designing with composite deck

17
Designing With Composite Deck Richard B. Heagler Author R ichard B. Heagler is director of engineering for Nicholas J. Bouras, Inc., and United Steel Deck, Inc. of Summit, New Jersey. He received his bachelor of science and master of science and professional degrees in civil engineering from the University of Missouri at Rolla. He has been involved in the steel deck industry for over thirty-five years. In 1962 he began his career at Granco Steel Products, St. Louis, Missouri and joined Nicholas J. Bouras, Inc. in 1977. Mr. Heagler has written articles on connecting steel deck and on designing with steel deck, and is the author of Engineers Notebook for the Design of Composite Steel Beams and Girders with Steel Deck. He is also the principal author of the Steel Deck Institute's Composite Deck Design Handbook. Mr. Heagler is the chairman of the Steel Deck Institute's Technical Committee on Floor Deck, and is the chairman of the American Society of Civil Engineer Standards Committee on Composite Deck. He is also an ex-president of the Steel Deck Institute. Mr. Heagler is a Registered Professional Engineer in the state of Missouri, New Jersey, and New York. strength of column testing. More than 40 tee joints were fabricated with high-strength (690 MPa yield strength) "pull" plates welded transversely to opposite flanges of short 610 mm lengths of heavy column sections. The second half of this session will detail the performance of steel in high-demand full-scale connec- tion tests. Several designs were examined, including a new, sim- ple and economical connection solution. Issues and recommen- dations related to design, detail- ing, fabrication, failure modes and material performance are presented. Summary I n the beam-to-column connec- tion used in welded moment frames, the through-thickness strength of the column flange is relied upon to transmit the cyclic forces from the beam flanges to the column. The first part of this session focuses on the results from SAC's research project "Through- Thickness Strength of Column Flanges in Welded Moment Connections," which was designed to resolve questions about the through-thickness 16-1 © 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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Page 1: Designing With Composite Deck

Designing WithComposite Deck

Richard B. Heagler

Author

Richard B. Heagler is director ofengineering for Nicholas J.

Bouras, Inc., and United SteelDeck, Inc. of Summit, NewJersey. He received his bachelorof science and master of scienceand professional degrees in civilengineering from the University ofMissouri at Rolla. He has beeninvolved in the steel deck industryfor over thirty-five years. In 1962he began his career at GrancoSteel Products, St. Louis,Missouri and joined Nicholas J.Bouras, Inc. in 1977.

Mr. Heagler has written articleson connecting steel deck and ondesigning with steel deck, and isthe author of Engineers Notebookfor the Design of Composite SteelBeams and Girders with SteelDeck. He is also the principalauthor of the Steel DeckInstitute's Composite DeckDesign Handbook.

Mr. Heagler is the chairman ofthe Steel Deck Institute'sTechnical Committee on FloorDeck, and is the chairman of theAmerican Society of CivilEngineer Standards Committeeon Composite Deck. He is alsoan ex-president of the Steel DeckInstitute.

Mr. Heagler is a RegisteredProfessional Engineer in the stateof Missouri, New Jersey, and NewYork.

strength of column testing. Morethan 40 tee joints were fabricatedwith high-strength (690 MPa yieldstrength) "pull" plates weldedtransversely to opposite flanges ofshort 610 mm lengths of heavycolumn sections.

The second half of this sessionwill detail the performance of steelin high-demand full-scale connec-tion tests. Several designs wereexamined, including a new, sim-ple and economical connectionsolution. Issues and recommen-dations related to design, detail-ing, fabrication, failure modes andmaterial performance arepresented.

Summary

In the beam-to-column connec-tion used in welded moment

frames, the through-thicknessstrength of the column flange isrelied upon to transmit the cyclicforces from the beam flanges tothe column.

The first part of this sessionfocuses on the results from SAC'sresearch project "Through-Thickness Strength of ColumnFlanges in Welded MomentConnections," which wasdesigned to resolve questionsabout the through-thickness

16-1

© 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.

Page 2: Designing With Composite Deck

Designing with Composite DeckTwo very different considerations have the most influence on choosing a composite deck system. These areconstruction spans, and fire ratings. The third consideration is the ability to carry the service loads but thiscan usually be done by a simple review. It is interesting to note that the third consideration (service load),while being perhaps the least important, has received the most attention and the most research effort. Ingeneral, fire requirements set the concrete type and cover while construction loading dictates the deck depthand gage - shoring is always avoided. Only now, after almost fifty years of composite deck use, is acampaign being launched to produce a more rational set of fire resistance rules.

The following two topic discussions on working platform and fire ratings were copied from the SDI CompositeDeck Design Handbook of 1997.

The Deck as a Working Platform and a Form.

