LRFD Program Description 4 · Girders and Spans This is the primary geometry definition screen. The...

Introduction This program was originally conceived to aid in the design and optimization of structures built using the simple for dead load, continuous for live load system. The program performs the analyses required for determining the applied loading both dead load and live load. The program also calculates the capacity at various limit states as determined using the AASHTO LRFD Bridge design Specifications 2004 and interims through 2006.

It is important to note that an important goal at the outset was to develop a fast and lightweight application requiring a minimum of input. Also note that the output is geared towards initial section selection and not comprehensive design documentation. Two examples deserving comment that illustrate this philosophy and its implementation have to do with lateral bracing and web stiffening.

Web stiffening is addressed by simply reporting the maximum allowable stiffener spacing at interior supports. Likewise, lateral bracing is addressed by reporting the maximum allowable brace spacing at each analysis point. This accomplishes the stated goals thusly.

Stiffener and bracing locations are numerous, highly variable, and often subject to outside influences, such as aesthetics and arbitrary minimum values. Manual positioning, especially during preliminary design, is difficult and wastefully time consuming. Computer optimized positioning can be computationally expensive and is usually later modified to accommodate the outside influences. Therefore, these time-consuming niceties have been dispensed with altogether. Reporting of the maximum allowable values allow relative options to be compared against each other, leaving the final detailing for later. To this end, the intermediate values required for subsequent calculations are provided at each of the analysis points.

At its core, the program simply takes the input geometry and calculates the loading and resistances of the structure. Other than aborting due to run time errors or encountering situations explicitly disallowed by the LRFD Specifications there is no logical processing of the results. That is, under strength conditions are not identified, nor are obvious input errors or omissions trapped. The interface provides a front end to this core and facilitates the inputting of information and viewing the results.

It should also be cautioned that the interface is by no means bullet proof and can be made to crash. Data referential integrity relies on internal default handling. Therefore, some of the error dialogs may appear confusing at first. In general, press the continue button when available as this will often work.

The following sections provide a brief introduction to the program interface. The values shown in the dialogs are taken from the sample structure described in Appendix A.

Main Screen The main screen, shown below, is a navigator for the different components of the program. Starting a new structure from scratch, one would typically proceed through each of the modules in order.

Main Navigator

Base Variables This is the screen for entering the structure wide variables. The program is only designed to handle prismatic structures, that is, the width cannot vary through the length. Therefore, variables such as girder spacing and deck width are constant through the length.

Girders and Spans This is the primary geometry definition screen. The girder cross sections are defined as well the structure spanning and analysis point locations. In general, the input paradigm employed throughout the program separates property definitions from their usage locations. This minimizes the volume of input required by allowing reuse of property definitions.

Slab This screen is used to define the slab sections and their usage locations. In most cases, a single slab section is defined through the length of the bridge. One possible exception would be a variation in haunch depth to facilitate certain camber situations.

Rebar The rebar definitions allow for two layers of reinforcement.

Bottom Slab The program was originally written for the express purpose of analyzing box girders utilized in a simple for dead, continuous for live application. This system uses a concrete slab cast into the bottom of the box near the interior support to stiffen the bottom flange, which is in compression at this location. This screen is used to define the properties of this bottom slab, if it exists.

Save The save button saves the input definition in an xml formatted file which may be opened at a later date.

Open The open button allows the user to choose a file to open.

Export / Execute The export button generates the files required by the analysis engine and performs the analysis.

Output The output screen is used to view each of the output modules.

Base Variables This is the screen for entering the structure wide variables. The program is only designed to handle prismatic structures, that is, the width cannot vary through the length. Therefore, variables such as girder spacing and deck width are constant through the length.

Base Variables

Each of the variables are described below.

Skew Angle Angle of skew with respect to the supports. Only constant skew is allowed.

Number of Girders Total number of girder lines.

Only one girder type is allowed at any given section.

Girder Spacing Constant Spacing along Length

Equal Girder Spacing Assumed

Total Slab Width Out to Out dimensions of the slab. This value is used to determine overhang distances. It is assumed that the slab is centered on the girders so the overhangs are equal.

Miscellaneous Steel Factor This factor accounts for bracing and other steel components. The total cross-sectional steel weight is multiplied by this value.

