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LONGITUDINAL STIFFENERS ON COMPRESSION PANELS Chai H. Yoo, Ph.D., P.E., F. ASCE Professor Emeritus Department of Civil Engineering Auburn University CIVL 7690 July 14, 200 9 History ● The most efficient structural form is truss

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longitudinal stiffeners on compression panels

LONGITUDINAL STIFFENERS ONCOMPRESSION PANELS

Chai H. Yoo, Ph.D., P.E., F. ASCE

Professor Emeritus

Department of Civil Engineering

Auburn University

CIVL 7690

July 14, 2009

history
History

● The most efficient structural form is truss

with regard to its weight-to-strength ratio provided that all other conditions are equal.

Old section of NY Metro Subway system,

Tower crane post and arms,

Space station,

New Orleans Super dome, etc.

slide8
Brooklyn Bridge, New York
  • Designed by Roebling, Opened in 1883
history10
History

● For containment type structures

maintaining two or more separate pressure

or temperature zones, continuous barriers,

membranes, plates and shells, are

required.

Aircraft fuselage,

Dome roof,

Submarines, etc.

history11
History

● When the loads (both transverse and

longitudinal) are

small→membrane, i.e., placard

medium→plates

heavy→stiffened plates

topic of discussion

background
BACKGROUND

AASHO Standard Specifications for Highway Bridges, 9th ed., 1965 adopted for the first time the minimum moment of inertia of the longitudinal stiffener:

where

There was no further stipulation as to the correct value for k.

background13
BACKGROUND

For composite box girder compression flanges stiffened longitudinally and transversely, AASHTO requites the minimum moment of inertia of the longitudinal stiffener:

It is of interest to note that the absence of a length parameter

of the longitudinal stiffener in both AASHTO equations.

A longitudinal stiffener attached to the compression flange is

essentially a compression member.

background14
BACKGROUND

It was found that an old bridge, (curved box girder approach spans to the Fort Duquesne Bridge in Pittsburg) designed and built before the enactment of the AASHTO criteria on longitudinal stiffeners, did not rate well for modern-day traffic, despite having served for many years.

background15
BACKGROUND

Despite the practicing engineers’ intuitive realization of the unreasonableness of the equations, they are still in force in both AASHTO Standard Specifications for Highway Bridges, 17th ed. (2002) and AASHTO LRFD Bridge Design Specifications, 4th ed. (2007) with a limitation imposed on the number of longitudinal stiffeners not to exceed “two.”

background16
BACKGROUND

In a relatively short period of time, there were a series of tragic collapses occurred during the erection of the bridges

Danube in 1969

Milford Haven Bridge in Wales in 1970

West Gate Bridge in Australia in 1970

Koblenz Bridge in Germany in 1971

background17
BACKGROUND

These tragic collapses drew an urgent attention to steel box girder bridge design and construction. Some of the researchers, primarily in the U.K., responded to the urgency include:

Chatterjee

Dowling

Dwight

Horne

Little

Merrison

Narayana

background18
BACKGROUND

Although there were a few variations tried, such as

Effective Width Method

Effective Length Method

these researchers were mainly interested in “Column Behavior” of the stiffened compression flanges.

background19
BACKGROUND

Barbré studied the strength of longitudinally stiffened compression flanges and published extensive results in 1937.

background20
BACKGROUND

Bleich (1952) and Timoshenko and Gere (1961) introduced Barbré’s study (published in German) to English speaking world using the following model:

slide22
Consider the load carrying mechanics of a plate

element subjected to a transverse loading

● Very thin plates depend on the membrane action as

that in placards and airplane fuselages

● Ordinary plates depend primarily on the bending action

● Very thick plates depend on bending and shear

action

Our discussions herein are limited to the case of ordinary plate

Elements (no membrane action, no shear deformation)

background23
BACKGROUND

It was known from the early days that stiffened plates with weak stiffeners buckle in a symmetric mode while those with strong stiffeners buckle in an antisymmetric mode. The exact threshold value of the minimum moment of inertia of the stiffener, however, was unknown.

slide24
Symmetric or antisymmetric buckling is somewhat confusing. It appears to be just the remnant of terminology used by Bleich. It is obvious that

symmetric buckling implies column behavior and

antisymmetric buckling implies plate behavior

slide25
It appears to be the case, at least in the earlier days, that the column behavior theory was dominant in Europe, Australia, and Japan while in North America, particularly, in the U.S., a modified plate behavior theory prevailed.
slide26

