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AISC-LRFD93 Design Methodology Page 1 of 22

©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001

COMPOSITE BEAM DESIGN AISC-LRFD93Technical Note

General and Notation

This Technical Note provides an overview of composite beam design using theAISC-LRFD93 design specification.

AISC-LRFD93 Design MethodologyThe flowchart in Figure 1 shows the general methodology for composite beamdesign of a single beam element using the AISC-LRFD93 specification. Thenumbered boxes in the flowchart correspond to the "Box" identifiers used inthe text of this Technical Note. The flowchart is intended to convey the im-portant features of the AISC-LRFD93 design methodology. It should not beliterally construed as a flowchart for the actual computer code included in theprogram.

Box 1 - Start HereBefore you begin, note that the flowchart is set up for a single beam. Thusyou must apply the flow process shown to each beam designed. Do not con-fuse the beam that is being designed with a trial section for that beam. Thebeam that is being designed is an actual element in the model. A trial sectionis simply a beam section size that is checked for the beam that is being de-signed.

Box 2 - Design Load CombinationsThe program creates default design load combinations for composite beamdesign using the AISC-LRFD93 specification. Also any user-specified designload combinations can be interpreted and implemented. Refer to TechnicalNote Design Load Combinations Composite Beam Design AISC-LRFD93 for adescription of the AISC-LRFD93 default design load combinations.

Box 3 - Design Check LocationsThe program determines all of the design check locations for a given beam.Also refer to Technical Note Beam Unbraced Length and Design Check Loca-tions Composite Beam Design.

Composite Beam Design AISC-LRFD93 General and Notation


Figure 1: Flowchart for AISC-LRFD93 Design of a Single Beam

No

Start here to designa beam element.

Determine designload combinations.

Determine designcheck locations.

Determine checkingorder for beams.

Select a trial beamsection.

Is the sectioncompact or

noncompact?

Is there another trialsection available that

may qualify as theoptimum beam

section?Yes

No The design for thisbeam element is

complete.

Determinetransformed section

properties for fullcomposite action.

Considering fullcomposite

connection, are themaximum moment

and deflectionacceptable?

No

Is the vibrationcriteria satisfied?

No

Yes

Yes

Is there axial load onthe beam for any

design loadcombination?

Yes

Considering fullcomposite action, is the

interaction for thecombined maximum

axial and bendingstresses acceptable?

Determine price ofsection.

Calculate requiredcamber.

Is beam shearacceptable?

Yes

No

Determine if trialsection is the current

optimum section.

YesDo the required

shear connectors fiton the beam?

Determine therequired number ofshear connectors.

Determine theminimum acceptablepercent composite

connectionconsidering

combined stressesand deflection

criteria.

No

No

Yes

123

4

5

6

8

9

10

11

12 13

14

15

16

17

18

19

2120

No

Based on compactsection requirements,determine whether to

use a plastic or anelastic stressdistribution to

calculate the momentcapacity, Mn.

Yes

7



Box 4 - Checking Order for BeamsYou must determine the checking order for a beam if the beam is assigned anauto selection property. The program considers the beams in the auto selectlist in the sequence described “How the Program Optimizes Design Groups” inTechnical Note General Design Information Composite Beam Design.

Box 5 - Trial Beam SectionThe program allows you to select the next trial beam section to be checkedfor conformance with the AISC-LRFD93 specification and any additional user-defined criteria. Refer to “How the Program Optimizes Design Groups” inTechnical Note General Design Information Composite Beam Design for a de-scription of this selection process.

Box 6 - Compact and Noncompact RequirementsFor AISC-LRFD93 design of composite beams, the program requires that thebeam section be either compact or noncompact. Slender sections are not de-signed. The program checks to make sure the beam is not slender. Refer toTechnical Note Compact and Noncompact Requirements Composite Beam De-sign AISC-LRFD93 for a description of how the program checks compact andnoncompact requirements.

