Composit Beam

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General and Notation Page 1 of 23

©COMPUTERS AND STRUCTURES, INC., BERKELEY, C ALIFORNIA JUNE 2009

COMPOSITEBEAMDESIGN AISC-LRFD360-05

Technical Note

General and Notation

This Technical Note provides an overview of composite beam design using the

AISC-LRFD360-05 design specification.

AISC-LRFD360-05 Design Methodology

The flowchart in Figure 1 shows the general methodology for composite beam

design of a single beam element using the AISC-LRFD360-05 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 AISC-LRFD360-05 design methodology. It should not

be literally 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 sectionis 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 AISC-LRFD360-05 specification. Also any user-specified de-

sign load combinations can be interpreted and implemented. Refer to the

Composite Beam Design AISC-LRFD360-05 Technical Note Design Load Com-

binations for a description of the default design load combinations for this

code.

Box 3 - Design Check LocationsThe program determines all of the design check locations for a given beam.

Also refer to the Composite Beam Design Technical Note Beam Unbraced

Length and Design Check Locations.

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General and Notation Composite Beam Design AISC-LRFD360-05

Technical Note Page 2 of 23

Figure 1: Flowchart for AISC-LRFD360-05 Design o f a Single Beam

No

Start here to design

a beam element.

Determine design

load combinations.

Determine design

check locations.

Determine checking

order for beams.

Select a trial beam

section.

Is the section

compact or

noncompact?

Is there another trial

section available that

may qualify as the

optimum beam

section?Yes

NoThe design for this

beam element is

complete.

Determine

transformed section

properties for full

composite action.

Considering full

composite

connection, are the

maximum moment

and deflection

acceptable?

No

Is the vibration

criteria satisfied?

No

Yes

Yes

Is there axial load on

the beam for any

design load

combination?

Yes

Considering full

composite action, is the

interaction for the

combined maximum

axial and bending

stresses acceptable?

Determine price of

section.

Calculate required

camber.

Is beam shear

acceptable?

Yes

No

Determine if trial

section is the current

optimum section.

Yes

Do the required

shear connectors fit

on the beam?

Determine the

required number of

shear connectors.

Determine the

minimum acceptable

percent composite

connection

considering

combined stresses

and 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 compact

section requirements,

determine whether to

use a plastic or anelastic stress

distribution to

calculate the moment

capacity, Mn.

Yes

7



Composite Beam Design AISC-LRFD360-05 General and Notation


Box 4 - Checking Order for Beams

The checking order must be determined for a beam if the beam is assigned anauto select property. The program considers the beams in the auto select list

in the order described in the section entitled “How ETABS Optimizes Design

Groups” in Composite Beam Design Technical Note General Design Informa-

tion.

Box 5 - Trial Beam Section

The program allows the user to select the next trial beam section to be

checked for conformance with the AISC-LRFD360-05 specification and any

additional user-defined criteria. Refer to the section entitled “How ETABS Op-

timizes Design Groups” in Composite Beam Design Technical Note General

Design Information for a description of this selection process.

Box 6 - Compact and Noncompact Requirements

For AISC-LRFD360-05 design of composite beams, the program requires that

the beam section be either compact or noncompact. Slender sections are not

designed. The program checks to make sure the beam is not slender. Refer to

Composite Beam Design AISC-LRFD360-05 Technical Note Compact and Non-

compact Requirements for a description of how the program checks compact

and noncompact requirements.

Box 7 - Stress Distribution Used to Calculate Moment Capacity

The program determines whether to use plastic or elastic stress distribution

when calculating the moment capacity for AISC-LRFD360-05 design. SeeComposite Beam Design AISC-LRFD360-05 Technical Note Compact and Non-

compact Requirements for more information.

Box 8 - Transformed Section Properties

The program computes the transformed section properties of the trial beam

section. If there is only positive bending in the beam, only the transformed

section properties for positive bending are calculated. Similarly, if there is

only negative bending in the beam, only the transformed section properties

for negative bending are calculated. If there is both positive and negative

bending in the beam, transformed section properties for both positive and

negative bending are calculated.

Refer to Composite Beam Design Technical Note Effective Width of the Con-

crete Slab for a description of how the program calculates the effective width

of the concrete slab for the composite beam. Refer to Composite Beam De-












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sign AISC-ASD89 Technical Note Transformed Section Moment of Inertia for

description of how the program calculates the transformed section properties.

In AISC-LRFD360-05 design, the transformed section properties are used for

calculating 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 Check

The program checks that the moment capacity of the beam using full compos-

ite connection is greater than or equal to the applied factored moment. It also

checks if the deflection using full composite connection is acceptable. The

main purpose of this check is to quickly eliminate inadequate beam sections.

Refer to Composite Beam Design AISC-LRFD360-05 Technical Note Bending

and Deflection Checks for more information.

Box 10 - Vibration Criteria Check

The program calculates the vibration parameters. If vibration is specified to

be used as one of the tools for selecting the optimum beam size, the program

checks if the vibration parameters satisfy the specified limits. If the vibration

check is satisfied, the design using the current trial section continues; other-

wise, the design for this section is terminated. For more detailed information

on the vibration checks, refer to Composite Beam Design Technical Note

Beam Vibration.

Box 11 - Axial Load

The 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 is

subsequently checked, as indicated in box 14. If there is no axial load on the

beam, the axial capacity is not determined and the interaction check (box 14)

is skipped. Refer to Composite Beam Design AISC-LRFD360-05 Technical Note

Compact and Noncompact Requirements for a description of how the program

calculates axial load capacity.

Box 12 - P-M Interaction Check

If there is axial load on the beam, the program checks the P-M interaction

equations. If the interaction check is satisfied, the design using the current

trial section continues; otherwise, the design for this section is terminated.

Refer to Composite Beam Design AISC-LRFD360-05 Technical Note Moment

Capacity for Steel Section Alone for more information.


























Box 13 - Partial Composite Action

A significant amount of design is performed at this point in the process. Theprogram determines the smallest amount of composite connection for which

the beam is adequate. Both flexural checks and deflection checks are made at

this point. In addition, the program considers axial load on the beam if it ex-

ists and is specified to be considered. Flexural checks also are made for the

construction loads.

For more information refer to Composite Beam Design AISC-LRFD360-05

Technical Note Partial Composite Connection with a Plastic Stress Distribution

and Composite Beam Design AISC-LRFD360-05 Technical Note Bending and

Deflection Checks. Also refer to Composite Beam Design AISC-ASD89 Techni-

cal Note Elastic Stresses with Partial Composite Connection.

Box 14 - Required Number of Shear Connectors

The program calculates the required number of shear connectors on the beam

and the distribution of those shear connectors. For more information refer to

Composite Beam Design AISC-LRFD360-05 Technical Note Shear Connectors.

Also refer to Composite Beam Design Technical Note Distribution of Shear

Studs on a Composite Beam and Composite Beam Design Technical Note The

Number of Shear Studs that Fit in a Composite Beam Segment. Finally refer

to Composite Beam Design Technical Note Effective Width of the Concrete

Slab for limitations associated with composite beams and formed metal deck.

Box 15 - Checking i f 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 Composite Beam De-

sign Technical Note Number of Shear Studs that Fit in a Composite Beam

Segment. If the connectors fit on the beam, the design using the current trial

section continues; otherwise, the design for this section is terminated.

Box 16 - Beam Shear

The program checks the beam shear for the reactions at each end of the

beam. See Composite Beam Design AISC-LRFD360-05 Technical Note Beam

Shear Capacity for more information. If the beam shear check is satisfied, the

design using the current trial section continues; otherwise, the design for thissection is terminated.









































Box 17 - Camber

The program determines the camber for the beam, if it is specified to havecamber. Refer to Composite Beam Design Technical Note Beam Deflection and

Camber for more information.

Box 18 - Section Price

Determination of price of section applies only when price has been specified

by 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 Price

to Select Optimum Beam Sections” in Composite Beam Design Technical Note

General Design Information for more information.

Box 19 - Check if a Section is the Current Optimum Section

This check applies only if price has been specified as the method of selectingthe optimum section. The program checks if the price of the current trial

beam is less than that of any other beam that satisfied the design criteria. If

so, the current beam section becomes the current optimum beam section.

Refer to “Using Price to Select Optimum Beam Sections” in Composite Beam

Design Technical Note General Design Information 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 the

heaviest beams and thus the first beam found to work is the optimum beam.

Box 20 - Check for Possible Addit ional 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 might

qualify as the optimum beam section. Refer to “How ETABS Optimizes Design

Groups” in Composite Beam Design Technical Note General Design Informa-

tion for more information.

Box 21 - Design Complete

At this point, the design for this particular beam element is complete. If the

beam has been assigned an auto selection property, the current optimum

section, 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 in

the auto selection list.





















If the beam is assigned a regular, non-auto selection property, the design for

that 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 design

module that are not directly addressed in the flowchart shown in Figure 1.

Those include designing beams in groups and designing beams with partial

length cover plates.

For more information on the design by group feature, refer to the section

"How the Program Optimizes Design Groups" in Composite Beam Design

Technical Note General Design Information. The extension of the methodology

described in Part 3 to designing by groups is relatively simple and is assumed

to be apparent to the reader.

When a beam has a partial length cover plate, the program checks not only

the design at the point of the maximum moment (box 8 of Figure 1), but also

the design at the point of the largest moment where the cover plate does not

exist.

Notation

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

Ac Area of concrete within slab effective width that is above the

elastic neutral axis (ENA) for full composite action, in2. For

beams with metal deck ribs running perpendicular to the beam

span, only the concrete above the metal deck and above the

ENA is included. For beams with metal deck ribs running paral-

lel to the beam span, the concrete above the metal deck and

the concrete in the deck ribs are included if it is above the

ENA. This value may be different on the left and right sides of

the 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 cover

plate) of a user-defined steel section, in

2

. Note that the totalarea of a user-defined steel section is found by summing the

area of the top flange, web, and bottom flange.

ASb Initial displacement amplitude of a single beam resulting from

a 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 web

thickness t w , in

2

.

B1 Moment magnifier, unitless.

C b Bending coefficient dependent on moment gradient, unitless.

C bot Cope depth at bottom of beam, in.

C C 1 Compressive force in the concrete slab above the metal deck,

kips. If no metal deck exists, this is the compressive force in

the slab.

C C 2 Compressive force in concrete that is in the metal deck ribs,

kips. This force occurs only when the metal deck ribs are ori-

ented parallel to the steel beam, and the plastic neutral axis is

below the top of the metal deck.

C FT Compressive force in the top flange of the steel beam, kips.

This force occurs only when the plastic neutral axis is below

the top of the beam.

C KT Compressive force in the top fillets of a rolled steel beam,

kips. This force occurs only when the plastic neutral axis is be-

low the bottom of the top flange of the beam.

C R Compressive force in the slab rebar, kips. This force occurs

only when the plastic neutral axis is below the rebar, and the

user has specified that the rebar is to be considered.





C top Cope depth at top of beam, in.

C w Warping constant for a section, in6.

C Web Compressive force in the steel beam web, kips. This force oc-

curs only when the plastic neutral axis is within the beam web.

D Damping ratio, percent critical damping inherent in the floor

system, unitless.

E c Modulus of elasticity of concrete slab, ksi. Note that this could

be different on the left and right sides of the beam. Also note

that this is different for stress calculations and deflection cal-

culations.

E s Modulus of elasticity of steel, ksi.

F cr Critical stress for columns in compression, ksi.

F L Smaller of (F yf - F r ) or F yw , ksi.

F r Compressive residual stress in flange, ksi. Taken as 10 kips

per square inch for rolled shapes and 16.5 kips per square

inch for welded shapes.

F u Minimum specified tensile strength of structural steel or shear

stud, ksi.

F y Minimum specified yield stress of structural steel, ksi.

F ycp Minimum specified yield stress of cover plate, ksi.

F yf-bot Minimum specified yield stress of steel in beam bottom flange,

ksi.

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

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

G Shear modulus of elasticity of steel, ksi.

H s Length of shear stud connector after welding, in.





I eff Effective moment of inertia of a partially composite beam, in4.

I O Moment of inertia of an element of the composite steel beam

section taken about its own center of gravity, in4.

I s Moment of inertia of the steel beam alone plus cover plate if

applicable, in4.

I tr Transformed section moment of inertia about elastic neutral

axis of the composite beam, in4.

I x , I y Moment of inertia about the x and y axes of the beam, respec-

tively, in4.

I yc Moment of inertia of compression flange about the y axis, or if

there is both positive and negative bending in the beam, the

smaller moment of the two flanges, in4.

J Torsional constant for a section, in4.

K Effective length factor for prismatic member, unitless.

K f A unitless coefficient typically equal to 1.57 unless the beam is

the overhanging portion of a cantilever with a backspan, in

which case K f is as defined in Figure 1 of Composite Beam De-

sign Technical Note Beam Vibration, or the beam is a cantile-

ver that is fully fixed at one end and free at the other end, in

which case K f 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 that

are braced against lateral displacement of the compression

flange or braced against twist of the cross section, in.

Lc Limiting unbraced length for determining allowable bending

stress, in.









LCBS Length of a composite beam segment, in. A composite beam

segment spans between any of the following: (1) physical endof the beam top flange; (2) another beam framing into the

beam being considered; (3) physical end of concrete slab. Fig-

ure 1 Composite Beam Design Technical Note Distribution of

Shear Studs on a Composite Beam illustrates some typical

cases for LCBS.

Lcsc Length of channel shear connector, in.

L p Limiting laterally unbraced length of beam for full plastic bend-

ing capacity, uniform moment case (C b = 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 to

the beam span and at least one of the points is at the end of

the beam, then Ls is taken as the distance between the two

points minus 3 inches.

L1 Distance from point of maximum moment to the closest point

of 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 point

of zero moment or physical end of beam top flange, or physi-

cal end of concrete slab measured on the other side of the

point of maximum moment from the distance L1, in.









L3 Distance from point load to the point of zero moment, physical

end of beam top flange, or physical end of concrete slabmeasured on the appropriate side of the point load, in. If the

point load is located on the left side of the point of maximum

moment, the distance is measured from the point load toward

the left end of the beam. If the point load is located on the

right side of the point of maximum moment, the distance is

measured toward the right end of the beam.

M Moment, kip-in.

M A Absolute value of moment at the quarter point of the unbraced

beam segment, kip-in.

M B Absolute value of moment at the centerline of the unbraced

beam segment, kip-in.

M C Absolute value of moment at the three-quarter point of the

unbraced beam segment, kip-in.

M cr Elastic buckling moment, kip-in.

M max Maximum positive moment for a beam, kip-in.

M n Nominal flexural strength, kip-in.

M p Plastic bending moment, kip-in.

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

M r Limiting buckling moment, M cr , when = r and C b = 1.0, kip-

in.

M u Required flexural strength, kip-in.

MPF conc Maximum possible force that can be developed in the concrete

slab, and rebar in slab, if applicable, kips.

MPF steel Maximum possible force that can be developed in the steel

section, and cover plate, if applicable, kips.





N CBS The number of uniformly distributed shear connectors the pro-

gram specifies for a composite beam segment, unitless.

N eff The effective number of beams resisting the heel drop impact,

unitless.

N r Number of shear stud connectors in one rib at a beam inter-

section; not to exceed three in computations, although more

than three studs may be installed, unitless.

N 1 Required number of shear connectors between the point of

maximum moment and an adjacent point of zero moment (or

end of slab), unitless.

N 2 Required number of shear connectors between a point load

and 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 two

points a distance of Ls apart, unitless.

P Axial load, kips.

P e Euler buckling load, kips.

P n Nominal axial strength (tension or compression), kips.

P nc Nominal compressive axial strength, kips.

P nt Nominal tensile axial strength, kips.

P O Heel drop force, kips. This force is taken as 0.6 kips.

P u Required axial strength (tension or compression), kips.

P y Axial compressive yield strength , kips.

PCC Percent composite connection, unitless. The exact formula for

this 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 connec-

tors, unitless.

RSmax Maximum number of rows of shear stud connectors that can fit

between two points a distance of Ls apart, unitless.

Sed Minimum edge distance from midheight of a metal deck rib to

the center of a shear stud, in. For an example see paragraph

1b of the section Solid Slab or Deck Ribs Oriented Parallel toBeam Span in Composite Beam Design Technical Note Number

of Shear Studs that Fit in a Composite Beam Segment. The

default value is 1 inch. You can change this in the preferences

and the overwrites.

Seff Effective section modulus of a partially composite beam with

respect 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, with respect to the tension flange, in3.

St -eff The section modulus for the partial composite section with re-

spect to the top of the equivalent transformed section, in3.

Stop Section modulus for the fully composite uncracked trans-

formed section with respect to the extreme compression fiber,

in3.

Str Section modulus for the fully composite uncracked trans-

formed section with respect to the extreme tension fiber of the

steel beam section (including cover plate), in3.

S x , Sy Section modulus about the x and y axes of the beam, respec-

tively, in3.









S xc Section modulus about the x axis of the outside fiber of the

compression flange, in

3

.

S xt Section modulus about the x axis of the outside fiber of the

tension flange, in3.

SRmax Maximum number of shear stud connectors that can fit in one

row across the top flange of a composite beam, unitless.

T B Tensile force in a composite rolled steel beam when the plastic

neutral axis is above the top of the beam, kips.

T CP Tensile force in the cover plate, kips.

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

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

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

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

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

V Shear force, kips.

V n Nominal shear strength, kips.

V u Required shear strength, kips.

W Total load supported by the beam, kips. The user specifies a

load combination that the program uses to determine this

weight.

X 1 Beam buckling factor defined by AISC-LRFD360-05 equation

F1-8.

X 2 Beam buckling factor defined by AISC-LRFD360-05 equation

F1-9.

Z Plastic section modulus of the steel beam alone plus cover

plate if applicable, in3.





Z x , Z y Plastic section modulus about the x and y axes of the beam

respectively, in

3

.

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 concrete

for partial composite connection when bottom of effective con-

crete is within the slab above the metal deck (or there is a

solid 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 when

elastic neutral axis is located in slab above metal deck, in.

a4 Distance from top of concrete slab to elastic neutral axis when

elastic neutral axis is located in slab above metal deck, in.

a5 Distance from bottom of metal deck to elastic neutral axis

when elastic neutral axis is located within height of metal

deck, in.

a6 Distance from top of metal deck to elastic neutral axis when

elastic 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 outside

face of bottom flange, in.

d avg Average depth of concrete slab, including the concrete in the

metal deck ribs, in.

d sc 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 between

flanges for other shapes, in.

hc For rolled shapes, twice the distance from the beam centroid

to the inside face of the compression flange less the fillet or

corner radius. In a user-defined section, twice the distance

from the centroid of the steel beam alone, not including the

cover 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 web

toe of a fillet, in.

k c Unitless factor used in AISC-LRFD360-05 Table B5.1, 0.35 kc

0.76.

k depth Distance from inner face of a rolled beam flange to the web

toe of a fillet, in.

k width Width of idealized fillet of rolled beam section, in.

l Controlling laterally unbraced length of a member, in.





l 22, l 33 Laterally unbraced length of a member for buckling about the

local 2 and 3 axes of the beam respectively, in.

l x , l y Laterally unbraced length of a member for buckling about the

x and y axes of the beam respectively, in.

m For a user-defined section, ratio of web yield stress to flange

yield stress, unitless.

r Governing radius of gyration, in.

