economical use of cambered steel beams

8/20/2019 Economical Use of Cambered Steel Beams

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Economical Use of Cambered Steel

Beams

Author Jay W. Larson received a bachelor of science degree in 1980 in civilengineering and a master of science degree In civil engineeringin 1985, from Lehigh University.

He is currently employed byBethlehem Steel Corporation asstructural consultant. His duties in-clude conducting preliminary steelframing studies for materialdeciders on building projects,maintaining and updating in-housestructural analysis computer programs, preparing promotionaland technical literature, and provid-ing technical assistance tofabricator and structural steeldesigners.

Mr. Larson is a member of theAmerican Society of Civil En-gineers, Lehigh Valley SectionBoard of Directors. He is aregistered professional engineer inthe state of Pennsylvania.

Author Robert K. Huzzard received abachelor of science in civil engineer-ing from the University of Pennsyl-vania, in 1963 and a master of science in civil engineering from Vil-

lanova University, in 1973. He is aregistered professional engineer inthe state of Pennsylvania.

Currently employed by Beth-lehem Steel as a sales engineer,his duties involve influencing en-gineers, architects, constructionmanagers and developers inmaterial selection for buildings andparking garages. Prior to hisemployment with Bethlehem Steel,Mr. Huzzard was constructionbridge engineer and project en-gineer with the PennsylvaniaDepartment of Transportation.

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SummaryThe overall economy and quality of a steel-framed building dependspartially on the method used to com-pensate for deflections of the beamsduring the placement of the concreteslab. Current practice ranges fromcambering or shoring beams to plac-ing extra concrete above thedeflected beam. For many buildings,cambering is the most cost effectivesolution. It could also result in themost level floor. Nevertheless, mis-conceptions and concerns regard-ing cambering persist.

The new AISC-LRFD proce-dures for composite constructionencourage the use of lighter, high-strength steel beams spanning

greater distances. This producesmore economical steel frames, butalso results in larger deflections tobe accommodated. Therefore, amore complete understanding of cambering is required.

Guidelines are suggested to as-sist in evaluating the cost effec-tiveness of cambering, correctlydetermining expected beam deflec-tons, understanding mill camber tolerances and limits, specifyingcamber properly, and maintaining

quality during construction.To illustrate, several recentsteel-framed office buildingprojects are discussed. In addition,field measured data is presented tosupport the suggested guidelines.

Jay W. Larson

Robert K. Huzzard

© 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.


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ECONOMICAL USE OF CAMBERED STEEL BEAMS

by

Jay W. Larson, P.E. and Robert K. Huzzard, P.E,Bethlehem Steel CorporationBethlehem, Pennsylvania

INTRODUCTION

The overall economy and quality of a steel-framed buildingdepends partially on the method used to compensate fordeflections of the beams during the placement of theconcrete slab. Current practice ranges from cambering orshoring beams to letting beams sag and pouring a varying

thickness slab. For many buildings, cambering is the mostcost effective solution. It could also result in the mostlevel floor. Nevertheless, misconceptions and concernsregarding cambering persist.

The new AISC-LRFD procedures for composite constructionencourage the use of lighter, high-strength steel beamsspanning greater distances. This produces more economicalsteel frames, but also results in larger deflections to beaccommodated. Therefore, a more complete understanding ofcambering is required.

This paper discusses the major issues related to the

economical use of cambering and concentrates on typicaloffice construction; i.e., simple span, interior, compositebeams and girders.

ACCOMMODATING DEAD LOAD DEFLECTIONS

There are four methods of accommodating beam dead loaddeflections during concrete placement and creating anacceptably level floor slab:

1) let beams sag and pour a varying thickness slab,2) overdesign beams to minimize deflections,

3) shore beams prior to concrete placement,4) camber beams to compensate for anticipated

deflections.

An economic analysis is necessary to select the bestapproach for accommodating beam dead load deflections. Eachof the methods mentioned above could be cost effectivedepending on material and labor costs in the location wherethe project will be built.