Box 7 - Stress Distribution Used to Calculate Moment CapacityThe program determines whether to use a plastic or an elastic stress distribu-tion when calculating the moment capacity for AISC-LRFD93 design. SeeTechnical Note Compact and Noncompact Requirements Composite Beam De-sign AISC-LRFD93 for more information.

Box 8 - Transformed Section PropertiesThe program computes the transformed section properties of the trial beamsection. If there is only positive bending in the beam, only the transformedsection properties for positive bending are calculated. Similarly, if there isonly negative bending in the beam, only the transformed section propertiesfor negative bending are calculated. If there is both positive and negativebending in the beam, transformed section properties for both positive andnegative bending are calculated.

Refer to Technical Note Effective Width of the Concrete Slab Composite BeamDesign for a description of how the program calculates the effective width ofthe concrete slab for the composite beam. Refer to Technical NoteTransformed Section Moment of Inertia Composite Beam Design AISC-ASD89



for description of how the program calculates the transformed section proper-ties.

In AISC-LRFD93 design, the transformed section properties are used for cal-culating deflection, and they are used when the moment capacity is deter-mined based on an elastic stress distribution; that is, when the web is non-compact.

Box 9 - Initial Moment Capacity and Deflection CheckThe program checks that the moment capacity of the beam using full com-posite connection is greater than or equal to the applied factored moment. Italso checks if the deflection using full composite connection is acceptable. Themain purpose of this check is to quickly eliminate inadequate beam sections.Refer to Technical Note Bending and Deflection Checks Composite Beam De-sign AISC-LRFD93 for more information.

Box 10 - Vibration Criteria CheckThe program calculates the vibration parameters. If vibration is specified tobe used as one of the tools for selecting the optimum beam size, the programchecks if the vibration parameters satisfy the specified limits. If the vibrationcheck is satisfied, the design using the current trial section continues; other-wise, the design for this section is terminated. For more detailed informationon the vibration checks, refer to Technical Note Beam Vibration CompositeBeam Design.

Box 11 - Axial LoadThe program checks if axial load exists on the beam for any design load com-bination. If so, the axial load capacity is determined and the interaction issubsequently checked, as indicated in box 14. If there is no axial load on thebeam, the axial capacity is not determined and the interaction check (box 14)is skipped. Refer to Technical Note Compact and Noncompact RequirementsComposite Beam Design AISC-LFRD93 for a description of how the programcalculates axial load capacity for AISC-LRFD93.

Box 12 - P-M Interaction CheckIf there is axial load on the beam, the program checks the P-M interactionequations. If the interaction check is satisfied, the design using the currenttrial section continues; otherwise, the design for this section is terminated.Refer to Technical Note Moment Capacity for Steel Section Alone CompositeBeam Design AICS-ASD89 for more information.



Box 13 - Partial Composite ActionA significant amount of design is performed at this point in the process. Theprogram determines the smallest amount of composite connection for whichthe beam is adequate. Both flexural checks and deflection checks are made atthis point. In addition, the program considers axial load on the beam if it ex-ists and is specified to be considered. Flexural checks are also made for theconstruction loads.

For more information refer to Technical Note Partial Composite Connectionwith a Plastic Stress Distribution Composite Beam Design AISC-LRFD93 andTechnical Note Bending and Deflection Checks Composite Beam Design AISC-LRFD93. Also refer to Technical Note Elastic Stresses with Partial CompositeConnection Composite Beam Design AISC-ASD89.

Box 14 - Required Number of Shear ConnectorsThe program calculates the required number of shear connectors on the beamand the distribution of those shear connectors. For more information refer toTechnical Note Shear Connectors Composite Beam Design AISC-LRFD93. Alsorefer to Technical Note Distribution of Shear Studs on a Composite BeamComposite Beam Design and Technical Note Number of Shear Studs that Fit ina Composite Beam Segment Composite Beam Design. Finally refer to Techni-cal Note Effective Width of Concrete Slab Composite Beam Design for limita-tions associated with composite beams and formed metal deck.