Additional DC1 Weight Additional dead weight (lbs/ft/girder) to be supported by the steel alone. Items such as stay in place forms would fall under this category.

Additional Construction Weight Additional construction weight (lbs/ft/girder) to be supported by the steel alone. This weight is only active during the constructability check and is factored by 1.5. Values to account for finishing equipment would be placed here.

DC2 Weight on Continuous Structure Additional weight to be supported by the composite structure assuming continuous behavior.

DC2 Weight on Simple Structure Additional weight to be supported by the composite structure assuming simply supported behavior. Certain scenarios utilizing prefabricated elements may require this value. Otherwise it is typically zero.

Future Wearing Weight This is the DW weight (lbs/ft/girder)

Pedestrian Weight This is the PL weight (lbs/ft/girder)

Distribution Factor Control This value controls what to use for a distribution factor

0 = Use Next Value

1+ = Reserved for Future

Distribution Factor Data If the Distribution Factor Control is equal to zero then use this value as the distribution factor.

Girder Location For a given run of the program an interior or exterior girder is assumed.

0 = Exterior

1 = Interior

Girders and Spans This is the primary geometry definition screen. In general, the input paradigm employed separates property definitions from their usage locations. This minimizes the volume of input required by allowing reuse of property definitions.

Note that defined sections do not necessarily need to be used in the structure. This is useful for trial designs where several candidate sections can be swapped in at out without redefining all of the properties.

Individual cross sections are first defined. These can then be referenced by ID number. The bridge is broken into spans and the spans are broken into segments. Each segment contains a reference to a previously defined cross section. Cross sections may be referenced by multiple segments (re-used).

Seg 1 Seg 2

Span 1 Span 2

Seg 2 Seg 1 Analysis point locations are also defined on this screen and are defined within the context of each span. Typically, the analysis points are evenly spaced within a span. However, individual analysis points may be added at specific locations if desired.

Geometry and Spans

Add New Section New section types can be added by pressing the Add a Section button which brings up a new dialog.

Currently only two types of sections are available, a straight sided box section and I girder. Highlight the type to create and include a description if desired.

Pressing the Add button will bring up the section editor dialog.

Add Section Dialog

Section Editor The section editor dialog is accessed by pressing the edit button in the row of the section to be edited. Additionally, this dialog is automatically entered after a new section is created.

Section Editor

The section editor provides prompting specific to the girder type being entered as described above. Currently only straight sided boxes and I girders are included. The required variables for both of these happen to appear identical.

Bfb – Width of bottom flange

Tfb – Thickness of bottom flange

Fyb – yield strength of bottom flange

Bft – Width of Top flange

Tft – Thickness of Top flange

Fyt – yield strength of Top flange

D – Depth of web plate (distance between inside faces of flange plates)

Tw – web thickness

Fyw – yield strength of web

Span Geometry The span geometry portion of the Girders and Spans dialog defines the spanning of the structure. Although the dialog has a place for end restraint condition, these values are currently unused by the program. To add a span, simply enter its length next to the asterisk (*). Note that the ID column is just that. The actual span configuration depends on the order that the spans are listed.

Geometry and Spans

Segment Definition Each of the spans can be broken into any number of segments where each segment is assigned a cross section. This information is entered in the segment definition region of the Girders and Spans dialog. Additional segments are added by filling in the line next to the asterisk (*). The SecID for a segment refers to the ID column of the section geometry defined at the top of the dialog.

Analysis Points The analysis points define where the analysis should be performed and output generated. Again, new lines are added by filling in the row adjacent to the asterisk. These can be either evenly space, absolutely positioned, or a fraction of the span. This information must be entered for each span. The definitions are additive. For example, in addition to the 10 evenly spaced points shown in the example, a single span fraction point could be added at 0.45.

Slab This screen is used to define the slab sections and their usage locations. In most cases, a single slab section is defined through the length of the bridge. One possible exception would be a variation in haunch depth to facilitate certain camber situations.

Slab

The input is broken into regions with the following values defined for each region:

Start – Starting location of the slab region (inches)

Length – Length of slab region (inches)

weightThickness – Initial slab thickness used for weight calculations (inches)

designThickness – Final slab thickness used for strength calculations (inches)

haunch – distance from top of top flange to bottom of slab

strength – f’c of the slab concrete

modular ratio – base modular ratio used for analysis

0 – use equation 57,000 * Sqrt(f’c) /29000

-1 – use Table C6.10.1.1.1b

Otherwise, use entered value

Rebar Input of rebar information is similar to the segment definitions. First, the various distinct reinforcement cross sections are defined and then their location is specified.

