E-TN-CBD-BS-5950-90-001

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BS 5950-90 Design Methodology Page 1 of 19 ©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA SEPTEMBER 2002 COMPOSITE BEAM DESIGN BS 5950-90 Technical Note General and Notation This Technical Note provides an overview of composite beam design using the BS 5950-90 design specification (BSI 1990a, 1990b). The various notations used in this series of Technical Notes are described herein. English as well as SI and MKS metric units can be used for input. But the code is based on Newton-Millimeter-Second units. For simplicity, all equations and descriptions presented in this series of Technical Notes correspond to New- ton-Millimeter-Second units unless otherwise noted. BS 5950-90 Design Methodology The flowchart in Figure 1 shows the general methodology for composite beam design of a single beam element using the BS 5950-90 specification. The numbered boxes in the flowchart correspond to the "Box" identifiers used in the text of this Technical Note. The flowchart is intended to convey the im- portant features of the BS 5950-90 design methodology. It should not be lit- erally construed as a flowchart for the actual computer code included in the program. Box 1 - Start Here Before you begin, note that the flowchart is set up for a single beam. Thus you 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. The beam that is being designed is an actual element in the model. A trial section is simply a beam section size that is checked for the beam that is being de- signed. Box 2 - Design Load Combinations The program creates default design load combinations for composite beam design using the BS 5950-90 specification. Also any user-specified design load combinations can be interpreted and implemented. Refer to Technical Note Design Load Combinations Composite Beam Design BS 5950-90 for a de- scription of the BS 5950-90 default design load combinations.

Transcript of E-TN-CBD-BS-5950-90-001

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BS 5950-90 Design Methodology Page 1 of 19

©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA SEPTEMBER 2002

COMPOSITE BEAM DESIGN BS 5950-90

Technical NoteGeneral and Notation

This Technical Note provides an overview of composite beam design using theBS 5950-90 design specification (BSI 1990a, 1990b). The various notationsused in this series of Technical Notes are described herein.

English as well as SI and MKS metric units can be used for input. But the codeis based on Newton-Millimeter-Second units. For simplicity, all equations anddescriptions presented in this series of Technical Notes correspond to New-ton-Millimeter-Second units unless otherwise noted.

BS 5950-90 Design MethodologyThe flowchart in Figure 1 shows the general methodology for composite beamdesign of a single beam element using the BS 5950-90 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 BS 5950-90 design methodology. It should not be lit-erally 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 BS 5950-90 specification. Also any user-specified design loadcombinations can be interpreted and implemented. Refer to Technical NoteDesign Load Combinations Composite Beam Design BS 5950-90 for a de-scription of the BS 5950-90 default design load combinations.

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Figure 1: Flowchart for BS 5950-90 Design of a Single Beam

11 12

19

No

Start here to designa beam element.

Determine designload combinations.

Determine designcheck locations.

Determine checkingorder for beams.

Select a trial beamsection.

Is the sectionplastic, compact or

semi-compact?

Yes No

The design for thisbeam element is

complete.

Considering fullcomposite

connection, are themaximum moment

and deflectionacceptable?

No

Is the vibrationcriteria satisfied?

No

Yes

Yes

Considering fullcomposite action, is

the interaction for thecombined stresses

acceptable?

Determine price ofsection.

Calculate requiredcamber.

Is beam shearacceptable?

YesNo

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 13

14

15

16

17

18

20

On the basis ofsection class requirements,

determine whetherto use a plastic oran elastic stress

distribution tocalculate the

moment capacity,Mn.

Yes

7

Determinetransformed section

properties for fullcomposite action.

Is there another trialsection available that

may qualify as theoptimum beam

section?

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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 Composite Beam Design.

Box 4 - Checking Order for BeamsYou must determine the checking order for a beam section if the beam is as-signed an auto selection property. The program considers the beam sectionsin the auto select list in the sequence described in “How the Program Opti-mizes Design Groups” in Technical Note General Design Information Compos-ite Beam Design.

Box 5 - Trial Beam SectionThe program allows you to select the next trial beam section to be checkedfor conformance with the BS 5950-90 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 - Section Class RequirementsFor BS 5950-90 design of composite beams, the program requires that thebeam section be Class 1 (Plastic), Class 2 (Compact) or Class 3 (Semi-Compact). Class 4 (Slender) sections are not designed. The program checksto make sure the beam is not Slender. Refer to Technical Note Classificationof Sections Composite Beam Design BS 5950-90 for a description of how theprogram classifies the sections.

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 BS 5950-90 design. See Tech-nical Note Classification of Sections Composite Beam Design BS 5950-90 formore 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.