Box 15 - Checking if Shear Connectors Fit on the BeamThe program checks if the number of shear connectors calculated (box 14)actually fit on the beam. For more information refer to Technical Note Numberof Shear Studs that Fit in a Composite Beam Segment Composite Beam De-sign. If the connectors fit on the beam, the design using the current trial sec-tion continues; otherwise, the design for this section is terminated.

Box 16 - Beam ShearThe program checks the beam shear for the reactions at each end of thebeam. See Technical Note Beam Shear Capacity Composite Beam DesignAISC-LRFD93 for more information. If the beam shear check is satisfied, thedesign using the current trial section continues; otherwise, the design for thissection is terminated.



Box 17 - CamberThe program determines the camber for the beam, if it is specified to havecamber. Refer to Technical Note Beam Deflection and Camber CompositeBeam Design for more information.

Box 18 - Section PriceDetermination of price of section applies only when price has been specifiedby the user as the method of selecting the optimum section. In such cases,the program determines the price of the current beam. Refer to “Using Priceto Select Optimum Beam Sections” in Technical Note General Design Infor-mation Composite Beam Design for more information.

Box 19 - Check if a Section is the Current Optimum SectionThis check applies only if price has been specified as the method of selectingthe optimum section. The program checks if the price of the current trialbeam is less than that of any other beam that satisfied the design criteria. Ifso, the current beam section becomes the current optimum beam section.Refer to “Using Price to Select Optimum Beam Sections” in Technical NoteGeneral Design Information Composite Beam Design for more information

If the optimum beam size is to be selected by weight, this check becomes ir-relevant because the beams are checked in order from the lightest to theheaviest beams and thus the first beam found to work is the optimum beam.

Box 20 - Checking for Possible Additional Optimum SectionsThis check applies only if the beam has been assigned an auto selection prop-erty. The program checks if another section in the auto selection list mightqualify as the optimum beam section. Refer to the section titled “How theProgram Optimizes Design Groups" in Technical Note General Design Infor-mation Composite Beam Design for more information.

Box 21 - Design CompleteAt this point, the design for this particular beam element is complete. If thebeam has been assigned an auto selection property, the current optimumsection, assuming one has been found, is the optimum section for the beam.The program will indicate if no beam with an optimum section is included inthe auto selection list.


Notation Page 7 of 22

If the beam is assigned a regular, non-auto selection property, the design forthat beam property will be provided or the beam will be indicated to be in-adequate.

There are some additional aspects included in the composite beam designmodule that are not directly addressed in the flowchart shown in Figure 1.Those include designing beams in groups and designing beams with partiallength cover plates.

For more information on the design by group feature, refer to How the Pro-gram Optimizes Design Groups in Technical Note General Design InformationComposite Beam Design.

When a beam has a partial length cover plate, the program checks not onlythe design at the point of the maximum moment (box 8 of Figure 1), but alsothe design at the point of the largest moment where the cover plate does notexist.

NotationAbare Area of the steel beam (plus coverplate) alone, in2.

Ac Area of concrete within slab effective width that is above theelastic neutral axis (ENA) for full composite action, in2. Forbeams with metal deck ribs running perpendicular to the beamspan, only the concrete above the metal deck and above theENA is included. For beams with metal deck ribs running par-allel to the beam span, the concrete above the metal deck andthe concrete in the deck ribs are included if it is above theENA. This value may be different on the left and right sides ofthe beam.

Af Area of compression flange, in2.

Ag Gross area of steel member, in2.

As Area of rolled steel section, or the total area (excluding coverplate) of a user-defined steel section, in2. Note that the totalarea of a user-defined steel section is found by summing thearea of the top flange, web and bottom flange.



ASb Initial displacement amplitude of a single beam resulting froma heel drop impact, in.

