RATE Spreadsheet User Guide - ftp.dot.state.tx.usftp.dot.state.tx.us/Pub/Txdot-info/Library/Pubs/Bus/Bridge/Rate-user-guide.pdfThe RATE Spreadsheet is used to calculate Load Factor

RATE Spreadsheet User Guide Bridge Division

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03/30/01 TxDOT Load Rating Spreadsheet

Table of Contents

Section Page #

Disclaimer 1General Information 2System Requirements 2Input Fields 3

System Information 3Bridge Information 4User Structural Data Input 4T-Beam Spans 5Pan Girder Spans 6Flat Slab Spans 7Prestressed Beam Spans 11Steel Stringer Spans 14Rolled Section Properties 17

Output Fields 18Theory 20

T-Beam Spans 20Pan Girder Spans 21Flat Slab Spans 21Prestressed Beam Spans 25Steel Stringer Spans 28

Appendix A 29References 30

03/30/01 TxDOT Load Rating Spreadsheet 1 of 30

Disclaimer

This program does not replace the judgment of an engineer familiar with the principles ofstructural analysis and load rating. Accordingly, the results of each analysis must bereviewed and sealed by a licensed professional engineer. An engineer’s judgment isneeded to recognize special situations where the routine, simplified procedures of thisprogram are inadequate. In addition, an engineer may be called upon to make decisionsabout the strength of materials, the accuracy of field reports, the stability of beams andsupports, and the need for additional field investigations.

No expressed or implied warranties are made by the Department for the accuracy,completeness, reliability, usability, or suitability of the program-associated data ordocumentation. The Department assumes no responsibility for incorrect results ordamages resulting from the use of the program.


General Information

TxDOT maintains a bridge inspection database of information about all of the on- andoff-system bridges in Texas as part of the National Bridge Inspection Standards (NBIS)required by the FHWA. Among the data in the Bridge Inventory file, is the Inventory andOperating rating for each bridge. The Inventory rating represents the heaviest loads thatcan safely use the bridge for an indefinite period of time. The Operating rating representsthe absolute maximum permissible live load to which the structure may be subjected.These ratings are dependent on the weight and configuration of the rating vehicle.Historically there have been two vehicles used for rating bridges in the bridge inspectiondatabase that is maintained by TxDOT. TxDOT is presently under a FHWA mandate touse HS load factor ratings in the database.

The RATE Spreadsheet is used to calculate Load Factor moment ratings of thesuperstructure for five different bridge types. The five types include: Concrete T-beams(slab and girder), Concrete Pan Girders, Concrete Flat Slabs, Prestressed Concrete I-Beams, and Steel I-beams. Only simple span structures may be load rated using thisprogram. Since this program rates superstructures based on the structural as-built details,the plans must be available, or accurate measurements must be made of the requireddetails. It is important to note that all ratings should include any structural deteriorationthat would affect the load carrying capacity of the structure.

The superstructure of a bridge usually controls the load rating for the structure, except inunusual circumstances, because it typically has a much smaller factor of safety than thesubstructure or the foundation of a bridge. In addition, flexure rather than shear usuallycontrols the load ratings of bridge superstructures. Judgment must be exercised whenmaking these assumptions to ensure that they are accurate assessments of the structure.One example of when an assumption might not be conservative occurs when a significantamount of deterioration is present in the substructure or foundation of a bridge. In thiscase the other bridge elements must also be load rated. When structures have beenwidened, each portion should be rated to determine the controlling section of thestructure. Typically, the oldest section will control the rating, but that is not always thecase. Multiple ratings must also be performed when a structure has more than one spantype (ie., pan girders and prestressed beams) or span length to determine the controllingspan. If multiple ratings are performed on a structure, a copy of each of the ratings shouldbe retained for documentation purposes.

Some bridge plans designate the standard used to build the bridge on the layout (forexample, G-18-28-40 is a T-Beam standard); however, the standard sheet is not includedin the plan set. In this case, the standard used to build the bridge can be located using thedate of construction and the standard designation. The Bridge Division can help locatethese standards.

System Requirements

To use the rating spreadsheets, Microsoft Excel 97 for Windows 95 or Windows NT 4.0or better needs to be installed on the computer.


Input Fields

To begin data entry, the sheet corresponding with the superstructure to be rated needs tobe selected by the tab titles at the bottom of the sheets. The sheet titles are as follows: T-Beam, Pan Girder, Flat Slab, Prestressed Beam, and Steel Stringer. Shaded areas indifferent locations on each sheet indicate fields for user data input. Note that none of thespreadsheets are case-sensitive.

System Information

The main use of this field is used to enter information about the individual that ran thecalculations. There is space available to enter the initials of the individual. This field alsonotes the date on which the calculations were performed and the program version beingrun. Figure 1 shows an example of a completed System Information field.

System InformationDate: 03/30/01

Rating Engineer's Initials:

Program Version: 3282001

Figure 1. System Information

There are two sheets in which the System Information field has been slightly modified:the Pan Girder Bridge and the Flat Slab Bridge sheets. For these two bridge types theinput data for a number of the standards has been recorded on the Standard Codes sheetand can be loaded automatically into the rating sheet. If a standard plan is used and it ison the list provided in the Standard Codes sheet of the program, then the standard planname can be cross-referenced with the appropriate code. Once known, the code can beselected from the Standard Code pull-down menu. To execute the data upload for thesheet the user will need to press the “Get Stnd Data” button below the SystemInformation field. It is important to note that certain assumptions have been made whenthe specific standard data was recorded. If these assumptions do not match what ispresent in the field, then the necessary cells will need to be modified. Figure 2 shows anexample of a System Information field in which a standard code has been selected (PanGirder field shown with CG-15 standard).

System InformationDate: 03/30/01

Rating Engineer's Initials:†Standard (if applicable): CGC-10 (1951/52)

Program Version: 3282001

Figure 2. Standard Code Example.


Bridge Information

This field is common to all the rating sheets. It contains specific information about thedistrict and county where the bridge is located, the structure number of the bridge, thecontrol-section-job (CSJ) number, the year the structure was built, and an abbreviateddescription of the physical location of the bridge. Lists of the counties throughout thestate are found in a drop-down menu for user input ease. The corresponding District willappear when the county is selected. The year built is an important piece of information tobe entered. Since the spreadsheet will make material strength recommendations based onthis date by referencing the AASHTO Manual for Condition Evaluation of Bridges, 1994.See Appendix A to verify recommended values. Two input lines are provided for thedescription of the location of the bridge. The only restriction is that the text must staywithin the borders of the field to be printed properly. It is recommended that the facilityand the feature crossed be included in the location description. Figure 3 shows anexample of a completed Bridge Information field.