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Refer to Technical Note Effective Width of the Concrete Slab Composite BeamDesign BS 5950-90 for a description of how the program calculates the effec-tive width of the concrete slab for the composite beam. Refer to TechnicalNote Transformed Section Moment of Inertia Composite Beam Design BS5950-90 for description of how the program calculates the transformed sec-tion properties.

In BS 5950-90 design, the transformed section properties are used for calcu-lating deflection, and they are used when the moment capacity is determinedbased on an elastic stress distribution.

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 Strength Checks Composite Beam Design BS 5950-90and Beam Deflection Checks Composite Beam Design BS 5950-90 for moreinformation.

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 BS 5950-90.

Box 11 - P-M Interaction CheckIf there is axial load on the beam, the program checks the P-M interactionequations for non-composite sections. If the interaction check is satisfied, thedesign using the current trial section continues; otherwise, the design for thissection is terminated. Refer to Technical Note Moment Capacity for Steel Sec-tion Alone Composite Beam Design BS 5950-90 for more information.

Box 12 - Partial Composite ActionA significant amount of design is performed at this point in the process. Theprogram determines the smallest amount of composite connection for which

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the beam is adequate. Both flexural checks and deflection checks are made atthis point. Flexural checks are also made for the construction loads.

For more information refer to Technical Notes Partial Composite ConnectionComposite Beam Design BS 5950-90, Strength Checks Composite Beam De-sign BS 5950-90, and Beam Deflection Checks Composite Beam Design BS5950-90.

Box 13 - 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 BS 5950-90. 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 BS 5950-90 for limitations associated with composite beams and formed metal deckand Technical Note Transverse Reinforcement Composite Beam Design BS5950-90 for checking longitudinal shear stress in concrete.

Box 14 - Checking if Shear Connectors Fit on the BeamThe program checks if the number of shear connectors calculated actually fiton the beam. For more information refer to Technical Note Number of ShearStuds that Fit in a Composite Beam Segment Composite Beam Design. If theconnectors fit on the beam, the design using the current trial section contin-ues; otherwise, the design for this section is terminated.

Box 15 - Beam ShearThe program checks the beam shear for the reactions at each end of thebeam. See Technical Note Beam Shear Capacity Composite Beam Design BS5950-90 for more information. If the beam shear check is satisfied, the de-sign using the current trial section continues; otherwise, the design for thissection is terminated.

Box 16 - CamberThe program determines the camber for the beam, if it is specified to havecamber. Refer to Technical Note Camber Calculation Composite Beam DesignBS 5950-90 for more information.

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Box 17 - 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 18 - 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 19 - 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 20 - 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.

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.

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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.

NotationAbare Area of the steel beam (plus cover plate), mm2.

Ac Area of concrete within slab effective width, mm2. For beamswith metal deck ribs running perpendicular to the beam span,only the concrete above the metal deck is included. For beamswith metal deck ribs running parallel to the beam span, theconcrete above the metal deck and the concrete in the deckribs are included. This value may be different on the left andright sides of the beam.

Ag Gross area of steel member, mm2.

As Area of rolled steel section, or the total area (excluding coverplate) of a user-defined steel section, mm2. 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, mm. Used in vibration analysis.

Asc Cross-sectional area of a shear stud connector, mm2.

Asv Area of transverse reinforcement with appropriate anchoringrequired within a spacing, mm2/mm.

Av2, Av3 Major and minor shear areas, mm2.

B Actual physical width of the concrete flange, mm. Also fullwidth of the steel flange, mm.

Bcp Width of steel cover plate, mm.

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Be Effective width of concrete flange of composite beam, mm.

B'e Effective width of concrete flange of composite beam inequivalent steel stiffness, mm.

B''e Effective width of concrete flange of composite beam inequivalent steel stiffness considering partial connection, mm.

Bf Width of the flange of a rolled steel beam, mm.

Bbot Width of bottom flange of a user-defined steel beam, mm.

Btop Width of top flange of a user-defined steel beam, mm.

Cbot Cope depth at bottom of beam, mm.

Ctop Cope depth at top of beam, mm.

D Depth of steel beam from outside face of top flange to outsideface of bottom flange, mm.

Dp Height of metal deck rib, mm.

Dr Damping ratio, percent critical damping inherent in the floorsystem, unitless. Used in vibration analysis.

Ec Modulus of elasticity of concrete slab, N/mm2. Note that thiscould be different on the left and right sides of the beam. Alsonote that this is different for stress calculations and deflectioncalculations.

Es Modulus of elasticity of steel, N/mm2.

Fconc,max The maximum concrete force that can be developed in a con-crete deck based on a concrete design strength of 0.45 fcu.Ribs are included if the concrete slab is ribbed, and if the ribsrun parallel to the beam, N.

Fsteel,max The maximum steel axial force that can be developed in acomposite beam based on the steel design strength py, N.