Asc Cross-sectional area of a shear stud connector, in2.

Atr Area of an element of the composite steel beam section, in2.

Aw Area of the web equal to the overall depth d times the webthickness tw, in2.

B1 Moment magnifier, unitless.

Cb Bending coefficient dependent on moment gradient, unitless.

Cbot Cope depth at bottom of beam, in.

CC1 Compressive force in concrete slab above metal deck, kips. Ifno metal deck exists, this is the compressive force in the slab.

CC2 Compressive force in concrete that is in the metal deck ribs,kips. This force only occurs when the metal deck ribs are ori-ented parallel to the steel beam, and the plastic neutral axis isbelow the top of the metal deck.

CFT Compressive force in the top flange of the steel beam, kips.This force only occurs when the plastic neutral axis is belowthe top of the beam.

CKT Compressive force in the top fillets of a rolled steel beam,kips. This force only occurs when the plastic neutral axis isbelow the bottom of the top flange of the beam.

CR Compressive force in the slab rebar, kips. This force only oc-curs when the plastic neutral axis is below the rebar, and youhave specified the rebar to be considered.

Ctop Cope depth at top of beam, in.

Cw Warping constant for a section, in6.

CWeb Compressive force in the steel beam web, kips. This force only



occurs when the plastic neutral axis is within the beam web.

D Damping ratio, percent critical damping inherent in the floorsystem, unitless.

Ec Modulus of elasticity of concrete slab, ksi. Note that this couldbe different on the left and right sides of the beam. Also notethat this is different for stress calculations and deflection cal-culations.

Es Modulus of elasticity of steel, ksi.

Fcr Critical stress for columns in compression, ksi.

FL Smaller of (Fyf - Fr) or Fyw, ksi.

Fr Compressive residual stress in flange, ksi. Taken as 10 kipsper square inch for rolled shapes and 16.5 kips per squareinch for welded shapes, converted to the appropriate.

Fu Minimum specified tensile strength of structural steel or shearstud, ksi.

Fy Minimum specified yield stress of structural steel, ksi.

Fycp Minimum specified yield stress of cover plate, ksi.

Fyf-bot Minimum specified yield stress of steel in beam bottom flange,ksi.

Fyf-top Minimum specified yield stress of steel in beam top flange, ksi.

Fyw Minimum specified yield stress of steel in beam web, ksi.

G Shear modulus of elasticity of steel, ksi.

Hs Length of shear stud connector after welding, in.

Ieff Effective moment of inertia of a partially composite beam, in4.

IO Moment of inertia of an element of the composite steel beamsection taken about its own center of gravity, in4.



Is Moment of inertia of the steel beam alone plus cover plate ifapplicable, in4.

Itr Transformed section moment of inertia about elastic neutralaxis of the composite beam, in4.

Ix, Iy Moment of inertia about the x and y axes of the beam respec-tively, in4.

Iyc Moment of inertia of compression flange about the y-axis, or ifthere is both positive and negative bending in the beam, thesmaller moment of the two flanges, in4.

J Torsional constant for a section, in4.

K Effective length factor for prismatic member, unitless.

Kf A unitless coefficient typically equal to 1.57 unless the beam isthe overhanging portion of a cantilever with a backspan, inwhich case Kf is as defined in Figure 1 of Technical Note BeamVibration Composite Beam Design, or the beam is a cantileverthat is fully fixed at one end and free at the other end, inwhich case Kf is 0.56.

L Center-of-support to center-of-support length of the beam, in.

Lb Laterally unbraced length of beam; length between points thatare braced against lateral displacement of the compressionflange or braced against twist of the cross section, in.

Lc Limiting unbraced length for determining allowable bendingstress, in.

LCBS Length of a composite beam segment, in. A composite beamsegment spans between any of the following: 1) physical endof the beam top flange; 2) another beam framing into thebeam being considered; 3) physical end of concrete slab.Figure 1 of Technical Note Distribution of Shear Studs on aComposite Beam Composite Beam Design illustrates sometypical cases for LCBS.