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

r 22, r 33 Radius of gyration about the local 2 and 3 axes of the beam

respectively, in.

r T Radius of gyration of a section comprising the compression

flange plus one-third of the compression web area taken about

an axis in the plane of the web, in.

r x , r y Radius of gyration about the x and y axes of the beam respec-

tively, in.

r yc Radius of gyration of the compression flange about the y-axis,

in.

sb Beam spacing, in.

t Thickness, in.

t c Thickness of concrete slab, in. If there is metal deck,this is the

thickness of the concrete slab above the metal deck.

t cp Thickness of cover plate, in.

t f Thickness of steel beam flange, in.

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

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





t O Time to the maximum initial displacement of a single beam

resulting from a heel drop impact, seconds.

t w Thickness of web of user-defined steel beam, in.

w a Additional metal deck rib width, in. This term is used to specify

metal deck ribs that are split over the beam. The width w a is

added to the width w r when determining the width of deck rib

available for shear studs.

w c Unit weight per volume of concrete, pounds/feet3.

w d Unit weight per area of metal deck, ksi.

wr Average width of metal deck rib, in.

x 1 The assumed gap distance from the supporting beam or col-

umn flange to the end of the beam flange, in. The default

value for this length is 0.5 inch.

y Distance from the bottom of the bottom flange of the steel

beam section to the elastic neutral axis of the fully composite

beam, in.

y bare The distance from the bottom of the bottom flange of the steel

beam to the neutral axis of the noncomposite steel beam plus

cover plate if applicable, in.

y e The distance from the elastic neutral axis of the bare steel

beam alone (plus cover plate, if applicable) to the elastic neu-

tral axis of the fully composite beam, in.

y eff The distance from the bottom of the bottom flange of the steel

beam to the neutral axis of the partially composite beam, in.

y 1 Distance from the bottom of the bottom flange of the steel

beam section to the centroid of an element of the composite

beam section, in.





y 2 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.

y 3 Distance from the bottom of the top flange of a rolled steel

beam section to the plastic neutral axis when the plastic neu-

tral axis is within the fillets, in.

y 4 For a rolled steel beam, the distance from the bottom of the

top fillet to the plastic neutral axis when the plastic neutral

axis is within the beam web, in. For a user-defined steel beam,

the distance from the bottom of the top flange to the plastic

neutral axis when the plastic neutral axis is within the beam

web, in.

y p Distance from the plastic neutral axis of composite section to

the bottom of the beam bottom flange (not cover plate), in.

z Distance from the elastic neutral axis of the steel beam (plus

cover plate, if it exists) alone to the top of the concrete slab,

in. Note that this distance may be different on the left and

right sides of the beam.

z p Distance from the plastic neutral axis of composite section to

the top of the concrete slab, in. Note that this distance may be

different on the left and right sides of the beam.

A Sum of the areas of all of the elements of the steel beam sec-

tion, in2.

Atr Sum of the areas of all of the elements of the composite steel

beam section, in2.

( Atr y 1) Sum of the product Atr times y 1 for all of the elements of the

composite steel beam section, in3.

( Ay 1) Sum of the product A times y 1 for all of the elements of the

steel beam section, in3.





( Ay 12) Sum of the product A times y 1

2 for all of the elements of the

steel beam section, in

4

.

( Atr y 12)= Sum of the product Atr times y 1

2 for all of the elements of the

composite steel beam section, in4.

I O Sum of the moments of inertia of each element of the compos-

ite steel beam section taken about the center of gravity of the

element, in4.

Qn Sum of nominal strength of shear connectors (shear stud or

channel) between point considered and point of zero moment,

kips.

Qn-pcc Required nominal strength of shear connectors (shear stud or

channel) between point considered and point of zero moment

for partial composite connection percentage, PCC , kips.

Qn-100 Required nominal strength of shear connectors (shear stud or

channel) between point considered and point of zero moment

for full (100%) composite action, kips.

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 composite

connection.

Resistance factor, unitless.

b Resistance factor for bending in a noncomposite beam,

unitless. The default value is 0.9.

bcc Resistance factor applied to concrete for bending in a compos-

ite section, unitless. Note that this is a resistance factor that is

not defined by AISC. It is included by CSI to give the user

more control over the strength of the composite section. The

default value is 1.0.





bcne Resistance factor for negative bending in a composite beam

when M n is determined from an elastic stress distribution,unitless. The default value is 0.9.

bcnp Resistance factor for negative bending in a composite beam

when M n is determined from a plastic stress distribution,


bcpe Resistance factor for positive bending in a composite beam

when M n is determined from an elastic stress distribution,


bcpp Resistance factor for positive bending in a composite beam

when M n is determined from a plastic stress distribution,unitless. The default value is 0.90.

bcs Resistance factor applied to steel for bending in a composite

section, unitless. Note that this is a resistance factor that is

not defined by AISC. It is included by CSI to give the user

more control over the strength of the composite section. The

default value is 1.0.

bs Resistance factor for strength of shear studs, unitless. Note

that this is a resistance factor that is not defined by AISC. It is

included by CSI to give the user more control over the

strength of the composite section. The default value is 1.0.

c Resistance factor for axial compression, unitless. The default

value is 0.9.

t Resistance factor for axial tension, unitless. The default value

is 0.9.

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

0.9.





Controlling slenderness parameter, unitless. It is the minor

axis slenderness ratio Lb /ry for lateral-torsional buckling. It isthe flange width-thickness ratio b/t as defined in AISC LRFD

Manual Specification section B5.1 for flange local buckling. It is

the web depth-thickness ratio h/tw as defined in AISC LRFD

Manual Specification section B5.1 for web local buckling.

c Column slenderness parameter, unitless.

p Limiting slenderness parameter for a compact element, largest

value of for which Mn = Mp, unitless.

r Limiting slenderness parameter for a noncompact element,

largest value of for which buckling is inelastic, unitless.



Preferences Page 1 of 9



Technical Note

Preferences

General

The composite beam design preferences are basic assignments that apply to

all composite beams. Use the Options menu > Preferences > Composite

Beam Design command to access the Preferences form; the form can be

used to view and revise the composite beam design preferences. The Com-

posite Beam Design Preferences form has five separate tabs: Factors, Beam,Deflection, Vibration, and Price.

Default values are provided for all composite beam design preferences. Thus,

it is not necessary to specify or change any of the preferences. However, the

preference items should be reviewed to make sure they are acceptable.

Using the Preferences Form

To view preferences, select the Options menu > Preferences > Composite

Beam Design. The Preferences form will display. When the Preferences form

displays, review and, if necessary, change the specified design code in the

drop-down box near the bottom of the form.

Click on the desired tab: Factors, Beam, Deflection, Vibration or Price. The

preference options included under each of the tabs are displayed in a two-

column spreadsheet. The left column of the spreadsheet displays the prefer-

ence item name. The right column of the spreadsheet displays the preference

item value.

To change a preference item, left click the desired preference item in either

the left or right column of the spreadsheet. This activates a drop-down box or

highlights the current preference value. If the drop-down box appears, select

a new value. If the cell is highlighted, type in the desired value. The prefer-ence value will update accordingly.



Preferences Composite Beam Design AISC-LRFD360-05


When the preference item is clicked in either column, a short description of

that item displays in the large text box just below the list of items. This de-scription explains the purpose of each preference item without referring to the

documentation.

To set all of the composite beam preference items on a particular tab to their

default values, click on that tab to view it and then click the Reset Tab but-

ton. This button resets the preference values on the currently selected tab.

To set all of the composite beam preference items on all tabs to their default

values, click the Reset All button. This button immediately resets all of the

composite beam preference items.

I m p o r t a n t n o t e a b o u t r e s e t t i n g p r e f er e n c es : The defaults for the prefer-ence items are built into the program. The composite beam preference values

that were in a .edb file used to initialize a model may be different from the

built-in default values. Clicking a reset button resets the preference values to

built-in values, not to the values that were in the .edb file used to initialize

the model.

Preferences

For purposes of explanation in this Technical Note, the preference items are

presented in tables. The column headings in these tables are described as fol-

lows:

Item: The name of the preference item as it appears in the cells at the

left side of the Preferences form.

Possible Values: The possible values that the associated preference

item can have.

Default Value: The built-in default value that the program assumes for

the associated preference item.

Description: A description of the associated preference item.



Composite Beam Design AISC-LRFD360-05 Preferences


Factors TabPhi Factors

Table 1 lists the preference items available for phi factors in AISC-LRFD360-

05 design. Some of these phi factors are specified by the AISC specification.

Others have been created by CSI to allow more control over the capacities for

the composite section. Note that the default value for all of the phi factors

specifically created by CSI (and not specified by AISC) is 1.0, and thus by de-

fault they have no effect on the design.

Table 1 AISC-LRFD360-05 Phi Factor Preferences

ItemPossibleValues

DefaultValue Description

phi-b >0 0.9 Resistance factor for bending capacityin a steel beam alone, b. See AISC-LRFD360-05 Composite Beam DesignTechnical Note Moment Capacity forSteel Section Alone.

phi-bcne > 0 0.9 Resistance factor applied to the nega-tive bending capacity in a compositebeam section when the bending capac-ity, Mn, is determined from an elastic stress distribution, bcne. See AISC-LRFD360-05 Composite Beam DesignTechnical Note Composite SectionElastic Moment Capacity.

phi-bcnp > 0 0.9 Resistance factor applied to the nega-tive bending capacity in a compositebeam section when the bending capac-ity, Mn, is determined from a plastic stress distribution, bcnp.

phi-bcpe > 0 0.9 Resistance factor applied to the posi-tive bending capacity in a compositebeam section when the bending capac-ity, Mn, is determined from an elastic stress distribution, bcne. See AISC-LRFD360-05 Composite Beam DesignTechnical Note Composite Section

Elastic Moment Capacity.


























Table 1 AISC-LRFD360-05 Phi Factor Preferences

Item PossibleValues DefaultValue Description

phi-bcpp > 0 0.9 Resistance factor applied to the posi-tive bending capacity in a compositebeam section when the bending capac-ity, Mn, is determined from a plastic stress distribution, bcnp. See AISC-LRFD360-05 Composite Beam DesignTechnical Note Composite Plastic Mo-ment Capacity for Positive Bending.

phi-v > 0 0.9 Resistance factor for shear capacity insteel beam, v. See AISC-LRFD360-05Composite Beam Design Technical

Note Beam Shear Capacity.Refer to the Technical Notes mentioned in the Description column of the table

for more information.

Beam Tab

Table 2 lists the composite beam preference items available on the Beam tab

in the Preferences form.

Table 2: Composite Beam Preferences on the Beam Tab

ItemPossibleValues


Shored? Yes/No No Toggle for shored or unshored con-struction.

Middle Range(%)

0% 70%

Length in the middle of the beam overwhich the program checks the effectivewidth on each side of the beam, ex-pressed as a percentage of the totalbeam length.

Pattern LiveLoad Factor

0 0.75Factor applied to live load for specialpattern live load check for cantileverback spans and continuous spans.

Stress RatioLimit

>0 1.0The acceptable stress ratio limit. Thisitem applies only to design optimiza-tion.
















Deflection Tab

Table 3 lists the composite beam preference items available on the Deflection

tab in the Preferences form.

Table 3: Composite Beam Preferences on the Deflection Tab

ItemPossibleValues


Live LoadLimit, L/

> 0 360Live load deflection limitation denomi-nator (inputting 360 means that the de-flection limit is L/360).

Total LoadLimit, L/

> 0 240Total load deflection limitation denomi-nator (inputting 240 means that the de-flection limit is L/240).

Camber DL(%)

> 0 100%Percentage of dead load (not includingsuperimposed dead load) on whichcamber calculations are based.

See Composite Beam Design Technical Note Beam Deflection and Camber for

description of beam deflection and camber.

Vibration Tab

Table 4 lists the composite beam preference items available on the Vibration

tab in the Preferences form.

Table 4: Composite Beam Preferences on the Vibration Tab

ItemPossibleValues


VibrationCriterion

Walking,Rhythmic,Sensitive

Equipment andNone

Walking Excitation types to estimate the peakacceleration or vibrational velocities.









Preference Applicable to Walking

OccupancyCategory

Paper Office,Electronic

Office,Residential,

church, Assembly,

Dining,ExerciseRoom,

Shopping mall,Indoor foot-bridge, Out-

door footbridgeand Other.

Paper Office Toggle to consider the occupancycategory to be used for determining if abeam section is acceptable.

Damping Ratio > 0 0.025Damping ratio, which depends onoccupancy category.

AccelerationLimit, ao/g

> 0 0.005 Acceleration limits for a specificoccupancy.

Preference Applicable to Rhythmic Excitation

OccupancyCategory


Office,Residential,

church, Assembly,




Exercise Room Toggle to consider the occupancycategory to be used for determining if abeam section is acceptable.

Damping Ratio > 0 0.02Damping ratio, which depends onoccupancy category.

Rhythmic

Activity Type

Aerobics,

Dancing, LiveConcert,Sports Event,

Other

Aerobics Type of rhythmic activity due to

occupants activity.







AffectedOccupancyCategory


Office,Residential,

church, Assembly,


Shopping mall,Indoor foot-

bridge, Out-door footbridgeand Other.

Paper Office Type of occupancy in the area adjacentof Rhythmic activity.


> 00.005 Acceleration limits for a specific

occupancy.

Upper StepFrequency > 0

2.75 Estimated loading during rhythmicevent in accordance with DG11 Table5.2.

Lower StepFrequency

> 0

2.00 Estimated loading during rhythmicevent in accordance with DG11 Table5.2. Maximum three harmonic frequen-cies for Jumping exercise.

Preference Applicable to Sensitive Equipment

OccupancyCategory


Office,Residential,

church, Assembly,





Damping Ratio > 0 0.06 Damping ratio which depends on occu-pancy category.







Equipment orUse Category

ComputerSystem, Lab

Robots, Class A, Class B,

Class C, ClassD and Class E

ComputerSystem

Type of equipment and use category.

VibrationalVelocity Limit

> 0 0.008Vibrational velocity limits for a specificoccupancy.

FootfallImpulse fo(Fast)

> 0 1.4Values of footfall impulse parametersfrom DG11 Table 6.2.

FootfallImpulse fo(Moderate)


FootfallImpulse fo(Slow)


FootfallImpulse Fm(Fast)

> 0 315 lbs.Values of footfall impulse parametersfrom DG11 Table 6.2.

FootfallImpulse Fm(Moderate)


FootfallImpulse Fm(Slow)


See Composite Beam Design AISC360-05/IBC2006 Technical Note Floor Vi-

bration for a description of floor vibration.

Price Tab

Table 5 lists the composite beam preference items available on the Price tab

in the Preferences form.









Table 5: Composite Beam Preferences on the Price Tab


Optimize forPrice? Yes/No No

Toggle to consider price rather thansteel weight when selecting the opti-mum beam section from an auto selectsection list.

Stud Price ($) 0 $0 Installed price for a single shear stud

connector.

Camber Price($) 0 $0

Camber price per unit weight of steelbeam (including cover plate, if itexists).

See "Using Price to Select Optimum Beam Sections" in Composite Beam De-

sign Technical Note General Design Information for additional information on

the "Optimize for Price?" item.

Note that the price per unit weight for the steel beam (plus cover plate, if ap-

plicable) is input as part of the material property specification for the beam.

The material properties can be reviewed or defined using the Define menu >

Material Properties command. Be sure to use the same currency units (for

example, U.S. dollars) for the steel price in the material properties, the stud

price in the preferences, and the camber price in the preferences.







Overwrites Page 1 of 17



Technical Note

Overwrites

This Technical Note provides instructions on how to use the Composite Beam

Overwrites form and describes the items available on each of the tabs in the

form. One section is devoted to each of the tabs.

General

The composite beam design overwrites are basic assignments that apply onlyto those composite beams to which they are assigned. After selecting one or

more composite beams, use the Design menu > Composite Beam Design

> View\Revise Overwrites command to access the Composite Beam Over-

writes form; the form can be used to view and revise the composite beam de-

sign overwrites. Default values are provided for all composite beam overwrite

items. Thus, it is not necessary to specify or change any of the overwrites.

However, at least review the default values for the overwrite items to make

sure they are acceptable. When changes are made to overwrite items, the

program applies the changes only to the elements to which they are specifi-

cally assigned; that is, to the elements that are selected when the overwrites

are changed.

The Composite Beam Overwrites form has eight tabs. They are Beam, Bracing

(C), Bracing, Deck, Shear Studs, Deflection, Vibration and Miscellaneous. De-

scriptions of the various overwrite options available on each tab are provided

later in this Technical Note.

Using the Composite Beam Overwrites Form

After selecting one or more composite beams, use the Design menu >

Composite Beam Design > View\Revise Overwrites command to access

the Composite Beam Overwrites form. Click on the desired tab.

The Composite Beam Overwrites are displayed on each tab with a column of

check boxes and a two-column spreadsheet. The left column in the spread-



Overwrites Composite Beam Design AISC-LRFD360-05

Page 2 of 17 Overwrites

sheet contains the name of the overwrite item. The right column in the

spreadsheet contains the overwrite value.

Initially, the check boxes are all unchecked and all of the cells in the spread-

sheet have a gray background to indicate they are inactive and that the items

in the cells currently cannot be changed. The names of the overwrite items in

the first column of the spreadsheet are visible. The values of the overwrite

items in the second column of the spreadsheet are visible only if one beam

was selected before the Composite Beam Overwrites form was accessed. If

multiple beams were selected, no values show for the overwrite items in the

second column of the spreadsheet.

After selecting one or multiple beams, check the box to the left of an over-

write item to change it. Then left click in either column of the spread sheet to

activate a drop-down box or to highlight the contents of the cell in the right

column of the spreadsheet. If the drop-down box appears, select a value from

the box. If the cell is highlighted, type in the desired value.

When a check box is checked or one of the columns in the spreadsheet is

clicked, a short description of the item in that row displays in the large text

box just below the list of items. This description explains the purpose of the

overwrite iteml.

When changes to the composite beam overwrites have been made, click the

OK button to close the form. The program then changes all of the overwriteitems whose associated check boxes are checked for the selected beam(s).

You must click the OK button for the changes to be accepted by the program.

If you click the Cancel button to exit the form, any changes made to the

overwrites will be ignored and the form will be closed.

Resetting Composite Beam Overwrites to Default Values

To set all of the composite beam overwrite items on a particular tab to their

default values, click on the tab and then click the Reset Tab button. This but-

ton resets the overwrite values on the tab currently selected.

To set all of the composite beam overwrite items on all tabs to their defaultvalues, click the Reset All button. This button immediately resets all of the

composite beam overwrite items. Alternatively, clicking the Design menu >



Composite Beam Design AISC-LRFD360-05 Overwrites


Composite Beam Design > Reset All Composite Beam Overwrites

command will accomplish the same thing.

I m p o r t a n t n o t e a b o u t r es e t t in g o v e r w r i t e s: The defaults for the over-

write items are built into the program. The composite beam overwrite values

that were in a .edb file used to initialize a model may be different from the

built-in program default values. When the overwrites are reset, the program

resets the overwrite values to its built-in values, not to the values that were

in the .edb file used to initialize the model.

Overwrites

For purposes of explanation in this Technical Note, the overwrite items are

presented in tables. The column headings in these tables are described as fol-lows.

Item: The name of the overwrite item as it appears in the cells at the left

side of the Composite Beam Overwrites form.

Possible Values: The possible values for the associated overwrite item.

Default Value: The built-in default value that the program assumes for

the associated overwrite item.

Description: A description of the associated overwrite item.

Beam Tab

Table 1 lists the composite beam overwrite items available on the Beam tab in

the Composite Beam Overwrites form.

Table 1: Compos ite Beam Overwrites on the Beam Tab

ItemPossibleValues


Shored? Yes/No No(unshored)

Toggle for shored or unshored con-struction.