Japanese design of rectangular box sections of a horizontally curved continuous girder

slide27
In the column behavior theory, the strength of a stiffened plate is determined by summing the column strength of each individual longitudinal stiffener, with an effective width of the plate to be part of the cross section, between the adjacent transverse stiffeners.
slide28
It should be noted that in symmetric buckling (column behavior), the stiffener bends along with the plate whereas in antisymmetric buckling (plate behavior), the stiffener remains straight although it is subjected to torsional rotation.
slide29

Symmetric Mode

Antisymmetric Mode

slide30
Hence, it became intuitively evident that in order to ensure antisymmetric buckling, the stiffener must be sufficiently strong.
slide31
A careful analysis of data from a series of finite element analyses made it possible to determine numerically the threshold value of the minimum required moment of inertia of a longitudinal stiffener to ensure antisymmetric buckling.
slide32

Symmetric Antisymmetric

Critical Stress vs Longitudinal Stiffener Size

slide33
Selected example data are shown in the table. During the course of this study, well over 1,000 models have been analyzed.
slide34

Comparison of Ultimate Stress, Fcr (ksi)

(Note: 1 in. = 25.4 mm; 1 ft = 0.305 m; 1 in4 = 0.416106 mm4; 1 ksi = 6.895 MPa)

slide35
Jaques Heyman, Professor emeritus, University of Cambridge, wrote in 1999 that there had been no new breakthrough since Hardy Cross published Moment Distribution method in 1931.
  • I disagree.
  • The most significant revolution in modern era is Finite Element method. Although the vague notion of the method was there since the time of Rayleigh and Ritz, the finite element method we are familiar with today was not available until in the late 1980s encompassing the material and geometric nonlinear incremental analysis incorporating the updated and/or total Lagrangian formulation.
slide36
Despite the glitter, Finite Element method is not a design guide.
  • Daily practicing design engineers need design guide in the form of charts, tables and/or regression formulas synthesizing and quantifying vast analytical data afforded from the finite element method.
  • There exist golden opportunities for engineering researchers to do just those contributions.
slide39
It was decided from the beginning of our study that we wanted to make sure that our stiffened compression flanges would buckle in an antisymmetric mode.
slide40
In the elastic buckling range of the width-to-thickness ratio, the critical stress of the plate is

with

slide41
AASHTO divides the sub-panel between longitudinal stiffeners or the web into three zones by the width-to-thickness ratio:

yield zone = compact

transition zone = noncompact

elastic buckling zone = slender

slide42
The regression equation for the minimum required moment of inertia of the longitudinal stiffener works equally well for the sub-panels in all three zones.

It also works for horizontally curved box girders.

slide44

Longitudinal stiffener arrangement, AASHTO

Longitudinal stiffener arrangement, Proposed

slide45

Japanese design of rectangular box sections of a horizontally curved continuous girder

tee shapes are stronger than rectangles
Consider the moment of inertia about the axis parallel to the flange and at the base of the stiffener.

Tee, WT9x25: A = 7.35 in2, tf = 0.57 in

Is = 53.5+7.35(8.995-2.12)2 = 400 in4

Rectangle, d/t = 0.38(E/Fy)1/2 = 9.15 with Fy = 50 ksi for compact section:

9.15t2 = 7.35, t = 0.9 in, d=7.35/0.9 = 8.17 in

Is = 0.9(8.17)3/3 =164 in4

Tee shapes are stronger than rectangles
concluding remarks
Concluding Remarks
  • The AASHTO critical stress equation appears to be unconservative in the transition zone with AWS acceptable out-of-flatness tolerances.
  • Residual stresses significantly reduce the critical stresses of slender plates.
  • Recognition of the postbuckling reserve strength in slender plates remains debatable with regard to the adverse effect of large deflection.
  • The regression equation derived appears now to be ready to replace two AASHTO equations without any limitations imposed.
concluding remarks continued
Concluding Remarks -continued
  • It has been proved that the plate behavior theory yields a more economical design than that by the column behavior theory.
  • In the numerical example examined, it is 20%-50% more economical.
slide57

Longitudinal stiffener arrangement, AASHTO

Longitudinal stiffener arrangement, Proposed

slide58

Symmetric Mode

Column Behavior Theory

Global Buckling

Antisymmetric Mode

Plate Behavior Theory

Local Buckling