Lcsc Length of channel shear connector, in.

Lp Limiting laterally unbraced length of beam for full plasticbending capacity, uniform moment case (Cb = 1.0), in.

Lr Limiting laterally unbraced length of beam for inelastic lateral-torsional buckling, in.

Ls Distance between two points used when the program is calcu-lating the maximum number of shear studs that can fit be-tween those points, in. If the deck span is oriented parallel tothe beam span and at least one of the points is at the end ofthe beam, Ls is taken as the distance between the two pointsminus 3 inches.

L1 Distance from point of maximum moment to the closest pointof zero moment or physical end of beam top flange, or physi-cal end of concrete slab, in.

L2 Distance from point of maximum moment to the nearest pointof zero moment or physical end of beam top flange, or physi-cal end of concrete slab measured on the other side of thepoint of maximum moment from the distance L1, in.

L3 Distance from point load to the point of zero moment, physicalend of beam top flange, or physical end of concrete slabmeasured on the appropriate side of the point load, in. If thepoint load is located on the left side of the point of maximummoment, the distance is measured from the point load towardthe left end of the beam. If the point load is located on theright side of the point of maximum moment, the distance ismeasured toward the right end of the beam.

M Moment, kip-in.

MA Absolute value of moment at the quarter point of the unbracedbeam segment, kip-in.

MB Absolute value of moment at the centerline of the unbracedbeam segment, kip-in.



MC Absolute value of moment at the three-quarter point of theunbraced beam segment, kip-in.

Mcr Elastic buckling moment, kip-in.

Mmax Maximum positive moment for a beam, kip-in.

Mn Nominal flexural strength, kip-in.

Mp Plastic bending moment, kip-in.

Mpt load Moment at the location of a point load, kip-in.

Mr Limiting buckling moment, Mcr, when λ = λr and Cb = 1.0, kip-in.

Mu Required flexural strength, kip-in.

MPFconc Maximum possible force that can be developed in the concreteslab, and rebar in slab, if applicable, kips.

MPFsteel Maximum possible force that can be developed in the steelsection, and cover plate, if applicable, kips.

NCBS The number of uniformly distributed shear connectors the pro-gram specifies for a composite beam segment, unitless.

Neff The effective number of beams resisting the heel drop impact,unitless.

Nr Number of shear stud connectors in one rib at a beam inter-section; not to exceed three in computations, although morethan three studs may be installed, unitless.

N1 Required number of shear connectors between the point ofmaximum moment and an adjacent point of zero moment (orend of slab), unitless.

N2 Required number of shear connectors between a point loadand a point of zero moment (or end of slab), unitless.

NR Available number of metal deck ribs between two points,



unitless.

NSmax Maximum number of shear stud connectors between twopoints a distance of Ls apart, unitless.

P Axial load, kips.

Pe Euler buckling load, kips.

Pn Nominal axial strength (tension or compression), kips.

Pnc Nominal compressive axial strength, kips.

Pnt Nominal tensile axial strength, kips.

PO Heel drop force, kips. This force is taken as 0.6 kips.

Pu Required axial strength (tension or compression), kips.

Py Axial compressive yield strength , kips.

PCC Percent composite connection, unitless. The exact formula forthis term is code dependent.

Qn Nominal strength of one shear connector (shear stud or chan-nel), kips.

R Wiss-Parmelee rating factor, unitless.

RF Reduction factor for horizontal shear capacity of shear con-nectors, unitless.

RSmax Maximum number of rows of shear stud connectors that can fitbetween two points a distance of Ls apart, unitless.

Sed Minimum edge distance from midheight of a metal deck rib tothe center of a shear stud, in. For an example see paragraph1b of the section entitle Solid Slab or Deck Ribs Oriented Par-allel to Beam Span in Technical Note Number of Shear Studsthat Fit in a Composite Beam Segment Composite Beam De-sign. The default value is 1 inch. You can change this in thepreferences and the overwrites.



