analytical method for calculating the reduction in...
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Analytical Method for Calculating the Reduction in Strength Due to Shear Lag Effect in Tension Member Connections
SSEF Architecture and Engineering Educators Meeting 2008February 29 - March 1, 2008,Novotel Toronto Centre Hotel
Dominique Bauer
Novotel Toronto Centre HotelToronto, Ontario
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11 000 kN Universal
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Universal Testing Machine
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L = 100 mmLoad = 350 MPa
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von Mises stresses
50 mm30° 30°
200 mm
100 mm30°
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beff
Critical Section
Fy
Gusset Plate
30°L
Tension Member
30°
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Ty
wTension Member
L2 tan θ
σ2
σ3
σ4
L1 tan θ
θL2
dL
σ2 σ1
σ2
θ
Critical Section
dL
L1
σ1
qθ
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σ
L tan θ T
x tan θ
θ
dxL
y’, y
L
x
Critical Section
1α =
Critical Section α
θ
1α =
elementalα
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x x
Fy
(a) σ (b)
a
(c)
Fy
Fu
σ σ
L
Critical Section
θ θθ
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55
44
θ55
Stress resultant
Critical Section
11L
θ
33
22
44
θ
θ332211
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w
cθ
w
cLθ
σc tan θ
(c – L) tan θ
L1 1
L
c
σ
c tan θy
θ
3 3
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θ
L Ly
c
10
Critical Section
Fu
L tan 30°
Fu
Critical Section
L
θ L θ
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w w
Elements connected by a single longitudinal weld
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L1
Critical Section
θ
FuL1 tan θ
θL
Fu F2
L1 L2θ θ
θ θ
Fu F2
L1 tan θ
w
L2 L12
L2θ θ
w w
CriticalFu
F
L1 tan θ L1 tan θ
F
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L1
Critical Section
Fu
L1L2
L2
θ θθ θ
Fu
L = 50 mmLoad = 200 MPa
F.E.A.
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L = 100 mmLoad = 200 MPa
F.E.A.
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L = 200 mmLoad = 200 MPa
F.E.A.
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Elements connected by longitudinal welds along two parallel edges
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σmaxσmax
Angle
CompressionTension T
L
Shear Flow, qGusset
Weld
2h/3
xp
My
CompressionTensionR
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2h/3
h/3
h b1b2
Weld
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a b cτ
τ
σ
σO
Compressionσ
σ
τ
σ
τ τ
Tension
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Element a
Element b
Element c
a
> 45º
b c
= 45 º < 45 º
Principal Directions from Mohr’s Circles
<45º> 45º = 45 º
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Principal Directions from ANSYS
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Line of Action of Line of Action of
xp
y
ypx
Load in AngleLine of Action of
Reaction in Gusset
TG
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Neutral AxisMy
yxp
Principal Axis of SectionLoad Axis
α
Neutral Axis
Centroïd f A l
xMx
G
Centroïd of Gusset
β
yp
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of Angleof Gusset Plate
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Deflection
DeflectionTorsion
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Angle
xp
xT T
xp
y z
M < T. xp
My = T. xp = constant
First Order Analysis
M < T xSecond Order
Analysis
z
z
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My < T. xpAnalysis My = T. xp
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AngleCentroïdxAngle
xpxpTTT
xp1
xpT
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Axe de la membrure principale
xp (+)xp (–)
E t i ité iti E t i ité é ti
Lignes de travail
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Excentricité positive Excentricité négative
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Moment maximumau noeud dû à la rigidité de la diagonale
Membruresupérieure
Moment fléchissant le
long de la diagonale
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TractionCompression Diagonales
Contraintes résiduelles de
traction
Tr
Contraintes résiduelles de
i
Section critique
++
–Contraintes dues au
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compression(Réserve)Tr
refroidissement différentiel
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σT
z
É l
Loi de Hooke pour une pièce confinée :1) coefficient de Poisson connu2) σy connu en fonction de σz (σy = υσz)
1
Section critique
σz1
σz2
σy2σz3
1Fy
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Fy
σy
σz
Étranglement amplifié de la section
y2
3 σy3
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Critère de von MisesÉtat des contraintes
Acknowledgments
The present research was made possible by grants from :grants from :
• Steel Structures Education Foundation of the Canadian Institute of Steel Construction
• National Sciences and Engineering Research Council of Canada (No 238967-01)
• École de technologie supérieure
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• École de technologie supérieure
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Center of Gravity
Length of Shear Lag
Tension Force, T
Gravity
S tTension Stresses
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Support
Outstanding Leg
Length of Shear Lag
T
C t d
± 0,65 T
Tension
± 0,35 T
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Connected Leg
Tension Stresses
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St-Venant Uniform Strain St-VenantT T
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Bar
Uniform Shear Flow
Non-uniform Shear Flow
Non-uniform Shear Flow
T
Supporting Member
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T