As a working platform the builder may assume an allowable working load of 50 pounds per squarefoot; an investigation may be necessary to see if shoring needs to be in place to obtain this capacity.For construction information and guidelines the Steel Deck Institute Manual of Construction with SteelDeck is recommended.Deck performance as a form is determined using the loading criteria and coefficients shown in Figures1, 2, and 3. Where only uniform loads are shown, the loading consists of concrete weight, deckweight, and a construction (men and equipment) load of 20 psf. In the cases where a combination ofa uniform and a concentrated load is shown, the uniform loading consists of concrete and deckweights and the concentrated load is 150 pounds per foot of width. (The 150 pound load is thedistributed result of a 300 pound man load acting over two feet). The single span loading considerslimited manueverability. For single span loading the concrete load is the actual concrete weight (psf)plus either 0.5 times the concrete weight or 30 psf, whichever is less. This increase in concrete load isto provide an allowance for possible concrete piling. In the 1991 edition of the Composite DeckDesign Handbook the 0.5 added weight factor was used but was not limited to the 30 psf increaseover the actual weight.The equations in figures 1, 2, and 3 are general. It is the responsibility of the user to apply the correctload factors to the various combinations of loads. Example problem 1 shows how the factors areapplied to a three span condition. The maximum unshored spans for various slabs and deckcombinations are shown in the tables. The LRFD calculations for the maximum spans use theAmerican Iron and Steel Institute (AISI) load factors of 1.6 for concrete weight; 1.4 for men andequipment; and, 1.2 for deck weight. The resistance factors from the AISI are 0.95 for bending,and 0.90 or 1.0 for shear depending on the web length to thickness ratio. The tabulated values forshear are factored.

Web crippling is checked at interior supports based on a 5" bearing width. In most cases steel beamflanges will be at least 5" wide, but even if they are less than 5" the temporary nature of the loadingmakes the calculation conservative. Web crippling at exterior supports is not a factor because if endcrippling occurs the deck simply becomes hinged which is assumed in any case. For the calculationof maximum unshored spans web crippling is checked using ASD procedures for the deck uniformlyloaded with concrete, deck weight, and 20 psf construction load. The LRFD load factors and thefactor provide unacceptable results. This is the only instance where ASD is used in preparing thetables. Additionally, web crippling loads are very temporary so the traditional 1/3 stress increase isallowed in the ASD procedure. Slip off is much more critical so deck ends must be well connected tothe framing members. Combined bending and shear is checked at the interior supports on multispandeck.

16-3

© 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.

Page 3: Designing With Composite Deck

Designing with Composite Deck

* deflection is to be calculated using only concrete plus deck weights uniformly distributed over all spans.

16-4

Key

uniform concrete load uniform construction load (20 psf, Unfactored)

concentrated man or equipment load (150 Ibs./ft. of width Unfactored)

figure 1

figure 2

figure 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.

Page 4: Designing With Composite Deck

Designing with Composite DeckForm deflection under the uniform loading of concrete and deck weight is limited to 1/180 of the spanor 3/4"; no additional temporary construction loads or concrete loads are included in the calculationsfor the tables. For the purpose of the tables, the supporting structure is assumed to remain level asthe frame flexibility is not known nor can any camber be anticipated. For concrete quantitycalculations refer to the SDI publication Metal Deck and Concrete Quantities, 1994.

Fire Ratings

Hourly fire ratings are used as a measure of the ability of the composite deck slab to contain a fireand keep it from spreading from floor to floor. The "fire" is defined in ASTM E119. For the duration ofthe fire test the floor must carry the design load, not allow 250° F temperature rise through the slab,and not permit flames or hot gasses to penetrate the assembly. Local codes dictate the number ofhours required and, as shown in figure 4, the concrete cover is often controlled by the rating selected.There are also rated assemblies not shown in figure 4 that use a suspended ceiling as part of theconstruction; these assemblies generally have 2.5" of normal weight concrete cover for one and twohour ratings and 3.5" for three hours.The information in figure 4 is based on the constructions shown in the Fire Resistance Directorypublished by Underwriters Laboratories, Inc. In this directory the construction group "Floor CeilingDesigns - Concrete with Steel Floor Units and Beam Supports" (prefix D) provides important details ofconstruction for each design and must be consulted.