Rebar Definition

Rebar Definition Two layers of reinforcement may be input for each section. Only the longitudinal component of the reinforcement is required.

Arb – Area of rebar in bottom layer (in^2/ft)

Crb – Distance from rebar centroid to bottom face of slab (in)

Art – Area of rebar in top layer (in^2/ft)

Crt – Distance from rebar centroid to top face of slab (in)

Rebar zone Definition Each zone of rebar is defined by a starting location, and length, and the rebar section ID. Additional definitions are added by entering data in the row next to the asterisk. A rebar zone may be deleted by selecting the row and pressing the delete key.

Note that the zones are not additive and should not be defined to overlap.

Rebar Zone Definitions

Bottom Slab Definition This screen is used to define the properties of this bottom slab, if it exists.

Bottom Slab Definition

The input is broken into regions with the following values defined for each region:

Start – Starting location of the slab region (inches)

Length – Length of slab region (inches)

Thickness –slab thickness used for weight and strength calculations (inches)

strength – f’c of the slab concrete

modular ratio – base modular ratio used for analysis

0 – use equation 57,000 * Sqrt(f’c) /29000

-1 – use Table C6.10.1.1.1b

Otherwise, use entered value

Output The core analysis engine creates a number of comma delimited files. These files may be viewed through the interface by pressing the output button on the main window. These files may also be opened in excel if desired.

Output Viewer

The individual files may be accessed through the toggles at the top of the screen.

• Properties • Construction • Strength • Service • Loads • Summary

The following sections describe the individual output values contained in each of these files.

Appendix A: Sample Problem

Program OutputProgram Output

Most Columns Double HeadedMost Columns Double Headed

Interpreted as:Interpreted as:

Rows correspond to analysis point locationsRows correspond to analysis point locations

Positive Positive Positive Negative Negative Negativefbut fbu Fnc fbut fbu Fnc

fbut fbu Fnc fbut fbu FncPositive Negative

Variable NamingVariable Naming

Names come from code when applicableNames come from code when applicableThe exact definition depends on the referenceThe exact definition depends on the reference

Otherwise, a Otherwise, a semisemi--descriptive namedescriptive nameCompromise between space and clarityCompromise between space and clarity

Many variables are repeated in multiple placesMany variables are repeated in multiple placesOutput near their use for referenceOutput near their use for reference

Value of 9999 corresponds to no outputValue of 9999 corresponds to no output

LocationLocation

PointPointXLocXLoc

Distance along bridgeDistance along bridge

SpanSpanSpanPctSpanPct

Span PercentageSpan Percentage

PropertiesProperties

PropertiesProperties

Primary HeadingsPrimary HeadingsSectionSectionSlabSlabProportionsProportionsSteel OnlySteel OnlyShort TermShort TermLong TermLong TermNegativeNegativePierPier

Properties Properties -- SectionSection

Repeat of input valuesRepeat of input valuesNum Num –– XX--Section NumberSection NumberType of SectionType of Section

Box or IBox or I--ShapeShape

bfbbfb –– Width of Bottom FlangeWidth of Bottom Flangetfbtfb –– Thickness of Bottom FlangeThickness of Bottom FlangeFybFyb –– Yield Strength of Bottom FlangeYield Strength of Bottom Flange

Num Typ bfb tfb Fyb bft tft Fyt D tw Fyw As

Properties Properties -- SectionSection

bftbft –– Width of Bottom FlangeWidth of Bottom Flangetfttft –– Thickness of Bottom FlangeThickness of Bottom FlangeFytFyt –– Yield Strength of Bottom FlangeYield Strength of Bottom FlangeD D –– Depth of Web PlateDepth of Web Platetwtw –– Thickness of Web PlateThickness of Web PlateFywFyw –– Yield Strength of WebYield Strength of WebAs As –– Calculated area of steel in cross sectionCalculated area of steel in cross section