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Fstud, Fc The design concrete force that can be generated in a concretedeck considering the effect of composite shear connection, N.

Fp The value of Fstud or Fc for full composite connection, N.

Fv Required shear strength, N.

Fv2, Fv3 Major and minor shear loads, N.

G Shear modulus of elasticity of steel, N/mm2.

H Warping constant, mm6.

I22, I33 Minor and major moment of inertia, respectively, mm4.

Ibare Moment of inertia of a steel section, including the cover plateif present, mm4. Ibare becomes equal to Is if there is no coverplate welded to the beam.

Ieff Effective moment of inertia of a partially composite beam,mm4.

Ieff, 100 Effective moment of inertia based on 100% composite con-nection, i.e., for full composite connection, mm4.

Ig Transformed section moment of inertia about the elastic neu-tral axis of the gross uncracked section, mm4. If the neutralaxis remains within the steel section, Ip for full compositeshear connection becomes equal to Ig.

In Transformed section moment of inertia for negative momentabout the elastic neutral axis of the cracked composite section,mm4. Because the longitudinal rebars are ignored, In is thesame as Ibare if a cover plate is present, and Is if there is nocover plate.

Ip Transformed section moment of inertia for positive momentabout the elastic neutral axis of the cracked composite section,mm4.

Is Moment of inertia of the steel beam alone, mm4.

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Ix, Iy Moment of inertia about the x and y axes of the beam, re-spectively, mm4.

J Torsional constant for the section, mm4.

K Effective length factor.

K33, K22 Major and minor effective length factors.

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. This is used for vibration analysis.

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

L22 Effective length of the beam for minor (2-2) axis of bending,mm.

L33 Effective length of the beam for major (3-3) axis of bending,mm.

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, mm.

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, mm.

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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, mm. 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.

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, mm.

LCBS Length of a composite beam segment, mm. 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.

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, mm. If the deck span is oriented parallelto the beam span and at least one of the points is at the endof the beam, Ls is taken as the distance between the twopoints minus 75 mm.

M Applied moment, N-mm.

M33 Applied moment about major axis, N-mm.

M22 Applied moment about minor axis, N-mm.

MA Absolute value of moment at the quarter point of the unbracedbeam segment, N-mm.

MB Absolute value of moment at the centerline of the unbracedbeam segment, N-mm.

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

Mb Lateral-torsional buckling moment capacity of a non-compositesection, N-mm.

Mc Moment capacity, N-mm.

Mc22 Minor moment capacity, N-mm.

Mc33 Major moment capacity, N-mm.

Mmax Maximum positive moment for a beam, N-mm.

Mcv Plastic moment capacity of a composite beam section for aPCC after considering the reduced strength for the coexistentshear force, N-mm.

ME Elastic critical moment of a noncomposite section, N-mm.

Me Elastic moment capacity of a composite section, N-mm.

Mf Plastic moment capacity of a composite section about themajor axis for positive moment for a PCC with the assumptionthat the web does not contribute to the moment strength, N-mm.

Mp Plastic moment capacity of a composite section for positivemoment with an appropriate PCC, or for negative moment, asappropriate, N-mm.

N Axial load, N.

Na Required number of shear connectors between the point ofmaximum moment and an adjacent point of zero moment (orend of slab) for partial composite connection, unitless.

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

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Neff The effective number of beams resisting the heel drop impact,unitless. Used in vibration analysis.

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

Np Required number of shear connectors between the point ofmaximum moment and an adjacent point of zero moment (orend of slab) for full composite connection, 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.

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.

PCC Percent composite connection, unitless. This represents thepartial composite connection ratio, and it is expressed as apercentage.

PO Heel drop force, kips. This force is taken as 0.6 kips. This isused for vibration analysis.

Pv2, Pv3 Major and minor shear capacities, N.

Qk Character strength of one shear connector (shear stud), N.

Qn Design strength of one shear connector (shear stud) for nega-tive moment, N.

Qp Design strength of one shear connector (shear stud) for posi-tive moment, N.

R Wiss-Parmelee rating factor, unitless. Used in vibration analy-sis.

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

S Plastic section modulus of the steel beam alone plus coverplate if applicable, mm3.

S33, S22 Major and minor plastic section moduli, mm3.

Sed Minimum edge distance from midheight of a metal deck rib tothe center of a shear stud, mm. 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 25 mm. You can change this in thepreferences and the overwrites.

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

T Thickness of flange, mm.

Tbot Thickness of bottom flange of a user-defined steel beam, mm.

Ttop Thickness of top flange of a user-defined steel beam, mm.

Tcp Thickness of cover plate, mm.

W Total load supported by the beam, N. You specify a load com-bination that the program uses to determine this weight.

Ys Specified yield strength, N/mm2.