13-3© 2003 by American Institute of Steel Construction, Inc. All rights reserved.

This publication or any part thereof must not be reproduced in any form without permission of the publisher.


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Let Beams Sag

For beams without induced camber, the standard practice isto erect the beam with natural camber upward. The AISC

[2,3] tolerance for this camber is 1/8" per 10'-0 of length.This helps offset the deflection of the steel beam due toits own weight plus the weight of the steel deck andconcrete floor slab. However, a negative camber usuallyresults in the steel beam and additional concrete is neededto achieve a level floor.

The cost of this additional concrete can be substantial. Inaddition, the appearance of a sagging beam in the finishedstructure might be objectionable.

Overdesign BeamsThe size of the steel beam can be increased to reduce itsdeflection and the excess concrete requirement. This willalso generally reduce the number of shear studs required.However, this is rarely an economical solution. Almostinvariably the increase in cost for the heavier steel beamexceeds the cost of the concrete and shear studs saved.

Shoring

The true cost of shoring is difficult to quantify. The

labor and material costs for installing shoring can probablybe accurately estimated. However, it is impossible todetermine the added expense caused by the shoring'sinterference with subsequent operations such asfire protection and mechanical systems installation.

The use of shoring has another drawback. When the shoresare removed the floor system will deflect under its ownweight. This will cause a sag in a slab that was initiallylevel and probably a crack to form over the girderssupporting the filler beams. For this reason crack controlslab reinforcement should be used over girders [1].

Cambering

Cambering provides an initial curvature about a member'sstrong axis so that a desired profile results. Beams can becambered to accommodate part of the dead load deflection,the full dead load deflection, or the dead load deflectionplus part of the live load deflection.

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Cambering saves money by reducing or eliminating excessconcrete that may be required in a building due to thedeflection of the steel beam. The cost of cambering can beaccurately determined with no additional hidden costs.

STEEL BEAM COST COMPARISONS

In order to demonstrate the potential cost savings usingcambering, four cases were investigated: three differentlength filler beams, 30'-0, 38'-0, and 45'-0, spaced at10'-0, and one 30'-0 girder supporting the 30'-0 span fillerbeams. The results are listed in Tables 1 - 4 .

For each of the cases, four solutions were evaluated:cambered with A572 Grade 50 high-strength steel (50/C),

uncambered with A572 Grade 50 high-strength steel (50/U),cambered with A36 steel (36/C) and uncambered with A36 steel(36/U). Direct comparisons were then made to identify costsavings attributable to both camber and high-strength steel.

Assumptions

Design Method: AISC Allowable Strength Design (1978)

Loads: Live: floor load (reduced per BOCA): 80 psf

Dead: 3" 20 ga. composite steel deck

w/3-1/4" lightweight concrete: 46 psfsteel: 5 psfpartitions: 20 psfceiling/mechanical/etc: 10 psf

Note: The analysis did not include any additionalload due to ponding concrete.

Deflections: Actual deflections (due to weight of steelmember, deck and wet concrete) wereassumed to equal 3/4 of the theoreticalfor a simple span to account forconnection rigidity.

Costs: Steel: "Cost-per-foot Guide" [4] (material only)

Shear studs: $1.50 ea. (installed)

Camber: 0.03 $/# for sections thru 50 #/ft0.02 $/# for sections over 50 #/ft

Concrete: 60.00 $/cy (in-place material, doesnot include finishing)

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Results

The savings due to cambering alone is the difference betweenthe least cost cambered scheme and the least cost schemewith no camber. The savings due to high-strength steelalone is the difference between the uncambered A572 Grade 50and A36 schemes.

The most economical scheme for each case utilized camber andhigh-strength steel. Further, high-strength steel usuallyreduced member sizes permitting a savings in depth of 3".

The results of the steel beam cost comparisons aresummarized in the following table.