Bridge InformationDistrict: Waco (09)County: Hill (110)

Structure #:

2309-01-001

® CSJ: 2309-01-003Year Built: 1967Location: FM 1244 over North

Towash Creek

Figure 3. Bridge Information

User Structural Data Input

This field compiles member property information the spreadsheet needs to determinedead load moments and the moment capacity for the specified beam or slab. Below arethe descriptions of each property for all five bridge types. Diagrams have been includedto aid in understanding certain dimensions. Definitions that are common to most of thebridge load rating sheets are listed directly below:

Overlay is the depth of asphalt, or ACP, on the deck or slab, in inches. This value can bedetermined by a field inspection. If anything other than, or in addition to, asphalt hasbeen used as a top layer on the deck, include this weight in the Misc. Non-Comp. DeadLoad for the structure, not as overlay.

The spreadsheet makes recommendations on the material strengths to use based on theyear the bridge was built. This information is to be used if exact materials strengths arenot known. Fy is yield strength, in ksi, of steel. See the chart located in Appendix A forrecommended Fy values for steel, based on the year built. The Specified Compressive


Strength for a batch of concrete, or f’c, typically varies according to the age of thestructure, and is recorded in kips per square inch. Texas Class “A” concrete has had anf’c of 3 ksi since the mid 1930's. However, for bridges built before 1959 that were notbuilt by TxDOT, an f’c of 2.5 ksi should be used, unless the record or actual strength isotherwise known. See Appendix A for recommended values of Fy and f’c.

T-Beam Spans

The Overall Span is the total length center-to-center of bents, in feet, of the simply-supported T-beam, not the total structure length. Slab Thickness, seen in Figure 4, is thethickness, in inches, of the slab being supported by the beams. If the thickness differsfrom beam to beam, use engineering judgement to choose a nominal thickness. BeamSpacing is the perpendicular distance between the centerline of the beam being rated tocenterlines of adjacent beams, in feet. This tells the spreadsheet the amount of slabsupported by the beam. Therefore, if the adjacent beam spacings differ, use engineeringjudgement to determine a nominal beam spacing for input.

Beam Spacing

Fillet Size

SlabThickness

Slab&

Beam

BottomSteel

Distancefrom

Bottom

BeamWeb

Width

Top SteelDistance

from Bottom

Figure 4. T-Beam Diagram.

Slab plus Beam Depth is the distance, in inches, from the top of the slab to the bottom ofthe T-beam. The Beam Web Width is the width of the “T”, in inches. This informationallows the spreadsheet to determine the correct slab and beam weight for the dead loadmoment.

The Misc. Dead Load per Beam includes railing, sidewalks, medians, and curbs, inkip/ft per beam, and is distributed to the beam being rated according to the judgement ofthe Engineer. For simplicity, this number may be calculated by taking the totalmiscellaneous dead load for the entire span, in kips, and dividing it by the total length ofall beams on the entire span (the product of the number of beams and the length of thebeams). For example, if there are five-35’ T-beams supporting 5.25 kips ofmiscellaneous dead load, the value placed in the field is 5.25k/(5*35’)=0.03 k/ft.

Total Area of Steel, in square inches, refers to the reinforcing steel runninglongitudinally within the T-beam. The depth of this steel, from the center of the bars, ininches, is noted in the Distance from Bottom field. The spreadsheet allows for the input


of two layers of steel, however, more layers are possible. If this occurs the centroid ofthe effective cross-sectional area of reinforcing should be entered

The Span Bearing Length Deduction is the portion of the overall span, located at eachend of the span, in feet, that is between the centerline of the bearing and the centerline ofthe bent. See Figure 16. This is measured along the centerline of the beam and includesboth ends of the span. The amount that is entered for the Span Bearing LengthDeduction is the sum of the values from both ends of the span. The program subtractsthis value from the Overall Span and will allow the spreadsheet to calculate the effectiveflexural length of the beam.

Fillet Size is recorded as the perpendicular dimension of the typically 45° slopedconnection between the slab and the beam, in inches.

Pan Girder Spans

If a Standard Code is used to input the information for a Pan Girder, all values in the UserStructural Data Input Table field will be automatically filled in. See the SystemInformation field section for a detailed description of using Standard Codes. Rememberthat modifications may need to be made since all standard assumptions may not matchthe structure.

USER STRUCTURAL DATA INPUT TABLE AOverall Span (ft):

Beam+Slab Depth = 24 or 33 (in):Misc Dead Load per Beam (k/ft):

Top Layer of Long. SteelTotal Area of Steel (in^2):

Distance from bottom (in):Bottom Layer of Long. Steel

Total Area of Steel (in^2):Distance from bottom (in):

USER STRUCTURAL DATA INPUT TABLE BSpan bearing length deduct (ft):

Fy (ksi):f'c (ksi):

Overlay (in):

Figure 5. Pan Girder Structural Data Input.

The Overall Span is the total length center-to-center of bents, in feet, of the simply-supported pan girder, not the total structure length. Do not reduce it to the bearing centerline at this time. This is handled in the Span Bearing Length Deduction.


Beam plus Slab Depth is the distance from top of slab to the bottom of the beam. ForPan Girders, this dimension is always 24 or 33 inches for span lengths of 30'-4" and 40'respectively.

Slab plusBeam Depth

Bottom Steel Distance

from Bottom

Top SteelDistance

from Bottom

Figure 6. Pan Girder.

The Misc. Dead Load per Beam includes railing, sidewalks, medians, and curbs, inkip/ft per beam, and is distributed to the pan girder being rated according to thejudgement of the Engineer. For simplicity, this number may be calculated by taking thetotal miscellaneous dead load for the entire span, in kips, and dividing it by the totallength of all pan girders on the entire span (the product of the number of beams and thelength of the beams). For example, if there are five-40’ Pan Girder beams supporting 15kips of miscellaneous dead load, the value placed in the field is 15k/(5*40’)=0.075 k/ft.