RatingHours

11

1.51.5223344

LIGHTWEIGHTConcrete

cover2.5"(65mm)

2.5"(65mm)3"(75mm)

3.25"(85mm)2.5"(65mm)2.5"(65mm)

4.25"(110mm)2.5"(65mm)

3.25"(85mm)

NORMAL WEIGHTConcrete

cover3.5"(90mm)2.5"(65mm)2.5"(65mm)4"(100mm)

4.5"(115mm)2.5"(65mm)2.5"(65mm)

5.25"(135mm)2.5"(65mm)

Is fireproofing requiredon the deck?*

NoYesYesNoNoYesYesNoYesYes

* This column refers to the deck; beams and columns normally need some typeof fire protection.

figure 4

In the Underwriters Fire Resistance Directory the composite deck constructions show hourly ratingsfor restrained and unrestrained assemblies. ASTM E119 provides information in appendix X3 called"Guide for Determining Conditions of Restraint for Floor and Roof Assemblies and for IndividualBeams". After a careful review of this guide the Steel Deck Institute determined that all interior andexterior spans of multispan deck properly attached to steel framing are restrained. Additionally, allmultiple span composite deck slabs attached to bearing walls are restrained. In fact, there is almostno realistic condition that a composite deck-slab could not be considered to be restrained - perhaps asingle span deck system which is unattached to framing or a wall in order to provide a removable slab.

16-5

© 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.

Page 5: Designing With Composite Deck

Designing with Composite DeckService Loads - Uniform & Concentrated

The composite deck of the 1950's was reviewed for service loading by using conventional reinforced concretedesign techniques. As the market for composite deck expanded, and as more deck manufacturers enteredthe business, the need for a set of design standards became interesting to the American Iron and SteelInstitute (AISI). A research program was initiated at Iowa State University and was funded by the AISI. Thisprogram resulted in the "shear bond" method of analysis which was based on results from a simple span testillustrated in the figure.

figure 5

In general, composite slabs under this testing failed in the so called "shear bond" mode which wascharacterized by a crack under one of the load beams and the concrete sliding from the crack past the steeldeck edge. The failure could be described as "brittle"; however, in most cases the bottom flange of the steeldeck achieved yield.

In the early 1980's the SDI initiated research at West Virginia University to investigate "real world" effects oncomposite behavior. End restraints from common attachments, shear studs, and pour stops were tested.Also the effects of multiple panel widths and deck continuity were examined. In 1989 multi span full scaletesting began at Virginia Polytech. The SDI supported the existing shear bond method but wanted to showthat a more ductile failure resulted with common construction practices. The SDI program resulted inconfirmation of the ductile failure premise and also quantified the effect of shear studs which were the mostinfluential of the restraints investigated. The resulting design methodology is again consistent with reinforcedconcrete methods.

The tables from the United Steel Deck, Inc. design manual show the results of the SDI work.

The SDI also sponsored research at West Virginia University to determine concentrated load distributions incomposite slabs. The results of the research are summarized in figure 6.

16-6

© 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.

Page 6: Designing With Composite Deck

Designing with Composite Deck

The SDI tables show all of the necessary information for any composite slab design problem with the exception of diaphragm -composite diaphragms are covered in the SDI Diaphragm Design Manual.

figure 6

Service Loads - Composite Slabs and Vibrations

The foremost authority on floor vibrations in steel framed buildings is Professor Thomas M. Murray of VirginiaPolytechnic Institute. The AISC has publications and software written by Professor Murray on the subject.The SDI software on floor design (composite beams) calculates the damping requirements for floor systemsand shows the result in the printout.

The Murray criterion is the formula:(In USA units)

(In international units)

16-7

© 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.

Page 7: Designing With Composite Deck

Designing with Composite DeckIf the damping (D) provided by the system is greater than the right side of the inequality, then the system willnot exhibit annoying vibrations according to most scales. D is expressed as a percent of critical, is themaximum (initial) amplitude of the system, and f is the first natural frequency. Murray's paper, FloorVibrations in Buildings (presented at the Pacific Structural Conference of 1989, Gold Coast, Queensland,Australia) provides example calculations for and f and also gives damping ranges for differentconstructions. All three variables include the slab thickness and this means that analyzing vibrations is areview process. Our concern is the deck/slab combination which will provide a starting point for the review.

Most deck/slab combinations are selected to provide a fire rating and to be unshored during construction.These constraints will provide a deck/slab that will be a good starting point for the vibration analysis. Howeveran additional check would be to keep the span depth ratio below the following limits:

Ao

Single Span NW 25Single Span LW 22Multi Span NW 27Multi Span LW 25

Where heavier gage deck (16 or 18) is used the limit of the ratio can, in most cases, be increased by addingtwo.

These limits are based on an item in Murray's paper,

"Ellingwood and Tallin (1984) have recently suggested that, to provide sufficient static stiffness against floormotions during walking, a stiffness criterion of 1 mm due to a concentrated load of 1 kN should be used. Thecriterion is recommended by them for floors used for normal human occupancy (e.g. residential, office,school), particularly for light residential floors. This criterion does not include damping, which manyresearchers believe to be the most important parameter in controlling transient vibrations. In addition, no testdata is presented to substantiate the criterion. Since the criterion is relatively new, acceptance by structuraldesigners and performance of floor systems so designed is unknown at this time."

