the analysis of splice joint behaviour in heavily …clapeyron’s theorem of three moments has been...
TRANSCRIPT
THE ANALYSIS OF SPLICE JOINT BEHAVIOUR IN HEAVILY LOADED
TENSILE CHORDS OF WARREN TRUSSES
Lilita Ozola
Asoc. Prof., Dr.Sc.ing.
Department of Structural Engineering
Latvia University of Agriculture
PANACM 2015 1st. Pan-American Congress on Computational Mechanics
An IACM Special Interest Conference
Department of
Structural Engineering
Latvia University of Agriculture
19 Akademijas Str
Jelgava, LV-3001, LATVIA
E-mail :
Lilita.Ozola@ℓℓu.ℓv
Problem
• Comprehensive design practice entails some risk
when the most unfavourable loading situations for
the whole structure or stress-strain relationships
are not analysed.
• Tolerance of this risk varies widely among
countries and emerges from the legal code system
and content, and clarity in definitions of criteria
for the acceptability of construction products,
and even more from the intelligence of
professionals
• disputable topics in the truss design area deal
with the conformity between design model links
and a realistic behaviour phenomena of a system
1) suggestions for modelling of
splice joint in tensile chord
considering additional stresses
induced by bending moment;
2) drawing up the methodology for
analysis and numerical examples of
end-plate joint design considering
elastically deformed tensioned bolts
and stiffness on end-plate
The Objectives of a Study:
The Method selected
The specified method used is the
phenomenological approach to the
splice joint behaviour problem
illustrated by the results of
numerical analysis based on a real
design solution.
The benefit to be expected:
• to perfect the knowledge in
structural design
• deepening the understanding in
designing and promoting an
extensive judgement of structural
solutions accepted, especially when
the hard-loaded structures have
been designed for covering the spans
of public building areas
End-plate joint types under discussion
a) With extended
end-plates
b) With hidden
fasteners
between flanges
a)
b)
...used in tensile chord of Warren truss
A
280
A
g= 0.68 kN/m [0.05 kip/ft]
332.8
[137.8]
47.5 [10.7]
22
.4 [
5]
55
2.0
5 [
12
4.1
]
1364.1 1364.1
7.9
7.9
22.7
88.4
[112699]
[47499]
HEA260
CHS160
HEA260
HEA320
q= 44.95 kN/m [3.08 kip/ft]
239.
2
1157.2815.0332.8
618.85
613.1
567.
4
364.3
55
2.0
5
390.
1
1024,8
245.9
82.6
1284.7
1329.7
68.7
55
2.0
5
1369.51284.8
78.5
[18]
1.7 0,2
1,0
1.7
D
7.9
7.9
[1
.8]
22.7 [16743]
7.9
3000 [9'-10.11"] 3000 [9'-10.11"]
1575 [5'-2.01"]
2900 [9'-6.17"]
1500 [4'-11.06"]
24
00
[7
'-1
0.4
9"]
11975 [39'-3.46"]
kN; kNm [kipf; lbf*ft]
[74.8]613.1
152.864.4
[65200]
[307.9][288.8]
78,9
[18]
[306.7] [306.7]
D
Middle bar effect in countour
u 1u 2
u' 1
u' 2
12000
1500
q= 65 kN/m
HEA320
CHS160
u = 48.5 mm
u = 40.5 mm
1
2
u = 44.6 mm
u = 44.4 mm1
2
'
'
Models effect on values of internal forces in Warren
truss heavily loaded elements
Splice joint with extended end-plates
Assembly
Loading scheme
Consideration on Behavior of Connection
Due to the coexistence of bending moment and axial force
in continuous chord sections there will be regions of
distinctive stress concentrations, even though the mean
stress across the section remains well below yield.
Thus, the end-plate is modelled as a continuous beam on
discrete elastically deformed supports (representing tying
bolts), and loaded by concentrated forces transferred by
flanges and the web of I section.