Table 1: Compos ite Beam Overwrites on the Beam Tab


Beam type Composite, NCw studs, or NC

w/o studs

Composite Type of beam design. NC w studs isshort for Noncomposite with minimumshear studs. NC w/o studs is short forNoncomposite without shear studs.

b-eff leftCondition

Programcalculated oruser-defined

Programcalculated

Toggle specifying how the effectivewidth of the concrete slab on the leftside of the beam is determined

b-eff left 0 Programcalculated

value

User-defined effective width of concreteslab on left side of beam, beff left.

b-eff rightCondition

Programcalculated oruser-defined

Programcalculated

Toggle specifying how the effectivewidth of the concrete slab on the rightside of the beam is determined

b-eff right 0 Programcalculated

value

User-defined effective width of concreteslab on right side of beam, beff right

Beam Fy 0 Specified inMaterial

Properties

Yield stress of the beam, Fy. Specifying0 in the overwrites means that Fy is asspecified in the material properties

Beam Fu 0 Specified inMaterial

Properties

Minimum tensile strength of the beam,Fu. Specifying 0 means that Fu is asspecified in the material properties

Cover PlatePresent?

Yes/No No Toggle switch indicating if a full lengthcover plate exists on the bottom of thebeam bottom flange.

Plate width 0 0 Width of cover plate, bcp.

Plate thickness 0 0 Thickness of cover plate, tcp.

Plate Fy > 0 0 Cover plate yield stress, Fycp. Specify-ing 0 means that Fycp is set to that

specified in the beam material proper-ties





The Shored item affects both the deflection calculations and the flexural

stress calculations for the beam. See Composite Beam Design Technical NoteBeam Deflection and Camber for a description of beam deflection. If the beam

is shored, no checks are performed for the construction loading design load

combination.

Note: The Middle Range item is specified on the Beam tab in the composite

beam preferences and is described in "Location Where Effective Slab Width isChecked" of Composite Beam Design Technical Note Effective Width of the

Concrete Slab.

Typically, when a beam is designed using the Composite Beam Design post-

processor, that beam is designed as a composite beam if it has a deck section

(not slab section) assigned along the full length of the specified Middle Range

on at least one side of the beam. The Beam Type overwrite allows a beam

that would ordinarily be designed as a composite beam to be specified to be

designed as a noncomposite beam. The overwrite does not and cannot force a

beam that has been designed as a noncomposite beam, because there is no

deck section along at least one side, to be designed as a composite beam.

When using the Composite Beam Design postprocessor, a beam that does not

have a deck section along at least one side is always designed as a noncom-

posite beam, regardless of what is specified in the Beam Type overwrite.

When a beam is designed as noncomposite with minimum shear studs, the

beam is designed as a noncomposite beam. Then shear studs are specified for

the beam with as large a spacing as possible, without exceeding the specified

maximum longitudinal spacing. The maximum longitudinal spacing can be

overwritten on the Shear Studs tab.

See Composite Beam Design Technical Note Effective Width of the Concrete

Slab for a description of the beam effective width.

The beam yield stress and the cover plate yield stress both default to the

yield stress specified for the material property associated with the beam sec-

tion. When the Define menu > Frame Sections command is used to define

a beam section, the material property associated with the beam section

should also be defined. The material property is defined using the Definemenu > Material Properties command.

In this program, the cover plate can have a yield stress that is different from

that of the beam, if desired. The cover plate width, thickness and F y items are


















not active unless the "Cover Plate Present" item is set to Yes. See "Cover

Plates" in Composite Beam Design Technical Note Composite Beam Propertiesfor a description of cover plates.

Bracing (C) Tab and Bracing Tab

The unbraced length overwrite items included on the Bracing (C) tab and the

Bracing tab are exactly the same. The items on the Bracing (C) tab apply to

construction loading design load combinations. The items on the Bracing tab

apply to final condition design load combinations.

The first two items that appear in the Bracing (C) tab and the Bracing tab are

shown in Table 2a. Additional items may also appear in the tabs, depending

on your choice for the Bracing Condition item. These additional items areshown in Tables 2b and 2c.

Table 2a: First Two Composi te Beam Overwrite Items on theBracing (C) Tab and the Bracing Tab

ItemPossibleValues


Cb factor 0 Programcalculated

Unitless factor used in determining al-lowable bending stress, Cb. Specifying0 in the overwrites means that thisvalue is program calculated

BracingCondition

Programcalculated,

bracingspecified or

lengthspecified

Programcalculated

This item defines how the unbracedlengths are determined for bucklingabout the beam local 2-axis. They areprogram calculated, based on user-specified uniform and point bracing, orbased on a user-specified maximumunbraced length.

When the C b factor is program calculated, the program uses Equation 1 to

calculate it unless the Bracing Condition has been identified as Length Speci-

fied.

b

M M

C . . . .M M

2

1 1

2 21 75 1 05 0 3 2 3 Eqn. 1

where,







M 1 and M 2 are the end moments of any unbraced span of the beam. M 1 is

numerically less than M 2.

The ratio M 1 /M 2 is positive for double curvature bending and negative for

single curvature bending within the unbraced beam span.

If any moment within the unbraced beam span is greater than M 2, the

numeric value of C b is 1.0.

The numeric value of C b is 1.0 for cantilever overhangs.

When the C b factor is program calculated and the Bracing Condition is set in

the overwrites to Length Specified, the program uses 1.0 for C b.

When the Bracing Condition is specified as Program Calculated, the program

assumes the beam is braced as described in "Determination of the Braced

Points of a Beam" in Composite Beam Design Technical Note Beam Unbraced

Length and Design Check Locations. Note that the program automatically con-

siders the bracing for construction loading and for the final condition sepa-

rately. For the construction loading condition, the program assumes that the

concrete fill does not assist in bracing the beam.

When the Bracing Condition is specified as Bracing Specified, two items ap-

pear in the tab in addition to those shown in Table 2a. Those additional items

are shown in Table 2b.

Table 2b: Additional Composi te Beam Overwri te Items on the Bracing (C) Tab andthe Bracing Tab When the Bracing Condition Is Specified as BracingSpecified

ItemPossibleValues


No. PointBraces

0 0 The number of user-specified pointbrace locations. Clicking in this boxopens the Point Braces form where youspecify the point braces.

No. UniformBraces

0 0 The number of user-specified uniformbraces. Clicking in this box opens theUniform Braces form where you specify

the uniform braces.

The No. Point Braces and No. Uniform Braces items allow you to specify actual

bracing for the beam. These items are described in "User-Specified Uniform









and Point Bracing" in Composite Beam Design Technical Note Beam Unbraced

Length and Design Check Locations.

When the Bracing Condition is specified as Length Specified, two items appear

in the tab in addition to those shown in Table 2a. The two additional items are

shown in Table 2c.

Table 2c: Addi tional Composite Beam Overwrite Items on the Bracing (C) Tab andthe Bracing Tab When the Bracing Condition Is Specified as LengthSpecified

ItemPossibleValues


AbsoluteLength?

Yes/No NoToggle switch for whether the maxi-mum unbraced length is given as anabsolute length or a relative length.

Unbraced L22 0 and beam length

Length ofbeam

Maximum unbraced length for bucklingabout the beam local 2 axis.

When the maximum unbraced length is specified as an absolute length, the

actual maximum unbraced length is specified. When the maximum unbraced

length is specified as a relative length, the value specified is equal to the

maximum unbraced length divided by the length of the beam. The relative

length specified is always between 0 and 1, inclusive.

See Composite Beam Design Technical Note Beam Unbraced Length and De-sign Check Locations for additional information about the unbraced length of

the beam.

Deck Tab

Table 3 lists the composite beam overwrite items available on the Deck tab in

the Composite Beam Overwrites form.













Table 3: Compos ite Beam Overwrites on the Deck Tab


Deck ID Left Programcalculated, anydefined deckproperty, or

None

Programcalculated

Deck ID assigned to left side of beam.

Deck directionLeft

Programcalculated,parallel, or

perpendicular

Programcalculated

Span direction of the metal deck ribs onleft side of beam relative to the spandirection of the beam.

Deck ID Right Programcalculated, anydefined deckproperty, or

None

Programcalculated

Deck ID assigned to right side of beam.

Deck directionRight

Programcalculated,parallel, or

perpendicular

Programcalculated

Span direction of the metal deck ribs onthe right side of beam relative to thespan direction of beam

When the Deck ID is program calculated, you must refer to the output data to

see what the program assumed for this item. It is not shown in the over-

writes.

If the deck direction is program calculated, do not overlook the important

note about deck orientation in "Multiple Deck Types or Directions Along theBeam Length" in Composite Beam Design Technical Note Effective Width of

the Concrete Slab.

Shear Studs Tab

Table 4 lists the composite beam overwrite items available on the Shear

Studs tab in the Composite Beam Overwrites form.

Table 4: Compos ite Beam Overwrites on the Shear Studs Tab

ItemPossibleValues


User Pattern? Yes/No No Toggle to indicate if a user-definedshear connector pattern is defined.









Table 4: Compos ite Beam Overwrites on the Shear Studs Tab


UniformSpacing

0 0, indicatingthere are no

uniformlyspaced

connectors

Uniform spacing of shear studs alongthe beam. There is one shear stud perrow along the beam.

No. AdditionalSections

0 0, indicatingthere are noadditional

connectorsspecified

Number of sections in which additionaluniformly spaced shear studs arespecified. Clicking in this box opens the

Additional Sections form where youspecify the section length and the num-ber of uniformly spaced connectors inthe section.

Min LongSpacing

> 0 6ds (i.e., six studdiameters)

Minimum longitudinal spacing of shearstuds along the length of the beam.

Max LongSpacing

> 0 36 inches Maximum longitudinal spacing of shearstuds along the length of the beam.

Min TranSpacing

> 0 4ds (i.e., four stud

diameters)

Minimum transverse spacing of shearstuds across the beam flange.

Max Studsper Row

> 0 3 Maximum number of shear studs in asingle row across the beam flange.

Qn Programcalculated or

> 0

Programcalculated

Capacity of a single shear stud. Speci-fying 0 in the overwrites means that thisvalue is program calculated.

The Uniform Spacing and No. Additional Sections items are available only if

the User Pattern item is set to Yes. See Composite Beam Design Technical

Note User-Defined Shear Stud Patterns for a more information.

The program default value for the minimum longitudinal spacing of shear

studs along the length of the beam is six shear stud diameters. Note that this

item is input as an absolute length, not as a multiplier on the stud diameter.

The program default value for the maximum longitudinal spacing of shear

studs along the length of the beam is 36 inches. The design code used may

specify the maximum longitudinal spacing is eight times the total slab thick-

ness (rib height, hr , plus concrete slab above metal deck, t c ). AISC-LRFD-360-

05 Specification Section specifies that the maximum longitudinal spacing of

shear studs along the length of a beam shall not exceed 36 inches for beams









when the span of the metal deck is perpendicular to the span of the beam. If

your total slab thickness is less than 36"/8 = 4.5", the program default valuemay be unconservative and should be revised.

The program default value for the minimum transverse spacing of shear studs

across the beam flange is four shear stud diameters. This is consistent with

the last paragraph of AISC-LRFD-360-05 Specification Section I5. Note that

this item is input as an absolute length, not as a multiplier on the stud diame-

ter. See Composite Beam Design Technical Note Distribution of Shear Studs

on a Composite Beam for an additional description of how shear studs are dis-

tributed on composite beams.

The "Max Studs per Row" item indicates the maximum number of shear studs

that is allowed in a row across the beam flange. For wider beams, the Min

Tran Spacing item might indicate that more studs could be accommodated

across the beam flange but the Max Studs per Row item will limit the number

of studs in any row. See Composite Beam Design Technical Note Distribution

of Shear Studs on a Composite Beam for an additional description of how

shear studs are distributed on beams.

See "Shear Stud Connector" in Composite Beam Design AISC-ASD89 Techni-

cal Note Shear Studs for a description of how the program calculates the al-

lowable shear load for a single shear stud. Note that when a q value is speci-

fied in the overwrites, the program assumes that the specified value of q has

already been modified by any applicable reduction factors for the metal deck.Finally, note that specifying 0 (zero) in the overwrites for this item means

that the allowable shear stud load is calculated by the program, not that it is

zero.

Shear studs are described in more detail in Composite Beam Design Technical

Note Distribution of Shear Studs on a Composite Beam, Technical Note The

Number of Shear Studs that Fit in a Composite Beam Segment, and Technical

Note User-Defined Shear Stud Patterns.

Deflection Tab

Table 5 lists the composite beam overwrite items available on the Deflection

tab in the Composite Beam Overwrites form.





























Table 5: Composite Beam Overwrites on the Deflection Tab


Deflection Absolute?

Yes/No No Toggle to consider live load and totalload deflection limitations as absoluteor as divisor of beam length (relative).

Live Load Limit > 0 Specified inPreferences

Deflection limitation for live load. Forrelative deflection, inputting 360 meansthat the limit is L/360.

Total LoadLimit

> 0 Specified inPreferences

Deflection limitation for total load. Forrelative deflection, inputting 240 meansthat the limit is L/240.

CalculateCamber?

Yes/No Yes Toggle for the program to calculatebeam camber.

Fixed Camber 0 0 User-specified camber when the pro-gram does not calculate beam camber

See Composite Beam Design Technical Note Beam Deflection and Camber for

a description of beam deflection and camber.

Vibration Tab

Table 6 lists the composite beam overwrite items available on the Vibration

tab in the Composite Beam Overwrites form.

Table 6: Composite Beam Overwrites on the Vibration Tab

Item

Possible

Values

Default

Value Description

VibrationCriterion

Walking,Rhythmic,Sensitive

Equipment andNone

Walking Excitation types to estimate the peakacceleration or vibrational velocities.

No. EffectiveBeams

1 1.0 Effective number of beams resisting aheel drop impact.










OccupancyCategory


Office,Residential,

church, Assembly,



door footbridgeand Other

Paper Office Toggle to consider the occupancycategory to be used for determining if abeam section is acceptable.

Damping Ratio > 0 0.025Damping ratio, which depends on oc-cupancy category.

Bay Frequency 0 0


> 0 0.005 Acceleration limits for a specific occu-pancy.

AdditionalDead Load

> 0 4 Additional Dead load acting on floorsystem.

Live Load > 0 11Live load for computing the beam fre-quency.

Colateral load 0 0 Colateral load for computing beam fre-quency.

Preference Applicable to Rhythmic Excitation

OccupancyCategory


Office,Residential,

church, Assembly,


Shopping mall,

Indoor foot-bridge, Out-









Damping Ratio > 0 0.02Damping ratio, which depends on oc-cupancy category.

Bay Frequency 0 0

Rhythmic Ac-tivity Type

Aerobics,Dancing, Live

Concert,Sports Event,

Other

Aerobics Type of rhythmic activity due to occu-pants activity.

Affected Occu-pancy Cate-gory


Office,

Residential,church, Assembly,




Paper Office Type of occupancy in the area adjacentof Rhythmic activity.


> 0 0.005 Acceleration limits for a specific occu-pancy.

Upper StepFrequency > 0 2.75 Estimated loading during rhythmicevent in accordance with DG11 Table

5.2.

Lower StepFrequency > 0 2.00

Estimated loading during rhythmicevent in accordance with DG11 Table5.2. Maximum three harmonic frequen-cies for Jumping exercise.

AdditionalDead Load


Live Load > 0 11Live load for computing the beamfrequency.

Colateral load 0 0Colateral load for computing beamfrequency.








OccupancyCategory


Office,Residential,

church, Assembly, Din-

ing, ExerciseRoom,




Damping Ratio > 0 0.06 Damping ratio, which depends onoccupancy category.

Bay Frequency 0 0

Equipment orUse Category

Computer Sys-tem, Lab Ro-bots, Class A,Class B, ClassC, Class D and

Class E

ComputerSystem


Vibrational

Velocity Limit

> 0 0.008Vibrational velocity limits for a specific

occupancy.FootfallImpulse fo(Fast)


FootfallImpulse fo(Moderate)


FootfallImpulse fo(Slow)


FootfallImpulse Fm

(Fast)


FootfallImpulse Fm(Moderate)








FootfallImpulse Fm(Slow)


AdditionalDead Load


Live Load > 0 11Live load for computing the beamfrequency.

Colateral load 0 0Colateral load for computing beamfrequency.

See Composite Beam Design Technical Note Beam Vibration for a description

of beam vibration.

See Composite Beam Design AISC360-05/IBC2006Technical Note Floor Vibra-

tion for a description of Floor vibration.

Miscellaneous Tab

Table 7 lists the composite beam overwrite items available on the Miscellane-

ous tab in the Composite Beam Overwrites form.

Table 7: Composite Beam Overwrites on the Miscellaneous Tab


ConsiderBeam Depth?

Yes/No No Toggle to select if beam depth is to beconsidered in an auto select sectionlist. If yes, maximum and minimumdepths must be input.

MaximumDepth

>0 44 inches Maximum actual (not nominal) beamdepth to be considered in auto selectsection list.

MinimumDepth

0 0 Minimum actual (not nominal) beamdepth to be considered in auto selectsection list.

MaximumPCC(%) >0 100% Maximum percent composite connec-tion considered for the beam.

Minimum PCC(%)

>0 25% Minimum percent composite connectionconsidered for the beam.











Table 7: Composite Beam Overwrites on the Miscellaneous Tab


LL ReductionFactor

0<, >1.0 1.0 Reducible live load is multiplied by thisfactor to obtain the reduced live load. Ifzero is selected, the program calcu-lated valued is used.

ReactionFactor

0<, >1.0 1.0 The reported reaction forces are multi-plied by this factor. Specifying 1 in theoverwrites means that the program cal-culated load-factored end reaction forceis to be reported.

IgnoreSimilarity

Yes/No No This item is Yes if story level similarity(to a master story level) is to be ignored

when designing the beam.



Design Load Combinations Page 1 of 4


COMPOSITEBEAMDESIGN AISC-LRFD 360-05

Technical Note

Design Load Combinations

This Technical Note defines the default AISC-LRFD 360-05 composite beam

design load combinations. General information about composite beam design

load combinations is provided by Composite Beam Design Technical Note De-

sign Load Combinations.

Default composite beam design load combinations can be used for design, or

the user may define design load combinations, or both default and user-defined combinations can be used for design. The default design load combi-

nations can be modified and deleted as necessary. Use the Design Menu >

Composite Beam Design > Select Design Combo command to access the

design load combinations selection form.

Strength Check for Construction Loads

The program performs only the check using the construction load design load

combination if the beam is unshored. If the beam is shored, the check for

construction loads is not performed and any specified design load combina-

tions for construction loads are not relevant.

The automatically created design load combination, using the AISC-LRFD 360-

05 specification, for checking the strength of an unshored beam subjected to

construction loads is given by Equation 1.

1.6 (WDL) + 1.6 [0.2 (LL + RLL)] Eqn. 1

where,

WDL = The sum of all wet dead load (WDL) load cases defined for

the model. Note that if a load case is simply defined as dead

load, it is assumed to be a WDL load case.

LL = The sum of all live load (LL) load cases defined for the

model.







Design Load Combinations Composite Beam Design AISC-LRFD 360-05

Page 2 of 4 Design Load Combinations

RLL = The sum of all reducible live load (RLL) load cases defined

for the model.

In Equation 1 the term 0.2 (LL + RLL) is an assumed construction live load.

Note that the load factor for dead loads is assumed the same as that for live

load when considering construction loads (e.g., placing of concrete, and the

like). See R. Vogel (1991).

Strength Check for Final Loads

The automatically created design load combinations for checking the strength

of a composite beam under final loads are given by Equations 2 and 3.