Total Area of Steel for top and bottom layers of longitudinal steel, in square inches,refers to the reinforcing steel running longitudinally within each stem of the Pan Girder.The depth of this steel for each layer, from the center of the bars, in inches, is noted in theDistance from Bottom field.


Flat Slab Spans

There are two types of flat slabs that this spreadsheet can be used to rate. The first isanalyzed using the traditional ASSHTO strip analysis method as detailed in section3.24.3.2 of the AASHTO Standard Specifications for Highway Bridges, 1996. Thesecond type is referred to as an FS slab and is based on research conducted at theUniversity of Illinois. The findings of the research and resulting design procedures aredocumented in a series research bulletins beginning with Illinois Bulletin 346. FS slabbridges have structural curbs that contribute to the load-carrying capacity, while anycurbs on the other type of flat slab bridges do not. Structural curbs are usually 18" inheight and are reinforced top and bottom with large size rebar, usually either #9s or #11s


If a Standard Code is used to input the information for an FS slab, all values in the UserStructural Data Input Table field will be filled in. See the System Information Fieldsection for a detailed description of using Standard Codes. Remember that modificationsmay be needed since all standard assumptions may not match the structure.

USER STRUCTURAL DATA INPUT TABLE AOverall Span along Roadway (ft):

Overall Bridge Width (ft):Skew (deg):

Slab Thickness (in):Slab Steel Direction (P or N):

P = Parallel to rdwy, N = Normal to supportsAs-slab, Area of Slab Tension Steel (in2/ft):

Distance to As-slab from bottom of Slab (in): Left (C)urb, (B)eam, or (N)one: C

Curb Height above Slab (in):Top of Curb Width (in):

Bottom of Curb Width (in):Misc. Dead Load on Curb (k/ft):

Area of Curb Tension Steel (in2):Distance from bottom of Slab (in):

Area of Curb Comp. Steel (in2):Distance from top of Curb (in):

Right (C)urb, (B)eam, or (N)one: CCurb Height above Slab (in):

Top of Curb Width (in):Bottom of Curb Width (in):

Misc. Dead Load on Curb (k/ft):Area of Curb Tension Steel (in2):

Distance from bottom of Slab (in):Area of Curb Comp. Steel (in2):Distance from top of Curb (in):

USER STRUCTURAL DATA INPUT TABLE BSpan bearing length deduct (ft):

Fy (ksi):f'c (ksi):

Overlay (in):Number of Live Load Lanes (2 to

4):

Figure 7. Flat Slab Structural Data Input.

The Overall Span along Roadway is the total length center-to-center of bents, in feet, ofthe simply-supported slab, not the total structure length. This is always measured parallelto the centerline of the roadway, even for skewed bridges. The Overall Bridge Width,in feet, is measured perpendicular to the roadway centerline for all Flat Slab bridges. SeeFigure 8. Slab Thickness is the thickness of the Slab, in inches.


Span Length

BridgeWidth

BridgeWidth

Span Length

Figure 8. Flat Slab Geometry.

For a majority of flat slab bridges the bottom steel runs parallel to the centerline of thebridge, while flat slab bridges that have a skew greater than 30 degrees, the bottom steelgenerally runs normal to the supports (See Figure 9). Skew is defined as the anglebetween the line perpendicular to the centerline of the roadway and the centerline of abent or support. The As-slab Area of Slab Tension Steel, in square inches per foot, refersto the bottom tension reinforcing steel found within a 1’ strip. The Total Area of Steelcan be calculated as (12/S) * (bar area), where S equals bar spacing, in inches, see Figure9. Include the contribution of “galloping” bars if they are effective at midspan. Thedimension of the tension steel from the bottom of the slab is noted as the Distance to As-

slab from Bottom of Slab, and is measure to the center of the bars, in inches.

S

L RoadwayC

(N)ormal(P)arallel

S

Figure 9. Flat Slab Steel Direction.

If structural curbs exist on a flat slab bridge, “C” or “c” should be entered next to theheader. Curb Height above Slab, in inches, does not include the slab thickness. Top ofCurb Width, in inches, is shown in Figure 10. Bottom of Curb Width, in inches, ismeasured at the top of the slab. The Misc. Dead Load on Curb, in k/ft, is for curbs onboth sides of the slab and includes railing, but does not include curb self-weight.

Area of Curb Tension Steel, in square inches, considers all bars within the width of thebottom of the curb, as long as the bars run parallel with the curb. Distance from Bottomof Slab, in inches, is measured from the center of the bars in tension to the extreme slabbottom. Area of Curb Compression Steel considers bars in the top of the curb. TheDistance from Top of Curb is from the center of the compression steel to the topextreme edge of the curb. See Figure 10.

03/30/01 TxDOT Load Rating Spreadsheet 10 of30

Top ofCurb width

Distancefrom

Top ofBeam

Distancefrom

Bottom ofCurb

Bottom ofCurb Width

SlabThickness

Curb Heightabove Slab

Figure 10. Flat Slab Curbs.

If there are Beams below the slab instead of curbs, a “B” or “b” should be entered next tothe header. Beam Depth Below Slab, in inches, does not include the slab thickness, andshould give the dimension that the beam extends beyond the bottom of the curb. Bottomof Beam Width, in inches, is measured at the bottom surface of the beam. Refer toFigure 11 for the dimensions of a beam. Top of Beam Width, in inches, is measured atthe bottom of the slab. Misc. Dead Load on Beam, in k/ft, is for beams on both sides (ifapplicable) and includes railing, but does not include beam self-weight.Area of Beam Tension Steel, in square inches, considers all bars within the width of thebottom of the beam, as long as the bars run parallel with the beam. Distance fromBottom of Beam, in inches, is measured from the center of the bars in tension to theextreme beam bottom.

The next line instructs the user to input an Fy-beam that is greater than or equal to 33 ksi.This is only necessary if Fy-beam is different than Fy that is used for the slab. “This cellshould be empty” only appears if there is a value in the adjoining cell when analyzing anFS slab with beams. Delete any value to get rid of this statement.

Top ofBeam Width

Distancefrom

Bottom ofBeam

SlabThickness

Beam DepthBelow Slab

Bottom ofBeam Width

Figure 11. Flat Slab Beams.


If the plans do not show curbs or beams that contribute to the structural capacity of theslab, an “N” or “n” should be entered in the appropriate cell, and all other descriptions inthe curb/beam section will disappear.