STEEL BEAM COST COMPARISONS

Shoring vs Cambering

Shoring can only be competitive with cambering if its costis lower. Combining the results for Cases 1 and 4 of thepreviously discussed analysis would indicate the total

camber cost for a typical 30' x 30' bay.

Hence, camber cost =

(3)(camber cost per beam) + (1)(camber cost per girder)

floor area

= [(3)(0.78 $/ft)(30')+(l)(1.50 $/ft)(30')] / [(30')(30')]

= 0.078 $/sf + 0.050 $/sf = 0.128 $/sf

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Case

# Description

1 30'-0 beam@10'-0 o.c.

2 38'-0 beam@10'-0 o.c.

3 45'-0 beam@10'-0 o.c.

4 30'-0 girder@30'-0 o.c.

Savings dueto Camber$/ft ($/sf)

0.22 (0.022)

0.49 (0.049)

0.45 (0.045)

1.05 (0.035)

Savings dueto H.S.Steel$/ft ($/sf)

1.43 (0.143)

1.21 (0.121)

1.76 (0.176)

1.86 (0.062)

OverallSavings

$/ft ($/sf)

1.65 (0.165)

1.70 (0.170)

2.21 (0.221)

2.91 (0.097)


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Therefore, for this case, the total cost of shoringincluding crack control slab reinforcement over girderswould have to cost less than 0.13 $/sf to be more economical

than cambering. In addition there is the added expensecaused by shoring's interference with subsequent operations.

CAMBERING OF STEEL BEAMS

Gag, or cold cambering of beams is generally more economicalthan heat cambering and is more widely used. It isgenerally done at the steel mill or fabricator shop and isaccomplished with the use of applied force [5,6]. Thetolerances, limitations and costs are described below.

Tolerances

The AISC [2,3] tolerance for mill camber of members 50 ft orless is minus 0" and plus 1/2". Over 50 ft, the plustolerance increases 1/8" for each 10 ft in excess of 50 ft.

The AISC also states that "Camber is measured at the milland will not necessarily be present in the same amount inthe section of beam as received due to release of stressinduced during the cambering operation. In general, 75% ofthe specified camber is likely to remain."

Limitations

Gag camber requires the development of large inelasticstrains. Beyond a certain point, local buckling of themember can occur. Therefore, the maximum amount of camberthat can be put into a member is limited and is dependent onthe particular cross section, length and material grade.There may also be equipment limitations by the producer.The minimum amount of camber is generally a practicalconsideration and is mainly dependent on economics.

MAXIMUM AND MINIMUM INDUCED CAMBER

Sections Nominal Depth

In.

W shapes, 24 and over

W shapes, 14 to 21, incl. and

S shapes, 12 in. and over

Specified Length of Beam, Ft

Over 30to 42, incl.

Over 42to 52, incl.

Over 52to 65, incl.

Over 65to 85, incl.

Over 85to 100, incl.

Max. and Min. Camber Acceptable, In.

1 to 2,incl.

¾ to 2½,incl.

1 to 3,incl.

1 to 3,incl.

2 to 4,incl.

2 to 4,incl.

3 to 5,incl.

2½ to 5,incl.

3 to 6,incl.

Inquire

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The preceding table, from the AISC [2,3], providesreasonable guidelines for minimum and maximum inducedcambers. However, obtaining the larger cambers on lighter

weight beams with shorter lengths within a range,particularly for grades other than A36, is more difficult.For example, a 2-1/2" camber in an A572 Grade 50 W16x26#that is only 30'-0 long would be difficult to achieve.Therefore, it is prudent to consult the producer prior tospecifying cambers near these extremes.

Costs

Cambering is definitely economical. For example, BethlehemSteel's published price book offers cambering for $60/ton onbeams up to 50 lbs/lf, and $40/ton for beams over 50 lbs/lf.

Many fabricators with the proper equipment can do their owncambering at prices that are competitive with this.

