Bridge Design Diaphragms Ch11notes_pdf

Bridge Engineering 1

Chapter 11Diaphragms and Cross Frames


Introduction –Functions of diaphragms and cross frames

Used to resist lateral wind loads by transferring them from the superstructure up into the deckLarge stiffness of the deck in horizontal plane will carry the loads to the supportsAt the supports, the diaphragms or cross frames transfer the loads down from the deck to bearings


Introduction –Functions of diaphragms and cross frames

They also improve vertical loads distribution to longitudinal membersIf closely spaced and placed at supports, they transfer live loads more uniformlyThey create lateral stability during construction.


Different types of bracings and diaphragms

Cross framesX typeK type

Non-composite diaphragmsComposite diaphragmsTop chord bracingDistortional bracingTie, etc.

Steel box girder



Bracings to reduce distortion and rotation

TiesDistortional bracingTorsion boxTop chord bracingEnd diaphragms






Design considerations

Intermediate onesCarry proportional to tributary area

End ones Carry all accumulated loads to the bearings

Do not use too manyCode practice, more or less arbitrary


Beam-and-Slab Bridges

Improve load distribution charactersiticsCharacterizing parameters of such bridges are:

Minimum 2 diaphragms or bracings perspan near to one third of the span, or

25.0

5.021

)(2)(

⎟⎟⎠

⎞⎜⎜⎝

⎛=

+++=

y

x

yx

yxxy

DD

Lb

DDDDDD

θ

α


Beam-and-Slab BridgesMinimum 3, placed at quarter and mid span pointsReduced form of is valid for characterizing load distributions in beam and slab bridges

=(total flexural rigidity of deck plus diaphragm)/spanIn calculating ignore the torsional rigidity of the diaphragms

5.0)(2)(

yx

yxxy

DDDD +

=α

yD

α

α


Beam-and-Slab Bridges

Recommended design procedureUse method for slab-on-girder bridges, if there min. 2 diaphragms per span, or 3 spans per spanCalculate as follows:

=(total flexural rigidity of deck plus diaphragm)/span

( )θα ,

α

( )( ) 5.02 yx

yxxy

DDDD +

=α

yD


Beam-and-Slab BridgesIf plate type diaphragms, obtain effectiveflexural rigidity by considering diaphragm bending about its neutral axisIf cross-bracings, calculate effective moment of inertia as follows

is the cross-sectional are of diagonal members

3

23

6 d

deffective L

hsAI =

dA


is the length of diagonal members

s is the spacing of the longitudinal girdersh is the depth of the cross bracing

Relate diaphragm size to optimum value of No need for heavy diaphragms to achieve optimum transverse load distribution.

22 hsLd +=

Ad

s

h

θ


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Steel Box Girder Bridge

Bracings and diaphragms are to resistwind and construction loads and maintain stabilityStresses due to bending and torsion as a result of eccentric live loads are:

Bending stressMixed torsion stressBending distortion stressTorsional distortion stress



Bracing systemsTiesDistortional bracingsTorsion BoxTop chord bracingsEnd Diaphragms


Steel Box Girder Bridgeex

P Pc Pc Pt Pt

Pc Pc

Pt Pt

Loading Components

Longitudinal bending Bending distorsion

Mixed torsion Torsional distorsion










Recommendations for design1) Distortion during construction

Place ties at top flanges every 1/8 length of the span (overcome distortion from concentric construction loads)Place transverse web stiffeners that increase transverse web stiffness at least 50 times (overcome distortion due to construction twist loads)



Horizontal bracing shall be placed belowthe level of top flangesInter-connecting bracings shall be mounted between boxes. These bracing systems shall be placed at the same sections as the interior distortional bracings



2) Overall Stability during construction

If , where is the mid-span

bending moment and is the cracking moment

Use linear analysis with St. Venant and warping stiffness to compute girder rotations

For higher loads,Calculate real rotations and warping stiffnessconsidering non-linear effects

15.00 <crM

M0M

crM


CHBDC requirements

1) General requirements5.4.6. (p 170)A 5.1 d (p 202)

2) Concrete8.18.5 Diaphragms (p 367)8.20.8 Concrete girder (p 371)8.22.3 Segmental construction (p 372)


CHBDC requirements

3) Steel10.10.9 (p 462) lateral bracing, cross –frames and diaphragms10.10.9.1 and 10.10.9.2, 10.10.9.3Load distribution & stability

10.10.9 Composite beams and girders (p 462) load distribution and stability10.12.6 Composite box girders (p 473)

10.13.5 Horizontally curved girders (p 474)10.14.3 Trusses (p 480)10.16.5 Orthotropic Decks (p 482)


Specific requirements


CHBDC Specifications

End floor beams and end diaphragms under expansion joints that are exposed to surface runoff should be easily maintainableFloor beams and diaphragms at piers and abutments to be designed to allow jacking of the superstructure, unless longitudinal members can be jacked directly.