The limits were calculated by assuming the 1 kN load was only distributed over a 12" width which would bevery conservative. Although Murray says the criterion is relatively new, it is quite familiar to some as beingclose to the "rule of thumb" used in the early sixties and is not too far off of the limits suggested in the ASCEStandard on Composite Deck Slabs.

Murray also cites Ellingwood and Tanner (1986) as recommending a stiffness criterion for commercial, i.e.shopping centers, as limiting deflection to 0.02" (1/2 mm) under a load of 450 pounds (2kN).

The previous listing of deck/slab span to depth ratios was determined by assuming a 12" load distribution.The following example shows that these limits are a good guide for commercial applications when the load isproperly distributed.

Example:The deck span is 10'; use a span to depth ratio of 27.

(use normal weight concrete).With 19 gage 2" Lok Floor shoring is not needed for continuous spans.

16-8

Ao

© 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.

Page 8: Designing With Composite Deck

Designing with Composite DeckUsing and putting the load at center span:

load distribution per foot of width

Deflection of a continuous beam with a point load at center:

Transformed l of 19 gage with 4.5" slab = 6.7 in.4 per foot of width.With which is O.K. for officeand residential.With which is O.K. for commercial.

Both Ellingwood requirements are satisfied. Any beam that is selected should be checked with the point loadat center span, but it is probably rare for either criterion to control the beam selection.

It could be argued that the deck/slab should be checked as a single span rather than as continuous.

Murray's paper does not deal with the deck/slab individually, but states that the floor system will besatisfactory if the critical damping, D, is greater than (in USA units).

is the initial amplitude from a heel drop (600 lbs.). f is the first natural frequency, 10% to 25% of thedesign live load can be included in the frequency calculation.

For the 19 gage 2" Lok Floor with the 4.5" slab assume a live load of 80 psf. In Murray's example problem heestimates the damping, D, of a particular system to be:

slab + beamhung ceilingduct workD

Partitions, not included in his example problem, could add significantly to the damping.

If the bay size were 40' x 40' a floor beam might be selected to limit the concrete deflection toConcrete + Deck = 44 psfSteel = 6 psf

16-9

© 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.

Page 9: Designing With Composite Deck

Designing with Composite Deck

Either a 21 x 44 or 18 x 50 (with reduced studs) could be used For the vibration analysis the complete(100%) composite l is used regardless of the number of studs. The Murray paper provides the requiredformulas.

With only the dead load applied:O.K.slightly greater than D

With 10% of the live load and the dead:O.K.

The Murray paper does an excellent job of providing insight and guidelines into vibration problems. However,we must realize that the analysis is not precise. Even the definition of "annoying" is fuzzy. So, from a deck/slab standpoint the span to depth ratio limits are probably the best way to check the "normal" starting point.The normal starting point is to fulfill the fire rating needs and to do the job without shoring.

Service Loads - Horizontal Loads

There are two references used in the United States for evaluating the diaphragm strength and stiffness ofcomposite deck slabs. These references are the Army, Navy, Air Force publication Seismic Design forBuildings (The Tri Service Manual) and the Steel Deck Institute, Diaphragm Design Manual, Second Edition.Part of the imput for calculating the SDI diaphragms is the weld size attaching the deck to the frame. When3/4" diameter welds and sidelap welds are used in the SDI formulas, the values obtained are close to thoseobtained using the Tri Service Manual. Both references present design strength values. The SDI Manualshows the safety factor for these concrete diaphragms as 3.25, so, to obtain the ultimate strength thetabulated SDI values can be multiplied by 3.25

The stiffness using the SDI formulas is given as G' in kips per inch. The SDI stiffness can be converted to thetri service flexibility factor, F, by the relation F = 1000/G'. In most cases composite slab diaphragms would beclassified as "rigid".

Typical SDI Design Diaphragm StrengthsSpan/Gage

8/2010/2012/1814/16

Q, plf1810180018801950

G', kips per inch2500250025402560

Note: 5/8" welds to structure - Side lap welds @ approximately 2'.

16-10

O.K.

© 2003 by American Institute of Steel Construction Inc All rights reserved

Page 10: Designing With Composite Deck

Example ProblemsThese example problems use 20 gage (t = 0.0358") 2" x 12" composite deck made from steel with a 33 ksi(minimum) yield point. The deck properties (per foot of width) have been calculated in accordance with theAmerican Iron and Steel Institute (AISI) Specifications and are: (sectionmodulus in positive bending); (section modulus in negative bending);lbs.; is the ASD interior web crippling capacity based on a 5" bearing andis the factored deck shear strength. SDI tolerances apply. The concrete properties are: density =145 pcf. The ratio of the moduli, The LRFD method is used in all of the example problems.Since the examples are "hand worked" there may be some round off differences from computer generatedanswers shown in the table.