Seff Effective section modulus of a partially composite beam re-ferred to the extreme tension fiber of the steel beam section(including cover plate), in3.

Sr Center-to-center spacing of metal deck ribs, in.

Ss Section modulus of the steel beam alone plus cover plate ifapplicable referred to the tension flange, in3.

St-eff The section modulus for the partial composite section referredto the top of the equivalent transformed section, in3.

Stop Section modulus for the fully composite uncracked trans-formed section referred to the extreme compression fiber, in3.

Str Section modulus for the fully composite uncracked trans-formed section referred to the the extreme tension fiber of thesteel beam section (including cover plate), in3.

Sx, Sy Section modulus about the x and y axes of the beam respec-tively, in3.

Sxc Section modulus about the x axis of the outside fiber of thecompression flange, in3.

Sxt Section modulus about the x axis of the outside fiber of thetension flange, in3.

SRmax Maximum number of shear stud connectors that can fit in onerow across the top flange of a composite beam, unitless.

TB Tensile force in a composite rolled steel beam when the plasticneutral axis is above the top of the beam, kips.

TCP Tensile force in the cover plate, kips.

TFB Tensile force in the bottom flange of a steel beam, kips.

TFT Tensile force in the top flange of a steel beam, kips.

TKB Tensile force in the bottom fillets of a rolled steel beam, kips.



TKT Tensile force in the top fillets of a rolled steel beam, kips.

TWeb Tensile force in the web of a steel beam, kips.

V Shear force, kips.

Vn Nominal shear strength, kips.

Vu Required shear strength, kips.

W Total load supported by the beam, kips. You specify a loadcombination that the program uses to determine this weight.

X1 Beam buckling factor defined by AISC-LRFD93 equation F1-8.

X2 Beam buckling factor defined by AISC-LRFD93 equation F1-9.

Z Plastic section modulus of the steel beam alone plus coverplate if applicable, in3.

Zx, Zy Plastic section modulus about the x and y axes of the beamrespectively, in3.

a clear distance between transverse stiffeners, in.

ar For a user-defined section, ratio of web area to flange area,but not more than 10, unitless.

a1 Distance from top of concrete to bottom of effective concretefor partial composite connection when bottom of effective con-crete is within the slab above the metal deck (or there is asolid slab with no metal deck), in.

a2 Distance from top of metal deck to bottom of effective con-crete for partial composite connection when bottom of effec-tive concrete is within the height of the metal deck, in.

a3 Distance from top of metal deck to elastic neutral axis whenelastic neutral axis is located in slab above metal deck, in.

a4 Distance from top of concrete slab to elastic neutral axis whenelastic neutral axis is located in slab above metal deck, in.



a5 Distance from bottom of metal deck to elastic neutral axiswhen elastic neutral axis is located within height of metaldeck, in.

a6 Distance from top of metal deck to elastic neutral axis whenelastic neutral axis is located within height of metal deck, in.

b Width, in.

bcp Width of steel cover plate, in.

beff Effective width of concrete flange of composite beam, in.

bf Width of flange of a rolled steel beam, in.

bf-bot Width of bottom flange of a user-defined steel beam, in.

bf-top Width of top flange of a user-defined steel beam, in.

d Depth of steel beam from outside face of top flange to outsideface of bottom flange, in.

davg Average depth of concrete slab, including the concrete in themetal deck ribs, in.

dsc Diameter of a shear stud connector, in.

f First natural frequency of the beam in cycles per second.

f'c Specified compressive strength of concrete, ksi.

g Acceleration of gravity, in/seconds2.

h Clear distance between flanges less the fillet or corner radiusat each flange for rolled shapes and clear distance betweenflanges for other shapes, in.