1.4 (WDL + SDL) Eqn. 2

1.2 (WDL + SDL) + 1.6 (LL + RLL) Eqn. 3

where,

SDL = The sum of all superimposed dead load (SDL) load cases

defined for the model.

and the remainder of the terms are as defined for Equation 1.

Deflection Check for Final Loads

The automatically created design load combination for checking the deflection

of a composite beam under final loads is given by Equation 4.

WDL + SDL + LL + RLL Eqn. 4

where all of the terms are as described for Equations 1 through 3. Note that

all of the load factors for this serviceability check are 1.0.

If the beam is unshored, the WDL portion of the deflection is based on the

moment of inertia of the steel beam alone and the remainder of the deflection

is based on the effective moment of inertia of the composite section. If the

beam is shored, the entire deflection is based on the effective moment of in-

ertia of the composite section.



Composite Beam Design AISC-LRFD 360-05 Design Load Combinations

Design Load Combinations Page 3 of 4

Reference

Vogel, R. 1991. “LRFD-Composite Beam Design with Metal Deck,” Steel Tips,

Technical Information & Product Service, Steel Committee of Califor-

nia, March





Compact and Noncompact Requirements Page 1 of 7



Technical Note

Compact and Noncompact Requirements

This Technical Note describes how the program checks the AISC-LRFD 360-05

specification requirements for compact and noncompact beams. The basic

compact and noncompact requirements checked are in AISC-LRFD 360-05

Chapter B, Table 4.1. The program checks the width-to-thickness ratios of the

beam compression flange, beam web, and, if it exists and is in compression,

the cover plate. When a singly symmetric beam is designed for noncomposite

behavior, it is also checked for lateral torsional buckling requirements.

Overview

The program classifies beam sections as either plastic, compact, noncompact

or slender. It checks the plastic, compact and noncompact section require-

ments at each design location along the beam for each design load combina-

tion separately. A beam section may be classified differently for different de-

sign load combinations. For example, a beam may be classified as compact

for design load combination A and as noncompact for design load combination

B. Two reasons that a beam may be classified differently for different design

load cases are as follows:

The compact section requirements for beam webs depend on the axial

load in the beam. Different design load combinations may produce differ-

ent axial loads in the beam. This is only an issue when beam axial loads

are specified to be considered in the composite beam analysis and design.

The compression flange may be different for different design load combi-

nations. If the sizes of the top and bottom flanges are not the same, clas-

sification of the section may depend on which flange is determined to be

the compression flange.

At each design location, for each design load combination, the program first

checks a beam section for the compact section requirements for the compres-

sion flange, web, cover plate (if applicable) and lateral torsional buckling (if

applicable) described herein. If the beam section meets all of those require-

ments, it is classified as compact for that design load combination. If the



Compact and Noncompact Requirements Composite Beam Design AISC-LRFD 360-05


beam section does not meet all of the compact section requirements, it is

checked for the noncompact requirements for the flanges, web, cover plate (ifapplicable) and lateral torsional buckling (if applicable) described herein. If

the beam section meets all of those requirements, it is classified as noncom-

pact for that design load combination. If the beam section does not meet all

of the noncompact section requirements, it is classified as slender for that de-

sign load combination, and the program does not consider it for composite

beam design.

Limiting Width-to-Thickness Ratios for Flanges

This section describes the limiting width-to-thickness ratios considered by the

program for beam compression flanges. The width-to-thickness ratio for

flanges is denoted b /t , and is equal to bf /2t f for I-shaped sections and bf /t f for

channel sections.

Compact Section Limits for Flanges

For compact sections, the width-to-thickness ratio for the compression flange

is limited to that indicated by Equation 1.

0.38 ,yf

b E

t F for compact sections Eqn. 1

where F yf is the specified yield stress of the flange considered. Equation 1 ap-

plies to both rolled sections selected from the program's database and touser-defined sections.

Noncompact Section Limits for Flanges

I - S h a p e d R o l l e d B e am s a n d Ch a n n e l s

For noncompact I-shaped rolled beams and channels, the width-to-thickness

ratio for the compression flange is limited to that indicated by Equation 2.

y

b E

t F 1.0 , for noncompact sections Eqn. 2

where F y is the specified yield stress of the beam or channel.



Composite Beam Design AISC-LRFD 360-05 Compact and Noncompact Requirements


User-Defined and Hybrid Beams

For noncompact user-defined and hybrid beams, the width-to-thickness ratiofor the compression flange is limited to that indicated by Equation 3.

c

L

K E b

t F 0.95 , for noncompact sections Eqn. 3

where F yf is the yield stress of the compression flange and,

c c

w

k k h

t

4

but not less than 0.35 0.76 Eqn. 4

F L=0.7F y for minor-axis bending, major axis bending of slender-web built-up

I-shaped members with S xt /S xc ≥ 0.7; F L = F y S xt /S xc ≥ 0.5F y for major axis

bending of compact and noncompact web built-up I-shaped members with

S xt /S xc < 0.7.

Limi ting Width-to-Thickness Ratios for Webs

This section describes the limiting width-to-thickness ratios considered by the

program for beam webs.

Compact Section Limits for Webs

When checking a beam web for compact section requirements, the width-to-thickness ratio used is h /t w . The equation used for checking the compact sec-

tion limits in the web depends on the ratio of the elastic neutral axis to theplastic neutral axis and the ratio of

p y M /M :

The program uses b = 0.9 for both elastic and plastic stress distribution

resulting from flexure.

Equation 5 defines the compact section limit for webs. For flexure in webs

of doubly symmetric I-shaped sections and channels:

3.76w y

h E

t F Eqn. 5a

For flexure in webs of singly-symmetric I-shaped sections:





2 5.70

0.54 0.09

c y

py

w p y

hE F

hh E F t M M

Eqn. 5b

In Equations 5a and 5b, the value of F y used is the largest of the F y values for

the beam flanges and the web.

Noncompact Section Limit s for Webs

When checking a beam web for noncompact section requirements, the width-

to-thickness ratio used is h /t w . The noncompact section limits depend on

whether the flanges of the beam are of equal or unequal size.

Equation 6 defines the noncompact section limit for webs:

w y

h E

t F5.70 Eqn. 6

Limi ting Width-to-Thickness Ratios for Cover Plates

The width-to-thickness checks made for the cover plate depend on the width

of the cover plate compared to the width of the beam bottom flange. Figure 1

illustrates the conditions considered.

In Case A of the figure, the width of the cover plate is less than or equal to

the width of the beam bottom flange. In that case, the width-to-thickness ra-

tio is taken as b1 /t cp, and it is checked as a flange cover plate.

In Case B of Figure 1, the width of the cover plate is greater than the width of

the beam bottom flange. Two conditions are checked in that case. The first

condition is the same as that shown in Case A, where the width-to-thickness

ratio is taken as b1 /t cp and is checked as a flange cover plate. The second

condition checked in Case B takes b2 /t cp as the width-to-thickness ratio and

checks it as a plate projecting from a beam. This second condition is only

checked for the noncompact requirements; it is not checked for compact re-quirements.





Compact Section Limits for Cover Plates

For both cases A and B shown in Figure 1, the cover plate is checked for com-pact section requirements as shown in Equation 7.

cp y

b E

t F1 1.12 Eqn. 7

where b1 is defined in Figure 1.

Figure 1: Conditions Considered When Checking Width-to-Thickness Ratios ofCover Plates

Noncompact Section Limits for Cover Plates

The checks made for noncompact section requirements depend on whether

the width of the cover plate is less than or equal to that of the bottom flange

of the beam, Case A in Figure 1, or greater than that of the bottom flange of

the beam, Case B in Figure 1.

b1 t c

p

b1 t c

p

b2b2

Case A Case B

Beam

Cover plate

Beam

Cover plate





Cover Plate Width Beam Bottom Flange Width

When the cover plate width is less than or equal to the width of the beambottom flange, Equation 8 applies for the noncompact check for the cover

plate.

1 1.40

cp y

b E

t F Eqn. 8

The term b1 in Equation 8 is defined in Figure 1.

Cover Plate Width > Beam Bottom Flange Width

When the cover plate width exceeds the width of the beam bottom flange,

both Equations 8 and 9 apply for the noncompact check for the cover plate.

2 1.12

cp y

b E

t F Eqn. 9

The term b2 in Equation 9 is defined in Figure 1.

Lateral Torsional Buckl ing

When a singly symmetric beam is designed for noncomposite behavior, it is

checked for lateral torsional buckling requirements. If the singly symmetric

beam is unshored, this check occurs for any construction design load case. It

also occurs for beams that have negative bending that are not specified toconsider the composite action provided by the slab rebar. Finally, the check

occurs for any singly symmetric beam specified to be noncomposite.

When reviewing for lateral torsional buckling requirements, the value of Lb /r yc

is checked. Lb is the laterally unbraced length of beam; that is, the length be-

tween points that are braced against lateral displacement of the compression

flange. The term r yc is radius of gyration of the compression flange about the

y-axis.

Compact Limi ts for Lateral Torsional Buckling

The compact section limit for lateral torsional buckling is given in Equations

10, 11, and 12.

For double-symmetric compact I-shaped members and channels bent

about their major axis:





1.76b

yc y

L E

r F

Eqn. 10

For double-symmetric I-shaped members with compact webs and non-

compact or slender flanges bent about their major axis:

1.76b

yc y

L E

r F Eqn. 11

For double-symmetric compact I-shaped members and channels bent

about their major axis:

1.1b t

yc y

L E

r F Eqn. 12

In Equation 10, 11, and 12, the term F yf is the yield stress of the compression

flange.



Composite Plastic Moment Capacity for Positive Bending Page 1 of 30



Technical NoteComposite Plastic Moment Capacity for

Positive Bending

This Technical Note describes how the program calculates the positive bend-

ing moment capacity for a composite section assuming a plastic stress distri-

bution.

Overview

Figure 1 illustrates a generic plastic stress distribution for positive bending.

Note that the concrete is stressed to 0.85 f' c and the steel is stressed to F y .

The distance y p is measured from the bottom of the beam bottom flange (not

cover plate) to the plastic neutral axis (PNA). The distance z p is measured

from the top of the concrete slab to the PNA; it can be different on the two

sides of the beam, as described later. The illustrated plastic stress distribution

is the basic distribution of stress used by the program when considering a

plastic stress distribution for positive bending. Note that if the metal deck ribs

are parallel to the beam, the concrete in the ribs also is considered.

Figure 1: Generic Plastic Stress Distribution for Positive Bending

Beam Section Beam Elevation Plastic Stress

Distribution

CConc

CSteel

TSteel

0.85f’c

Fy

Fy

a

Plastic neutral axis (PNA)

y p

z p



Composite Beam Design AISC-LRFD 360-05 Composite Plastic Moment Capacity for Positive Bending


Figure 2 illustrates how the program idealizes a steel beam for calculating the

plastic stress distribution. Two different cases are shown, one for a rolled sec-tion and the other for a user-defined section. The idealization for the rolled

section considers the fillets, whereas the idealization for the user-defined sec-

tion assumes there are no fillets because none are specified in the section

definition. Although not shown in those figures, the deck type and orientation

may be different on the left and right sides of the beam, as shown in Figure 2

of Composite Beam Design Technical Note Effective Width of the Concrete

Slab.

For a rolled steel section, the fillets are idealized as a rectangular block of

steel. The depth of this rectangular block, k depth, is:

k depth = k – t f Eqn. 1

The width of this rectangular block, k width, is:

k width = ( As – 2bf t f – (d – 2k )t w ) / 2k depth Eqn. 2

The basic steps in computing the positive plastic moment capacity are:

Determine the location of the PNA using Equations 3a through 10.

Calculate the plastic moment capacity of the composite section using Equa-

tion 11 together with the appropriate table chosen from Tables 2 through

11 depending on the location of the PNA. Note that for user-defined sec-tions, the terms related to the top and bottom fillets are ignored.









Figure 2: Idealization of a Rolled Section and a User-Defined Section used forCalculating the Plastic Stress Distribu tion

bcp

bf-bot

kwidth

kwidth

tw

bf-top

h r

t c

t f - t o p

k

k

d h

k d e p t h

k d e p t h

t c p

t f -

b o t

Idealization for Rolled Section

bcp

bf-bot

tw

bf-top

h r

t c

t f - t o p

d h

t c p

t f -

b o t

Idealization for User-Defined Section





Location of the Plastic Neutral Axis

The program determines the location of the PNA by comparing the maximum

possible compressive force that can be developed in the concrete, MPF conc,

with the maximum possible tensile force that can be developed in the steel

section (including the cover plate, if applicable), MPF steel.

The maximum concrete force, MPF conc, is calculated from Equation 3a if there

is no metal deck, or if the metal deck ribs are oriented perpendicular to the

beam span. Equation 3b is used if the deck ribs are oriented parallel to the

beam span. Note that the maximum concrete force has contributions from the

left and right sides of the beam that are treated separately and may be dif-

ferent.

MPF conc = bcc [(0.85f 'c beff t c )left + (0.85f 'c beff t c )right] Eqn. 3a

MPF conc = bcc [(0.85f 'c beff r r

c

r

w ht

S

)left +

(0.85f 'c beff r r

c

r

w ht

S

)right Eqn. 3b

The maximum steel force, MPFsteel, is calculated from Equation 4a if the beamis a rolled section or Equation 4b if it is a user-defined section.

MPF steel = bcs ( AsF y + bcp t cp F ycp) Eqn. 4a

MPF steel = bcs (bf -topt f -topF yf -top + t w h +

bf -bott f -botF yf -bot + bcp t cp F ycp) Eqn. 4b

Note that bcc and bcs are resistance factors defined by CSI, not CISC. They

are provided to give you more control over section capacity, if desired or

needed. They essentially allow you to have a different resistance factor for

steel and concrete. Note the bcc factor is applied to the reinforcing steel in theconcrete slab (if this steel is considered). By default, both of those resistance

factors are set equal to 1.0.





When computing the location of the PNA, it is important to remember that the

concrete is assumed to take no tension. Also, the concrete in the metal deckribs is considered effective in compression only if the metal deck ribs are ori-

ented parallel to the beam span.

The maximum concrete and steel forces are compared to determine if the

PNA is within the concrete slab or the steel section. If MPF conc > MPF steel, the

PNA is within the concrete slab. If MPF steel > MPF conc, the PNA is within the

steel section. If MPF steel = MPF conc, the PNA is at the top of the steel beam.

If the PNA is within the slab, the fact that the concrete slab can be different

on each side of the beam complicates locating the PNA. If the PNA is within

the steel section, there are several general locations for it. After the general

locations have been identified, it is a straightforward process to determine the

location of the PNA. The general locations are as follows:

Within the beam top flange.

Within the beam top fillet (applies to rolled shapes from the program's

section database only).

Within the beam web.

Within the beam bottom fillet (applies to rolled shapes from the program's

section database only).

Within the beam bottom flange.

Within the cover plate (if one is specified).

Note it is very unlikely that the PNA would be below the beam web but there

is nothing in the program to prevent it. This condition would require a very

large beam bottom flange and/or cover plate. Each of the PNA locations in the

steel section is described following the description of the PNA in the concrete

slab.

PNA in the Concrete Slab Above the Steel Beam

The program considers the condition where the slab on the left and right sidesof the beam are different. When the program determines that the PNA is

above the top of the steel section, that is, when MPF conc > MPF steel, it puts the

following four items in order, from highest elevation to lowest:





Top of concrete slab on the left side of the beam.

Top of concrete slab on the right side of the beam.

Top of metal on the left side of the beam.

Top of metal on the right side of the beam.

Next the program sums the compressive forces of those four items, starting

with the item at the highest elevation and proceeding downward. As each

item is added into the sum, the sum of compressive forces is compared with

the maximum tension value, which is the sum of MPF steel. As soon as the sum

of forces exceeds MPF steel, the program recognizes that the last location con-

sidered is below the PNA, and the second to last location considered is abovethe PNA. Using this information, the program can solve directly for the loca-

tion of the PNA.

Figures 3a and 3b show the internal forces for a rolled steel section and a

user-defined steel section, respectively, for the condition where the PNA is in

the concrete slab above the metal deck.

Figure 3a: Rolled Steel Section with PNA in Concrete Slab Above Metal Deck,Positive Bending

CC 1

Beam Section Beam Elevation Beam Internal Forces

TC P


TF B

TK B

TWeb

TK TTF T

y p

z p





Figure 3b: User-Defined Steel Section with PNA in Concrete Slab Above Metal

Deck, Positive Bending


user-defined steel section, respectively, for the condition where the PNA is

within the height, hr , of the metal deck ribs.

Figure 4a: Rolled Steel Section with PNA within Height, hr , of Metal Deck, Positive

Bending

C C 1

Beam Section Beam Elevat ion Beam In ternal Forces

C C 2 T F T

T F B T Web T C P

Plastic neutral axis (PNA)p

zp

CC 1


TF T

TF B

TWeb

TC P

Plastic neutral axis (PNA) y p

z

p





Figure 4b: User-Defined Steel Section with PNA with in Height, hr , of Metal Deck,

Positive Bending

Note that in Figures 3a through 4b the concrete compression forces (C C 1 and

C C 2) may have different magnitudes and locations (elevations) for the left and

right sides of the beam.

PNA wi thin the Beam Top FlangeFigures 5a and 5b show the internal forces for a rolled steel section and a


within the beam top flange. The term y 2, which is the distance from the top of

the steel beam to the PNA, is shown in these figures and is defined by Equa-

tion 5.

steel conc

bcs f top yf top

MPF MPF y

b F

2

2 Eqn. 5

CC 1


CC 2

TF T

TF B

TWeb

TC P


z p





Figure 5a: Rolled Steel Section with PNA within Beam Top Flange, PositiveBending

Figure 5b: User-Defined Steel Section with PNA within Beam Top Flange, Posi tiveBending

CC 1


CC 2

TF TTK T

TF B

TK B

TWeb

TC P


CF T

y 2

y p

z p

CC 1


CC 2

TF T

TF B

TWeb

TC P


CF T

y 2

y p

z p





PNA within the Beam Top Fillet

The PNA lies within the beam top fillet only if the beam section is a rolled sec-tion. Figure 6 shows the internal forces for this condition. The term y 3, which

is the distance from the bottom side of the beam top flange to the PNA, is

shown in Figure 6 and is defined by Equation 6.

steel conc bcs f top f top yf top

bcs width yw

MPF MPF b t F y

k F

3

2

2 Eqn. 6

Figure 6: Rolled Steel Section with PNA with in Beam Top Fillet, Positive Bending

PNA wi thin the Beam Web



within the beam web. The term y 4, which for a rolled steel beam is the dis-

tance from the web toe of the top fillet to the PNA and for a user-defined

beam is the distance from the bottom side of the beam top flange to the PNA,

is shown in Figures 7a and 7b and is defined by Equation 7.

CC 1


CC 2

CK TTK T

TF B

TK B

TWeb

TC P


CF T y 3

y p

z p






bcs w yw

bcs width depth yw

bcs w yw

MPF MPF b t F y

t F k k F

t F

4

2

22

2

Eqn. 7

The last term in Equation 7 applies only to rolled steel beams; it reduces to

zero for user-defined beams.

Figure 7a: Rolled Steel Section with PNA within Beam Web, Positive Bending

Figure 7b: User-Defined Steel Section with PNA within Beam Web, PositiveBending

CC1


CC2

CWeb

TF B

TWeb

TCP


CF T

y 4

y p

z p

CC1


CC2

CK T

CWeb

TF B

TKB

TWeb

TCP


CF T

y 4

y p

z p





PNA within the Beam Bottom Fillet

The PNA is within the beam bottom fillet only if the beam section is a rolledsection. Figure 8 shows the internal forces for this condition. The term y 5,

which is the distance from the top side of the beam bottom fillet to the PNA,

is shown in Figure 8 and is defined by Equation 8.


bcs width yw

bcs width depth yw bcs w yw

bcs width yw bcs width yw

MPF MPF b t F y

k F

k k F ht F

k F k F

5

2

2

2 2

2 2

Eqn. 8

Note that it is unlikely that the PNA will be this low. It requires a very large

beam bottom flange and/or cover plate.