Example Problem Number 1. Unshored Span Calculation

Calculate the maximum unshored clear span for the three span condition of the deck (20 gage 2" x12") with a 4.5" slab.The resistance factors and the load factors are provided by the AISI Specifications. The load factorsare 1.6 for concrete weight, 1.4 for construction loading of men and equipment, and 1.2 for the deckdead load. It is important to remember that these factors are for the deck under the concreteplacement loads; when the slab has cured, and the system is composite, the factors are different.

Check negative bending with two spans loaded:

Check positive bending with one span loaded with concrete and the concentrated load:

Web crippling, shear, and the interaction of bending and web crippling are checked with two spansloaded.

Check interior web crippling (note the 1/3 stress increase allowed for ASD temporary loading for webcrippling):

Check shear:

Shear alone will not control, but the interaction of shear and bending could. The AISI equation forinteractions is:

16-11

© 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.

Page 11: Designing With Composite Deck

Example Problems

Solving forCheck deflection with and with limits;

These "hand" calculations show the maximum unshored span is controlled by combined shear and bending. The computergenerated tables show a maximum unshored span of 9.27'.

Example Problem 2. Composite section properties

Calculate the composite section properties and the allowable uniform load for the deck slabcombination of Example Problem Number 1. The clear span is 9'. No negativebending reinforcing is used over the beams, so the composite slab will be a simple span.

and l are per foot of width.

Determine the "cracked" I. This calculation is the standard ASD calculation which assumes allconcrete below the neutral axis is cracked. The concrete is transformed into equivalent steel.

Moments (of areas) about the neutral axis (N.A.) are summed in order to locate the N.A.

Solving for a shows

The cracked section modulus The table printoutshows 1.26, which checks.

Determine the "uncracked" moment of inertia The concrete is again transformed into equivalentsteel.

16-12

© 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.

Page 12: Designing With Composite Deck

Example Problems

16-13

Using the top of the slab as the reference line:

and the uncracked l is:

Calculate the Unfactored (allowable) live load for the case with no studs. The clear span is 9'.The factored moment is; , where is the section modulus of the cracked section aspreviously determined, and the f factor is 0.85.

inch pounds = 35.34 inch kips. The printout shows 35.43 whichchecks within 1%.Unless negative bending reinforcement is present, the composite slab is assumed to be single span.For a single span, the Unfactored uniform (live) load is found by:

Solving for shows rounded to the nearest 5 psf.

Check the deflection if the applied load is 150 psf.With no negative reinforcing, the composite slab is a single span.

which is and should be OK

Check the factored vertical shear capacity:

Check the concrete shear control limit:

5450 < 6080 pounds. (The tabulated value is 5450 - checks)The Unfactored (allowable) live load if shear controls is found by:

So obviously shear does not control the Unfactored liveload.The number of studs required to develop 100% of the factored moment is given by:

the numerator of this equation is specific to the deckbeing used and the denominator is AISC equation 15-1. For this 20 gage 2" x 12" deck

(The printout shows 0.43 because of round off.)The inverse 1.0/0.43 = 2.33 which means a stud is required every 2.33' in order to achieve the fullfactored moment.The full factored moment is In this equation a is the depth of the concretecompression block and is given by where b is 12".a = 0.54(33000)/(0.85 x 3000 x 12) = 0.58"; d is measured from the top of the slab to the centroid ofthe deck and is 3.5".

The printout shows 48.60 inch kips, whichchecks.Since studs spaced at 1' and 2' will develop the full factored moment of48.60 inch kips, and with no studs the composite slab develops 35.43 inch kips. If studs are spaced at3' (1/3 =0.33 studs per foot) then the composite slab capacity is found by interpolation:

© 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.

Page 13: Designing With Composite Deck

Example ProblemsExample Problem 3. Point Load

This problem is designed to demonstrate how to check the ability of a composite slab to carry a2000 lb point load over an area of 4.5" x 4.5" occurring anywhere in the span. (See figure 6 for distributionformulas.)

There will be no other live load acting simultaneously, and there is no negative bending reinforcement presentover the supports, therefore we assume a single span condition.

For this example the following data obtained from problems 1 and 2 are used:

Clear Span - 9 ft.Slab Thickness - 4.5 in.

