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Unformatted text preview: MECHANICS OF DIAGONAL
TENSION FIELD ACTION
TENSION
Chai H. “Jay” Yoo, Ph.D., P.E., F. ASCE
Professor Emeritus
Department of Civil Engineering
Auburn 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 A pdf file of the paper can be downloaded
from http://www.asce.org/
Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Functions of Webs in Plate
Girders?
Girders?
1. Maintain the relative distance
between two flanges.
2. Carry the induced shear. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Bending Moment & Shear
Bending
Bending Moment =αwl Shear = βwl Auburn University 2 MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS AASHTO LRFD (2007) Article 6.10.2
AASHTO
CrossSection Proportion
D / tw £ 300 with longitudinal stiffeners
D / tw £ 150 without longitudinal stiffeners
b f / ( 2t f ) £ 12 bf ³ D / 6
t f ³ 11tw
.
Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS 28" 28" 1
2"
2 1
2"
2 5
"
8 84" y = 42176"
. 27" 3" M y = 18 ,717 kft
Auburn University 27" 3" M y flg = 0.95 M y MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Minimum Steel Thickness?
Minimum
5/16 (0.3125) in. for all main members
per AASHTO LRFD Article 6.7.3
 corrosive environment
 weldability Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Background
Background
• It is desired to use as thin a web panel as you can get by
⇒ elastic buckling becomes a major concern
• In 1886, Wilson considered the possibility of utilizing
postbuckling strength
• In 1931, Wagner demonstrated the tension field action Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS A postbuckling mode shape of a super thin high
strength wire is shown. Although a considerable postbuckling strength is
available at this stage of deformation, it is highly
impractical to use in practical design.
Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Shear Strength Curve
Shear
C Elastic buckling curve
AASHTO LRFD (2007) 1.0 T1 T2
Yield
zone
0
Auburn University Transition Elastic buckling
zone
zone
1.12 1.40 λ= D
tw Ek
Fyw MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Postbuckling is a very complex nonlinear response. 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. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Incorrect Tension Field Models
Incorrect
Plastic Hinge (a) Basler (1963) (b) Fujii (1968, 1971) Plastic Hinge (c) Porter et al. (1975) (d) Steinhardt and
Schroter (1971) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Free body diagram (Basler 1963)
Free
B A
b/2
C V V
b/2 C φ
A do B Fs Fw
Ff Auburn University Cφ
V/2 tσt
O C
V/2 Fw
Ff +ΔFf MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Both Basler and Rockey theories were calibrated with
extensive test data. “Calibration=Finagling?” 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. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Ultimate Strength vs. Flange Size
Ultimate Shear Force (kN) 900 600 Simply Supported Panel
Light Flange
Moderate Flange
Heavy Flange 300 0
0 10 20 Outofplane displacement at center of web panel
(mm) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Stress Development
at Prebuckling Stage
at
τ τ τ
σ σ
τ
(a) Shear stress Auburn University τ (b) Diagonal tension (c) Diagonal compression MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Incomplete Stress State
after Buckling
after
σ2 σ2
τ τ cr
σ1 τ τ cr
σ1
σt (a) Diagonal tension
Auburn University (b) No diagonal compression
MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Outofplane Displacement
Outofplane Shear Force (kN) 900
Phase3 Phase4 600
Phase2
Phase1 300 0 Vertical and horizontal strips Auburn University 0 5
10
15
20
Displacement (mm)
at the center of the panel 25 MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Normal Stresses in Vertical Strip
Normal Horizontal direction Vertical direction Phase1 0.50 0.25 Phase2 Wep Depth Wep Depth Phase1
Phase2
Phase3
Phase4 0.00 0.25 0.50 σ1 /Fyw Auburn University Phase3
Phase4 0.50 0.25 0.00 0.25 0.50 σ2 /Fyw MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Normal Stresses in Horizontal Strip
Normal Horizontal direction Vertical direction 0.50 0.50 0.25 0.25 σ 1 0.00 σ 2 0.00 Fy
w 0.25 Phase1
Phase2
Phase3
Phase4 Fy
w 0.25 Phase1
Phase2
Phase3
Phase4 0.50 0.50
Web width Auburn University Web width MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Principal Stresses under Pure Shear
Principal
Buckling stage Ultimate stage ↔ Tension Compression Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Diagonal Stress Diagram
at Ultimate Stage
at
Diagonal tension Vu/2 Diagonal
compression Vu/2 Vu Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Lateral Deflection
along Compression Diagonal
along
2 Phase1
Phase2 1 Phase3
Phase4 w0
tw 1
2
3
Compression diagonal of web panel Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS TensionField in Plate Girder
TensionField Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Effect of Transverse Stiffener
Effect
0.50 0.25 S. S. Simple Support
Transverse
Stiffener
S. S.
S. S. S. S. Transverse
Stiffener Left Edge σ2 0.00
Fyw
0.25 1I=Is
4Is Is
I=4
6 I=6Is 0.50 Web Width
(Left Panel) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS 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 MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS 28" 28" 1
2"
2 1
2"
2 5
"
8 84" y = 42176"
. 27" 3" M y = 18 ,717 kft
Auburn University 27" 3" M y flg = 0.95 M y MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Conclusions
Conclusions All previous tension field (postbuckling) models including those by
Basler and Rockey were incorrect. All forces developed during
postbuckling are in a selfequilibrating force system. 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. There is no truss action that takes place as suggested by Basler
(American model). Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Incorrect Tension Field Models
Incorrect
Plastic Hinge (a) Basler (1963) (b) Fujii (1968, 1971) Plastic Hinge (c) Porter et al. (1975) (d) Steinhardt and
Schroter (1971) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Conclusions (continued)
Conclusions There is no need to have sturdy flanges present in order to develop
tension field action as suggested by Rockey (British model ). 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. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS Questions?
Questions? Samford Hall,
Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION
MECHANICS ...
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 Summer '10
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 Civil Engineering

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