Figure 8: Rolled Steel Section with PNA within Beam Bottom Fillet, Positive Bend-

ing

PNA within the Beam Bottom Flange


user-defined steel section, respectively, for the condition where the PNA lies

CC 1


CC 2

CK T

CK B

TF B

TK B

CWeb

TC P

CF T

y 5


y p

z p





within the beam bottom flange. The term y 6, which is the distance from the

top of the beam bottom flange to the PNA, is shown in Figures 9a and 9b andis defined by Equation 9.


bcs f-bot yf-bot


bcs f -bot yf -bot bcs f -bot yf -bot

MPF MPF b t F y

b F

k k F ht F

b F b F

6

2

2

4 2

2 2

Eqn. 9

Note that it is unlikely that the PNA will be this low. It requires a very large

beam bottom flange and/or cover plate.

Figure 9a: Rolled Steel Section with PNA within Beam Bottom Flange, Posi tiveBending

CC 1


CC 2

CK T

CK B

TF B

CF B

CWeb

TC P

CF T

y 6


z p





Figure 9b: User-Defined Steel Section with PNA within Beam Bottom Flange, Posi-

tive Bending

PNA within the Cover Plate


user-defined steel section, respectively, for the condition where the PNA lies

within the cover plate. The term y 7, which is the distance from the top of the

cover plate to the PNA, is shown in Figures 10a and 10b and is defined by

Equation 10.


bcs cp ycp


bcs cp ycp bcs cp ycp

bcs f bot f bot yf bot

bcs cp ycp

MPF MPF b t F y

b F

k k F ht F

b F b F

b t F

b F

7

2

2

4 2

2 2

2

2

Eqn. 10

Note that it is unlikely that the PNA will be this low. It requires an extremely

large cover plate. In the event that the PNA were in the cover plate, the dis-

tance y p would become negative.


CC 1

CC 2

TF B

CF B

CWeb

TC P

CF T

y 6


y p

z p





Figure 10a: Rolled Steel Section with PNA within Cover Plate, Positi ve Bending

Figure 10b: User-Defined Steel Section with PNA within Cover Plate, PositiveBending

CC 1


CC 2

CK T

CK B

CCP

CF B

CWeb

TC P

CF T

y 7


z p



CC 1

CC 2

CCP

CF B

CWeb

TC P

CF T

y 7

y p

z p





Calculating the PNA Location

To calculate the location of the PNA for positive bending, the program startsby comparing the value of MPF conc to that of MPF steel to determine if the PNA is

in the steel section or in the concrete slab above the steel section. As de-

scribed in an earlier section of this Technical Note, if MPF conc > MPF steel, the

PNA is within the concrete slab. If MPF steel > MPF conc, the PNA is within the

steel section. If MPF steel = MPF conc, the PNA is at the top of the steel beam.

If the PNA is in the concrete slab above the steel section, the procedure de-

scribed in the previous subsection of this Technical Note entitled "PNA in the

Concrete Slab Above the Steel Beam" is followed.

If the PNA is within the steel section, the program assumes that the PNA oc-

curs in the top flange of the beam. The distance y 2 is calculated using Equa-

tion 5. The calculated distance y 2 is then checked to see if it actually is within

the beam top flange. If it is, the location of the PNA has been identified.

If the calculated distance y 2 is not within the beam top flange, the program

continues by assuming that the PNA occurs in the beam top fillet. (Note that if

the beam is a user-defined beam, there is no top fillet and the program skips

directly to assuming that the PNA is in the beam web.) The distance y 3 is cal-

culated using Equation 6. The calculated distance y 3 is then checked to see if

it actually is within the beam top fillet. If it is, the location of the PNA has

been identified.

If the calculated distance y 3 is not within the beam top fillet, the program

continues by assuming that the PNA occurs in the beam web. The distance y 4

is calculated using Equation 7. The calculated distance y 4 is then checked to

see if it actually is within the beam web. If it is, the location of the PNA has

been identified.

In any practical case, the PNA is not expected to be below the beam web.

However, in the event the PNA has not yet been located, the program contin-

ues down the beam section through the bottom fillet, the bottom flange and

finally the cover plate until the location of the PNA has been identified.

Plastic Moment Capacity for Positive BendingThe plastic moment capacity for positive bending in a composite section is

calculated from Equation 11:





bcpp n bcpp piece PNA piece

Piece

bcpp piece PNA piece

Piece

M T x

C x

12

1

12

1

Eqn. 11

where:

C piece = Compression force in a piece of the composite beam,

kips.

M n = Plastic moment capacity for positive bending, kip-in.

T piece = Tension force in a piece of the composite beam, kips.

x PNA-piece = Distance from centroid of tension or compression force

in a piece of a composite beam to the PNA, in.

bcpp = Resistance factor for positive bending when plastic

stress distribution is assumed, unitless.

In Equation 11, the ten pieces are as follows:

Concrete above the metal deck, not including rebar, on the left side

of the beam: The concrete can carry only a compression force; tension is

not allowed in the concrete.

Concrete above the metal deck, not including rebar, on the right

side of the beam: The concrete can carry only a compression force; ten-

sion is not allowed in the concrete.

Concrete within the height of the metal deck on the left side of the

beam: The concrete can carry only a compression force; tension is not al-

lowed in the concrete.

Concrete within the height of the metal deck on the right side of the

beam: The concrete can carry only a compression force; tension is not al-

lowed in the concrete.

Beam top flange: The force in the beam top flange can be tension, com-

pression, or compression in the upper portion of the flange and tension in

the lower portion.





Beam top fillet: The force in the beam top fillet can be tension, compres-

sion, or compression in the upper portion of the fillet and tension in thelower portion.

Beam web: The force in the beam web can be tension, compression, or

compression in the upper portion of the web and tension in the lower por-

tion.

Beam bottom fillet: The force in the beam bottom fillet can be tension,

compression, or compression in the upper portion of the fillet and tension in

the lower portion.

Beam bottom flange: The force in the beam bottom flange can be ten-

sion, compression, or compression in the upper portion of the flange andtension in the lower portion.

Cover plate: The force in the cover plate can be tension, or compression in

the upper portion of the cover plate and tension in the lower portion.

In Equation 11 the values used for T piece, C piece and x PNA-piece depend on the lo-

cation of the PNA. The appropriate values for these items are given in Tables

2 through 11. Table 1 serves as a guide to which of those tables to use based

on the location of the PNA.

Note, because the metal deck and concrete slab can be in different locations

relative to the PNA on the two sides of the beam, you may need to use valuesfrom two different tables listed in Table 1.





Table 1:Table to determine which table to use in conjunction with Equation 11 to determinethe plastic moment capacity of composite section for positive bending.

Location of PNA Table

Above rebar in concrete above metal deck 2

In concrete within metal deck 3

In beam top flange 4

In beam top fillet 5

In beam web 6

In beam bottom fillet 7

In beam bottom flange 8

In cover plate 9

Table 2:When the PNA is above the centroid of the rebar in the concrete above the metal deck,use the equations specified in this table together with Equation 11 to determine the plas-tic moment capacity of composite section for positive bending.

Piece T xPNA C xPNA

Concrete above metal deck (left) N. A. N. A. 12a 21a

Concrete above metal deck (right) N. A. N. A. 12a 21a

Concrete in metal deck (left) N. A. N. A. 0 N. A.

Concrete in metal deck (right) N. A. N. A. 0 N. A.Beam top flange 15a 23a 0 N. A.

Beam top fillet 16a 24a 0 N. A.

Beam web 17a 25a 0 N. A.

Beam bottom fillet 18a 26a 0 N. A.

Beam bottom flange 19a 27a 0 N. A.

Cover plate 20a 28a 0 N. A.





Table 3:When the PNA is in the concrete within the metal deck, use the equations specified inthis table together with Equation 11 to determine the plastic moment capacity of com-posite section for positive bending.

Piece T xPNA C xPNA

Concrete above metal deck (left) N. A. N. A. 12b 21b

Concrete above metal deck (right) N. A. N. A. 12b 21b

Concrete in metal deck (left) N. A. N. A. 14a 22a

Concrete in metal deck (right) N. A. N. A. 14a 22a

Beam top flange 15a 23a 0 N. A.

Beam top fillet 16a 24a 0 N. A.Beam web 17a 25a 0 N. A.




Table 4:When the PNA is in the beam top flange, use the equations specified in this table to-gether with Equation 11 to determine the plastic moment capacity of composite sectionfor positive bending.

Piece T xPNA C xPNA

Concrete above metal deck (left) N. A. N. A. 12b 21bConcrete above metal deck (right) N. A. N. A. 12b 21b

Concrete in metal deck (left) N. A. N. A. 14b 22b


Beam top flange 15b 23b 15c 23c

Beam top fillet 16a 24a 0 N. A.

Beam web 17a 25a 0 N. A.








Table 5:When the PNA is in the beam top fillet, use the equations specified in this table togetherwith Equation 11 to determine the plastic moment capacity of composite section forpositive bending.

Piece T xPNA C xPNA




Concrete in metal deck (right) N. A. N. A. 14b 22b

Beam top flange 0 N. A. 15d 23d

Beam top fillet 16b 24b 16c 24cBeam web 17a 25a 0 N. A.




Table 6:When the PNA is in the beam web, use the equations specified in this table togetherwith Equation 11 to determine the plastic moment capacity of composite section forpositive bending.

Piece T xPNA C xPNA






Beam top fillet 0 N. A. 16d 24d

Beam web 17b 25b 17c 25c








Table 7:When the PNA is in the beam bottom fillet, use the equations specified in this table to-

gether with Equation 11 to determine the plastic moment capacity of composite sectionfor positive bending.

Piece T xPNA C xPNA







Beam web 0 N. A. 17d 25d

Beam bottom fillet 18b 27b 18c 26cBeam bottom flange 19a 27a 0 N. A.


Table 8:When the PNA is in the beam bottom flange, use the equations specified in this tabletogether with Equation 11 to determine the plastic moment capacity of composite sec-tion for positive bending.

Piece T xPNA C xPNA


Concrete above metal deck (right) N. A. N. A. 12b 21bConcrete in metal deck (left) N. A. N. A. 14b 22b




Beam web 0 N. A. 17d 25d

Beam bottom fillet 0 N. A. 18d 26d

Beam bottom flange 19b 27b 19c 27c






Table 9:When the PNA is in the cover plate, use the equations specified in this table togetherwith Equation 11 to determine the plastic moment capacity of composite section forpositive bending.

Piece T xPNA C xPNA






Beam top fillet 0 N. A. 16d 24dBeam web 0 N. A. 17d 25d

Beam bottom fillet 0 N. A. 18d 26d

Beam bottom flange 0 N. A. 19d 27d

Cover plate 20b 28b 20c 28c

Equations 12a and 12b are used for the compression force in the concrete

above the metal deck. Note that these equations are applied to each side of

the beam separately.

C C 1 = 0.85 bcc f 'c beff z p Eqn. 12a

C C 1 = 0.85 bcc f 'c beff t c Eqn. 12b

Note: For partial composite connection, Equation 12b is replaced with Equa-

tion 3 of Composite Beam Design AISC-LRFD 360-05 Technical Note Partial

Composite Connection with a Plastic Stress Distribution.

Equations 13a and 13b are used for the tension and compression forces in the

rebar in the concrete slab above the metal deck. Note that these equations

are applied to each side of the beam separately.

T R =

bcc A

r F

yr Eqn. 13a

C R = bcc Ar F yr Eqn. 13b









Equations 14a and 14b are used for the compression force in the concrete

within the metal deck. Note that these equations are applied to each side ofthe beam separately. Also note that these equations apply only if the span of

the metal deck ribs is oriented parallel to the beam span. If the metal deck

ribs are oriented perpendicular to the beam span, no compression force is al-

lowed on the concrete within the metal deck ribs.

r p c ' C bcc c eff

r

w z t C . f b

S

2 0 85 Eqn. 14a

' r r C bcc c eff

r

w hC . f b

S 2 0 85 Eqn. 14b

Note: For partial composite connection Equation 14b is replaced with Equation

4 in Composite Beam Design AISC-LRFD 360-05 Technical Note Partial Com-

posite Connection with a Plastic Stress Distribution.

Equations 15a through 15d are used for the tension and compression forces

in the beam top flange.

T FT = bcs bf -top t f -top F yf -top Eqn. 15a

T FT = bcs bf -top (t f -top y 2) F yf -top Eqn. 15b

C FT = bcs bf -top y 2 F yf -top Eqn. 15c

C FT = bcs bf -top t f -top F yf -top Eqn. 15d


in the beam top fillet. Note that these equations do not apply to user-defined

sections.

T KT = bcs k width k depth F yw Eqn. 16a

T KT = bcs k width (k depth y 3) F yw Eqn. 16b

C KT = bcs k width y 3 F yw Eqn. 16c

C KT = bcs k width k depth F yw Eqn. 16d










in the beam web.

T Web = bcs t w h F yw Eqn. 17a

T Web = bcs t w (h y 4) F yw Eqn. 17b

C Web = bcs t w y 4 F yw Eqn. 17c

C Web = bcs t w h F yw Eqn. 17d


in the beam bottom fillet. Note that these equations do not apply to user-

defined sections.

T KB = bcs k width k depth F yw Eqn. 18a

T KB = bcs k width (k depth y 5) F yw Eqn. 18b

C KB = bcs k width y 5 F yw Eqn. 18c

C KB = bcs k width k depth F yw Eqn. 18d


in the beam bottom flange.

T FB = bcs bf -bot t f -bot F yf -bot Eqn. 19a

T FB = bcs bf -bot (t f -bot y 6) F yf -bot Eqn. 19b

C FB = bcs bf -bot y 6 F yf -bot Eqn. 19c

C FB = bcs bf -bot t f -bot F yf -bot Eqn. 19d

Equations 20a through 20c are used for the tension and compression forces in

the cover plate.

T CP = bcs bcp t cp F ycp Eqn. 20a

T CP = bcs bcp (t cp y 7) F ycp Eqn. 20b

C CP = bcs bcp y 7 F ycp Eqn. 20c





Equations 21a and 21b are used for the distance from the center of the force

in the concrete above the metal deck to the PNA. Note that these equationsare applied to each side of the beam separately.

x PNA = z

2 Eqn. 21a

x PNA =c

p

t z

2 Eqn. 21b

Note: For partial composite connection Equation 21b is replaced with Equation

5 in Composite Beam Design AISC-LRFD 360-05 Technical Note Partial Com-

posite Connection with a Plastic Stress Distribution.

Equations 22a and 22b are used for the distance from the center of the force

in the concrete within the metal deck ribs to the PNA. Note that these equa-

tions are applied to each side of the beam separately.

xPNA =c z t

2 Eqn. 22a

xPNA =r

p c

h z t

2 Eqn. 22b

Note: For partial composite connection, Equation 22b is replaced with Equa-

tion 6 in Composite Beam Design AISC-LRFD 360-05 Technical Note Partial

Composite Connection with a Plastic Stress Distribution.

Equations 23a through 23d are used for the distance from the center of the

force(s) in the beam top flange to the PNA.

xPNA =f -top

p

t y d

2 Eqn. 23a

xPNA =f -topt y 2

2 Eqn. 23b

xPNA =y 22

Eqn. 23c













xPNA =f top

p c r d

t z t h r

2

Eqn. 23d

Note the terms z p, t c , hr and r d in Equation 23d must all be for the left side of

the beam or all for the right side of the beam. It does not matter which side

of the beam is used, but all of the terms must be consistent.


force(s) in the beam top fillet to the PNA.

xPNA =depth

p f top

k y d t

2 Eqn. 24a

xPNA =depthk y 3

2 Eqn. 24b

xPNA =y 32

Eqn. 24c

xPNA =depth

p c r d f top

k z t h r t

2 Eqn. 24d





force(s) in the beam web to the PNA.

xPNA = p f top depth

hy d t k

2 Eqn. 25a

xPNA =h y 4

2 Eqn. 25b

xPNA =y 4

2

Eqn. 25c

xPNA = p c r d f top depth

h z t h r t k

2 Eqn. 25d






the beam or all for the right side of the beam. It does not matter which sideof the beam is used, but all of the terms must be consistent.


force(s) in the beam bottom fillet to the PNA.

xPNA =depth

p f top

k y d t h

3

2 Eqn. 26a

xPNA =depthk y 5

2 Eqn. 26b

xPNA = y 52

Eqn. 26c

xPNA =depth

p c r d f top

k z t h r t h

3

2 Eqn. 26d





force(s) in the beam bottom flange to the PNA.

xPNA =f -bot

p f top depth

t y d t k h 2

2 Eqn. 27a

xPNA =f -bot t y 6

2 Eqn. 27b

xPNA =y 62

Eqn. 27c

f -bot PNA p c r d f top depth

t x z t h r t k h 2

2 Eqn. 27d








Equations 28a through 28c are used for the distance from the center of the

force(s) in the cover plate to the PNA.

cp

PNA p f top depth f -bot

t x y d t k h t 2

2 Eqn. 28a

xPNA =cpt y 7

2 Eqn. 28b

xPNA =y 72

Eqn. 28c





Composite Section Elastic Moment Capacity Page 1 of 3



Technical Note

Composite Section Elastic Moment Capacity

This Technical Note describes how the program calculates the moment capac-

ity of a composite section when an elastic stress distribution is assumed.

Positive Moment Capacity with an Elastic StressDistribution

To calculate the positive moment capacity with an elastic stress distribution,the program first calculates the location of the elastic neutral axis (ENA) and

the transformed section moment of inertia. Information on how the program

calculates the location of the ENA and the transformed section moment of in-

ertia for full composite connection is provided in Composite Beam Design

AISC-ASD89 Technical Note Transformed Section Moment of Inertia. Informa-

tion on how the program calculates the location of the ENA and the trans-

formed section moment of inertia for partial composite connection is provided

in Composite Beam Design AISC-ASD89 Technical Note Elastic Stresses with

Partial Composite Connection.

The positive moment capacity for a composite beam with an elastic stress dis-tribution is determined by considering five locations in the composite section.

These locations are as follows:

The top of the concrete on the left side of the beam.

The top of the concrete on the right side of the beam.

The top of the top flange of the beam.

The bottom of the bottom flange of the beam.

The bottom of the cover plate.

A moment capacity is calculated based on the allowable stress and the section

modulus at each of these five locations that is applicable to the beam consid-

ered. The smallest moment capacity calculated is the positive moment capac-











Composite Section Elastic Moment Capacity Composite Beam Design AISC-LRFD 360-05


ity for the beam. Figure 1 illustrates the allowable stress assumed for each of

these locations.

Figure 1: Allowable Stresses for Positive Bending at Various Key Locations ofthe Composite Beam Section

Equations 1a through 1e are used to calculate the positive moment capacity

at the seven key locations in the beam section. Table 1 lists the location to

which each equation applies. Note that in these equations, if there is full

composite connection, the term y is substituted for the term y eff .

Table 1:

Table to determine which of Equations 1a through 1e apply to a particular location in

a composite beam Location in Beam Equation

Top of concrete on left side of beam 1a

Top of concrete on right side of beam 1b

Top of beam top flange 1c

Bottom of beam bottom flange 1e

Bottom of cover plate 1f

h r

t c

d

t c p

y e f f

Elastic neutral axis (ENA)

bcsFycp

bcsFyf-bot

bcsFyf-top

bccFyr

0.85bccf’cEs

Ec

Composite B eam

All owable Elast ic

Stress at Key Points

Compression

Tension

Note: For a fully composite beam yeff = y.



