Post on 20-Dec-2015
MECHANICS OF DIAGONAL MECHANICS OF DIAGONAL TENSION FIELD ACTIONTENSION FIELD ACTION
Chai H. “Jay” Yoo, Ph.D., P.E., F. ASCEProfessor Emeritus
Department of Civil EngineeringAuburn University
CIVL 7690
July 14, 2009
Yoo, C.H., and Lee, S.C., “Mechanics of Web Panel Postbuckling Behavior in Shear,” Journal of Structural Engineering, ASCE, Vol. 132, No. 10, October, 2006
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
A pdf file of the paper can be downloaded from
http://www.asce.org/
Functions of Webs in Plate Functions of Webs in Plate Girders?Girders?
1. Maintain the relative distance
between two flanges.
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
2. Carry the induced shear.
Bending Moment & ShearBending Moment & Shear
Bending Moment 2w
w
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Shear
AASHTO LRFD (200AASHTO LRFD (20077) Article 6.10.2) Article 6.10.2Cross-Section ProportionCross-Section Proportion
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
"28 "28
"1
22
"27 "27"3
y . "=42176
"84
"58
"1
22
"3
k-ftyM ,=18717 flgy yM . M=095
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Minimum Steel Thickness?Minimum Steel Thickness?
5/16 (0.3125) in. for all main members
per AASHTO LRFD Article 6.7.3
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
- corrosive environment
- weldability
BackgroundBackground
• It is desired to use as thin a web panel as you can get by elastic buckling becomes a major concern
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
• In 1886, Wilson considered the possibility of utilizing postbuckling strength
• In 1931, Wagner demonstrated the tension field action
A postbuckling mode shape of a super thin high strength wire is shown.
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Although a considerable postbuckling strength is available at this stage of deformation, it is highly impractical to use in practical design.
Shear Strength CurveShear Strength Curve
1.12 1.40
1.0
0
C
Yield zone
Transition zone
Elastic bucklingzone
T1 T2
Elastic buckling curve
AASHTO LRFD (2007)
w yw
D Ekt F
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Postbuckling is a very complex nonlinear response.
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
There were no reliable analytical tools available to examine nonlinear behavior in the 1960s and 1970s.
More than a dozen simplified and linearized models and their derivatives for the postbuckling behavior of web panels subjected to shear were a futile exercise.
The analysis of web panels has remained elusive for nearly 50 years and various researchers have agreed to disagree.
Incorrect Tension Field ModelsIncorrect Tension Field Models
(a) Basler (1963) (c) Porter et al. (1975)
Plastic Hinge
(b) Fujii (1968, 1971)
Plastic Hinge
(d) Steinhardt and
Schroter (1971)
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Free body diagram (Basler 1963)Free body diagram (Basler 1963)
Fw
BA do
Fs
tσt
C CO
Ff
V/2 Fw
Ff +ΔFf
V/2
φ
V Vb/2
b/2
CC
A B
φ
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Both Basler and Rockey theories were calibrated with extensive test data. “Calibration=Finagling?”
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
The aspect ratio of those specimens were mostly equal to one.
The steel industry wants to increase the aspect ratio for economic reasons.
As the test data cannot be extrapolated, old design provisions stuck.
Ultimate Strength vs. Flange SizeUltimate Strength vs. Flange Size
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Out-of-plane displacement at center of web panel (mm)
0
300
600
900
0 10 20
She
ar F
orce
(kN
)
Simply Supported Panel
Light Flange
Moderate FlangeHeavy Flange
Stress Development Stress Development at Prebuckling Stageat Prebuckling Stage
(a) Shear stress (b) Diagonal tension
(c) Diagonal compression
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Incomplete Stress State Incomplete Stress State after Bucklingafter Buckling
(a) Diagonal tension(a) Diagonal tension
-cr
t
-cr
(b) No diagonal compression(b) No diagonal compression
2
11
2
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Out-of-plane DisplacementOut-of-plane Displacement
Vertical and horizontal strips
0
300
600
900
0 5 10 15 20 25
Shea
r For
ce (k
N)
Phase1
Phase2
Phase3 Phase4
Displacement (mm)at the center of the panel
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Normal Stresses in Vertical StripNormal Stresses in Vertical Strip
Horizontal direction Vertical direction
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
-0.50 -0.25 0.00 0.25 0.50
Wep
Dep
th
Phase1Phase2Phase3Phase4
1 /Fyw
-0.50 -0.25 0.00 0.25 0.50
Wep
Dep
th
Phase1
Phase2
Phase3
Phase4
2 /Fyw
Normal Stresses in Horizontal StripNormal Stresses in Horizontal Strip
-0.50
-0.25
0.00
0.25
0.50
Web width
Phase1Phase2Phase3Phase4
1
Fyw
-0.50
-0.25
0.00
0.25
0.50
Web width
Phase1Phase2Phase3Phase4
2
Fyw
Horizontal direction Vertical direction
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Principal Stresses under Pure ShearPrincipal Stresses under Pure Shear
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Buckling stage Ultimate stage
Tension Compression
Diagonal Stress Diagram Diagonal Stress Diagram at Ultimate Stageat Ultimate Stage
Diagonal tension
Diagonal compression
Vu/2
Vu/2
Vu
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Lateral Deflection Lateral Deflection along Compression Diagonalalong Compression Diagonal
-3
-2
-1
0
1
2Phase1
Phase2
Phase3
Phase4
Compression diagonal of web panel
wtw
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Tension-Field in Plate GirderTension-Field in Plate Girder
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Effect of Transverse StiffenerEffect of Transverse Stiffener
TransverseStiffener
Simple Support
S. S.
S. S.
S. S.
S. S.
-0.50
-0.25
0.00
0.25
0.50
1
4Is
6
I=Is
I=4Is
I=6Is
2
Fyw
Web Width(Left Panel)
TransverseStiffener
Left Edge
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Since the moment of inertia of the transverse stiffener is proportional to the cube of the width of the stiffener, the width only needs to be increased to 1.8 times the old width [6^(1/3)=1.8].
The placement of transverse stiffeners helps shipping and handling of the slender girders by making the girder torsionally stiff. Wider transverse stiffeners are beneficial to this concern.
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
"28 "28
"1
22
"27 "27"3
y . "=42176
"84
"58
"1
22
"3
k-ftyM ,=18717 flgy yM . M=095
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
ConclusionsConclusions
All previous tension field (postbuckling) models including those by Basler and Rockey were incorrect. All forces developed during postbuckling are in a self-equilibrating force system.
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
There is no truss action that takes place as suggested by Basler (American model).
There is no net axial compressive force developed in an intermediate transverse stiffener. Hence, the current area requirement for a transverse stiffener is irrelevant.
There is no need to distinguish the end panel from the interior panel. Tension field action can take place in the end panel.
Incorrect Tension Field ModelsIncorrect Tension Field Models
(a) Basler (1963) (c) Porter et al. (1975)
Plastic Hinge
(b) Fujii (1968, 1971)
Plastic Hinge
(d) Steinhardt and
Schroter (1971)
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Conclusions (continued)Conclusions (continued)
There is no need to have sturdy flanges present in order to develop tension field action as suggested by Rockey (British model ).
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION
Transverse stiffeners need to have sufficient stiffnesses (moment of inertia) in order to form and maintain nodal lines during the history of postbuckling.
All design specifications regarding the tension field action, AISC, AASHTO, BS 5400, Eurocode 3, must be revised.
All current steel design textbooks in the world incorporating erroneous theories must be revised.
Questions?Questions?
Samford Hall,Auburn University
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMECHANICS OF DIAGONAL TENSION FIELD ACTION