__

~~

- _ _ _

Fig.

28 -

Bolted truss support connections

welded stud

Fig. 29

-

Bolted purlin connections

a

b

Fig.

30 -

Bolted end connections

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For flange oint connections various investigations have been carried out (27,81. However,

for simple designs he recommendations which are ncluded in the 1990 edition of he

Japanese Recommendations for the Design and Fabricationof Tubular Structures in Steel

1291 are most simple and are givenn Fig. 31.

Implicit in these connection details s an allowance for prying forces amountingo 1/3 of the

total bolt forceat the ultimate imit state and the assumption thathe tube yield strength must

be developed.

The modesof failure assumed n determining these details are those dueo plastification of

flange plates and not due to tensile failure of high strength bolts. The standard details

shown in Fig. 31 are for STK41 tubes. (specified minimum f = 235N/mm2 and minimum

ultimate ensilestrength = 402N/mm2), SS41 plates specifiedminimumyieldstrength

= 245 N/mm2) andFlOT bolts (about equal

o

10.9 bolts with a specified minimum ultimate

tensile strength of 981 Nlmm).

1

d

e l e

max. tube

dimensions

dl x

tl

(mm)

60.5 x 4.0

through

89.1 x 4.0

101.6 x 4.0

through

114.3

x

3.6

114.3 5.6

through

139.8

x

4.5

165.2x 5.0

190.7x 5.0

V6.3 x 6.0

36.3 8.0

Z67.4 9.0

318.5 7.0

355.6

x

12.0

106.4x 9.0

thickness of

of bolts diameter

lange plate

minimum no. nominal

tl

(mm)

mm)

of bolt

Fig. 31

-

Standard details for flange joint connections (fullstrength connections)

According to

1281

he flange plate thickness, can be determined from:

where

N, = tensile member orce

f = yield strength of plate

Y,, ,

= 1 l (partial safety factor)

f =

dimensionless to be obtained from Fig. 32

t, = thickness

of

plate

edge

distance

el = e2

(mm)

25

25

30

35

35

35

40

40

40

40

40

43


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Fig.

10

8

6

3

1 4

2

0

32

- Parameter

3

for us e in Eq.5.1 for the design of a CHS f lange plate conn ect ions

Tubu lar frame roof sup port

44


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45/68

The dimension e l (see Fig. 31) should be kept as low as possible to minimize prying action

(around 1.5 d to 2.0 d; d = bolt diameter), but the clearance between the nut and the weld

should be at least 5mm.

The number of bolts n canbe determined from:

where

r, = (d,/2 + 2el)

r2 = (d,/2+ el )

T = ultimate tensile resistance of a bolt

Other factors;see eq. 5.1.

Fig. 33

-

Some examples

of

bolted connections

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46/68

6 Worked

out

desing examples

6.1 a) Uni-planar truss

Truss

lay out:

The following dimensions are assumed:

Span

=

36 m, Trusses

L

12m centres

Purlins, L 6m centres

Trussdepth - =

2.40

m (considering overall costs, e. g.costsof all cladding of the

buildung, deflections, etc. U15 s generally an economical

height)

span

~

l

.l- -

l =

6 X 6000 = + 36000

2.4

3

an

H

=

0.8 B

=

38.7O

Fig. 34 Truss layout

A

warren type truss with K-joints is chosen to limit the number of joints.

The factored design load P from the purlins including the weight of the truss have been

calculated as P = 108 kN.

Member oads kN )

A

pin-jointed analysis of the truss gives the following member forces:

338 878 1 1 4 8 j

A

Fig.

35

-Truss member axi-'

a1 luaus

675 k N

1080

1215'

Des ign

of members

In this example the chords will be made from steel with a yield stress of 355 N/mm2 and

bracing from steel with a yield stress of 275N/mm2.

For memberselection use either member resistance tables forhe applicable effective length

or the applicable buckling curve. Check the availability

of

the member sizes selected. Since

the joints at the truss ends are generally decisive, the chords should not beoo thin walled.

A s

a consequence a continuous hord with the same wall thickness over the whole truss length

is often the best choice.

top

chord

use a continuous chordwith an effective in-plane and out-of-plane ength of:

le =

0.9

x 6000

=

5400mm 17, 161,ee chapter 2.2

No = 1148 kN

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-

f Y

. .A,

*

dolt,

,

ossible

e

O

sections

Nlmm

W )

mm2)mm)m)kN)

355

1189.71.94 30.9728219.1

-

7.1

1245

.61

.09 19.4

771

193.7-10.0

.400

148

0 219.1

-

8.0

1159 0.78.843.7

202244.5- 5.6

1329

.71

.95

7.4

305

0

244.5- 6.3

1298

.78

.84

8.8

714

* Eurocode 3 buckling curve

a

From a material point of view the sections44.5

x

5.6 and0 219.1-7.1 are mostefficient;

however, these two dimensions are, forhe supplier considered n this example, not available

from stock (only to be delivered from factory). These dimensions can onlye used

if

a large

quantity is required, which s assumed in this example.

Bottom

chord

possible

sections

Diagonals

Try to select members which satisfy 2.0; i.e.

355

71 2 2.0 or t,5 4.5 mm, see eq. 4.2.7.