Num Typ bfb tfb Fyb bft tft Fyt D tw Fyw As

ts tsinit haunch fc nmod Arb Art Crb Crt tsb fcb nmodb

Properties Properties -- SlabSlab

Continuation of input valuesContinuation of input valueststs –– Slab Thickness for DesignSlab Thickness for Designtsinittsinit –– Initial Thickness (for Weight)Initial Thickness (for Weight)haunch haunch –– Haunch ThicknessHaunch Thicknessfcfc –– Concrete StrengthConcrete Strengthnmodnmod –– Modular RatioModular Ratio

Actual Value Actual Value –– Calculated or SpecifiedCalculated or Specified



ArbArb –– Rebar Area (inRebar Area (in22/ft) in Bottom Layer/ft) in Bottom LayerArt Art –– Rebar Area (inRebar Area (in22/ft) in Top Layer/ft) in Top LayerCrbCrb –– Rebar Centroid Distance Rebar Centroid Distance

Bottom Layer to Bottom Face of SlabBottom Layer to Bottom Face of Slab

CrtCrt –– Rebar Centroid DistanceRebar Centroid DistanceTop Layer to Top Face of SlabTop Layer to Top Face of Slab



tsbtsb –– Bottom Slab ThicknessBottom Slab Thicknessfcbfcb –– Strength of Concrete in Bottom SlabStrength of Concrete in Bottom Slabnmodbnmodb –– Modular Ratio of Bottom Slab Concrete Modular Ratio of Bottom Slab Concrete

WebHand WebHandMax FlangeHand FlangeHandMax Bf BfMin tf tfMin BoxSpace BoxSpaceMin BoxSpaceMax

Properties Properties -- ProportionsProportions

WebHandWebHand ––

WebHandMaxWebHandMax –– 150.0 (6.10.2.1.2150.0 (6.10.2.1.2--1)1)

FlangeHandFlangeHand ––

FlangeHandMaxFlangeHandMax –– 12.0 (6.10.2.212.0 (6.10.2.2--1)1)

wtD

f

f

tb2



bf bf –– Flange Width (Top)Flange Width (Top)

bfMinbfMin ––

tftf –– Flange Thickness (Top)Flange Thickness (Top)

tfMintfMin ––

6D

wt1.1



BoxSpaceBoxSpace –– Clear Space Between GirdersClear Space Between GirdersDistance between webs of adjacent girdersDistance between webs of adjacent girdersCurrently Assumes Vertical WebsCurrently Assumes Vertical WebsCurrently Assumes 1Currently Assumes 1”” Web Center to Edge of Bottom Web Center to Edge of Bottom FlangeFlange

BoxSpaceMinBoxSpaceMin –– 0.8 0.8 ×× Girder WidthGirder WidthBoxSpaceMaxBoxSpaceMax –– 1.1 1.1 ×× Girder WidthGirder Width

Box SpacingBox Spacing

6.11.2.36.11.2.3

H As YBar I Sxb Sxt Sxr Dcp Dt Dp Mp My Dc FBI

Calculated Section PropertiesCalculated Section Properties

The same subheads are used forThe same subheads are used forSteel OnlySteel OnlyShort TermShort TermLong TermLong TermNegativeNegativePierPier

Not all values are calculated for each TypeNot all values are calculated for each Type



H H –– Total Depth of SectionTotal Depth of SectionAs As –– Total Steel Area of SectionTotal Steel Area of Section

Equivalent Steel Area of Composite SectionsEquivalent Steel Area of Composite Sections

YBarYBar –– Neutral Axis LocationNeutral Axis LocationFrom Bottom of Bottom FlangeFrom Bottom of Bottom Flange

I I –– Moment of InertiaMoment of Inertia



SxbSxb –– Section Modulus Section Modulus w.r.tw.r.t. Bottom Flange. Bottom FlangeSxtSxt –– Section Modulus Section Modulus w.r.tw.r.t. Top Flange. Top FlangeSxrSxr –– Section Modulus Section Modulus w.r.tw.r.t. Rebar. Rebar



DcpDcp –– Depth of Web in CompressionDepth of Web in CompressionAt Plastic Moment At Plastic Moment

DtDt –– Total Section DepthTotal Section DepthDpDp –– Depth of Neutral Axis from Top of SectionDepth of Neutral Axis from Top of SectionMp Mp –– Plastic MomentPlastic MomentMy My –– Yield Moment Yield Moment Dc Dc –– Depth of Web in CompressionDepth of Web in Compression

