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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
Construction with Hollow Steel Sections - Design guide for circular hollow section (CHS) joints under predominantly static loading
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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
Construction with Hollow Steel Sections - Design guide for circular hollow section (CHS) joints under predominantly static loading
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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
14
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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)
chord plastification
(eq. 4.2.2)
I K
and
N
gap or overlapoints
I
chord plastification
(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
chord plastification
fJnJ
Ml p = 4.85 f . g .
P
' d l .
chord plastification
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.
35
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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
36
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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
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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
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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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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
W
Construction with Hollow Steel Sections - Design guide for circular hollow section (CHS) joints under predominantly static loading
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Createdon24May2008
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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