Useorhebracingsoaded in compressionan initial effectiveength

=

0.75 J2.4

+

3.02

2.88

m

17, 161, see chapter 2.2.

f

. to

f .

,

275 .t,

Compression diagonals

of .75 . P

-

f,

A1

ossible

e

I

. . A,*

sections

Nlmm

(mm2)

mm)m)

kN)

275

462.90.57862

168.3-3.6.881 432

0 139.7-4.5

448

.85

.69

911

275 266.77.85252114.6-3.6.88159

0 101.6-4.0

235 0.70

.96

226

275

92.61

.08

46

88.9-2.0.8816

* *

0 76.1 2.6

80

.49.28

00

* Eurocode 3 buckling curve a

* *

the wall thickness

is

rather small for welding

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Tension diagonals

f Y

F

$2 .A2

A2

ossible

sections

Nlmrn

( W

mm2)

mm)

kN)

275 445 1621

L3 133.3-4.0

32

275

2656488.9- 3.6

59

275 91

32

48.3- 2.36

Member selection

The number of sectional dimensions depends on the total tonnage to be ordered. In this

example for he bracings only twodifferent dimensions will beselected.

Comparison of the members suitable for the tension members and those suitable for the

compression members shows thathe following sections are most convenient:

- bracings: 39.7- 4.5

- top chord: 19.1 7.1

- bottom chord: C7 193.7- 6.3 (Thesechordsizesallowgap oints;no eccentricity is

0 88.9-3.6

required).

It

is recognized that the doho atios

of

the chords selected are high. This may give joint

strength problems in joints

2

and 5.

0 2 1 9 . 1 ~ 7 ~~~ 0 8 8 . 9 X - 3 6

r -

l

1

l

Fig. 36

-

Member dimensions

Commentary and revision

Joint 1

Jotnt 1 In joint

1

between plate and bracing agap g

=

2

t o

ischosen.This

r no ten 1 joint is checked s K(N) oint.

+h? -

ection A should

be able

to

resist the shear of 2.5

P

=

2.5

x

108

Attention should be paid

to

the top chord shear capacity, i. e. cross

Since oint 1 is

ratherheavily oaded t is recommended to use

= 270 kN.

-l*

2

to

\r

conservatively the elastic hear capacity of the top chord, i .e.:

Fig . 37

0.5A0.-yo

=

0.5 .4728. = 485kN > 270kN

.355

\3 v3

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Check jo in t s t reng th

joint

1

2

3

4

5

6

7

chord

(mm)

219.1 -7.1

219.1 -7.1

219.1 -7.1

219.1 -7.1

193.7- 6.3

193.7- 6.3

193.7

-

6.3

bracings

(mm)

plate

139.7

-

4.5

139.7-4.5

88.9 - 3.6

139.7-4.5

88.9

-

3.6

88.9

-

3.6

88.9

-

3.6

139.7- 4.5

139.7

-

4.5

88.9- 3.6

139.7-4.5

88.9

-

3.6

88.9 - 3.6

T

joint parameter

0.64

0.64

0.64

0.41

0.72

0.72

0.46

dolt,

30.9

30.9

30.9

30.9

30.7

30.7

30.7

2.0

12.8'

12.8

18.5

2.9

9.4

15.8

not appl.

- 0.20

-

0.52

- 0.68

0.82

0.32

0.82 0.23

0.98

0.49.23

0.32

0.32.26

0.32

0.82

0.82 0.29

0.98

0.49.23

0.32

0.32 0.25

-

fyo

' 10

f

.

11

2.04

2.04

2.55

2.04

2.55

2.55

2.55

1.81

1.81

2.26

1.81

2.26

2.26

N*

1.60 > 1.00

1.49 0.70

> 1 oo

1.22 0.58

> 1 oo

1.05 0.70

0.70

0.85

1.60 0.85

> 1 oo

1.60 0.67

0.91

1.60.91

P

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50/68

Joint

2

The strength of joint2 is not sufficient. The

~~ easiestay

to

obtain sufficient oint strengthill

be to decrease the gap rom12.8 to to 3 to

resulting in a joint efficiencyof0.86 > 0.82.

However, this means that a (negative) ccentri-

city of e

=

28 mm is introduced resulting in a

moment due

o

eccentricities of:

4

o

- h e

t- '

338 kN i ? 878 kN

Fig. 38 M

= (878-338).28.10--3=15.12kNm.

Since the length and the stiffness El of the top chord members betweenoints 1 - 2 and 2 3

are the same (see Fig. 36) this moment can be equally distributed over both members, i.e.

both members have o be designed additionally for

M

= 7.56 kNm.

The chord members betweenoints

1

- 2 and -3 have nowo be checked as a beam-column.

From these, the chord member 2

-

3 is most critical. This check depends onhe national code

to

be used.

However, the criterion to be checked hasgenerally a formof:

(6.1.1.)

where:

= plastic resistance (W,

.

fyo)of the chord (class1 or 2 sections);

use for class 3 elastic moment resistance (Weo-fyo)

and moment diagram (in this case use triangle)

k = factor including second order effects depending on slenderness, section classification

878.56

113.3

0.74 + 0.067 k

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