The Span Bearing Length Deduction is the portion of the overall span, located at eachend of the span, in feet, that is between the centerline of the bearing and the centerline ofthe bent. See Figure 16. This is measured along the centerline of the roadway andincludes both ends of the span. The amount that is entered for the Span Bearing LengthDeduction is the sum of the values from both ends of the span. The program subtractsthis value from the Overall Span and will allow the spreadsheet to calculate the effectiveflexural length of the beam.

The Number of Live Load Lanes (2 to 4) tells the program the number of wheel lines toplace on the flat slab during analysis. According to Illinois Bulletin #346, a flat slabbridge can carry two, three, or four lanes of traffic. Any other lane loading is notallowed.

Prestressed Beam Spans

The Overall Span is the total length, in feet, of the simply-supported prestressed beamspan, not the total structure length. Slab Thickness is the thickness, in inches, of the slabbeing supported by the beams. If the thickness changes from beam to beam, useengineering judgement to choose a nominal thickness.

Currently there are nine prestressed Beam Types available to the user—A, B, C, 48, 54,60, 66, 72, and IV. The numeric types refer to the depth of that beam in inches. TypesA, B, C, and IV beams have larger bottom flanges than the numeric types, thus providingmore area for additional prestressing strands. This can be seen in Table A.

Beam Spacing

C.G.

Height to Centroid

Eccentricity Yb

Figure 12. Prestressed Beam.

Beam Spacing is the perpendicular distance between the centerline of the beam beingrated to centerlines of adjacent beams, in feet. This tells the spreadsheet the amount of


slab supported by the beam. If the adjacent beam spacings differ, use engineeringjudgement in the specification of the beam spacing.

USER STRUCTURAL DATA INPUT TABLEOverall Span (ft):

Slab Thickness (in):Beam Type (A,B,C,IV,48,54,60,66,72):

Beam Spacing (ft):Number of Strands:

Eccentricity at Mid-Span (in):Number of Interior Diaframs (0 to 4):

Misc Comp DL per Beam (k/ft):Span bearing length deduct (ft):

Area of Strand (in2):Strand Type (SR### or LR###):

f'c-slab (ksi):f'c-beam (ksi):f'ci-beam (ksi):

Slab Embedment ("-"ve for haunch,in):

Modulus of rupture factor, fr/root(f'c):Overlay (in):

Loss Calc Method (LS or CALC):

Figure 13. Prestressed Beam Structural Data Input.

The Number of Strands refers to the total number of prestressed strands, both straightand draped. This value can be determined from looking at the beam cross-section on theplans. Typically, a set of plans for prestressed beams will include a sheet labeled “GpA1” that shows many different beam views, including the cross-section. When “as-built”prestressed beam shop plans are available for the bridge they should be used to determinethe number of strands.

Eccentricity at Midspan is the distance, in inches, between the concrete beam center ofgravity and the centroid of the prestressed strands at midspan as seen in Figure 12. It isaffected by the beam type and number of strands. Values for the distance, in inches, fromthe bottom of the beam to the beam center of gravity, Yb, and the distance from the top ofthe beam to the center of gravity, Yt, are located in Table A. When available, useprestressed beam shop drawings to aid in the determination of strand locations, sinceoften optional strand patterns are utilized by the fabrication to optimize production. Shopdrawings are usually found in the back of the final bridge plans.


Table A. Prestressed Beam Dimensions.BeamType

Width – TopFlange, in

Width – BottomFlange, in

Beam Depth,in

Yt,in

Yb,in

A 12 16 28 15.39 12.61B 12 18 34 19.07 14.93C 14 22 40 22.91 17.0948 14 14 48 25.13 22.8754 16 16 54 28.47 25.5360 18 18 60 31.59 28.4166 20 20 66 34.93 31.0772 22 22 72 38.27 33.73IV 20 26 54 29.25 24.75

Non-composite dead load moment is influenced by the Number of InteriorDiaphragms . Note that the non-composite dead load is calculated by the spreadsheet.However, the Misc. Composite DL per Beam, in kips per foot, must be calculated bythe user. Composite dead load includes such things as railing, sidewalks, medians, andcurbs.


Area of Strand is for a single prestressing strand in a beam, in square inches. Under thecross-section of the specified beam, normally on plan sheet “Gp A1” or in the “as-built”prestressed beam shop drawings, the strand diameter is noted. Appendix A then relatesstrand diameter and its area. However, this value is dependent on the material propertiesof the strand. Input Strand Type as the type (SR or LR), then the grade of steel. Twotypes of prestressing strands exist: Stress-Relieved (S.R.) and Low-Relaxation (L.R.). AnS.R. strand consists of seven cold-drawn prestressing wires, six of which are wrappedaround the seventh, larger wire. After this strand is drawn it is stress-relieved, meaning itis placed in a continuous heat treatment until the desired mechanical properties have beenattained. L.R. strands are S.R. strands that have been heated to a blueing temperature fora very short period of time, and as a last step are then tensioned to a very high stressduring this heating stage. This additional step permanently lengthens the strand so it willnot “relax” or elongate over time as much as the S.R. strand. L.R. strands are thestandard type strands produced today.

The two grades available are 250 and 270 ksi, indicating the minimum guaranteedultimate stress. Strand grade may be back-calculated from the loading on the strands byassuming this strand strength and the appropriate type. According to the AASHTO“Standard Specifications for Highway Bridges, 1996”, Section 9.15.1, stress in an S.R.strand in a pretensioned member equals 0.70 f’s and L.R. strand stress equals 0.75 f’s,


where f’s is the ultimate stress of the strand. There will be a note on the plans thatmentions the amount of tension placed on different strand sizes. For example, a set ofplans show 7/16” diameter strands to be stressed to 18.9 kips. Assume the strand grade tobe 250 ksi (SR250). From Appendix A, 7/16” diameter strands of 250 ksi strength havean Area of Strand equal to 0.108 in2. 0.70 f’s = (0.70)[(250 ksi)*(0.108 in2)] = 18.9 kips.This checks, and proves that the Strand Type is SR250 for this 7/16” diameter strand, andhas an Area of Strand equal to 0.108 in2. If the answer did not equal the load in thestrands shown on the plans, try a strand strength of 270 ksi.

f’c will differ for the slab and the prestressed beam, and should be input in kips per squareinch. Recommended values for f’c-slab, based on year built, can be found in Appendix Aunder Reinforced Concrete Strengths. Texas Class “A” concrete, since the mid-1930’s,has had an f’c of 3 ksi. However, for slabs built before 1959 that were not built byTxDOT, an f’c of 2.5 ksi should be used. For f’c-beam (final 28-day compressive strengthof the concrete in the beam) note the recommended values, based on year built, inAppendix A under Prestressed Concrete Strengths. Where concrete strengths are shownon the plans, these values should be used.f’ci-beam is the initial specified compressive strength of the beam (for release), in kips persquare inch. It is used to calculate the initial beam modulus of elasticity and can be foundon the prestressed beam plan sheets. Slab Embedment, in inches, refers to the distancethe bottom of the slab is above or below the top of the beam. If there is a haunch, inputthe value as negative.