When deciding whether to camber or not, the above pricesshould permit a reasonable cost comparison.

FACTORS AFFECTING CAMBER

The amount of camber that is specified is crucial toobtaining a level floor with the proper slab thicknessThere are several factors which must be considered:

1) calculated dead load deflection,2) camber tolerances,3) camber losses,4) effect of connection end restraint.

Calculated Dead Load Deflection

In order to select the proper amount of camber for a beamthe desired finished floor profile must be considered. Itis most reasonable to attempt to construct a level slab atthe time the concrete is placed. Ideally, the slab wouldalso be of constant thickness. Therefore, the beam should

be level after the concrete is placed.

For this situation only the weight of the beam itself, themetal deck, and the wet concrete should be used in thecalculation of the dead load deflection. Additional items,such as partitions, mechanicals, ceiling and any live loadshould be excluded.




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Tolerances

There most likely will be additional camber induced at the

mill to assure that it is within tolerance. This could beas much as 1/2" !

Losses

Although the AISC states that "75% is likely to remain",there is no guarantee that some mill camber will be "lost"during shipment, fabrication, and erection. Anticipatingthis loss could be a mistake since excess camber may result.

End Restraint

Connections on the beams provide some degree of endrestraint. Therefore, the full calculated dead loaddeflection will probably not occur.

Determining the exact dead load deflection is probably notpossible or practical for each member and end conditionwithin a project. Many engineers reportedly specify camberamounts in the range of 2/3 to 3/4 of the calculated, simplespan dead load deflection to account for end restraint.

The "More is Better" Syndrome

In much of structural engineering and construction more isdeemed better. That is, using a heavier design load,exceeding the minimum tolerances, anticipating larger lossesand ignoring the end restraint provided by connections isusually thought to be conservative.

However, when it comes to the cambering of steel beams to beused in typical building construction, this can result inexcessive camber in the steel beams and extreme difficultiesin achieving level floors and required slab thickness. Allparticipants of the design/construction team need to realizethat it is usually easier and more economical in the field

to accommodate under-cambered beams rather thanover-cambered beams.

FIELD MEASURED DATA

In an attempt to verify the factors influencing amount ofcamber that should be specified, 9 girders and 9 fillerbeams were monitored.

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The girders were 30'-0 simple span W24x55#, A572 Grade 50,members supporting 30'-0 simple span filler beams spaced at10'-0. The filler beams were 30'-0 span W16x31#, A572

Grade, members spaced at 10'-0. The floor slab consisted of18 gage 2" composite steel deck with 3-1/2" 115 pcf concretetopping.

Measurements of actual camber were taken:

1) immediately after cambering at the mill,2) after shipment and unloading at the fabrication

shop, but prior to fabrication,3) after shipment, unloading and erection at the job

site with composite steel deck and shear studserected, but prior to placement of the concreteslab,

4) after the placement of the concrete slab but priorto any additional dead or live loading.

At the mill and fabrication shop measurements were made witha string line and foot rule, and were taken to the nearest1/16". In the field, measurements on the erected memberswere made using a surveying level and rod, and were taken tothe nearest 0.005'. Table 5 shows the complete set of data.

It must be remembered that data was collected for only onespan length; 30'-0. Further investigation of other spans isprobably warranted.

Tolerances

A comparison of the desired camber and the actual camber ismade in Table 6. This shows that girders were cambered 1/4"to 1/2" beyond the specified amount (typically 1/4").Similarly, beams were cambered 1/8" to 5/16" beyond thespecified amount (typically 1/4").

All members were cambered within AISC tolerances.

Losses

A comparison of the expected erected camber and the actualerected camber is made in Table 7. The expected erectedcamber was determined by subtracting the calculateddeflection due to the weight of the steel members and deckfrom the actual mill camber. The effect of connection endrestraint, probably less than 1/32" at this stage, wasignored for this table.