Composite Beam Design AISC-LRFD 360-05 Composite Section Elastic Moment Capacity


' s eff bcpe n bcpe bcc c-left

c-left r -left c-left eff

E I M . f

E d h t - y

0 85 Eqn. 1a

' s eff bcpe n bcpe bcc c-right

c-left r-right c-right eff

E I M . f

E d h t y

0 85 Eqn. 1b

In Equation 1c, the term "ABS" means to take the absolute value of the

amount in the associated brackets.

eff bcpe n bcpe bcs yf -top

eff

I M F

ABS d y

Eqn. 1c

eff bcpe n bcpe bcs yf - bot

eff

I M F y

Eqn. 1d

eff bcpe n bcpe bcs ycp

eff cp

I M F

y t

Eqn. 1e

The positive moment capacity of a composite beam with an elastic stress dis-

tribution is the smallest of the moment capacities obtained from the equations

included in Equations 1a through 1e that are applicable to the beam consid-

ered. If the denominator of Equation 1c is zero, the program does not con-

sider the moment capacity associated with that equation.

Note that the term bcpe in these equations is the resistance factor for positive

bending in a composite beam when M n is determined from an elastic stress

distribution.



Moment Capacity for Steel Section Alone Page 1 of 20



Technical Note

Moment Capacity for Steel Section Alone

This Technical Note describes how the program calculates the moment capac-

ity of a noncomposite steel beam, including a cover plate, if applicable.

Overview

The program calculates the moment capacity, M n, only if the beam is compact

or noncompact. It does not calculate M n if the section is slender.

The plastic moment, M p, for a noncomposite rolled steel beam section without

a cover plate is calculated as M p = ZF y .

The exact methodology used to compute the plastic moment capacity in the

other cases depends on whether the beam, including the cover plate if it ex-

ists, is doubly or singly symmetric, and whether the beam web is classified as

compact or noncompact.

Figure 1 shows a flowchart that identifies the appropriate section in this tech-

nical note for calculating the moment capacity of the steel section alone. The

figure has boxes labeled a through g; start in the box labeled a. Note that thecriteria used by the program to determine if a section is compact or noncom-

pact for the AISC-LRFD 360-05 specification is described in Composite Beam

Design AISC-LRFD 360-05 Technical Note Compact and Noncompact Re-

quirements.

Steel Beam Properties

If properties for the steel section alone are available directly from the pro-

gram's section database, those properties are used to compute the moment

capacity. For other cases, such as a user-defined section or a section with a

cover plate, the section properties are calculated in a manner similar to thatdescribed in Composite Beam Design AISC-ASD89 Technical Note Trans-

formed Section Moment of Inertia, except that there is no concrete or rein-

forcing steel to consider.













Composite Beam Design AISC-LRFD 360-05 Moment Capacity for Steel Section Alone


After the moment of inertia has been calculated, the section moduli and ra-

dius of gyration are calculated using standard formulas. This process is re-

peated to get properties about both axes. The torsional constant is deter-

mined by summing the torsional constants for the various components of the

section. For example, it may be determined by summing the J's of a rolled

section and the cover plate, if applicable, or in a user-defined section, by

summing the J's for the top flange, web, bottom flange and cover plate, if ap-

plicable.

Moment Capacity for a Doubly Symmetric I- Beam

The nominal flexural strength for major axis bending depends on compact-

ness of the web and flanges.

Compact Webs with Compact Flanges

The nominal flexural strength is the lowest value obtained according to the

limit states of yielding (plastic moment) and lateral-torsional buckling.

Yielding

n p y M M F Z 33, (AISC F2-1)

Is section doubly

symmetric or achannel?

Yes

No

Refer to

“Moment

Capacity for a

Doubly Symmetric

Beam or a

Channel Section”

in this

Technical Note.

Is the beam webcompact?

Yes

No

Is the beam webnoncompact?

Yes

No Beam section isclassified as

slender and is not

designed. Go to

next trial section.

Refer to

“Moment

Capacity for a

Singly Symmetric

Beam with a

Compact Web”

in this

Technical Note.

Refer to

“Moment

Capacity for a

Singly Symmetric

Beam with a

Noncompact

Web” in this

Technical Note.

a b c

d

e f g

Figure 1: Flowchart For Determining Which Section of this Chapter Applies inCalculating Plastic Moment for Steel Section Alone





where, Z 33 is the plastic section modulus about the major axis.

Lateral-Torsional Buckling

p b p

b p

n b p p y p p b r

r p

cr p p r

M , if L L ,

L LM C M M . F S M , if L L L , and

L L

F S M , if L L ,

33

33

0 7

(AISC F2-1, F2-2, F2-3)

where,33

S is the elastic section modulus taken about the major

axis, bL is the unbraced length, pL and r L are limiting lengths, and

cr F is the critical buckling stress. cr F , pL , and r L are given by:

b bcr

tsb

ts

C E L Jc F

S h r L

r

22

233 0

1 0.078 , (AISC F2-4)

p y

y

E L r

F 1.76 , (AISC F2-5)

y

r ts

y

F S hE Jc L r

F S h E Jc

2

33 0

33 0

0.71.95 1 1 6.76 ,

0.7 (AISC F2-6)

where,

y w

ts

I C r

S2

33

, (AISC F2-7)

c , 1 and (AISC F2-8a)

0h is the distance between flange centroids.





Compact Webs with Noncompact or Slender Flanges

The nominal flexural strength is the lowest value obtained from the limitstates of lateral-torsional buckling and compression flange local buckling.


The provisions of lateral-torsional buckling for "Compact Web and

Flanges" as described in the provision pages also apply to the nomi-

nal flexural strength of I-Shapes with compact webs and noncompact

or slender flanges bent about their major axis.

p b p

b p

n b p p y p p b r

r p

cr p p r

M , L L ,

L LM C M M . F S M , L L LL L

F S M , L L .

33

33

if

0 7 if , and

if

(AISC F3.1, F2-1, F2-2, F2-3)

Compression Flange Local Buckling

pf

p p y

rf pf n

c

M M . F S

M . Ek S

,

33

33

2,

0 7 , for noncompact flanges,

0 9

for slender flanges

(AISC F3-1, 3-2)

where pf , and rf are the slenderness and limiting slenderness for

compact and noncompact flanges from Table 3.5, respectively,

2

f

f

b ,

t

pf

y

E . ,

F

0 38 (AISC Table B4.1, F3.2)





y

rf

c

L

E .

F

k E .

F

1 0 (Rolled),

0 95 (Welded),

(AISC Table B4.1, F3.2)

and c k is given by

c c

w

k , . k . .h t

4

0 35 0 76 (AISC F.3.2)

Noncompact Webs with Compact, Noncompact and Slender Flanges

The nominal flexural strength is the lowest values obtained from the limitstates of compression flange yielding, lateral-torsional buckling, and compres-

sion flange local buckling.

Compression Flange Yielding

n pc y M R M , (AISC F4-1)

where, pc R is the web plasticity factor, which is determined as fol-

lows:

p

pw y

pc

p p pw p

pw w rw

y y rw pw y

M

, ,M R

M M M , ,

M M M

if

1 if

(AISC F4-9a, F4-9b)

where,

pM = y y Z F . S F 33 331 6 (AISC F4-2)

S33 = elastic section modulus for major axis bending

w = c

w

h

t (AISC F4.2, Table B4.1)





pw = p , the limiting slenderness for a compact web, as given in

Table 3-5 (AISC Table B4.1)

rw = r , the limiting slenderness for a noncompact web, as

given in Table 3-5 (AISC Table B4.1)

and y M is the yield moment, which is determined as follows:

y M = y S F 33 (AISC F4-1)


pc y b p

b p

n b pc y pc y L 33 pc y p b r

r p

cr 33 pc y b r

R M , L L ,

L LM C R M R M F S R M , L L L ,

L L

F S R M , L L ,

if

if

if

(AISC F4-1, F4-2, F4-3)

where,

b c bcr

o t b

t

C E J LF .

S h r Lr

22

2

33

1 0 078 (AISC F4-5)

f t

w

br

h ha

d h d

20

0

112

6

(AISC F4-10)

c w w

f f

h t a

b t 10 (AISC F4-11)

yc y

yc y

, I I .

C I I .

1 if 0 23

0, if 0 23 (AISC F4.2)





p t

y

E L . r

F

1 1 (AISC F4-7)

L or t

L o

E J F S hL . r .

F S h E J

2

33

33

1 95 1 1 6 76 (AISC F4-8)

L y F . F 0 7 (AISC F4-6a)

pc R web plastification factor, which is determined using a

formula described previously (AISC F4-9)

yc I moment of inertia of the compression flange about the

minor axis

y I moment of inertia of the entire section about the minor

axis.


pc y

pt

n pc y pc y L

rf pt

c

R M ,

M R M R M F S ,

. Ek S , ,

33

33

2

if flanges are compact,

if flanges are noncompact, and

0 9if flanges are slender

(AISC F4-1, F4-12, F4-13)

where,

LF = 0.7 y F (AISC F4-6a, F4.3)

pc R = is the web plastification factor, which is determined using

a formula described previously (AISC F4-9, F4.3)

c k =w

,h t

4 c k . 35 0 76 (AISC F4.3, Table B4.1)





= f

f

b

t 2

pf = p , the limiting slenderness for compact flange, as given

in Table 3-5 (AISC Table B4.1, B4.3)

rf = r , the limiting slenderness for noncompact flange, as

given in Table 3-5 (AISC Table B4.1, B4.3).

Slender Webs with Compact, Noncompact, and Slender Flanges

The nominal flexural strength is the lowest value obtained from the limit

states of compression flange yielding, lateral-torsional buckling, and compres-

sion flange local buckling.


n pg y M R F S 33, (AISC F5-1)

where pgR is the bending strength reduction factor given by

c w pg

w w y

ha E R

a t F

1 5.7 1.0,1200 300

(AISC F5-6)

w w

f f

ht ab t

10, (AISC F5.2, F4-11)

where 0h is the distance between flange centroids (AISC F2.2).


n pg cr M R F S 33, (AISC F5-2)

where cr F is the critical lateral-torsional buckling stress given by





y b p

b p

cr b y y y p b r

r p

2

by p r 2

b

t

,

F , L L ,

L LF C F 0.3F F L L L

L L

C E F , L L

L

r

if

, if , and

if

(AISC F5-1, F5-3, 5-4)

where,

p t

y

E L r

F 1.1 (AISC F5.2, 4-7)

.r t

y

E L r

F

0 7 (AISC F5-5)

f t

w

br

h ha

d h d

20

0

112

6

(AISC F5.2, F4-10)

pgR is the bending strength reduction factor, which has been de-

scribed in the previous section.


n pg cr M R F S 33, (AISC F5-7)

where cr F is the critical buckling stress given by





y

pf

cr y y

rf pf

c y 2

f

f

F , ,

F F 0.3F ,

0.9Ek F ,

b

2t

if flanges are compact


if flanges are slender,

(AISC F5-1, F5-8, F5-9)

and , pf , and rf are the slenderness and the limiting slenderness

ratios for compact and noncompact flanges from Table 3.5, respec-tively, and ck is given by

c c

w

k . k . .h t

4

where 0 35 0 76 (AISC 5.3)

Moment Capacity for a Singly Symmetric I- Beam

The nominal of flexural strength for major axes bending depends on com-

pactness of the web and flanges.

Compact and Noncompact Webs with Compact, Noncompact and Slender Flanges

The nominal flexural strength is the lowest values obtained from the limit

sates of compression flange yielding, lateral-torsional buckling, compression

flange local buckling, and tension flange yielding.


n pc yc M R M , (AISC F4-1)

where, pc R is the web plasticity factor, which is determined asfollows:





p

pw

yc

pc

p p pw p

pw w rw

yc yc rw pw yc

M , ,

M RM M M

, ,M M M

if

1 if

(AISC F4-9a, F4-9b)

where,

M = y c y Z F . S F 33 331 6 (AISC F4-2)

c S33 = elastic section modulus for major axis bending referred

to compression flange

t S33 = elastic section modulus for major axis bending referred

to tension flange

= c

w

h


pw = p , the limiting slenderness for a compact web, as




and yc M is the yield moment for compression flange yielding,

which is determined as follows:

yc M = c y S F .33 (AISC F4-1)






if

if

if

pc yc b p

b p

n b pc yc pc yc L 33c pc yc p b r

r p

cr 33c pc yc b r

R M , L L

L LM C R M R M F S R M , L L L ,

L L

F S R M , L L ,

(AISC F4-1, F4-2, F4-3)

where,

b c bcr

o t b

t

C E J LF

S h r Lr

22

2

33

1 0078. (AISC F4-5)

fc t

w

br

h ha

d h d

20

0

112

6

(AISC F4-10)

c w w

fe fc

h t a

b t 10 (AISC F4-11)

yc y

yc y

, I I .

C I I .

1 if 0 23

0, if 0 23 (AISC F4.2)

p t

y

E L . r

F 1 1 (AISC F4-7)

L c or t

L o

E J F S hL . r .

F S h E J

2

33

33

1 95 1 1 6 76 (AISC F4-8)

t y

c

Lt t

y y

c c

S. F , .

S

F S SF . F , .

S S

33

33

33 33

33 33

0 7 if 0 7

0 5 if 0 7 (AISC F4-6a, F4-6b)





pc R web plastification factor, which is determined using a

formula describe previously (AISC F4-9)

yc I moment of inertia of the compression flange about the

minor axis

y I moment of inertia of the section about the minor axis.


pc yc

pt

n pc yc pc yc L c

rf pt

c c

R M ,

M R M R M F S ,

. Ek S , ,

33

33

2



0 9if flanges are slender

(AISC F4-1, F4-12, F4-13)

where,

LF = is a calculated stress, which has been defined previ-

ously

(AISC F4-6a, F4-6b, F4.3)

pc R = is the web plastification factor, which is determined

using a formula described previously (AISC F4-9,

F4.3)

c k =w

,h t

4 c k . 35 0 76 (AISC F4.3, Table B4.1)

= fc

fc

b

t 2

pf = p , the limiting slenderness for compact flange, asgiven in Table 3-5 (AISC Table B4.1, B4.3)






given in Table 3-5 (AISC Table B4.1, B4.3).

Tension Flange Yielding

33 33

33 33

if

if

p t c

n

pt yt t c

M , S SM

R M , S S

(AISC F4-14)

where, pt R is the web plastification factor corresponding to the ten-

sion flange yielding limit state. It is determined as follows:

if

1 if

p

pw

yt pt

p p pw

pw rw

yt yt rw pw

M ,

M RM M

,M M

(AISC F4-15a, F4-15b)

where,

pM = 33 y Z F (AISC F4-2)

33c S = elastic section modulus for major axis bending referred

to compression flange

33t S = elastic section modulus for major axis bending referred

to tension flange

w = c

w

h


pw = p , the limiting slenderness for a compact web, as



given in Table 3-5. (AISC Table B4.1)





Slender Webs with Compact, Noncompact and Slender Flanges

The nominal flexural strength is the lowest value obtained from the limitstates of compression flange yielding, lateral-torsional buckling, compression

flange local buckling, and tension flange yielding.


33 ,n pg y c M R F S (AISC F5-1)

where, pgR is the bending strength reduction factor given by

1 5.7 1.01200 300

c w pg

w w y

ha E R

a t F

(AISC F5-6)

10w w

f f

ht a

b t (AISC F5.2, F4-11)

where, 0h is the distance between flange centroids (AISC F2.2).


33 ,n pg cr c M R F S (AISC F5-2)

where, cr F is the critical lateral-torsional buckling stress given by

if

, if , and

if

y b p

b p

cr b y y y p b r

r p

2

by p r 2

b

t

,

F , L L ,

L LF C F 0.3F F L L L

L L

C E F , L L

L

r

(AISC F5-1, F5-3, 5-4)

where,





1.1 p t

y

E L r

F

(AISC F5.2, 4-7)

0.7r t

y

E L r

F (AISC F5-5)

20

0

112

6

fc t

w

br

h ha

d h d

(AISC F5.2, F4-10)

pgR is the bending strength reduction factor, which has been

described in a previous section.


33 ,n pg cr c M R F S (AISC F5-7)

where, cr F is the critical buckling stress given by

if flanges are compact


if flanges are slender,

y

pf cr y y

rf pf

c y 2

fc

fc

F , ,

F F 0.3F ,

0.9Ek F ,

b

2t

(AISC F5-1, F5-8, F -9)

and , pf , and rf are the slenderness and the limiting slenderness

ratios for compact and noncompact flanges from Table 3.5, respec-tively, and c k is given by





4where 0 35 0 76c c

w

k , . k . .

h t

(AISC 5.3)

Tension Flange Yielding

33 33

33 33 33

if

if

p t c

n

y t t c

M S S ,M

F S S S .

(AISC F5-10)

Moment Capacity for a Channel Sections

The nominal flexural strength is the lowest value obtained according to the

limit states of yielding (plastic moment), lateral-torsional buckling, and com-

pression flange local buckling.

Yielding

33,n p y M M F Z (AISC F2-1)

where Z 33 is the plastic section modulus about the major axis.


33

33

if

0 7 if , and

if

p b p

b p

n b p p y p p b r

r p

cr p p r

M , L L ,

L L

M C M M . F S M L L LL L

F S M , L L ,

(AISC F2-1, F2-2, F2-3)

where 33S is the elastic section modulus taken about the major axis,

bL is the unbraced length, pL and r L are limiting lengths, and cr F is the

critical buckling stress. cr F , pL and r L are given by

22

233 0

1 0.078b bcr

tsb

ts

C E L Jc F S h r L

r

(AISC F2-4)





1.76 p y

y

E L r

F

(AISC F2-5)

2

33 0

33 0

0.71.95 1 1 6.76

0.7

y

r ts

y

F S hE Jc L r

F S h E Jc

(AISC F2-6)

where

2

33

y w

ts

I C r

S (AISC F2-7)

1 for Double Channel sections

for Channel sections2

y o

w

C I h

C

(AISC F2-8a, F2-8b)

and oh is the distance between flange centroids.


The nominal strength for compression flange local buckling is deter-

mined based on whether the web is compact, noncompact, or slen-

der.

If the web is compact,

for compact flanges,

for noncompact flanges, and

for slender flanges,

n

p

pf

p p y 33

rf pf

c 33

2

M

M ,

M M 0.7F S ,

0.9Ek S ,

(AISC F2-1, F3-1, F3-2)

if the web is noncompact,





for compact flange,

for noncompact flanges, and

for slender flanges,

n

pc y

pf

pc y pc y L 33

rf pf

c 33

2

M

R M ,

R M R M F S ,

0.9Ek S ,

(AISC F4-1, F4-12, F4-13)

and if the web is slender,

33n pg cr M R F S (AISC F5-7)

where,cr

F is the critical buckling stress give by

2


0 3 if the flanges are noncompact,

0 9if the flanges are slender,

y

pf

cr y y

rf pf

c y

F ,

F F . F ,

. Ek F ,

where,

= 2f

f

b

t

pf = p , the limiting slenderness for compact flange, as given

in Table 3-5 (AISC Table B4.1, B4.3)


given in Table 3-5 (AISC Table B4.1, B4.3)

c k =4

w

,h t

35 0 76c k . (AISC F4.3, Table B4.1)

LF = 0 7 y . F (AISC F4-6a, F4.3)





pc R =

if

1 if

p

w pw

y

p p pw p

pw w rw

y y rw pw y

M ,

M M M M

,M M M

(AISC F4-9a, F4-9b)

pg R = 1 5 7 1 01200 300

w c

w w y

a h E . .

a t F

(AISC F5-6)

33S = elastic section modulus for major axis bending,

w = c

w

h

t

pw = p , the limiting slenderness for compact web, as given in

Table 3-5 (AISC Table B4.1)



pgR is the bending strength reduction factor, which has been de-

scribed in a previous section.