ElasticElastic



FBI FBI –– Full Bridge Moment of InertiaFull Bridge Moment of InertiaUsed in Iterative DesignUsed in Iterative DesignCompared with required Value Entered in Geometry FileCompared with required Value Entered in Geometry FileUsed to Check Live Load DeflectionUsed to Check Live Load Deflection

LoadsLoads

LoadsLoads

Moment and ShearMoment and ShearDC1DC1DC2DC2DWDW

Max and Min Max and Min –– Moment and ShearMoment and ShearLLLLPLPLFatigueFatigue

-50000

-40000

-30000

-20000

-10000

0

10000

20000

30000

40000

50000

60000

0 500 1000 1500 2000 2500 3000

DC1DC2DWLLLLFATFAT

-200

-150

-100

-50

0

50

100

150

200

0 500 1000 1500 2000 2500 3000

DC1DC2DWLLLLFATFAT

ConstructabilityConstructability

fbb fbt WebSlend WebSlendMax Slender rho beta Rb Rh FlSlend FlComp FlNonC FncBase Fnc Dc rt Cb Lp Lr Lb FncltbBase k Fcrw


fbbfbb –– Bottom Fiber Stress Due to BendingBottom Fiber Stress Due to Bending

fbtfbt –– Top Fiber Stress Due to BendingTop Fiber Stress Due to Bending

Construction loads not directly includedConstruction loads not directly includedCan be accounted for in SIP valuesCan be accounted for in SIP values



Follows IFollows I--Girder Provisions (6.10.3.2)Girder Provisions (6.10.3.2)Without aid of Appendix AWithout aid of Appendix A



Equation 1 Not checked whenEquation 1 Not checked whenfl fl = 0= 0andand

Web is slenderWeb is slender

Equation 2 Always CheckedEquation 2 Always Checked

Equation 3 only Checked for SlenderEquation 3 only Checked for Slender



Determine SlendernessDetermine Slenderness

WebSlendWebSlend ––

WebSlendMaxWebSlendMax ––

SlenderSlender1 = Slender1 = Slender0 = Not Slender0 = Not Slender



Need Hybrid and Web Load Shedding FactorsNeed Hybrid and Web Load Shedding FactorsUsed in various locations throughout Equation 1Used in various locations throughout Equation 1--33Some intermediate values are provided for referenceSome intermediate values are provided for reference



rhorho –– Intermediate Value in Intermediate Value in RhRh

beta beta –– Intermediate Value in Intermediate Value in RhRh

RbRb –– Web Bend Buckling Reduction FactorWeb Bend Buckling Reduction Factor(6.10.1.9)(6.10.1.9)

RhRh –– Hybrid Factor Hybrid Factor (6.10.1.10.1(6.10.1.10.1--1)1)



Equation 2 Requires Equation 2 Requires FncFnc smaller ofsmaller ofFlange Local BucklingFlange Local Buckling

oror

Lateral Torsional BucklingLateral Torsional Buckling

Flange Local Buckling Require Flange Flange Local Buckling Require Flange Slenderness StateSlenderness State



Determine Flange SlendernessDetermine Flange SlendernessFlSlendFlSlend -- Flange Slenderness RatioFlange Slenderness Ratio

6.10.8.2.26.10.8.2.2--33

FlCompFlComp -- Compact LimitCompact Limit6.10.8.2.26.10.8.2.2--44

FlNonCFlNonC -- NonNon--Compact LimitCompact Limit6.10.8.2.26.10.8.2.2--55



FncBaseFncBase –– BaseBaseCompactCompact

FncFnc –– FinalFinalReduced by Local Buckling if NonReduced by Local Buckling if Non--CompactCompact



LTB Bracing Requirements (6.10.8.2.3)LTB Bracing Requirements (6.10.8.2.3)Solves for Maximum Allowable Brace SpacingSolves for Maximum Allowable Brace Spacing

Satisfies equations Satisfies equations 6.10.8.2.36.10.8.2.3--1, 2, or 3 1, 2, or 3 as applicableas applicable



Dc Dc –– Depth of Web in CompressionDepth of Web in CompressionElasticElastic

rtrt –– effective radius of gyrationeffective radius of gyration6.10.8.2.36.10.8.2.3--99