The Modulus of rupture factor, fr/root(f’c), is a factor used to calculate cracking stressfound in AASHTO 9.15.2.3. This value is typically 7.5 but has been assumed to be ashigh as 12.0. This decision must be made with sound engineering judgement. The valueselected can have a significant effect where the inventory load rating is controlled by thecracking moment.

Loss Calc Method (LS or CALC) refers to the method used to analyze prestressinglosses. According to AASHTO, a beam can be designed for 45,000 psi pretressing loss;this is considered the Lump Sum (LS) method. The spreadsheet can now calculate theexact losses on the prestressing strands, using CALC. If there are few strands in thebeam, the calculated losses should be less than the assumed 45,000 psi loss, so usingCALC aids in giving a higher rating for the beam. However, if there are a large numberof strands in the beam, the assumed losses should be less than the actual, calculatedlosses and using LS will raise the rating. Inputting LS or CALC will only affect therating if it is controlled by the cracking moment. To generate calculated losses press the“Click to Converge Calculated Losses” button after all values have been input toconverge the losses. If any input is changed after pressing the button, it should be pressedagain to converge calculations. This only applies when the CALC method is used andwhen the rating is controlled by the cracking moment.

Steel Stringer Spans

The Overall Span is the total length, in feet, of the simply-supported steel stringer span,not the total structure length, and is typically the distance from centerline of bent to


centerline of bent measured along the centerline of the beam. Slab Thickness is thethickness, in inches, of the slab being supported by the stringers. If the thickness changesfrom one stringer to the next, engineering judgement must be used in specifying thecorrect thickness. Beam Spacing is the distance between beam centerlines of adjacentbeams, in feet. This tells the spreadsheet the amount of slab supported by the beam.Therefore, if the adjacent beam spacings differ, use engineering judgement in thespecification of beam spacing. See Figure 15.

USER STRUCTURAL DATA INPUT TABLEOverall Span (ft):

Slab Thickness (in):Beam Spacing (ft):

Misc Non-Comp Dead Load per Beam (k/ft):Misc Comp Dead Load per

Beam (k/ft):Top Cover Plate Width (in):

Top Cover Plate Thickness (in):Bottom Cover Plate Width (in):Bottom Cover Plate Thickness

(in):Span Bearing Length Deduct

(ft):Fy (ksi):f'c (ksi):

Overlay (in):Slab Embedment (in):

Composite Action (y/n):

§ Select a historical rolled section DESIGNATION, using the pulldownmenu below, and click the "Get Sect Data" button. Or else, enter aDESIGNATION along with the appropriate data in the shaded cellsbelow. If input DESIGNATION changes to "NA" after clicking the "GetSect Data" button, it is not in the rolled section data base; manualentry of section data is then required.

§ ROLLED SECTION INFORMATION

Rolled Section Depth (in):Web Thickness (in):

Flange Width (in):Top Flange Thickness (in):

Bottom Flange Thickness (in):Fillet Radius (in):

Figure 14. Steel Stringer Structural Data Input.

Steel Stringer bridges divide their miscellaneous dead load per beam into two portions,the composite dead load and the non-composite. The Misc. Non-Composite Dead Load


per Beam takes into account what the beam alone supports beyond self weight before theslab is cast. It is listed in kip/ft of beam. This dead load includes the diaphragms.

Calculate this number by taking the total non-composite dead load for the entire span, inkips, and dividing it by the total length of all stringers on the entire span (the product of

the number of stringers and their lengths). For example, if there are six-60’ stringerssupporting 3.6 kips of miscellaneous dead load, the value placed in the field is

3.6/(6*60’)=0.01 k/ft. Note that the slab weight is not included in this item because thespreadsheet calculates slab weight separately.

The Misc. Composite Dead Load per Beam is only applicable when the stringer hascomposite action with the slab. This includes the railing, sidewalks, median, and curbs, inkips per foot of beam. Calculate this value as it was done in the previous step. Noteagain that the overlay is taken into account in a separate area on the spreadsheet.

If the stringer is not composite with the slab, the weight of the railing, sidewalks, median,and curbs must be included with the diaphragms in the Misc. Non-Composite Dead Loadper Beam to ensure proper loading.

Cover plates are often attached in the maximum moment regions. This additional steelarea is taken into account in the Top/Bottom Cover Plate Width and Top/BottomCover Plate Thickness fields, both documented in inches.

Shear Stud

SlabThickness

Bottom CoverPlate Width

BottomCoverPlate

Thickness

Beam Spacing

Figure 15. Steel Stringer.



Figure 16. Span Length Deduction.

Some steel structures have slabs that embed the top flange of the stringer in the slab.Slab Embedment is the amount the stringer is embedded, in inches. If the plans showshear studs on the top flanges, then enter “YES”, “yes”, or “y” under Composite Action.Also, if the plans show a haunch over the top of the beam, the depth can be entered in theSlab Embedment cell as a negative value.One assumption that the spreadsheet makes in analyzing steel stringers is to assume thatthe top flange is fully braced. This is based on research conducted at the University ofTexas at Austin. The study included examples of concrete decks supported on steelstringers. It was found that if the top flange of a steel stringer was in contact with aconcrete deck throughout its full length, then the beam behaved as if it were braced. Ifanother deck is used then this assumption made by the spreadsheet should be re-evaluatedto ensure its applicability.

Rolled Section Properties**

The Rolled Section Information has been compiled from the AISC publication IRONAND STEEL BEAMS 1873 to 1972, otherwise known as Historical Record Dimensionsand Properties, ROLLED SHAPES, Steel and Wrought Iron BEAMS & COLUMNS, asrolled in U.S.A. Period 1873 to 1852, With sources as noted, compiled and edited byHerbert W. Ferris.