Partial Composite Connection with a Plastic Stress Distribution Page 1 of 6



Technical NotePartial Composite Connection w ith a Plastic

Stress Distribution

This technical note describes how the positive moment capacity of the com-

posite beam using plastic stress distribution is calculated for partial composite

connection. Partial composite connection for an elastic stress distribution is

described in Composite Beam Design AISC-ASD89 Technical Note Elastic

Stresses with Partial Composite Connection and Composite Beam Design

AISC-LRFD 360-05 Technical Note Composite Section Elastic Moment Capac-ity.

Estimating the Required Percent Composite Connection

The program uses Equation 1 to estimate the required percent composite

connection (PCC) for a composite beam.

2

u n steel beam

n X% comp n steel beam

M M PCC X%

M M

Eqn. 1

where,

PCC = Required percent composite connection, unitless.

M u = Required flexural strength, that is, the applied factored

moment, kip-in.

M n X% comp = Nominal flexural strength (capacity) of composite section

with X% composite connection, kip-in.

M n steel beam = Nominal flexural strength (capacity) of the steel beam

section alone as determined from Composite Beam Design

AISC-LRFD 360-05 Technical Note Moment Capacity forSteel Section Alone, kip-in.



















Partial Composite Connection with a Plastic Stress Distribution Composite Beam Design AISC-LRFD 360-05


X % = Percent composite connection that M n X % comp is based

on, unitless. For 50% composite connection use X % =0.50.

= Resistance factor that was used when calculating M n for

full composite connection, unitless. It is either bcpe or

bcpp.

Equation 1 is based on Example 3 in Vogel (1991). Equation 1 might be con-

sidered the LRFD equivalent to Equation 2 in Composite Beam Design AISC-

ASD89 Technical Note Elastic Stresses with Partial Composite Connection,

with some rearrangement of terms.

The program initially uses Equation 1 with M n X% comp equal to the M n for full(100%) composite connection to estimate the required PCC for a composite

beam. The program checks the moment capacity using this PCC . If the mo-

ment capacity is adequate, the iteration is complete. If the moment capacity

is not adequate, the program calculates a new PCC , using the last considered

PCC for X % and M n X% comp, and determines a new moment capacity. This

process continues until a PCC that provides an adequate moment capacity is

found.

Calculating MPF conc

The program calculates MPF conc as the smaller of the values obtained from theequations specified in Table 1 for the particular circumstances of the beam

considered.

Table 1:

Table identifying equations to be used to calculate initial value of Qn for partial com-

posite connection Deck Orientation

Beam Type Deck Ribs Parallel

to Beam Span

Deck Ribs Perpendicular to

Beam Span, or

No Metal Deck Exists

(Solid Concrete Slab)

Rolled Beam from Database 2b, 2c 2a, 2c

User-Defined Beam 2b, 2d 2a, 2d







Composite Beam Design AISC-LRFD 360-05 Partial Composite Connection with a Plastic Stress Distribution


MPF conc = bcc (PCC ) [(0.85f 'c beff t c )left + (0.85f 'c beff t c )right] Eqn. 2a

MPF conc = bcc (PCC ) [(0.85f 'c beff r r

c

r

w ht

S

left +

(0.85f 'c beff r r

c

r

w ht

S

right ] Eqn. 2b

MPF conc = bcs(PCC ) ( AsF y + bcp t cp F ycp) Eqn. 2c

MPF conc = bcs(PCC ) (bf -topt f -topF yf -top +

t w h + bf -bott f -botF yf -bot + bcp t cp F ycp) Eqn. 2d

In Equations 1a through 1d, the term PCC is the percent composite connec-

tion. For 50 percent composite connection, PCC is 0.5, not 50. The next sub-

section describes how the program initially estimates PCC .

Location of the PNA

The location of the PNA for partial composite connection with a plastic stress

distribution is calculated using the method described in Composite Beam De-sign AISC-LRFD 360-05 Technical Note Composite Plastic Moment Capacity

for Positive Bending for full composite connection, except that the value used

for MPF conc is obtained from one of the preceding Equations 2a through 2d, as

appropriate, instead of the value obtained from Equation 3a or 3b of that

technical note.

Determining the Effective Portion of the Concrete Slab

When different composite decks or spans are specified on each side of the

beam, the effective portion of the slab is determined as follows: The program

first puts the following six items in order, from highest elevation to lowest, to

determine how much of the concrete slab is effective for partial compositeconnection:

Top of concrete slab on the left side of the beam.











Top of concrete slab on the right side of the beam.

Top of metal on the left side of the beam.

Top of metal on the right side of the beam.

Bottom of metal on the left side of the beam.

Bottom of metal on the right side of the beam.

Next the program sums the compressive forces of these eight items, starting

with the item at the highest elevation and proceeding downward. As each

item is added into the sum, the sum of compressive forces is compared with

the MPF conc as determined by one of Equations 2a through 2d.

As soon as the sum of forces exceeds MPF conc, the program recognizes that

the last location considered is below the bottom of the effective concrete, and

the second to last location considered is above the bottom of the effective

concrete. Using this information, the program can solve directly for the loca-

tion of the bottom of the effective concrete.

Figure 1a shows the internal concrete forces for a rolled steel section (a user-

defined steel section is similar) for the condition where the bottom of the ef-

fective concrete is in the concrete slab above the metal deck.

Figure 1a: Rolled Steel Section With Bottom of Effective Concrete in ConcreteSlab Above Metal Deck, Positive Bending With Partial CompositeConnection

CC1


Bottom of effective concrete

a 1



Composite Beam Design AISC-LRFD 360-05 Partial Composite Connection with a Plastic Stress Distribution


In that case, a1 represents the distance from the top of the concrete slab to

the bottom of the effective concrete. Note that the distance a1 can be differ-ent on the left and right sides of the beam.

Figure 1b shows the internal concrete forces for a rolled steel section (a user-

defined steel section is similar) for the condition where the bottom of the ef-

fective concrete is within the height, hr , of the metal deck ribs. In that case,

a2 represents the distance from the top of the metal deck ribs to the bottom

of the effective concrete. Note that the distance a2 can be different on the left

and right sides of the beam.

Figure 1b: Rolled Steel Section With Bottom of Effective Concrete Within theHeight, hr , of the Metal Deck Ribs, Positive Bending With PartialComposite Connection

The program obtains the distances a1 and a2 using an iterative solution tech-

nique.

If the bottom of effective concrete is in the concrete above the metal deck, a2

is set equal to 0. If the bottom of effective concrete is within the height of the

metal deck, a1 is set equal to t c .

Moment Capacity of a Partially Composite Beam with aPlastic Stress Distribution

The moment capacity for partial composite connection with a plastic stress

distribution is calculated using the method described for full composite con-

nection in the section entitled "Plastic Moment Capacity for Positive Bending"

CC1


CC2

Bottom of effective concrete

a 2





in Composite Beam Design AISC-LRFD 360-05 Technical Note Composite Plas-

tic Moment Capacity for Positive Bending with the following changes:

Replace Equation 12b in that Technical Note with Equation 3.

C C 1 = 0.85 bcc f 'c beff a1 Eqn. 3


22 0 85 ' r

C bcc c eff

r

w aC . f b

S Eqn. 4


x PNA =1

2 p

a z Eqn. 5

Replaced Equation 22b in that Technical Note with Equation 6.

x PNA =2

12

p

a z a Eqn. 6

When calculating the moment capacity, concrete or reinforcing steel below

the bottom of the effective concrete is not considered in the calculation.

Note that the PNA for a partially composite beam always lies within the steel

beam section, not the concrete slab. Thus it is not necessary to check for thePNA location within the concrete slab.

Reference

Vogel, R. 1991. “LRFD-Composite Beam Design with Metal Deck,” Steel Tips,

Technical Information & Product Service, Steel Committee of Califor-

nia, March.







Bending and Deflection Checks Page 1 of 2

©COMPUTERS AND STRUCTURES, INC., BERKELEY, C ALIFORNIA DECEMBER 2008


Technical Note

Bending and Deflection Checks

This Technical Note describes how the program checks bending and deflection

for AISC-LRFD 360-05 design.

Bending Check Locations

For each design load combination the program checks bending at the follow-

ing locations:

Point of maximum moment for the design load combination considered.

Point load locations for the design load combination considered.

Bending Check at Point of Maximum Moment

For beams with no axial load, or when axial loads are not considered, the

program uses Equation 1 to perform bending checks for both composite and

noncomposite beams. If there is axial load to be considered, the interaction

formulas described in Composite Beam Design AISC-LRFD 360-05 Technical

Note Moment Capacity for Steel Section Alone are used rather than Equation1.

u

n

M1.0

M Eqn. 1

where,

Mu = The maximum required flexural strength, that is, the maximum

applied factored moment, kip-in.

Mn = Moment capacity for full composite connection or partial com-

posite connection, as applicable, kip-in.

= Resistance factor for bending, unitless. For positive bending in a

composite beam with an assumed plastic stress distribution,



Composite Beam Design AISC-LRFD 360-05 Bending and Deflection Checks

Bending and Deflection Checks Page 2 of 2

bcpp is used. For negative bending in a composite beam with an

assumed plastic stress distribution, bcnp is used. For positivebending in a composite beam with an assumed elastic stress

distribution, bcpe is used. For negative bending in a composite

beam with an assumed elastic stress distribution, bcne is used.

If the beam is specified to be noncomposite, b is used.

If there is axial load to be considered, the interaction formulas described in

Composite Beam Design AISC-LRFD 360-05 Technical Note Moment Capacity

for Steel Section Alone are used rather than Equation 1.

Bending Check at Point Loads

The bending check at point load locations is performed by applying Equation 9in Composite Beam Design AISC-LRFD 360-05 Technical Note Shear Connec-

tors at the point load location. See the next section entitled "Bending Checks"

for additional information.

Deflection Check

Deflection is calculated as described in Composite Beam Design Technical

Note Beam Deflection and Camber. For full composite connection Itr is used in

the deflection calculations. For partial composite connection Ieff is used in the

deflection calculations.





Technical Note

Shear Connectors

This Technical Note begins by defining the program's default allowable shear

connector loads for AISC-LRFD 360-05 composite beam design. Shear con-

nector capacities are defined for both shear studs and channel shear connec-

tors. Next the equations used for determining the number of shear connectors

on the beam are provided.

Shear Stud ConnectorsThe capacity for a single shear stud is calculated using Equation 1.

Qn = 0.5sc Asc ' c c f E RgR p Asc F u, Eqn. 1

Rg and R p are defined as follows:

Condition R g R p

Decking oriented parallel to the steel shape

1.5r

r

w

h

1.5r

r

w

h

1.0

0.85**

0.75

0.75

Decking oriented perpendicular to the steel shape.

Number of studs occupying the same deck rib

1

2

3 or more

1.0

0.85

0.7

0.6

0.6

0.6

where,

hr = nominal rib height, in.



Shear Connectors Composite Beam Design AISC-LRFD 360-05

Shear Connectors Page 2 of 5

w r = average width of concrete rib or haunch, in.

** - For a single stud

Equation 1 is based on AISC-LRFD93 specifications Equation I5-1. The bs fac-

tor in Equation 1 is not specified by AISC. It is provided by CSI to allow addi-

tional control over the allowable shear connector load. The default value for

this factor is 1, but that value can be modified using both the preferences and

the overwrites.

If there is formed metal deck, the value of qrs obtained from either Equation 1

or from the overwrites, if specified, is reduced by a reduction factor, RF that

is specified in Composite Beam Design AISC-ASD89 Technical Note Shear

Studs. Note that the reduction factor is different depending on if the span ofthe metal deck ribs is oriented parallel or perpendicular to the span of the

beam.

The reduction factor, RF, applies only to the 0.5 sc Asc ' c c f E term in Equation

1. It does not apply to the RgR p Asc F u term.

The terms f ’ c and E c can be different on the two sides of the beam. The pro-

gram calculates qrs for each side of the beam separately using Equation 1 and

uses the smaller value in the calculations.

Channel Shear ConnectorsThe capacity for channel shear connectors is calculated using Equation 2.

Qn = 36.5 bs (t + 0.5t w )Lcsc '

cf E Eqn. 2

Equation 2 is based on AISC-LRFD 360-05 specifications Equation I5-2. The

bs factor in Equation 2 is the same as that described for Equation 1 in the

previous section.

Because the program does not allow channel shear connectors to be used

with formed metal deck, there is no reduction factor that needs to be applied

to the value of Qn calculated using Equation 2.







Composite Beam Design AISC-LRFD 360-05 Shear Connectors


The terms f ’ c and E c can be different on the two sides of the beam. The pro-

gram calculates Qn for each side of the beam separately using Equation 2 anduses the smaller value in the calculations.

The terms f ’ c can be different on the two sides of the beam. The program cal-

culates qrs for each side of the beam separately using Equation 2 and uses the

smaller value in the calculations.

Horizontal Shear for Full Composite Connection

Between Maximum Moment and Point of Zero MomentPositive Bending

The total horizontal shear to be resisted between the point of maximum p o s i -

t i v e moment (where the concrete is in compression) and the points of zeromoment for full composite connection, qrs -100, is given by the smaller of

Equations 3, 4a or 4b as applicable. Table 1 defines the conditions where the

various equations are applicable and it defines what to use for Ac left and Ac right

(both simply called Ac in the table) in Equation 3 for each condition.

Table 1: Table Defining Equations to be used to Calculate Horizontal Shear for

Full Composite Connection

Deck Rib

Span Relative

to Beam Span Beam Section

Use Smaller

of These

Equations

Note About Ac in

Equation 3

Rolled sectionfrom the pro-

gram database

3 as noted

and 4aPerpendicular

User-defined3 as noted

and 4b

Ac in Equation 3 is the area ofconcrete in the slab above the

metal deck that is above the

elastic neutral axis of the fully

composite beam

Rolled section

from the pro-

gram database

3 as noted

and 4a

Parallel

User-defined3 as noted

and 4b

Ac in Equation 3 is the area of

concrete in the slab, including

the concrete in the metal deck

ribs, that is above the elastic

neutral axis of the fully compos-

ite beam

100 left left right right0 85 0 85n c c c c Q . f A . f A Eqn. 3



Shear Connectors Composite Beam Design AISC-LRFD 360-05


100n s y cp cp ycpQ A F b t F Eqn. 4a

100 top top top bot bot botn f - f - yf - w yw f - f - yf - cp cp ycpQ b t F ht F b t F b t F Eqn. 4b

Number of Shear Connectors

Between Maximum Moment and Point of Zero Moment

For full composite action, the number of shear connectors between a point of

maximum positive or negative moment and adjacent points of zero moment,

N 1, is given by Equation 5.

1001

n

n

QN

Q

Eqn. 5

In Equation 5, Qn-100 is as determined in the previous section entitled "Hori-

zontal Shear for Full Composite Connection" and Qn is determined as de-

scribed in either the previous section entitled "Shear Stud Connectors" or the

previous section entitled "Channel Shear Connectors" depending on the type

of shear connector used.

For partial composite connection, the number of shear connectors between a

point of maximum p o s i t i v e (not negative) moment and adjacent points of

zero moment, N 1, is given by Equation 6.

1

n PCC

n

Q

N Q

Eqn. 6

In Equation 6, Qn-PCC is equal to the percent composite connection times Qn-

100. For example, if there is 70% composite connection, Qn-PCC = 0.7 Qn-100.

Thus, the percent composite connection, PCC, for AISC-LRFD93 design is

given by Equation 7.

100

n PCC

n

QPCC

Q

Eqn. 7

Between Point Load and Point of Zero Moment

The program uses Equation 8 to check that the number of shear connectorsprovided between a point load and a point of zero moment is sufficient. Equa-

tion 8 is not specified by AISC but is used by CSI as the LRFD equivalent of

Equation I4-5 in the AISC-ASD89 specification.



Composite Beam Design AISC-LRFD 360-05 Shear Connectors


steel alone

2 1

comp steel alone

u n

n n

M M N N

M M

Eqn. 8

In Equation 8,

M n comp = Maximum moment capacity of composite beam, consider-

ing partial composite connection if applicable, kip-in.

M n steel alone = Moment capacity of steel beam alone, kip-in.

M u = Moment at point load location, kip-in.

N 1 = Number of shear connectors required between the point of

maximum moment and the point of zero moment, or endof the slab, unitless.

N 2 = Number of shear connectors required between the point

load considered and the point of zero moment, or end of

the slab, unitless.

= Resistance factor used to determine moment capacity of

composite beam, unitless. This is equal to bcpe, bcpp, bcne,

or bcnp depending on if there is positive or negative bend-

ing and if the stress distribution considered is elastic or

plastic.

Equation 8 is checked at each point load location.





Technical Note

Beam Shear Capacity

This Technical Note describes how the program calculates the allowable shear

stress for AISC-LRFD 360-05 composite beam design.

Shear Capacity

AISC-LRFD 360-06 Equations G2-1 through G2-5 are reproduced here as

Equations 1 through 5 respectively.

The nominal shear strength, V n, of unstiffened or stiffened webs is given by:

0.6n y w v V F A C Eqn.1

(a) For webs of rolled I-shaped members with 2.24w y

h E

t F :

v=1.00 and v C =1.00 Eqn.2

(b) For webs of all other doubly symmetric shapes and singly symmetric

shapes and channels, the web shear coefficient, v C , is determined as fol-

lows:

For 1.10 v

w y

k E h

t F , v C =1.00 Eqn.3

For 1.10 1.37v v

y y

k E k E h

F tw F ,

1.10 /v y

v

w

k E F C

ht

Eqn.4

For 1.37 v

w y

k E h

t F ,

21.51 v

v w y

k E C

h t F Eqn.5

In the preceding equations , k v is the web plate buckling coefficient, and it is

defined as:



Beam Shear Capacity Composite Beam Design AISC-LRFD 360-05

Beam Shear Capacity Page 2 of 3

(i) For unstiffened webs with h /t w < 260, k v = 5

(ii) For stiffened webs,

2

55v k

ah

2

2605 for 3.0v

w

a ak or h h h t

where,

a = clear distance between transverse stiffeners, in.

h = for rolled shapes, the clear distance between flanges

less the fillet or corner radii, in.

Note that in preceding Equations, Aw , the area of the web, is calculated as

shown in Equation 4 where C top and C bot are the depths of copes, if any, at the

top and bottom of the beam section. The copes are specified in the over-

writes.

Aw = (d C top C bot) t w Eqn. 6

Checking the Beam Shear

The program checks the beam shear at the ends of the beam using Equation

7.

1.0u

v n

V

V Eqn. 7

where,

V u = The required shear strength, that is, the applied factored shear,kips.

V n = Shear capacity, kips. This term is calculated from Equation 1.



Composite Beam Design AISC-LRFD 360-05 Beam Shear Capacity

Beam Shear Capacity Page 3 of 3

v = Resistance factor for shear, unitless.

Limi tations of Beam Shear Check

Following are some limitations of the program's beam shear check for com-

posite beams.

No check is made for shear on the net section considering the bolt holes.

No check is made for shear rupture on a beam with the top flange coped as

described in AISC-LRFD 360-05 specification.