hc For rolled shapes, twice the distance from the beam centroidto the inside face of the compression flange less the fillet orcorner radius. In a user-defined section, twice the distancefrom the centroid of the steel beam alone, not including thecover plate even if it exists, to the inside face of the compres-



sion flange, in.

hr Height of metal deck rib, in.

k Distance from outer face of a rolled beam flange to the webtoe of a fillet, in.

kc Unitless factor used in AISC-LRFD93 Table B5.1, 0.35 ≤ kc ≤0.763.

kdepth Distance from inner face of a rolled beam flange to the webtoe of a fillet, in.

kwidth Width of idealized fillet of rolled beam section, in.

l Controlling laterally unbraced length of a member, in.

l22, l33 Laterally unbraced length of a member for buckling about thelocal 2 and 3 axes of the beam respectively, in.

lx, ly Laterally unbraced length of a member for buckling about thex and y axes of the beam respectively, in.

m For a user-defined section, ratio of web yield stress to flangeyield stress, unitless.

r Governing radius of gyration, in.

rd Distance from top of beam flange to bottom of metal deck, in.

r22, r33 Radius of gyration about the local 2 and 3 axes of the beamrespectively, in.

r T Radius of gyration of a section comprising the compressionflange plus one-third of the compression web area taken aboutan axis in the plane of the web, in.

rx, ry Radius of gyration about the x and y axes of the beam respec-tively, in.

ryc Radius of gyration of the compression flange about the y-axis,in.



sb Beam spacing, in.

t Thickness, in.

tc Thickness of concrete slab, in. If there is metal deck, this isthe thickness of the concrete slab above the metal deck.

tcp Thickness of cover plate, in.

tf Thickness of steel beam flange, in.

tf-bot Thickness of bottom flange of a user-defined steel beam, in.

tf-top Thickness of top flange of a user-defined steel beam, in.

tO Time to the maximum initial displacement of a single beamresulting from a heel drop impact, seconds.

tw Thickness of web of user-defined steel beam, in.

wa Additional metal deck rib width, in. This term is used to specifymetal deck ribs that are split over the beam. The width wa isadded to the width wr when determining the width of deck ribavailable for shear studs.

wc Unit weight per volume of concrete, pounds/feet3.

wd Unit weight per area of metal deck, ksi.

wr Average width of metal deck rib, in.

x1 The assumed gap distance from the supporting beam or col-umn flange to the end of the beam flange, in. The defaultvalue for this length is 0.5 inches.

y Distance from the bottom of the bottom flange of the steelbeam section to the elastic neutral axis of the fully compositebeam, in.

ybare The distance from the bottom of the bottom flange of the steelbeam to the neutral axis of the noncomposite steel beam pluscover plate if applicable, in.



ye The distance from the elastic neutral axis of the bare steelbeam alone (plus cover plate, if applicable) to the elastic neu-tral axis of the fully composite beam, in.

yeff The distance from the bottom of the bottom flange of the steelbeam to the neutral axis of the partially composite beam, in.

y1 Distance from the bottom of the bottom flange of the steelbeam section to the centroid of an element of the compositebeam section, in.

y2 Distance from the top of the top flange of the steel beam sec-tion to the plastic neutral axis when the plastic neutral axis iswithin the beam top flange, in.

y3 Distance from the bottom of the top flange of a rolled steelbeam section to the plastic neutral axis when the plastic neu-tral axis is within the fillets, in.

y4 For a rolled steel beam, the distance from the bottom of thetop fillet to the plastic neutral axis when the plastic neutralaxis is within the beam web, in. For a user-defined steel beam,the distance from the bottom of the top flange to the plasticneutral axis when the plastic neutral axis is within the beamweb, in.

yp Distance from the plastic neutral axis of composite section tothe bottom of the beam bottom flange (not cover plate), in.

z Distance from the elastic neutral axis of the steel beam (pluscover plate, if it exists) alone to the top of the concrete slab,in. Note that this distance may be different on the left andright sides of the beam.

zp Distance from the plastic neutral axis of composite section tothe top of the concrete slab, in. Note that this distance may bedifferent on the left and right sides of the beam.