The results indicated that girders lost from 0" to 1/4" ofcamber during shipment, fabrication and erection.Similarly, beams lost from 1/8" to 5/16".

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These unexplained losses are consistent with the AISCstatement that "in general, 75% of the specified camber islikely to remain." However, these losses do not appear tobe very predictable or consistent. In some cases there were

no camber losses at all; therefore, anticipating lossescould be a mistake.

The net effect of mill tolerances, which generally providemore camber than desired, and camber losses, which reducethe amount of camber, tend to offset each other. However,the net result is usually slightly more camber thanspecified.

End Restraint

A comparison of the expected final camber and the actualfinal camber is made in Table 8. The expected final camberwas determined by subtracting the calculated deflection dueto the weight of the concrete slab from the actual erectedcamber. It was assumed that there were no additional lossessuch as those that would occur during shipment, fabrication,and erection.

The results indicated that the girders gained from -1/8"(loss) to 3/16" (gain) of camber. Similarly, beams gainedfrom 1/16" to 3/16" of camber. The gains with respect tothe theoretical camber are probably due to the restrainingeffect of the end connections which are typically ignored in

deflection calculations.

There is no apparent explanation for the loss of camber intwo of the girders. However, this was not a controlledscientific study. More extensive research would benecessary before specific recommendations can be made.

CONSTRUCTION METHODS

There are two basic methods used in the finishing ofconcrete slabs: constant thickness and constant elevation.In the constant thickness method, the top of the concrete

slab is established by measuring the desired thickness abovethe steelwork with a stick or rod. In the constantelevation method, either a conventional or laser level isused to aid the finisher in setting the desired top ofconcrete elevations. In either method, a small area issmoothed off to the desired elevation and is used as a guidefor the screeding operation.

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Both methods are greatly affected by the actual elevation ofthe erected steel and are more seriously affected by highpoints in the steel than by low ones. The only sure way todetermine the actual elevations of the erected steel is to

conduct a field survey of the erected steel. This surveyallows the computation of the anticipated finished slabelevation and profile. If these are not satisfactory, it isnot too late to make modifications to correct the problem.Without the survey, problems do not become apparent untilafter the slab is completed.

Constant Thickness Method

In the constant thickness method, floor levelness is themajor concern since the slab will follow the deflected

profile of the beam below. From the field survey thedeflected profile of the steel can be calculated bysubtracting the expected dead load deflections from themeasured elevations. By adding the desired slab thicknessto these elevations the expected floor profile can bedetermined.

High spots are the most serious concern, especially afterthe concrete has set. If portions of the floor, ascalculated, will be unacceptably high, it is probably wiseto resort to the constant elevation method; i.e., adjust thegrade for the entire floor.

If portions of the floor will be too low, the constantelevation method can be used in those areas. For theremaining portion of the floor the constant thickness methodcan be used. Alternatively, the offending beams could beshored to minimize their deflection and the entire floorcould be set from the steel.

Constant Elevation Method

In the constant elevation method, slab thickness is thepotential problem area. If too much camber is present inthe beams and the theoretical plan elevation is maintained

there will necessarily be a thin slab. Once again, a fieldsurvey should be performed to determine high points in theerected steel.

Final beam elevations, based on the expected dead loaddeflections, should be calculated. Then the desired slabthickness should be added to the highest calculated finalbeam elevation. This elevation should then be compared tothe plan finish grade and the final slab elevation should beadjusted up or down to account for any difference.

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The constant elevation method is also greatly affected bythe placement of wet concrete. It is important that screedelevations not be set until the entire wet concrete load ison the member. Thus, careful thought must be given to the

sequence of the concrete placement.

CONCLUSIONS

Cambering is often the most economical method ofaccommodating dead load deflections in beams. It savesmoney by reducing or eliminating excess concrete that may berequired. The cost of cambering can be accuratelydetermined with no additional hidden costs to consider.

in order to achieve the ultimate goal of a level slab havingthe correct thickness, it is imperative that camber in beamsbe specified properly, which in turn requires that accuratedead load deflections be calculated. Only the weight of thebeams, metal deck, and wet concrete should be used in thesecalculations. Additional items, such as partitions,mechanicals, ceiling and any live load should be excluded.

