MECHANICS OF DIAGONAL TENSION FIELD ACTION Chai H. “Jay” Yoo, Ph.D., P.E., F. ASCE Professor...

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.


2. Carry the induced shear.

Bending Moment & ShearBending Moment & Shear

Bending Moment 2w

w


Shear

AASHTO LRFD (200AASHTO LRFD (20077) Article 6.10.2) Article 6.10.2Cross-Section ProportionCross-Section Proportion


"28 "28

"1

22

"27 "27"3

y . "=42176

"84

"58

"1

22

"3

k-ftyM ,=18717 flgy yM . M=095


Minimum Steel Thickness?Minimum Steel Thickness?

5/16 (0.3125) in. for all main members

per AASHTO LRFD Article 6.7.3


- 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


• 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.


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


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.

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)


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


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.

Ultimate Strength vs. Flange SizeUltimate Strength vs. Flange Size


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


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


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


Normal Stresses in Vertical StripNormal Stresses in Vertical Strip

Horizontal direction Vertical direction


-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


1

Fyw

-0.50

-0.25

0.00

0.25

0.50

Web width


2

Fyw

Horizontal direction Vertical direction


Principal Stresses under Pure ShearPrincipal Stresses under Pure Shear


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


Lateral Deflection Lateral Deflection along Compression Diagonalalong Compression Diagonal

-3

-2

-1

0

1

2Phase1

Phase2

Phase3

Phase4

Compression diagonal of web panel

wtw


Tension-Field in Plate GirderTension-Field in Plate Girder


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


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.


"28 "28

"1

22

"27 "27"3

y . "=42176

"84

"58

"1

22

"3

k-ftyM ,=18717 flgy yM . M=095


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.


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)


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 ).


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


MECHANICS OF DIAGONAL TENSION FIELD ACTION Chai H. “Jay” Yoo, Ph.D., P.E., F. ASCE Professor...

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