CHBDC- Beams, Girders and Composite Beams

Spacing of intermediate diaphragms or cross-frames:

Lateral torsional buckling resistance of girdersNeed for transfer of lateral wind loadNeed for torsional resistance due to torsionloadDesign for lateral load + 1% of compressionflange force, if girder not solely for lateral loadsIf considered in analysis, design for their shareof load



The bracing should be stable under the compression force that it receives from the compression flangeSteel or concrete slab, if attached sufficiently to compression flange will sufficePlace perpendicular to main girder, when supportsare skewed more than and design to the forcethey attractUnless otherwise justified by analysis, girder spansin excess of 50 m shall be provided with lateralbracing at or close to bottom flanges

020



Use cross-frames and diaphragms at piers or abutments of beam or girder bridgesUse cross-frames as deep as practicalWhere practical, diaphragms shall support the end of the deck slab.


CHBDC- Composite Box Girders

Internal diaphragms, cross-frames or other means, at supports to resist transverse rotation, displacements and distortion and transfervertical, transverse and torsional loads to the bearingsConsider the effect of access holes and provide adequate reinforcementIntermediate cross-frames and diaphragms to be used during fabrication, transportation and construction.



Vertical stiffeners used as connecting plates for diaphragms or cross-frames shall be connectedto both flangesSingle box girder, place diaphragms and cross-frames every 8 m unless shown cross-sectional distortion is not criticalFor multiple open box girders, the bracing of top flanges of the boxes should be provided adequatelyPut lateral bracing at top flange of single, through box section girders.



Design the bracings for shear flow before concrete is cured. Also consider bending forces.The structural section assumed to resist the portion of factored horizontal wind or seismicloading in the plane of bottom flange shall consist of the bottom flange acting as the weband 12 times the thickness of the webs acting as the flanges.


Horizontally curved girdersUnless otherwise approved, the girders shall be connected at each support by diaphragms to resist twisting of the girdersPlace diaphragms or cross-frames on I girders betweensupports to resist twisting. Extend them across the whole width of the bridge.Place diaphragms or cross-frames between box girdersto resist torsion. Place them inside box girders in linewith those in between girders.Treat them as main elements. They shall be as deep asthe girders and shall carry all the load they attract.


Horizontally curved girdersIn addition, place extra diaphragms or cross-frames to resist the distortional effects of eccentric loads on the cross-section.Lateral bracing for construction, wind and service load shall be placed on top flange of Igirders or box girders.


TrussesThrough-truss, deck-truss shall have top and bottom lateral bracing systems.If shallower than the chord, the bracing needs approvalConnect the bracings to top and bottom chordseffectivelyFor through trusses, have portal bracing rigidlyconnected to the end post and top chordflanges.


TrussesFor through trusses, portal bracings should take the full reaction of the top chords, and end posts should be designed accordingly.For through trusses, sway bracings shall be installed at necessary points.For deck trusses, install sway bracing at the plane of end posts.For deck trusses, install sway bracing at intermediate panel points, unless analysisshows unnecessary.


Trusses

For deck trusses, the sway bracing shall have the full depth of the truss below the floor.For deck trusses, the end sway bracing shall carry the entire upper lateral forces to the supports through the end posts.Bracings between straight compressionmembers or flanges shall carry the shear forcedue to lateral loads plus 1% of the compressionforces in the supported members.


TrussesFactored compressive resistance of the columnshall be at least equal to the maximum force in any panel of the top chord resulting from loads at the ULS.Vertical truss members, floor beams, and connections between them shall not carry lessthan (ULS) 8 kN/m lateral force applied at the top chord panel points.


Orthotropic Decks

Place diaphragms or cross-frames at each support, sufficient to transmit lateral forcesto the bearings and to resist transverse rotation, displacement and distortion.Place diaphragms or cross-frames at intermediate locations consistent with the analysis of the girders.

Documents

Bridge Design Diaphragms Ch11notes_pdf