A drop-down list with 1562 entries from the above document is available. Scroll downthe list until the correct member is found, then press the “Get Sect Data” button to loadthe information into the spreadsheet.

**For Simple Span Steel Stringer Bridges Only

C

Overall Span

L BearingsC

L RoadwayCOverallBridgeWidth

OverallBridgeWidth

L BearingsC

Bearing Length Deduct

L Roadway

Bearing Length Deduct

Overall Span


Output Fields

After all information for a structure has been input, the HS-Rating will be calculated bythe spreadsheet. HS-ratings are based on the HS-20 loading specified by AASHTO in the“Standard Specifications for Highway Bridges”, Section 3.7. The standard truck withone 8 kip axle and two 32 kip axles is used, with lane loadings also considered. H-Ratingvalues are also calculated by these spreadsheets; however, the H-20 truck weighs lessthan the minimum allowed by AASHTO. This truck is no longer used as a standard forrating.

Inventory Rating (I.R.) and Operating Rating (O.R.) are defined by the AASHTO“Manual for Condition Evaluation of Bridges, 1994”. See the General Information pagefor an explanation.

The Calculated Values box shows some of the intermediate numbers determined by thespreadsheet. This box includes the Distribution Factor, Impact Factor, and the depth ofthe concrete ultimate stress block. The Flat Slab Bridge also includes the AnalysisMethod, Effective Slab Width, and “a” values for the slab and curbs. Distribution ofwheel loads in the longitudinal beams is handled in the Distribution Factor. For T-Beam and Pan Girder bridges with a concrete slab, the distribution factor equals S/6,where S = average stringer spacing, in feet. For Prestressed Beam and Steel Stringerbridges, the distribution factor is S/5.5. Distribution Factor information can be found inTable 3.23.1 in the AASHTO Specifications. The Impact Factor increases the amount oflive load on the structure to account for dynamic effects. It is based on the length of thespan, and cannot be more than an additional 30% of the live load. The Depth of theConcrete Ultimate Stress Block, “a”, is given in inches for all bridges, and is limited tothe thickness of the concrete slab except for prestressed concrete beam bridges where it islimited to slab thickness plus top flange depth to the chamfers.

Analysis Method for the Flat Slab Bridge is dependent on if it has curbs or beams, orneither. If the bridge has curbs or beams on the edge, the Illinois Bulletin 346 is used todistribute moments between the slab and its curbs or beams. If there are no curbs orbeams, AASHTO 3.24.3.2 is used instead. Effective Slab Width for a Flat Slab bridge isthe portion of the slab acting integrally with the curb or beam, equaling 4 times the slabthickness. There is no effective slab width when a beam or curb does not exist on astructure. Notice that the ultimate stress block depth is different for a slab with attachedcurbs or beams.

The Prestressed Beam bridge rating sheet informs the user that the shape of the compositesection is flanged or rectangular and whether or not the section is Over-Reinforced orUnder-Reinforced. If it is Over-Reinforced, the concrete will crush before the steelyields. Under-Reinforced beams will have a more ductile failure mode, allowing thesteel to yield before the concrete crushes. The AASHTO specifications allow either casefor prestressed concrete members only.

All dead and live load moments and moment capacities are displayed under the Momentsheading. The descriptions of their applied moments and moment capacities differ,depending on the structure type. Also located at the bottom of the spreadsheet is space


for documenting any Additional CSJ’s for the structure. When a bridge is widened orspecialized jobs are performed on a bridge, additional CSJ numbers are assigned to thestructure. Room for Additional Notes allows the user to list standards, explaindeviations from standards, or show how a calculation was computed, etc.


Theory

Following are all calculations required to determine the moment capacity for eachstructure type. All AASHTO references are according to the AASHTO StandardSpecifications for Highway Bridges, 16th Edition, 1996, with 1998 updates. All MCEBreferences are according to the AASHTO Manual for Condition Evaluation of Bridges,1994, with Interims.

T-Beam Spans

Notes

If “a” is less than slab thickness, beams are classified as rectangular (i.e. compressionzone is rectangular).

Equations

bf

FAa

c

ys

'85.0=

where a = depth of compression stress block, in inches, see AASHTO 8.16.3.2.As = total area of top and bottom longitudinal steel layers, inches2

Fy = rebar strength, ksif’c = concrete strength, see Appendix A.b = effective flange width, see AASHTO 8.10.1.1.

total

bt

s

bsts

A

dAdAhd

+−=

where d = distance from extreme compression fiber to centroid of tensionreinforcement (steel centroid to top of slab), in inches.

h = slab + beam depth Ast = total area of top layer of longitudinal steel dt = distance of top layer of longitudinal steel from bottomAsb = total area of bottom layer of longitudinal steel db = distance of bottom layer of longitudinal steel from bottom

−== 12/

2a

dFAMC ysnu φφ

where Cu = nominal member ultimate capacity used in MCEB Eq. 6-1a.Mn = nominal ultimate moment capacity of T-beam, in kip-feet, see

AASHTO 8.16.3.2, Eq. (8-16).φ = strength capacity reduction factor; 0.9 for flexure, see AASHTO

8.16.1.2.2.


Pan Girder Spans

Notes

For standard Pan Girder bridges, “b” will always equal the beam spacing, seen byfollowing the procedure in the noted AASHTO Specifications.

Equations

bf

FAa

c

ys

'85.0=

where a = depth of compression stress block, in inches, see AASHTO 8.16.3.2.As = total area of top and bottom longitudinal steel layers, inches2

Fy = rebar strength, ksif’c = concrete strength, see Appendix A.b = effective flange width, see AASHTO 8.10.1.1.

total

bt

s

bsts

A

dAdAhd

+−=

where d = distance from extreme compression fiber to centroid of tensionreinforcement (steel centroid to top of slab), in inches.

h = slab + beam depth Ast = total area of top layer of longitudinal steel dt = distance of top layer of longitudinal steel from bottom Asb = total area of bottom layer of longitudinal steel db = distance of bottom layer of longitudinal steel from bottom

−== 12/

2a

dFAMC ysnu φφ

where Cu = nominal member ultimate capacity used in MCEB Eq. 6-1a.Mn = ultimate moment capacity of T-beam, in kip-feet, see AASHTO

8.16.3.2.φ = strength capacity reduction factor; 0.9 for flexure, see AASHTO 8.16.1.2.2.