CbCb –– Moment gradient modifierMoment gradient modifierTaken as 1.0Taken as 1.0



LpLp –– Limiting Braced Length to achieve Base Limiting Braced Length to achieve Base StrengthStrength

RbRhFycRbRhFycUniform BendingUniform Bending

LrLr –– Limiting Braced Length to achieve Onset of Limiting Braced Length to achieve Onset of YieldingYielding

Considering Residual Stresses Considering Residual Stresses FyrFyrUniform BendingUniform Bending



Lb Lb –– Maximum Allowable Braced LengthMaximum Allowable Braced LengthTo achieve To achieve FncltbBaseFncltbBaseAssumes Fl=10.0Assumes Fl=10.0

FncltbBaseFncltbBase –– Base LTB StrengthBase LTB Strength



Bend Buckling Bend Buckling StregnthStregnth (No(No--Longitudinal)Longitudinal)k k –– web bend buckling coefficientweb bend buckling coefficient

6.10.1.9.16.10.1.9.1--22

FcrwFcrw –– Nominal Bend Buckling ResistanceNominal Bend Buckling Resistance6.10.1.9.16.10.1.9.1--11Limited to Min Limited to Min

RhRh FycFycFyw/0.7Fyw/0.7



Tension Flange (6.10.3.2.2Tension Flange (6.10.3.2.2--2)2)Bottom Flange of Box fl is negligibleBottom Flange of Box fl is negligibleAssume continuously bracedAssume continuously braced

FntFnt –– Strength of Tension FlangeStrength of Tension Flange

StrengthStrength

StrengthStrength

Primary HeadingsPrimary HeadingsPositivePositiveNegativeNegativePierPierShearShear

Mu Mn fbut Fnt fbu Fnc Dp DpLim WebSlend WebSlendMax Lrw Rb Rh rho beta My Mp del

Strength Strength -- PositivePositive

Loading and Strength SummarizedLoading and Strength SummarizedMuMu –– Applied MomentApplied MomentMnMn –– Section Moment StrengthSection Moment Strengthfbutfbut –– Applied Tension Flange StressApplied Tension Flange StressFntFnt –– Section Tension Flange StrengthSection Tension Flange Strengthfbufbu –– Applied Compression Flange StressApplied Compression Flange StressFncFnc –– Section Compression Flange StrengthSection Compression Flange Strength

Strength Strength --

PositivePositive

*

*

* Closed Boxes Modified forSt. Venant Torsion


Determine Compactness (6.11.6.2.2)Determine Compactness (6.11.6.2.2)FyFy ≤≤ 70.0 70.0 ksiksiWeb meets handling requirement D/Web meets handling requirement D/twtw ≤≤150150Box Spacing Ratio is Satisfied (6.11.2.3)Box Spacing Ratio is Satisfied (6.11.2.3)Box Flange is Fully Effective (6.11.1.1)Box Flange is Fully Effective (6.11.1.1)Web Slenderness limit is metWeb Slenderness limit is met

6.11.6.2.26.11.6.2.2--11



DpDp –– Depth of Neutral Axis from Top of SectionDepth of Neutral Axis from Top of SectionDpLimDpLim –– Maximum Depth of Maximum Depth of NetrualNetrual AxisAxis

6.10.7.36.10.7.3--11

WebSlendWebSlend –– Web SlendernessWeb SlendernessPlasticPlastic

WebSlendMaxWebSlendMax –– Maximum Web SlendernessMaximum Web Slenderness



If All Compactness Criteria are metIf All Compactness Criteria are metCalculate Calculate MnMnMp if Mp if Dp/DtDp/Dt>0.1>0.1

Box Section Strictly limited Box Section Strictly limited 6.10.7.1.26.10.7.1.2--22

Else Move to NonElse Move to Non--CompactCompact



NonCompactNonCompact Limited to YieldLimited to YieldCompression FlangeCompression Flange

6.11.7.2.26.11.7.2.2--22No Del for TubNo Del for Tub

Tension FlangeTension Flange6.10.7.2.26.10.7.2.2--55

Need Hybrid and Web Load Shedding FactorsNeed Hybrid and Web Load Shedding FactorsSome intermediate values are provided for referenceSome intermediate values are provided for reference