Clapeyron’s theorem of three moments has been used at
the first step assuming bolts as rigid supports for
continuous end-plate, and reactive forces expected to be
acting in bolts has been determined.
Design model of extended
end-plate: beam on
discrete elastic supports
Deformed axis of end-
plate modelled
Primary system for
analysis
In reality some axial deformation of the bolts takes place under tensile
forces according to Hooke’s law. So, at the next step a model of a
continuous beam on elastic supports has been examined taking into
account the additional rotations (ψn+1-ψn) due to differences of support
displacements. The condition of continuity of a deformed axis may be
expressed by the following equation:
01116
nlτ
nrτnψnψnMnM4nM
EJ
Input Data: ho, As, Af, Aw, Wy, Wyo, Ab, ℓ, Ntd, Md, σtd, Ftu, Ftb, qw
Compilation of three-moment equation systemSlide 22
Defining the fictive reactionsSlide 23
Finding the support moments solving the equation systemSlide 24
Determination of the support reactions Slide 25
Determination of elongation value of an individual boltSlide 26
Equation system for continuous beam on elastic supportsSlide 27
Solution of the system and determination of reactions in bolts
Differences →0
Yes End No
Algorithm for extended end-plate joint analysis
;0,
,1,
,
iB
iBiB
iBM
MM;0
,
,1,
,
iC
iCiC
iCM
MM0
,
,1,
,
iD
iDiD
iDM
MM
-200 -100 0 100 200 300 400 500 600
E
D
C
B
A
Force, kN
Bo
lt r
ow
lo
cati
on
Elastic Rigid
Results of approximation
E
A
Force per bolt row, kN
D
C
B
A
B
C
D
E
Rigid
Elastic
100 200 300 400 500 600 0 -100
Analysis of joint behavior with hidden fasteners
Three moment equation
Five moment equation
Moments in end-plate sections and reactive forces
in bolts for joint variant with hidden fasteners (1-st
approximation- rigid supports)
-1000 -500 0 500 1000
E
D
C
B
A
Force, kN
Bo
lt r
ow
lo
cati
on
Elastic Rigid
Results of analysis of joint behavior with
fasteners hidden between flanges
Force per bolt row, kN
D
C
B B
C
D
0 500 1000 -500 -1000
Summary of Results
• Bending moments generated in the tensile
bottom chord sections even of reasonably moderate
values itself affects significantly the force
distribution between the bolts depending on a
location. It has been found that in the case of
variant with closed fasteners solution the
overloading of bolts near flanges exceed 2,5 times in
comparison with the bolts of variant with extended
end-plates at the same position.
• No experimental tests have been carried out to
prove the results of this study. Significant effects on
the behaviour and force distribution in a real
structure may be expected due to friction surface-
on-surface, imperfections, some lateral actions,
plastic deformations possibly accumulated during
previous extreme loading cycles and other factors.
Anticipated force distribution between bolt rows
depending on location
-1000
-500
0
500
1000
1500
A B C D E
Bolt row location
Forc
e tr
ansf
erre
d,
kN
Variant I, elastic supports Variant I, rigid supports
Variant II, elastic supports Variant II, rigid supports
• Design models that disregard some
portion of the stresses or strains in
comparison with real structural behaviour,
may be assessed as overly simplified and
insufficient for the design of bearing
structures.
• It is potentially dangerous to assess or
design truss structures without thorough
analysis of possible models taking into
account more unfavourable loading
situations, the stresses generated and the
deformations developed.
CONCLUSIONS
• The continuous beam model on
elastically settled supports may be
advisable for the analysis of end-plate joint
behaviour in heavily loaded tensile chords
• The end-plate joint solution with
fasteners arranged between flanges (variant
with closed fasteners) may be assessed as
hazardous with regard to collapse
• Despite the proper account of code
conditions in the practical design it would
be reasonable to consider the potentials of
a structure when subjected to overloading
and/or unfavourable service conditions.
Latvia Riga
Jelgava
Ru
ss
ia
Latvia University of Agriculture
Thanks for your attentation !