ΣA Sum of the areas of all of the elements of the steel beam sec-tion, in2.



ΣAtr Sum of the areas of all of the elements of the composite steelbeam section, in2.

Σ(Atry1) Sum of the product Atr times y1 for all of the elements of thecomposite steel beam section, in3.

Σ(Ay1) Sum of the product A times y1 for all of the elements of thesteel beam section, in3.

Σ(Ay12) Sum of the product A times y1

2 for all of the elements of thesteel beam section, in4.

Σ(Atry12)= Sum of the product Atr times y1

2 for all of the elements of thecomposite steel beam section, in4.

ΣIO Sum of the moments of inertia of each element of the com-posite steel beam section taken about the center of gravity ofthe element, in4.

ΣQn Sum of nominal strength of shear connectors (shear stud orchannel) between point considered and point of zero moment,kips.

ΣQn-pcc Required nominal strength of shear connectors (shear stud orchannel) between point considered and point of zero momentfor partial composite connection percentage, PCC, kips.

ΣQn-100 Required nominal strength of shear connectors (shear stud orchannel) between point considered and point of zero momentfor full (100%) composite action, kips.

β Unitless factor used in calculating number of shear studs be-tween a point load and a point of zero moment equal to Str/Ss

for full composite connection and Seff/Ss for partial compositeconnection.

φ Resistance factor, unitless.

φb Resistance factor for bending in a noncomposite beam,unitless. The default value is 0.9.



φbcc Resistance factor applied to concrete for bending in a compos-ite section, unitless. Note that this is a resistance factor that isnot defined by AISC. It is included by CSI to give you morecontrol over the strength of the composite section. The defaultvalue is 1.0.

φbcne Resistance factor for negative bending in a composite beamwhen Mn is determined from an elastic stress distribution,unitless. The default value is 0.9.

φbcnp Resistance factor for negative bending in a composite beamwhen Mn is determined from a plastic stress distribution,unitless. The default value is 0.85.

φbcpe Resistance factor for positive bending in a composite beamwhen Mn is determined from an elastic stress distribution,unitless. The default value is 0.9.

φbcpp Resistance factor for positive bending in a composite beamwhen Mn is determined from a plastic stress distribution,unitless. The default value is 0.85.

φbcs Resistance factor applied to steel for bending in a compositesection, unitless. Note that this is a resistance factor that isnot defined by AISC. It is included by CSI to give you morecontrol over the strength of the composite section. The defaultvalue is 1.0.

φbs Resistance factor for strength of shear studs, unitless. Notethat this is a resistance factor that is not defined by AISC. It isincluded by CSI to give you more control over the strength ofthe composite section. The default value is 1.0.

φc Resistance factor for axial compression, unitless. The defaultvalue is 0.85.

φt Resistance factor for axial tension, unitless. The default valueis 0.9.

φv Resistance factor for beam shear, unitless. The default value is



0.9.

λ Controlling slenderness parameter, unitless. It is the minoraxis slenderness ratio Lb/ry for lateral-torsional buckling. It isthe flange width-thickness ratio b/t as defined in AISC LRFDManual Specification section B5.1 for flange local buckling. It isthe web depth-thickness ratio h/tw as defined in AISC LRFDManual Specification section B5.1 for web local buckling.

λc Column slenderness parameter, unitless.

λp Limiting slenderness parameter for a compact element, largestvalue of λ for which Mn = Mp, unitless.

λr Limiting slenderness parameter for a noncompact element,largest value of λ for which buckling is inelastic, unitless.

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D 2001 COMPOSITE BEAM DESIGN AISC-LRFD93 Technical Note General and Notation AISC ...extras.springer.com/2003/978-3-322-80049-7/INFORMATION... · AISC-LRFD93 Design Methodology Page