The effects of mill tolerances and camber losses tend tooffset each other; although, the net effect is usuallyslightly more actual camber than specified.

The effect of connection end restraint can usually beminimized by reducing the amount of camber specified. The

reported practice by many engineers of specifying camberamounts in the range of 2/3 to 3/4 of the calculated, simplespan dead load deflection to account for end restraintappears reasonable.

Camber 1/2" or less should probably not be specified; at1/2" the cost of cambering usually exceeds the potentialsavings in concrete, especially since natural mill camberwill probably be present.

It should be remembered that "more is not better" ! It isusually easier and more economical to accommodateunder-cambered beams than over-cambered beams. Much more

severe problems occur in the field with beams that are toohigh than with ones that are too low.

For either the constant elevation or thickness method offinishing, a field profile survey of the erected steel priorto pouring the slab can be invaluable in determining whetherthe desired slab thickness and grade can be obtained. If aproblem is detected, construction procedures can then bemodified prior to casting the slab.

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SUMMARY

Cambering is often the most economical method ofaccommodating dead load deflections in beams. It saves

money by reducing or eliminating excess concrete that may berequired. The cost of cambering can be accuratelydetermined with no additional hidden costs to consider.

Increasing the size of the steel beam in order to reduce itsdeflection and the excess concrete requirement is rarely aneconomical solution. Almost invariably the increase in costfor the heavier steel beam exceeds the cost of the concreteand shear studs saved.

Camber should be specified only after consideration of thefollowing:

1) calculated dead load deflection,2) camber tolerances and limitations,3) camber losses,4) effect of connection end restraint,5) The "More is Better" Syndrome.

Prior to placing concrete slabs a profile survey of beamelevations should be performed. Then, if the expected floorprofile is not satisfactory, a modification to the finishingapproach can be made.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the cooperation of thefabricator, Strait Manufacturing and Welding, Inc.,Greencastle, PA and the general contractor, GlenConstruction Company, Inc., Gaithersburg, MD, for theircooperation and assistance in obtaining field data duringthe construction of the Dulles Corner #6 office building,Fairfax, VA.

REFERENCES

1) Allison, Horatio, "Steel Design - SpecialConsiderations", in Building Structural Design Handbook,ed. White, Richard N. and Salmon, Charles, G., John Wiley& Sons, 1987, pp. 567-569, 572-573, 587-590.

2) American Institute of steel Construction, Manual ofSteel Construction - Allowable stress Design, 9thEdition, 1989, pp. 1-147, 1-150.

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3) American Institute of steel Construction, Manual ofSteel Construction - Load & Resistance Factor Design,1st Edition, 1986, pp. 1-167, 1-170.

4) Bethlehem Steel Corporation, "Cost-per-foot Guide",Bethlehem TB-300 A, 1989.

5) Kloiber, Lawrence A., "Cambering of steel Beams", inSteel Structures; Proceedings of the ASCE StructuresCongress, American society of civil Engineers,1989.

6) Ricker, David T., "Cambering steel Beams", in EngineeringJournal, American Institute of steel Construction, FourthQuarter, 1989.

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Table 1

COST COMPARISON: CASE 1

30'-0 span filler beam, 10'-0 o.c.