35.43 in.k48.60 in.k42 psf6.3 in4/ft

Thickness of concrete cover over the top of the deckThickness of any additional toppingTotal thickness exclusive of topping

For moment and for determining the distribution steel, put the load in the center of the span.where x is the location of the load x = l/2

However in feettherefore

Check vertical shear: Put the load one slab depth away from the beam

For MomentFor Shear

Live load moment (per foot of width) = Pl/4 = (1.6)(2000)(9/4)(12/59)(12)/1000Pl/4 = 17.54 in.k ; 1.6 is the load factor and 12/59 is the distribution factor

1.2 is the load factor.

Dead load moment

16-14

© 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.

Page 14: Designing With Composite Deck

Example ProblemsFactored resisting moment when studs are not present on the beams

Find the required distribution steel (welded wire mesh)

Assume the wire mesh is located 1/2 in above top of deck.

is the area per foot of the wire mesh which has an of 60 ksi. Ifthe bars are being investigated the would have to be adjustedaccordingly.

NOTE: in ACI but SDI uses 0.85

b=12in.Assume is the area of 6x6w1.4x1.4 mesh, which is SDI and ASCEminimum

2816 > 2582 O.K. SDI minimum welded wire mesh is sufficient

Check Deflection under concentrated load:

Put load in center of span and use concentrated load coefficients

Should be O.K.

16-15© 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.

Page 15: Designing With Composite Deck

Load Tables - 2 x 12" DECK 145 pcf concrete

The Deck Section Properties are per foot of width. The lvalue is for positive bending (in.4); t is the gage thickness ininches; w is the weight in pounds per square foot; andare the section moduli for positive and negative bending(in.3); and are the interior reaction and the shear inpounds (per foot of width); studs is the number of studsrequired per foot in order to obtain the full resisting moment,

The Composite Properties are a list of values for thecomposite slab. The slab depth is the distance from thebottom of the steel deck to the top of the slab in inches asshown on the sketch. U.L. ratings generally refer to thecover over the top of the deck so it is important to be awareof the difference in names. is the factored resistingmoment provided by the composite slab when the "full"number of studs as shown in the upper table are in place;inch kips (per foot of width). is the area of concreteavailable to resist shear, in.2 per foot of width. Vol. is thevolume of concrete in ft.3 per ft.2 needed to make up theslab; no allowance for frame or deck deflection is included.W is the concrete weight in pounds per ft.2. is the sectionmodulus of the "cracked" concrete composite slab; in.3 perfoot of width. is the average of the "cracked" and"uncracked" moments of inertia of the transformedcomposite slab; in.4 per foot of width. The transformedsection analysis is based on steel; therefore, to calculatedeflections the appropriate modulus of elasticity to use is29.5 x 106 psi. is the factored resisting moment of thecomposite slab if there are no studs on the beams (thedeck is attached to the beams or walls on which it isresting) inch kips (per foot of width). is the factoredvertical shear resistance of the composite system; it is thesum of the shear resistances of the steel deck and theconcrete but is not allowed to exceed pounds(per foot of width). The next three columns list themaximum unshored spans in feet; these values areobtained by using the construction loading requirements ofthe SDI; combined bending and shear, deflection, andinterior reactions are considered in calculating these

values. is the minimum area of welded wire fabricrecommended for temperature reinforcing in the compositeslab; square inches per foot.

DECK PROPERTIES

Gage

2220191816

t

0.02950.03580.04180.04740.0598

w

1.51.82.12.43.1

As

0.4400.5400.6300.7100.900

0.3380.4200.4900.5600.700

0.2840.3670.4450.5230.654

0.3020.3870.4580.5290.654

7141010133016802470

19902410281031803990

studs

0.360.430.510.570.72

22 g

age

20 g

age

19 g

age

18 g

age

16 g

age

COMPOSITE PROPERTIESSlabDepth4.505.005.255.506.006.256.507.007.257.504.505.005.255.506.006.256.507.007.257.504.505.005.255.506.006.256.507.007.257.504.505.005.255.506.006.256.507.007.257.504.505.005.255.506.006.256.507.007.257.50

40.2746.4449.5352.6158.7861.8764.9571.1274.2177.2948.6056.1859.9663.7571.3275.1178.9086.4790.2694.0555.8564.6869.1073.5282.3586.7791.19100.03104.44108.8662.0872.0477.0282.0091.9596.93101.91111.87116.85121.8362.0872.0477.0282.0091.9596.93101.91111.87116.85121.83

32.637.540.042.648.050.853.659.561.964.332.637.540.042.648.050.853.659.561.964.332.637.540.042.648.050.853.659.561.964.332.637.540.042.648.050.853.659.561.964.332.637.540.042.648.050.853.659.561.964.3

0.2920.3330.3540.3750.4170.4380.4580.5000.5210.5420.2920.3330.3540.3750.4170.4380.4580.5000.5210.5420.2920.3330.3540.3750.4170.4380.4580.5000.5210.5420.2920.3330.3540.3750.4170.4380.4580.5000.5210.5420.2920.3330.3540.3750.4170.4380.4580.5000.5210.542