Flat Slab Spans


Load rating analysis of a Flat Slab bridge is more complex than T-Beam and Pan Girderbridges. Many dimensions and variables are needed to describe the theory. Please referto the figures and diagrams to better understand these dimensions and variables.

Ratings are performed separately for the slab, beams, and curbs, but load effects aredetermined by considering the presence of all elements. The lowest of these three ratingscontrols the overall structure rating shown in the HS Rating field.

Curb Capacity

As-slab is reduced by cos2φ for reinforcement placed Normal to supports. In most cases,“a” will be less than “hcurb” as shown. As-slab considered in curb capacity calculations isonly that portion within the adjacent effective slab width.

b

n

1

top

As-prime

d

dcu

rb

dsl

ab

prim

e

As-curb

As-slab

b bot

hsl

ab

slab

hcu

rb

a

yco

nc

Effective Slab = 4h

Compression Steel Component

Make sure that steel is yielded by satisfying AASHTO Eq. (8-24), otherwise ignore thecompression steel. This makes As-prime = 0 and φMn1 = 0.

If the compression steel is yielded and, As-prime ≤ As-curb then:φMn1 = φAs-prime Fy (dcurb-dprime)

If the compression steel is yielded and As-prime ≥ As-curb then:φMn1 = φAs-curb Fy (dcurb-dprime) + φ(As-prime – As-curb) Fy (dslab-dprime)

Compressive Stress Block

The depth and centroid of the curbular stress block is derived by setting the compressiveforce in the curb equal to the available tension force in the net tension steel and solvingthe resulting quadratic equation for depth, a, resulting in the following formula:

( )n

b

nf

FAAA

n

ba top

c

yprimesslabscurbstop −−+

+

= −−−

'

2

85.0

2 where

curb

topbot

h

bbn

−=


The centroid at the trapezoidal compressive stress block, measured from the top of curb,is determined as

nab

naaby

top

topconc 36

23 2

+

+=

If a > hcurb, a more complex analysis is required. Such an analysis is beyond the scope ofthis spreadsheet.

Tension Steel Component

If As-prime ≤ As-curb, then the following equation applies:( ) ( ) ( )concslabyslabsconccurbyprimescurbsn ydFAydFAAM −+−−= −−− φφφ 2

If As-prime ≥ As-curb, then:( ) ( )concslabyprimescurbsslabsn ydFAAAM −−+= −−−φφ 2

Curb Capacity Equation

21 nnn MMM φφφ +=

Beam Capacity

In most cases, “a” will be less than “dslab”. If this is not the case, ignore the contributionof “As-slab”. Always ignore the compression steel in the beam. If reinforcement has beenplaced Normal to supports, As-slab is reduced by cos2φ. As-slab considered in beamcapacity calculations is only that portion within the adjacent effective slab width.

a

dsl

ab

dbe

am

As-beam

hsl

ab

b total

As-slab

slabEffective Slab = 4hb top

The depth of the stress block on the beam is as follows:

( )totalc

yslabsbeams

bf

FAAa

'85.0−− +

=


The capacity of the beam is:

−+

−= −− 22

adFA

adFAM slabyslabsbeamybeamsn φφφ

Slab Capacity

This is the third capacity on a Flat Slab bridge that must be computed. As-slab is reducedby cos2φ for reinforcement placed Parallel to roadway.

ad

hsla

b

As-slab per foot

b = 1'-0"

The depth of the stress block on the slab is as follows:

( )bfFA

ac

yslabs'85.0

−=

The capacity of the slab is:

−= − 2

adFAM yslabsn φφ

Flat Slab Bridge Assumptions

• Only slabs designed as FS slabs should consider the contribution of curbs or beams.Other slab bridges were not designed for the curbs to carry load; therefore, it cannotbe assumed that they have adequate development length, confinement, sheer capacity,etc., to be considered in the capacity.

• If curbs and/or beams are considered in the analysis, then each element of the bridge(left curb, slab, right curb), is assigned an Inventory and Operating rating according toits individual capacity and applied moments.


~ Inventory rating is based on the least strength element of the bridge (slab, beam,or curb), because this rating is governed by the serviceability required of everydayloads.

~ Operating rating is a weighted average with curb and slab ratings consideredproportionate to their tributary width as compared with the total bridge weight,because this rating is governed by strength required of unusual overloads.

• If curbs and/or beams are not considered in the capacity, their moments aredistributed according to AASHTO 3.24.3.2 (strip capacity of a one foot strip of slab).If the longitudinal edge beam is not checked, it is assumed that this is equal orstronger than the interior slab.

• Transverse steel is okay for distributing moments and will not control the ratings.This is justified based on experimental research (Illinois bulletin 346) and analyticalmodels which consider cracking.

• Skewed slab bridges are rated as equivalent right angle slabs.

~ Assumptions derived from Illinois Bulletins 369 & 386. See Attachment 2 & 3.

~ Span length normal to supports is that considered for design moments.

~ Slab steel area applied to slab capacity is reduced by cos2φ for slab steel runningparallel to roadway.

~ Slab steel area applied to curb capacity (FS slabs only) is reduced by cos2φ forslab steel running normal to supports.

~ Curb and/or beam dead and live load moments are increased by 10% to accountfor the additional length above that considered by span length normal to supports.

Prestressed Beam Spans

Equations

Mu calculations:

bf

FAa

slabc

ys

'85.0 −

=

where a = depth of compression stress block, see AASHTO 8.16.3.2, inchesAs = total area of prestressing strands, inches2

Fy = strand strength, ksif’c-slab = slab concrete strength, see Appendix A, ksi


b = effective flange width, see AASHTO 8.10.1.1, inches

If “a” is greater than the sum of the slab thickness, haunch at centerline of span, and topflange thickness, the spreadsheet is unable to compute an Mu value. If “a” is less thanthis sum and “asr” is greater than zero, Mu equals Mu(flanged). If “a” is less than thissum but “asr” is equal to or less than zero, Mu = Mu (rectangular).

asr = wf

fA

slabc

susr

**85.0 '−

where asr = depth of stress block for rectangular section, inchesAsr = steel area required to develop the compressive strength of the web of a flanged section, inches2. If “a” is greater than the slab

thickness, then Asr = As*- Asf. If “a” is less than the slab thickness,

then Asr = 0.fsu = average stress in prestressing steel at ultimate load, see AASHTO