Description $/ft $/sf

50/C) W16x26 grade 50 7.4120 studs 1.00theoretical deflection = 1.07"camber = 75% of defl. = 13/16" 0.78TOTAL 9.19 0.919

50/U) W16x26 grade 50 7.4120 studs 1.00theoretical deflection = 1.07"ponding conc.= 75% of defl.= 13/16" 1.00TOTAL 9.41 0.941

36/U) W16x31 grade 36 8.3734 studs 1.70theoretical deflection = 0.86"ponding conc.= 75% of defl. = 5/8" 0.77TOTAL 10.84 1.084

36/C) W16x31 grade 36 8.3734 studs 1.70theoretical deflection = 0.86"camber = 75% of defl. = 5/8" 0.93

TOTAL 11.00 1.100

Savings:

camber: 0.22 0.022high-strength steel: 1.43 0.143

TOTAL 1.65 0.165

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Table 2

COST COMPARISON; CASE 238'-0 span filler beam, 10'-0 o.c.


50/C) W18x35 grade 50 9.9836 studs 1.42theoretical deflection = 1.63"camber = 75% of defl. = 1 1/4" 1.05TOTAL 12.45 1.245

50/U) W18x35 grade 50 9.9836 studs 1.42theoretical deflection = 1.63"

ponding conc.= 75% of defl. = 1 1/4" 1.54TOTAL 12.94 1.294

36/U) W21x44 grade 36 11.8834 studs 1.34theoretical deflection = 0.99"ponding conc.= 75% of defl. = 3/4" 0.93TOTAL 14.15 1.415

36/C) W21x44 grade 36 11.8834 studs 1.34theoretical deflection = 0.99"camber = 75% of defl. = 3/4" 1.32

TOTAL 14.54 1.454

Savings:


TOTAL 1.70 0.170




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Table 3

COST COMPARISON; CASE 3

45'-0 span filler beam,10'-0 o.c.


50/C) W21x44 grade 50 12.5444 studs 1.47theoretical deflection = 1.94"camber = 75% of defl. = 1 7/16" 1.32TOTAL 15.33 1.533

50/U) W21x44 grade 50 12.5444 studs 1.47theoretical deflection = 1.94"

ponding conc.= 75% of defl. = 1 7/16" 1.77TOTAL 15.78 1.578


36/U) W24x55 grade 36 14.8546 studs 1.53theoretical deflection = 1.21"ponding conc.= 75% of defl. = 15/16" 1.16

TOTAL 17.54 1.754

Savings:


TOTAL 2.21 0.221




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Table 4

COST COMPARISON; CASE 4

30'-0 span girder supp't 30'-0 beams @ 10'-0 o.c.



50/U) W21X50 grade 50 14.2552 studs 2.60theoretical deflection = 0.89"

ponding conc.= 75% of defl. = 11/16" 2.55TOTAL 19.40 0.647


36/U) W24x62 grade 36 16.7458 studs 2.90theoretical deflection = 0.56"ponding conc.= 75% of defl. = 7/16" 1.62

TOTAL 21.26 0.709

Savings:


TOTAL 2.91 0.097




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Table 5: FIELD MEASURED DATA

ID

2345678

9

10

1112131415161718

Section

W24x55#W24x55#W24x55#W24x55#W24x55#W24x55#W24x55#W24x55#W24x55#

W16x31#

W16x31#W16x31#W16x31#W16x31#W16x31#

W16x31#W16x31#W16x31#

Span

30'-030'-030'-030'-030'-030'-030'-030'-030'-0

30'-0

30'-030'-030'-030'-030'-0

30'-030'-0

CamberDesired

5/8"5/8"5/8"5/8"5/8"5/8"5/8"5/8"5/8"

7/8"

7/8"7/8"7/8"7/8"7/8"

7/8"7/8"7/8"

Measured Camber

@Mill

7/8"1-1/8"1"

7/8"7/8"7/8"7/8"1-1/8"1"

1"

1"1-1/8"1-1/8"

1"1-1/8"1-1/8"1-3/16"

1"

@Fab

3/4"1-1/16"15/16"13/16"7/8"13/16"13/16"1-1/16"

1"

7/8"

15/16"1-1/16"1"

15/16"1"

1-1/8"1-1/16"1"

Erected

9/16"*3/4"3/4"5/8"9/16"11/16"15/16"5/8"

11/16"

11/16"3/4"13/16"11/16"13/16"7/8"3/4"11/16"

Final

1/16"*7/16"5/16"1/4"0"1/4"5/16"5/16"

1/8"

0"3/16"3/16"1/8"1/4"1/4"3/16"1/8"

* Girder could not be located in the field; therefore,this data is not available.