4248515460636673767942485154606366737679424851546063667376794248515460636673767942485154606366737679

1.051.231.321.421.611.711.812.012.112.211.261.481.601.711.952.072.192.432.552.671.451.711.841.972.242.382.522.802.943.081.621.902.052.202.502.662.813.133.283.441.992.352.532.723.103.293.483.884.084.28

5.98.09.210.513.515.317.121.223.526.06.38.69.811.314.516.318.222.625.027.66.79.010.411.915.217.119.223.826.329.07.09.510.912.415.917.920.024.827.430.27.710.411.913.617.419.521.827.029.832.8

29.4034.5337.1639.8145.2147.9550.7056.2659.0761.8835.4341.6544.8448.0754.6357.9661.3168.0971.5074.9340.6947.8751.5655.3062.9066.7670.6578.5082.4686.4545.3453.3657.4861.6670.1874.5078.8587.6692.1096.5745.3453.3657.4861.6670.1874.5078.8587.6692.1096.57

50305480572059606460672069807530775079705450590061406380688071407400795081708390585063006540678072807540780083508570879060806670691071507650791081708720894091606080698074507940846087208980953097509970

Max. unshored spans, ft.1span5.825.545.415.305.095.034.974.854.794.746.816.476.326.185.945.865.795.655.585.527.657.267.096.936.656.566.486.326.246.178.427.987.797.617.307.207.116.936.856.779.589.088.858.658.298.178.077.867.777.67

2span7.837.477.317.166.896.766.656.436.326.228.978.558.368.187.857.707.567.297.177.059.769.309.098.908.548.388.237.947.817.6810.489.999.779.569.189.018.858.548.408.2611.6311.1010.8510.6310.2110.029.849.509.359.20

3span7.927.567.397.246.976.846.726.516.416.319.278.838.638.458.117.957.807.537.417.2810.089.619.399.198.838.668.508.208.077.9410.8310.3210.109.889.499.319.148.828.688.5412.0211.4711.2210.9810.5510.3510.179.829.669.50

0.0230.0270.0290.0320.0360.0380.0410.0450.0470.0500.0230.0270.0290.0320.0360.0380.0410.0450.0470.0500.0230.0270.0290.0320.0360.0380.0410.0450.0470.0500.0230.0270.0290.0320.0360.0380.0410.0450.0470.0500.0230.0270.0290.0320.0360.0380.0410.0450.0470.050

16-16© 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.

Page 16: Designing With Composite Deck

Load Tables - 2 x 12" DECK 145 pcf concrete22

gag

e20

gag

e19

gag

e18

gag

e16

gag

e22

gag

e20

gag

e19

gag

e18

gag

e16

gag

e

SlabDepth

4.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.50

40.2746.4452.6158.7864.9571.1274.2177.2948.6056.1863.7571.3278.9086.4790.2694.0555.8564.6873.5282.3591.19100.03104.44108.8662.0872.0482.0091.95101.91111.87116.85121.8362.0872.0482.0091.95101.91111.87116.85121.8329.4034.5339.8145.2150.7056.2659.0761.8835.4341.6548.0754.6361.3168.0971.5074.9340.6947.8755.3062.9070.6578.5082.4686.4545.3453.3661.6670.1878.8587.6692.1096.5745.3453.3661.6670.1878.8587.6692.1096.57

6.00

400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400305360400400400400400400375400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400

6.50

365400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400255305350400400400400400315375400400400400400400370400400400400400400400400400400400400400400400400400400400400400400400

7.00

310360400400400400400400380400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400215255295340380400400400270315365400400400400400315370400400400400400400350400400400400400400400350400400400400400400400

L, Uniform Live Loads, psf *

7.50

265305350390400400400400325380400400400400400400380400400400400400400400400400400400400400400400400400400400400400400400185220255290325360380400230270315360400400400400270315365400400400400400300355400400400400400400300355400400400400400400

8.00

230265300335370400400400285330375400400400400400330385400400400400400400370400400400400400400400370400400400400400400400160185215250280310325345200235270310350390400400230275320365400400400400260310360400400400400400260310360400400400400400

8.50

200230260295325355370385245285325365400400400400290335380400400400400400325375400400400400400400325375400400400400400400135160190215240270285295170205235270300335355370200240275315355395400400230270315360400400400400230270315360400400400400

9.00

175200230255285310325340215250285320355390400400255295335375400400400400285335380400400400400400285335380400400400400400120140165185210235245260150175205235265295310325175210240275310350365385200235275315355395400400200235275315355395400400