LrwLrw –– Web Compact LimitWeb Compact Limit6.10.1.10.26.10.1.10.2--44Used in Used in RbRb CalculationCalculation

RbRb –– Web Bend Buckling Reduction FactorWeb Bend Buckling Reduction Factor6.10.1.96.10.1.9

RhRh –– Hybrid Factor Hybrid Factor 6.10.1.10.16.10.1.10.1--11

rhorho –– Intermediate Value in Intermediate Value in RhRhbeta beta –– Intermediate Value in Intermediate Value in RhRh



My My –– Yield MomentYield MomentD6.2.2D6.2.2

Mp Mp –– Plastic MomentPlastic MomentD6.1D6.1



del del –– St. St. VenantVenant Shear Modification FactorShear Modification Factor

fv = St. fv = St. VenantVenant Torsional shear stressTorsional shear stressT = TorqueT = TorqueA0 = Enclosed AreaA0 = Enclosed Areatfctfc=flange thickness=flange thickness

Fnc

Unstiffened

StiffenedCompression

Tension

Strength Strength -- NegativeNegative

fbut Fnt fbu Fnc Lrw Rb rho beta Rh del Fyr Lamf LamfC LamfNC


Loading and Strength SummarizedLoading and Strength Summarizedfbutfbut –– Applied Tension Flange StressApplied Tension Flange StressFntFnt –– Section Tension Flange StrengthSection Tension Flange Strengthfbufbu –– Applied Compression Flange StressApplied Compression Flange StressFncFnc –– Section Compression Flange StrengthSection Compression Flange Strength



Box Flange in CompressionBox Flange in CompressionUnstiffenedUnstiffened

6.11.8.2.26.11.8.2.2StiffenedStiffened

6.11.8.2.36.11.8.2.3

Tension FlangeTension Flange6.11.8.36.11.8.3

Need Hybrid and Web Load Shedding FactorsNeed Hybrid and Web Load Shedding FactorsSome intermediate values are provided for referenceSome intermediate values are provided for reference



LrwLrw –– Web Compact LimitWeb Compact Limit6.10.1.10.26.10.1.10.2--44Used in Used in RbRb CalculationCalculation

RbRb –– Web Bend Buckling Reduction FactorWeb Bend Buckling Reduction Factor6.10.1.96.10.1.9

RhRh –– Hybrid Factor Hybrid Factor 6.10.1.10.16.10.1.10.1--11




del del –– St. St. VenantVenant Shear Modification FactorShear Modification Factor6.11.8.2.26.11.8.2.2--55

fv = St. fv = St. VenantVenant Torsional shear stressTorsional shear stressT = TorqueT = TorqueA0 = Enclosed AreaA0 = Enclosed Areatfctfc=flange thickness=flange thickness



UnUn--Stiffened Box Flange in CompressionStiffened Box Flange in Compression



FyrFyr –– Smaller of Compression flange stress at onset Smaller of Compression flange stress at onset of yield or web yield strengthof yield or web yield strength

Considering Residual Stress and TorsionConsidering Residual Stress and Torsion6.11.8.2.26.11.8.2.2--77

LamfLamf –– Flange SlendernessFlange Slenderness

LamfCLamfC –– Compact LimitCompact Limit

LamfNCLamfNC –– NoncompactNoncompact LimitLimit



R1R16.11.8.2.26.11.8.2.2--88

R2R26.11.8.2.26.11.8.2.2--99

k=4.0k=4.0ksks=5.34=5.34



Stiffened Box FlangeStiffened Box FlangeLocations of Bottom Flange SlabLocations of Bottom Flange SlabProvide Sufficient Studs to Stiffen PlateProvide Sufficient Studs to Stiffen Plate

To Meet Equation 1 RequirementsTo Meet Equation 1 Requirements



Tension FlangeTension Flange

Mu Mp

Strength Strength -- PierPier

Tension FlangeTension FlangeMuMu –– Factored Applied MomentFactored Applied MomentMp Mp –– Plastic Moment Considering:Plastic Moment Considering:

Deck Reinforcement Providing ContinuityDeck Reinforcement Providing ContinuityBottom Flange in CompressionBottom Flange in CompressionWeb in CompressionWeb in Compression