Table 6: EFFECT OF MILL TOLERANCES

ID

123456789

101112131415161718

DesiredCamber

5/8"5/8"5/8"5/8"5/8"5/8"5/8"5/8"5/8"

7/8"7/8"7/8"7/8"7/8"7/8"7/8"7/8"7/8"

MillCamber

7/8"1-1/8"

1"7/8"7/8"7/8"7/8"1-1/8"

1"

1"1"

1-1/8"1-1/8"

1"1-1/8"1-1/8"1-3/16"1"

ExtraCamber

1/4"1/2"3/8"1/4"1/4"1/4"1/4"1/2"3/8"

1/8"1/8"1/4"1/4"1/8"1/4"1/4"5/16"1/8"

13-20

30'-0



20/20

Table 7: EFFECT OF LOSSES

ID

13

45

6

7

8

9

10

1112131415161718

Actual

MillCamber

7/8"1"

7/8"7/8"7/8"7/8"1-1/8"

1"

1"

1"1-1/8"1-1/8"

1"1-1/8"1-1/8"1-3/16"

1"

Calc.

Deflect.

1/8"1/8"1/8"1/8"1/8"1/8"1/8"1/8"

1/8"

1/8"1/8"1/8"1/8"1/8"1/8"1/8"1/8"

Expected

ErectedCamber

3/4"7/8"3/4"3/4"3/4"3/4"1"

7/8"

7/8"

7/8"1"1"

7/8"1"1"

1-1/16"

7/8"

Actual

ErectedCamber

9/16"3/4"3/4"5/8"9/16"11/16"15/16"5/8"

11/16"

11/16"3/4"13/16"11/16"13/16"

7/8"3/4"11/16"

Camber

Loss

3/16" (21%)1/8" (13%)0" (0%)1/8" (14%)3/16" (21%)1/16" (7%)1/16" (6%)1/4" (25%)

3/16" (19%)

3/16" (19%)1/4" (22%)3/16" (17%)3/16" (19%)3/16" (17%)1/8" (11%)5/16" (26%)

3/16" (19%)

Table 8: EFFECT OF END RESTRAINT

ID

13

456

78

9

101112131415161718

ActualErectedCamber

9/16"3/4"3/4"5/8"9/16"11/16"15/16"5/8"

11/16"11/16"

3/4"13/16"11/16"13/16"7/8"3/4"11/16"

Calc.Deflect.

1/2"1/2"1/2"1/2"1/2"1/2"1/2"1/2"

3/4"3/4"3/4"3/4"3/4"3/4"3/4"3/4"3/4"

ExpectedFinalCamber

1/16"1/4"1/4"1/8"1/16"3/16"7/16"1/8"

- 1/16"- 1/16"

0"1/16"

- 1/16"1/16"1/8"0"

- 1/16"

ActualFinalCamber

1/16"7/16"5/16"1/4"0"

1/4"5/16"5/16"

1/8"0"

3/16"3/16"1/8"1/4"1/4"3/16"1/8"

CamberDiff.

0" (0%)+ 3/16" (+25%)+ 1/16" (+8%)+ 1/8" (+20%)- 1/16" (-11%)+ 1/16" (+9%)- 1/8" (-13%)+ 3/16" (+30%)

+ 3/16" (+27%)+ 1/16"+ 3/16" (+25%)+ 1/8" (+15%)+ 3/16" (+27%)+ 3/16" (+23%)+ 1/8" (+14%)+ 3/16" (+25%)+ 3/16" (+27%)

(+9%)

economical use of cambered steel beams

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