9.50

155175200225250275285295190220250285315345360375225260295335370400400400255295335375400400400400255295335375400400400400105120140160185205215225130155180205230260270285155185215245275305320340175210240275310350365385175210240275310350365385

10.00

13515517520022024025026017019522525028030532033020023026529533036037539522526030033537540040040022526030033537540040040090105125140160180190200115135160180205230240250135160190215245270285300155185215245275310325340155185215245275310325340

10.50

1201401551751952152252301501752002252452702852951802052352652953203353502002352653003353653854002002352653003353653854008095110125140155165175100120140160180200210225120145165190215240255265140165190220245275290305140165190220245275290305

11.00

105125140155175190200205135155175200220240255265160185210235265290300315180210240270300330345360180210240270300330345360708095110125140145155901051251401601801902001051251501701902152252351251451701952202452602701251451701a95220245260270

11.50

9511012514015517017518512014016018019521522523514516519021523526027028016019021524527029531032516019021524527029531032560708595110120130135809511012514016016517595115130150170190200210110130150175195220230245110130150175195220230245

12.00

8595110125135150155165110125140160175195205210130150170190210235245255145170195220245270280290145170195220245270280290506575859510511512070859511012514015015585100120135155170180190100115135155175195210220100115135155175195210220

area above the arrowindicates 1 STUD/FT.

area below arrowindicates NO STUDS

* The Uniform Live Loads are based onthe LRFD equationAlthough there are other loadcombinations that may requireinvestigation, this will control most ofthe time. The equation assumes thereis no negative bending reinforcementover the beams and therefore eachcomposite slab is a single span. Twosets of values are shown; is usedto calculate the uniform load when thefull required number of studs is present;

is used to calculate the load whenno studs are present. A straight lineinterpolation can be done if theaverage number of studs is betweenzero and the required number neededto develop the "full" factored moment.The tabulated loads are checked forshear controlling (it seldom does), andalso limited to a live load deflection of1/360 of the span.

An upper limit of 400 psf has beenapplied to the tabulated loads. This hasbeen done to guard against equatinglarge concentrated to uniform loads.Concentrated loads may requirespecial analysis and design to takecare of servicibility requirements notcovered by simply using a uniform loadvalue. On the other hand, for any loadcombination the values provided by thecomposite properties can be used inthe calculations.

Welded wire fabric in the requiredamount is assumed for the table values.If welded wire fabric is not present,deduct 10% from the listed loads.

Refer to the example problems for theuse of the tables.

16-17© 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.

Page 17: Designing With Composite Deck

Load Tables - 2 x 12" DECK 145 pcf concrete

Slabdepth

4.505.005.506.006.507.007.257.50

wcpsf4248546066737679

Scin3

1.261.481.711.952.192.432.552.67

lbs.54485902637968797403795081718392

Acin2

32.637.542.648.053.659.561.964.3

lavin4

6.38.611.314.518.222.625.027.6

Max. Unshored Spans, ft.1 spans

6.816.476.185.945.795.655.585.52

2 spans8.978.558.187.857.567.297.177.05

3 spans9.278.838.458.117.807.537.417.28

WWF

0.0230.0270.0320.0360.0410.0450.0470.050

1 f

oo

t2

feet

3 f

eet

no

stu

ds

SlabDepth

4.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.504.505.005.506.006.507.007.257.50

48.6056.1863.7571.3278.9086.4790.2694.0548.6056.1863.7571.3278.9086.4790.2694.0545.5752.8360.1467.4874.8482.2385.9389.6435.4341.6548.0754.6361.3168.0971.5074.93

Superimposed Live Load, psf

6.0

400400400400400400400400400400400400400400400400400400400400400400400400375400400400400400400400

6.5

400400400400400400400400400400400400400400400400400400400400400400400400315375400400400400400400

7.0

380400400400400400400400380400400400400400400400355400400400400400400400270315365400400400400400

7.5

325380400400400400400400325380400400400400400400305355400400400400400400230270315360400400400400

8.0

285330375400400400400400285330375400400400400400265305350395400400400400200235270310350390400400

8.5

245285325365400400400400245285325365400400400400230265305340380400400400170205235270300335355370

9.0

215250285320355390400400215250285320355390400400200235265300335365385400150175205235265295310325

9.5

190220250285315345360375190220250285315345360375175205235265295325340355130155180205230260270285

10.0

170195225250280305320330170195225250280305320330155180210235260285300315115135160180205230240250

10.5

150175200225245270285295150175200225245270285295140160185210230255265280100120140160180200210225

11.0

13515517520022024025526513515517520022024025526512514516518520522524025090105125140160180190200

11.5

1201401601801952152252351201401601801952152252351101301451651852052152208095110125140160165175

12.0

110125140160175195205210110125140160175195205210100115130150165180190200708595110125140150155

16-18© 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.