Strength Strength --

ShearShear

Vu VP VnS VnU dMin Lamw d0 k LamwCS LamwNCS CS LamwCU LamwNCU CU

Strength Strength -- ShearShear

Loading and Strength SummarizedLoading and Strength SummarizedVu Vu –– Applied Shear (Factored)Applied Shear (Factored)VP VP –– Plastic Shear StrengthPlastic Shear Strength

Maximum Possible Shear CapacityMaximum Possible Shear Capacity

VnSVnS –– Nominal Shear Strength Nominal Shear Strength –– Stiffened WebStiffened WebStiffener Spacing = D (Max Allowed)Stiffener Spacing = D (Max Allowed)Only Used for Informational PurposesOnly Used for Informational Purposes

VnUVnU –– Nominal Shear Strength Nominal Shear Strength –– UnStiffenedUnStiffened WebWeb



dMindMin –– Maximum allowable spacingMaximum allowable spacingSolve for Solve for dd from from VnVn=Vu=VuOnly solved for at Interior SupportsOnly solved for at Interior SupportsUsed to select web thicknessUsed to select web thickness

If If dMindMin is small then excessive stiffeners are requiredis small then excessive stiffeners are required



Calculate shear strength with a panel width equal Calculate shear strength with a panel width equal to the web depth (Informational)to the web depth (Informational)

LamwLamw –– Web SlendernessWeb Slendernessd0 d0 –– panel widthpanel width

Taken as web depthTaken as web depth

k k –– shear buckling coefficientshear buckling coefficient



Stiffened WebStiffened WebLamwCSLamwCS –– Compact Web Slenderness LimitCompact Web Slenderness Limit

LamwNCSLamwNCS –– NonNon--Compact Web SlendernessCompact Web Slenderness

CS CS –– Shear Buckling RatioShear Buckling RatioShear Buckling Strength to Yield StrengthShear Buckling Strength to Yield StrengthStiffened WebStiffened Web



UnUn--Stiffened WebStiffened WebLamwCSLamwCS –– Compact Web Slenderness LimitCompact Web Slenderness Limit

LamwNCSLamwNCS –– NonNon--Compact Web SlendernessCompact Web Slenderness

CU CU –– Shear Buckling RatioShear Buckling RatioShear Buckling Strength to Yield StrengthShear Buckling Strength to Yield StrengthUnUn--Stiffened WebStiffened Web

ServiceService

fbut Fnt fbuc Fnc Rh rho beta FBI FBIMin

Service Service -- PositivePositive

Loading and Strength SummarizedLoading and Strength Summarizedfbutfbut –– Applied Tension Flange StressApplied Tension Flange StressFntFnt –– Section Tension Flange StrengthSection Tension Flange Strengthfbucfbuc –– Applied Compression Flange StressApplied Compression Flange StressFncFnc –– Section Compression Flange StrengthSection Compression Flange Strength



Loading and Strength SummarizedLoading and Strength SummarizedFollow 6.10.4.2.2 ExceptFollow 6.10.4.2.2 Except

6.10.4.2.26.10.4.2.2--2 fl=02 fl=06.10.4.2.26.10.4.2.2--3 Doesn3 Doesn’’t Applyt ApplyAll Sections 6.10.4.2.2All Sections 6.10.4.2.2--4 Unless 6.11.2.1.24 Unless 6.11.2.1.2

Use Use RhRh obtained from Strength Limit Stateobtained from Strength Limit State



Loading and Strength SummarizedLoading and Strength SummarizedRhRh –– Hybrid Factor Hybrid Factor

6.10.1.10.16.10.1.10.1--11


FBI FBI –– Full Bridge Moment of InertiaFull Bridge Moment of InertiaFBIMinFBIMin –– Minimum Full Bridge Moment of InertiaMinimum Full Bridge Moment of Inertia

Service Service -- NegativeNegative

Same Definitions as PositiveSame Definitions as PositiveOnly one set of provisionsOnly one set of provisions

Distinction due to different values of Distinction due to different values of RhRhAnd Structure of ProgramAnd Structure of Program

Service Service -- PierPier

Similar to NegativeSimilar to NegativeTension Strength Based on RebarTension Strength Based on Rebar

SummarySummary

SummarySummary

Critical ValuesCritical ValuesEach Limit StateEach Limit StatePreviously definedPreviously defined

LRFD Program Description 4 · Girders and Spans This is the primary geometry definition screen. The...

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