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### MECHANICS OF DIAGONAL TENSION FIELD ACTION

Chai H. “Jay” Yoo, Ph.D., P.E., F. ASCE

Professor Emeritus

Department of Civil Engineering

Auburn University

CIVL 7690

July 14, 2009

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

- 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 ACTIONFunctions of Webs in Plate Girders?

1. Maintain the relative distance

between two flanges.

2. Carry the induced shear.

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONBending Moment & Shear

Bending Moment

Shear

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONMinimum Steel Thickness?

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 ACTIONBackground

• 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

- 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.

C

Elastic buckling curve

AASHTO LRFD (2007)

1.0

T1

T2

Yield zone

Elastic buckling

zone

Transition zone

0

1.12

1.40

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Shear Strength Curve Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

- There were no reliable analytical tools available to examine nonlinear behavior in the 1960s and 1970s.

- Postbuckling is a very complex nonlinear response.

- 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.

Plastic Hinge

Plastic Hinge

(a) Basler (1963)

(b) Fujii (1968, 1971)

(d) Steinhardt and

Schroter (1971)

(c) Porter et al. (1975)

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Incorrect Tension Field ModelsB

A

b/2

V

V

C

C

b/2

φ

do

A

B

Fs

tσt

φ

C

C

O

V/2

Fw

Fw

V/2

Ff +ΔFf

Ff

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Free body diagram (Basler 1963) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

- 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.

Out-of-plane displacement at center of web panel (mm)

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Ultimate Strength vs. Flange Size

(a) Shear stress

(b) Diagonal tension

(c) Diagonal compression

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Stress Development at Prebuckling Stage2

2

-cr

-cr

1

1

t

(a) Diagonal tension

(b) No diagonal compression

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Incomplete Stress State after BucklingDisplacement (mm)

at the center of the panel

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Out-of-plane DisplacementVertical and horizontal strips

Horizontal direction

Vertical direction

1 /Fyw

2 /Fyw

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Normal Stresses in Vertical Strip Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

1

Fyw

2

Fyw

Normal Stresses in Horizontal StripHorizontal direction

Vertical direction

Buckling stage

Ultimate stage

- Tension

Compression

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Principal Stresses under Pure ShearDiagonal tension

Vu/2

Diagonal

compression

Vu/2

Vu

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Diagonal Stress Diagram at Ultimate StageCompression diagonal of web panel

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

w

tw

Lateral Deflection along Compression Diagonal Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONTension-Field in Plate Girder

Transverse

Stiffener

Left Edge

Simple Support

Transverse

Stiffener

S. S.

I=Is

I=4Is

I=6Is

S. S.

S. S.

S. S.

Web Width

(Left Panel)

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

2

Fyw

Effect of Transverse Stiffener Auburn University MECHANICS 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 MECHANICS OF DIAGONAL TENSION FIELD ACTION

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONConclusions

- 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 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).

Plastic Hinge

Plastic Hinge

(a) Basler (1963)

(b) Fujii (1968, 1971)

(d) Steinhardt and

Schroter (1971)

(c) Porter et al. (1975)

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

Incorrect Tension Field Models Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTIONConclusions (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.

Samford Hall,

Auburn University

Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

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