Z33, Z22 Section modulus about the 3-3 and 2-2 axes of the beam re-spectively, mm3.

a Robertson constant, unitless. Also the depth of the concretecompression block, mm.

br Average width of concrete rib, mm.

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d Clear distance between flanges less the fillet or corner radiusat each flange for rolled shapes and clear distance betweenflanges for welded shapes, mm.

davg Average depth of concrete slab, including the concrete in themetal deck ribs, mm. Used in vibration analysis.

dsc Diameter of a shear stud connector, mm.

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

fcu Characteristic cube strength of concrete, N/mm2.

fyr Yield strength of transverse reinforcement, N/mm2.

g Acceleration caused by gravity, mm/sec2.

hs Length of shear stud connector after welding, mm.

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

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

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

l Controlling laterally unbraced length of a member, mm.

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

le22, le33 Major and minor effective lengths, mm (K33l33, K22l22).

m Equivalent uniform moment factor.

m22,m33 Equivalent uniform moment factor for the minor (2-2) andmajor (3-3) axes of bending.

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n Slenderness correction factor dependent on moment gradient,unitless. This factor modifies the slenderness to consider theeffect of variation of moment along the length of the beam.This is used to calculate Mb.

pE Euler strength, N/mm2.

py Minimum specified yield stress of structural steel, N/mm2.

pycp Minimum specified yield stress of cover plate, N/mm2.

r Governing radius of gyration, mm. Also the ratio of averageaxial stress in steel to yield stress of steel, unitless.

r22, r33 Radius of gyration about the local 2-2 and 3-3 axes of thebeam respectively, mm.

sb Beam spacing, mm.

sr Center-to-center spacing of metal deck ribs, mm.

t Thickness of web of steel beam, mm.

tc Thickness of concrete slab, mm. If there is metal deck, this isthe thickness of the concrete slab above the metal deck, tc =Ds - Dp.

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

u Buckling parameter.

v Longitudinal shear force per unit length, N/mm.

vrc Maximum resistance per unit length imparted by concretealone to the longitudinal shear, N/mm.

vr,max Maximum resistance per unit length to the longitudinal shearthat is allowed with or without transverse reinforcement,N/mm.

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wa Additional metal deck rib width, mm. This term is used tospecify metal deck ribs that are split over the beam. The widthwa is added to the width br when determining the width ofdeck rib available for shear studs. Currently this term is al-ways zero.

x1 The assumed gap distance from the supporting beam or col-umn flange to the end of the beam flange, mm. The defaultvalue for this length is 10 mm.

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

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, mm.

yc Distance of the bottom of the compression block from thebottom of the beam bottom flange (no cover plate), mm.

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

yp Distance of the plastic neutral axis of composite section fromthe bottom of the beam bottom flange (no cover plate), mm.

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

α Axial compression stress level indicator for classification ofsection.

αs, αl Modular ratio Es/Ec for short term and long term loading, re-spectively, unitless.

αe Effective modular ratio for a specific value of ρl

β Ratio of smaller to larger end moments.

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δ Maximum span deflection considering the effect of PCC, mm.

δc Maximum span deflection for full composite connection, mm.

δLLMaximum span deflection for live load component of a loadcombination, mm.

δTLMaximum span deflection for total load of a load combination,mm.

δallow Allowable maximum span deflection, mm.

δcamber Maximum camber deflection, mm.

δLL,allow Allowable maximum span deflection for live load component ofa load combination, mm

δTL,allow Allowable maximum span deflection for total load of a loadcombination, mm.

ε Constant 2

1275

yp.

λ Slenderness parameter. It is the minor axis slenderness ratioLb / r22 for lateral-torsional buckling of non-composite beam.For composite beam, this parameter is not required.

λ0 Limiting slenderness.

λLT Equivalent slenderness.

λLo Limiting equivalent slenderness.

η Perry factor.

ηLT Perry coefficient.

ν Slenderness factor.

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References Page 19 of 19

ρl Proportion of the long term loading to the total loading in a

load combination. This ratio is taken by considering the ratioof the corresponding moments in the program, unitless. Itranges between 0 and 1.

ψ Monosymmetry index.

ReferencesBritish Standard Institution (BSI). 1990a. British Standard Structural Use of

Steelwork in Buildings. Part 1. Code of Practice for Design of Simpleand Continuous Construction: Hot Rolled Sections. 389 Chiswick HighRoad, London, U.K. W4 4AL.

British Standard Institution (BSI). 1990b. British Standard Structural Use ofSteelwork in Buildings. Part 3. Design in Composite Construction, Sec-tion 3.1 Code of Practice for Design of Simple and Continuous Com-posite Beams. 389 Chiswick High Road, London, U.K. W4 4AL.