9.17.4.1, ksif’c-slab = slab concrete strength, see Appendix A, ksiw = top flange width, inches

Asf = su

sslabc

ftwbf *)(*85.0 ' −−

where Asf = steel area required to develop the compressive strength of the overhanging portions of the flange, inches2

f’c-slab = slab concrete strength, see Appendix A, ksits = slab thickness, inchesb = effective width, inchesw = top flange width, inchesfsu = average stress in prestressing steel at ultimate load, see AASHTO 9.17.4.1, Eq. (9-17), ksi

fsu =

−

−'

'*

1

'

*

*1*slabc

ss

s f

fbdA

f βγ

where fsu = average stress in prestressing steel at ultimate load, see AASHTO 9.17.4.1, Eq. (9-17), ksiγ = factor for type of prestressing steel, see AASHTO 9.1.2 and 9.17 Low-Relaxation (L.R.) = 0.28 Stress-Relieved (S.R.) = 0.40As

* = total area of prestressing strands, inches2

β1 = ratio of depth of equivalent compression zone to depth from fiber of maximum compressive strain to the neutral axis. Value equals


0.85 for concrete strengths, f’c, up to and including 4,000 psi. For strengths above 4,000 psi, see AASHTO 8.16.2.7

fs’ = ultimate stress of prestressing steel; normally 250 to 270 ksib = effective flange width, see AASHTO 8.10.1.1, inchesd = distance from extreme compressive fiber to centroid of the prestressing force, see AASHTO 9.1.2, inchesf’c-slab = slab concrete strength, see Appendix A, ksi

Mu (flanged) calculations:

The Reinforcement Index = (Asr*fsu)/(w*d*f’ c-slab), see AASHTO Eq. (9-21)

If Reinforcement Index > 0.36β1 then it is Over-Reinforced, andMu (flanged) =

121

))](5.0(**)(*85.0***)08.036.0[( '2'211 ssslabcslabc tdtwbfdwf −−+− −−ββ ,

see AASHTO Eq. (9-23)

If Reinforcement Index < 0.36β1 then it is Under-Reinforced, and

Mu (flanged) = 12

2**2**

−

− s

susfsr

susrtdfAadfA

, see AASHTO Eq. (9-14)

Mu (rectangular) calculations:

The Reinforcement Index = (As**fsu)/(b*d*f’ c-slab), see AASHTO Eq. (9-20)

If Reinforcement Index > 0.36β1 then it is Over-Reinforced, and

Mu (rectangular) = ( )[ ]2'211 ***08.036.0

121

dbf slabc−− ββ , see AASHTO Eq. (9-22)

If Reinforcement Index < 0.36β1 then it is Under-Reinforced, and

Mu (rectangular) = ( )( )[ ]2*121 * adfA sus − , see AASHTO Eq. (9-13)


Steel Stringer Spans

Following is a flowchart for determining controlling moment capacities of non-hybrid,simply-supported, unstiffened, fully-braced, steel I-beams and plate girders according tothe provisions of AASHTO 10.48 through 10.50.

Per AASHTO 10.48.3, a transition (straight line interpolation) is allowed betweenEquations 10-92 and 10-98 as long as the web thickness always satisfies Equation 10-94.

Does SectionSatisfy

Equations 10-93, 10-94,and 10-95?

Mu is perEquation

10-92

DoesSectionSatisfy

Equations10-129 and10-129a?

DoesSectionSatisfy

Equations10-100?

In Equation10-129a, isDp/D’ less

than orequal to 1?

Mu is perEquation10-129b

DoesSectionSatisfy

Equations10-99 and10-100?

Is SectionNon-

Composite?

Mu is perEquation

10-98

Mu = My

Mu is perEquation10-129c

Section NoGood /BeyondScope

Section NoGood /BeyondScope

YES NO

YES

YES

YES

NO

NO

NO

DoesSectionSatisfy

Equation10-94?

YES

YES

NO

NO

YES NO


Appendix A

CONCRETE STRUCTURES

CONCRETE STRENGTHS REINFORCING STRENGTHS

Reinforced Concrete Prestressed Concrete Reinforced Concrete Prestressed Concrete

Prior to 1959f’c = 2500 psi **

f’ci = 4000 psi ## Prior to 1954fy = 33,000 psi **

Prior to 1970SR250 ##

After 1959f’c = 3000 psi **

f’c = 5000 psi ## After 1954fy = 40,000 psi **

After 1970SR270 ##

** From the AASHTO Manual for Condition Evaluation of Bridges; 1994 edition.## Based on historical records.

REINFORCING SIZES

REINFORCED CONCRETE PRESTRESSED CONCRETE ++

Bar Designation Area of Bar, in2 Strand Strength Strand Size Area of Strand, in2

#4 0.196 1/4" 0.036

#5 0.307 5/16" 0.058

#6 0.442 3/8" 0.080

#7 0.601 7/16" 0.108

#8 0.785

SR250

1/2" 0.144

#9 1.000 3/8" 0.085

#10 1.266 7/16" 0.115

#11 1.563

SR270

1/2" 0.153

++ From ASTM, vol. 01.04 (Steel-Structural, Reinforcing, Pressure Vessel, Railway), section A416.

STEEL STRUCTURES

Prior to 1905 - fy = 26,000 psi **

Between 1905 and 1936 - fy = 30,000psi **

Between 1936 and 1963 - fy = 33,000psi **

After 1963 - fy = 36,000 psi **

** From the AASHTO Manual for Condition Evaluation of Bridges; 1994 edition.


References

AASHTO Manual for Condition Evaluation of Bridges, 1994 edition.

AASHTO Standard Specifications for Highway Bridges, 16th Edition, 1996.

Lin, T.Y., and Ned H. Burns, Design of Prestressed Concrete Structures, 3rd Edition, JohnWiley & Sons, Inc., 1981.

FS Slab Bridge Load Rating Theory, Pat Bachman, Texas Department of Transportation.

Bridge Design Guide, Design Division, Texas Department of Transportation, 1990.

University of Illinois Bulletin Nos. 315, 332, 346, 369, 386.

Documents

RATE Spreadsheet User Guide - ftp.dot.state.tx.usftp.dot.state.tx.us/Pub/Txdot-info/Library/Pubs/Bus/Bridge/Rate-user-guide.pdfThe RATE Spreadsheet is used to calculate Load Factor