Beam shear is checked only at the ends of the beam. In unusual cases,

where some of the load cases act downward and some act upward, the

maximum shear may occur elsewhere. For example, consider a beam that

has a uniform load acting downward over its entire length and a single con-

centrated load acting upward at the center. Assume that the magnitude of

the upward concentrated load is equal to the magnitude of the uniform load

times its length. In that case, the end reactions are zero, and the maximum

shear occurs at the center of the beam. The program will check the shear at

the ends of the beam in that case but not at the center.



Overview Page 1 of 11


COMPOSITEBEAMDESIGN AISC360-05/IBC2006

Technical Note

Floor Vibration

Overview

For AISC360-05/IBC2006, by default the program performs the floor vibration

check in accordance with AISC Steel Design Guide 11 (DG11). The program

calculates the first natural vibration frequency, estimated peak acceleration(in units of g), pa g , and acceleration limit, oa g , for each beam and reports

this information to determine the adequacy of a composite beam section.

The acceleration limit of any floor system can be achieved by limiting the vi-

bration characteristics of beams or girders. The program optimize the floor

vibration by limiting the estimated peak acceleration of each individual beams

only.

Excitation Types

The program supports the following excitation types:

Walking Excitation

The recommended walking excitation criterion, the method for estimating the

required floor properties and design procedure, was first proposed by Allen

and Murray (1993). In DG11, the criterion is based on the dynamic response

of steel beam floor systems to walking forces. The criterion can be used to

evaluate structural systems supporting offices, shopping malls, footbridges

and similar occupancies.

Rhythmic Excitation

The rhythmic excitation criterion is based on the dynamic response of the

structural system to rhythmic exercise forces distributed over all or part of

the floor. This criterion is used to evaluate structural systems supporting

aerobics, dancing, audience participation and similar events, assuming that

loading function is known.



Composite Beam Design AISC360-05/IBC2006 Floor Vibration

Design for Walking Excitation Page 2 of 11

Walking near Sensitive Equipment

For sensitive equipment, a criterion is based on the vibrational velocitiesgiven in Table 6.1 of DG11. The following expression can be used to convert

given velocity, V , to the corresponding acceleration, a.

2a g fV g (DG11 Eqn. 6.1)

Design for Walking ExcitationEffective Panel Weight

The effective panel weights for the beam and girder panels modes are esti-

mated from the following equation:

W wBL (DG11 Eqn. 4.2)

where,

w = Supported weight per unit area

L = Beam or girder span

B = Effective width

For the beam panel mode, the effective width is

1 /4

2 3•FloorWidth j j s j j B C D D L (DG11 Eqn. 4.3a)

where,

j C = 2.0 for beams in most areas

= 1.0 for beams parallel to an interior edge

3 12s eD d n = Transformed slab moment of inertia per unit width

ed = Effective depth of concrete slab, taken as the depth of

concrete above the form deck plus one-half the depth of

the form deck

s c n E E = Modular ratio

sE = Modulus of elasticity of steel

c E = Modulus of elasticity of concrete j t D I S = Transformed beam moment of inertia per unit width

t I = Effective moment of inertia of T-beam

S = Beam spacing





j L = Beam span

For the girder panel mode, the effective width is

1 / 4

2 3•Floor Lengthg g j g gB C D D L (DG11 Eqn. 4.3b)

where,

C g = 1.6 for girders supporting beam connected to the girder flange

= 1.8 for girders supporting beam connected to the girder web

Dg = Girder transformed moment of inertia per unit width

= g j I L for all except edge girders

= 2g j I L for edge girders

Lg = Girder span

Where beams or girders are continuous over their supports and an adjacent

span is greater than 0.7 times the span under consideration, the effective

panel weight, W j or W g, can be increased by 50 percent.

For the combined mode, the equivalent panel weight is computed as follows:

j g j g+ +

j g j gW W W

(DG11 Eqn. 4.4)

Note: For vibration calculations, the program calculates the moment of inertia

assuming f ull (100%) composite connection, regardless of the actual percent

composite connection.

Vibration Frequency

The program calculates the first natural vibration frequency of a beam using

the Dunkerley relationship.

0.18

n j g

gf

(DG11 Eqn. 3.4)

where,





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

j and g

= Beam and girder deflections due to the weight supported,respectively

g = Acceleration of gravity

Damping

The damping associated with floor systems depends primarily on non-

structural components, finishing, furnishings and occupants. DG11 Table 4.1

provides the recommended values for THE modal damping ratio, . Recom-

mended modal damping ratios range between 0.01 to 0.05.

Computation of Peak AccelerationThe program calculates the peak acceleration, a , from the following expres-

sion for walking excitation criteria:

0.35 nf p oa P e

g W

(DG11 Eqn. 4.1)

Important Note About W , the Weight Used in the Frequency Calculation

The weight, W , used in the frequency calculations is determined by theprogram as the sum of all dead loads, plus the sum of all superimposeddead loads, plus the sum of additional dead load and the sum of live loads

on the beam specified in the design overwrites, regardless of whetherthose loads are included in a design load combination. The program de-

termines the type of load (dead, sdead, and so on) based on the type ofload specified in the load case definition. The Define menu > Static Load

Cases command can be used to define a load case.

Thus, for the program to correctly calculate the weight supported by the

beam, and thus correctly calculate the frequency, you must be sure to tagall of your load types correctly when you define your static load cases. Be

careful not to define the same load twice (i.e., in two different load cases)

as a Dead, Superimposed dead. If you want or need to define the sameload twice, you may want to tag the load as an Other-type load in the sec-ond case. Doing this keeps the program from double counting the load

when calculating the weight, W .




Design for Rhythmic Excitation Page 5 of 11

where,

P o = A constant force representing the excitation

f n = Fundamental natural frequency of a beam panel, a girder panel,

or a combined panel, as applicable

= Modal damping ratio

W = Effective weight supported by the beam panel, girder panel or

combined panel, as applicable.

Accelerat ion Limit

Acceleration limits depends on occupancy categories, and recommended val-

ues are provided in DG11 Table 4.1. The program uses Table 4.1 values asprogram defaults. However, the user has control to change the acceleration

limits in the design preferences or overwrites.

Design for Rhythmic ExcitationEffective Weight, w t

The effective panel weight is the effective weight per unit area of participants

distributed over the floor panel.

Rhythmic Loading Parameters: w p , i and f The effective total weight per unit area distributed over the floor panel

(weight of participants plus weight of floor system) is taken from DG11 Table

5.2. When areas are partially occupied by occupants, the value of w p is re-

duced on the basis of equivalent effect (moment or deflection) for a fully

loaded span. The values of i and f are also taken from DG11 Table 5.2.

Vibration Frequency


Dunkerley relationship.

0.18n

j g

gf (DG11 Eqn. 3.4)

where,




Design for Rhythmic Excitation Page 6 of 11


j and g = Beam and girder deflections due to the weight supported

respectively


Damping


structural components, finishing, furnishings and occupants. DG11 Table 4.1

provides the recommended values for modal damping ratio, . Recommended

modal damping ratios range between 0.01 to 0.05.

Computation of Peak Acceleration

The peak acceleration, a p, of the floor due to a harmonic rhythmic force is ob-

tained from the following expression:

22 2

1.3

21

p i p t

n n

a w w

gf f

f f

(DG11 Eqn. 2.4)

where,

i = Dynamic coefficient from DG11 Table 2.1

w p = Effective weight per unit area of participants distributed over

floor panel

w t = Effective distributed weight per unit area of floor panel, including

occupants

f n = Natural frequency of floor structure

f = Forcing frequency

= Modal damping ratio

The effective maximum acceleration, accounting for all harmonics is esti-

mated from the following combination rule (Allen 199a).

1 1.51.5

m i a a (DG11 Eqn. 2.6)

where,




Page 7 of 11

i a = Peak acceleration for the i th harmonic.

Accelerat ion Limit

Acceleration limits depends on occupancy categories, and recommended val-

ues are provided in DG11 Table 5.3. The program uses Table 5.3 values as

program defaults. However, the user has control to change the acceleration

limits in design preferences or overwrites.

Design for Sensitive Equipment

Floor VibrationThe following procedure is used for calculating the stiffness of a floor under a

concentrated force of 1kN per mm (5.7 kips per inch). The deflection of a

beam panel under concentrated forces, jP

, is estimated as

oj jP

eff N

(DG11 Eqn. 4.6)

where,

oj = The static deflection of a single, simply supported, tee-beam

due to a 1 kN (0.225 kips) concentrated force calculated us-

ing the same effective moment of inertia as was used for the

frequency calculation.

N eff = Number of effective beams or joists. The concentrated load is

to be placed so as to produce the maximum possible deflec-

tion of the tee-beam. The effective number of tee-beams can

be estimated from

24

90.49 34.2 9.0 10 0.00059 1.0 j j e

eff t

L Ld N

S I S

(DG11 Eqn. 4.7)

and,




Design for Sensitive Equipment Page 8 of 11

0 018 0 208ed

S

. .

46 64.5 10 257 10

j

t

L

I

2 30 j L

S

where,

d e = Effective slab depthS = Beam spacing

L j = Beam span I t = Transformed moment of inertia of the T-beam

The total floor deflection,P

, is then computed using the following equation:

2P jP gP

(DG11 Eqn. 4.8)

where,

gP = maximum deflection of the more flexible girder due to a 1 kN

(0.225 kips) concentrated load, using the same effective mo-

ment of inertia as used in the frequency calculation. The deflec-

tions are usually estimated using the following expression:

3

1

48 t

P L EI (DG11 Eqn. 4.9)

which assumes simple span conditions. To account for rota-

tional restraint provided by beam and girder web framing con-

nections, the coefficient 1/48 is reduced to 1/96, which is the

geometric mean of 1/48 (for simple span beams) and 1/192

(for beams with built-in ends).

Vibration Frequency


Dunkerley relationship.




Design for Sensitive Equipment Page 9 of 11

0.18n

j g

gf

(DG11 Eqn. 3.4)

where,


j and

g = Beam and girder deflections due to the weight supported,

respectively


Damping


structural components, finishing, furnishings, and occupants. DG11 Table 4.1

provides the recommended values for the modal damping ratio, . Recom-

mended modal damping ratios range between 0.01 to 0.05.

Peak Vibration of Floor Caused by Walking

The maximum displacement caused by a footfall impulse, the floor static dis-

placement, static X , due to a point load, mF , is computed as follows:

maxm static A X X (DG11 Eqn. 6.2)

where,

static m P X F

2

max 22

m P o

n

F f X

f

(DG11 Eqn. 6.3)

mF andP

are obtained form DG11 Table 6.2.

Because a floor vibrates at its natural frequency as a result of a footfall im-

pulse, the maximum velocity is determined from the following equation:

max max2 nV f X (DG11 Eqn. 6.4a)




References Page 10 of 11

Vibrational Velocity Limi t for Sensitive Equipment

For sensitive equipment, a criterion is based on the vibrational velocitiesgiven in Table 6.1 of DG11. The following expression can be used to convert

given velocity, V , to the corresponding acceleration, a.

2a g fV g (DG11 Eqn. 6.1)

References

Allen, D.L. 1974. Vibrational Behavior of Long Span Floor Slabs. Canadian

Journal of Civil Engineering. Vol. 1, No. 1. September.

Allen, D. E., and J.H. Rainer. 1976. Vibration Criteria for Long Span Floors.

Canadian Journal of Civil Engineering. Vol. 3, No.2. June.

Allen, D.E., J.H. Rainer, and G. Pernica. 1979. Vibration Criteria for Long Span

Concrete Floors. Vibrations of Concrete Structures. Publication SP-60.

American Concrete Institute. Detroit, MI.

Allen, D. E. and Murray, T. M., 1993, "Design Criterion for Vibrations due to

Walking," Engineering Journal, 4th Qtr, AISC, pp. 117-129.

Murray, T. M., Allen, D. E. and Unger, E. E., 1997, "Floor Vibrations due to

Human Activity," AISC Steel Design Guide Series 11.

Murray, T.H. 1975. Design to Prevent Floor Vibration. Engineering Journal .

American Institute of Steel Construction, Inc. Vol. 12, No. 3.

Murray, T.H. 1981. Acceptability Criterion for Occupant-Induced Floor Vibra-

tions. Engineering Journal. American Institute of Steel Construction,

Inc. Vol. 18, No. 2.

Murray, T.M. 1991. Building Floor Vibrations. Engineering Journal. American

Institute of Steel Construction, Inc. Vol. 28, No. 3.

Murray, T.M. and W.E. Hendrick. 1977. Floor Vibrations and CantileveredConstruction. Engineering Journal . American Steel Institute of Steel

Construction, Inc. Vol. 14, No. 3.




References Page 11 of 11

Naeim, F. 1991. Design Practice to Prevent Floor Vibration. Steel Tips, Techni-

cal Information & Product Service. Structural Steel Educational Coun-cil. September.



Input Data Page 1 of 7



Technical Note

Input Data

This Technical Note describes the composite beam design input data for AISC-

LRFD 360-05. The input can be printed to a printer or to a text file when you

click the File menu > Print Tables > Composite Beam Design command.

A printout of the input data provides the user with the opportunity to carefully

review the parameters that have been input into the program and upon which

program design is based. See Composite Beam Design Technical Note Input

Data for further information about using the print Composite Beam Design

Tables Form, as well as other non-code-specific input data for composite

beam design.

Beam Overwrites Input Data

The program provides the printout of the input data in a series of tables. The

tables typically correspond to the tabs used in the Composite Beam Over-

writes form. The column headings for input data and a description of what is

included in the columns of the tables are provided in Table 1 of this Technical

Note.

Recall that the composite beam overwrites apply to all beams to which they

have been specifically assigned. To access the composite beam overwrites,

select one or more beams and then click the Design menu > Composite

Beam Design > View/Revise Overwrites command. Information about

composite beam overwrites is available in Composite Beam Design AISC-LRFD

360-05 Technical Note Overwrites.











Input Data Composite Beam Design AISC-LRFD 360-05


Table 1 Beam Overwri tes Input Data

COLUMN HEADING DESCRIPTION

Beam Location InformationThis information does not correspond to one of the tabs in the composite beam over-writes. This data is provided to help identify the beam to which printed overwrites apply.

XGlobal X coordinate of the center of the beam to which theoverwrites apply.

YGlobal Y coordinate of the center of the beam to which theoverwrites apply.

LengthLength of the beam to which the overwrites apply.

Beam Properties

Composite Type Type of beam design. The choices are Composite, NC w/ studsand NC w/o studs. NC w/ studs is short for noncomposite withminimum shear studs. NC w/o studs is short for noncompositewithout shear studs. Note that this option allows you to design anoncomposite floor beam in the Composite Beam Design post-processor.

Shoring Provided This item is Yes if the composite beam is shored. Otherwise, itis No. Note that this item supersedes the Shored Floor item inthe composite beam preferences.

b-eff Left If the beff left width is program calculated, this item reads "ProgCalc." Otherwise, this item is the user-defined width for beff left.See Composite Beam Design Technical Note Effective Width ofthe Concrete Slab for description of the effective width of theslab.

b-eff Right If the beff right width is program calculated, this item reads "ProgCalc." Otherwise, this item is the user-defined width for beff right.See Composite Beam Design Technical Note Effective Width ofthe Concrete Slab for description of the effective width of theslab.

Beam Fy If the beam yield stress is based on the material property speci-fied for the beam, this item reads "Prog Calc." Otherwise, thisitem is the user-defined yield stress of the beam.

Beam Fu If the beam minimum tensile strength is based on the materialproperty specified for the beam, this item reads "Prog Calc."Otherwise, this item is the user-defined minimum tensilestrength of the beam.













Composite Beam Design AISC-LRFD 360-05 Input Data


Table 1 Beam Overwrites Input Data


Cover PlateThis information is included on the Beam tab of the overwrites.

Plate Width Width of the cover plate.

Plate Thick Thickness of the cover plate.

Plate Fy Yield stress of the cover plate.

Consider Cover Plate If this item is "Yes," the specified cover plate is considered inthe design of the beam. Otherwise, the cover plate is not con-sidered in the beam design.

Beam Unbraced LengthBeam unbraced length data is provided for both the construction condition and the finalcondition. The headings for these two types of beam unbraced lengths are “Beam Un-braced Length (Construction Loading)” and “Beam Unbraced Length (Final Loading).”The types of data provided in each of these tables is identical and is documented oncehere.

Bracing State This item can be "Prog Calc," "User Bracing," or "LengthGiven." Prog Calc means that the program determines thebraced points of the beam. User Bracing means that you havespecified the actual bracing for the beam. The user-definedbracing may be point or uniform bracing along the top and bot-tom flange of the beam. Length Given means that you havespecified a single maximum unbraced length for the beam.

Unbraced L22 If the Bracing State item is "Length Given," this item is the user-specified maximum unbraced length of the beam. Otherwise,this item is specified as N/A.

L22 Absolute If the Bracing State item is "Length Given," this item indicateswhether the user-specified maximum unbraced length of thebeam (the Unbraced L22 item) is an absolute (actual) length ora relative length. A relative length is the maximum unbracedlength divided by the length of the beam. If the Bracing Stateitem is not Length Given, this item is specified as N/A.

Cb Factor If the Cb factor is calculated by the program, this item reads"Prog Calc." Otherwise, the user-defined Cb factor that is usedin determining the allowable bending stress is displayed. (Notethat when the ω2 factor is program calculated, it may be differ-ent for each design load combination, and for a given designload combination, it may be different for each station consid-ered along the length of the beam.)







Point Braces

The heading of the point braces data table specifies whether the point braces are pro-gram calculated or user-defined, and whether the distances used to locate the pointbraces (Location item) are absolute (actual) distances or relative distances. A relativedistance is the distance divided by the length of the beam.

Location This is the distance from the I-end of the beam to the pointbrace. As described in the preceding description, it may be anabsolute or a relative distance.

Type The choices for this item are TopFlange, BotFlange orBothFlngs. TopFlange means only the top flange is braced at

this point. BotFlange means only the bottom flange is braced atthis point. BothFlngs means both the top and bottom flangesare braced at this point.

Uniform Braces

The heading of the uniform braces data table specifies whether the point braces are pro-gram calculated or user-defined, and whether the distances used to define the extent ofthe uniform braces (Start and End items) are absolute (actual) distances or relative dis-tances. A relative distance is the distance divided by the length of the beam.

Note:Details about the location and type of program calculated point and uniform braces is re-ported only after the design has been run. Before the design is run, this information is notavailable.

Start This is the distance from the I-end of the beam to the startingpoint of the uniform brace. As described in a previous descrip-tion, it may be an absolute or a relative distance.

End This is the distance from the I-end of the beam to the endingpoint of the uniform brace. This distance is always larger thanthe Start item. As described previously, it may be an absoluteor a relative distance.

Type The choices for this item are TopFlange, BotFlange orBothFlngs. TopFlange means only the top flange is uniformlybraced along the specified length. BotFlange means only thebottom flange is uniformly braced along the specified length.BothFlngs means both the top and bottom flanges are uniformly

braced along the specified length.







Deck Properties

Beam Side This item is either Left or Right. It indicates to which side of thebeam the deck label and deck direction specified in the samerow apply.

Deck Label This item is either “Prog Calc,” if the deck label is determinedby the program, or it is the label (name) of a defined deck sec-tion, if this is a user-specified overwrite, or it is "None" if nocomposite deck has been specified on the side of the beam.

Deck Direction This item is “Prog Calc,” “Parallel,” or “Perpendclr.” Prog Calcmeans that the direction of the deck span (parallel or perpen-dicular to the beam span) is program determined. Parallelmeans that the span of the metal deck is parallel to the beamspan. Perpendclr means that the span of the metal deck is per-pendicular to the beam span.

Shear Stud Properties

Min Long Spacing Minimum longitudinal spacing of shear studs along the beam.

Max Long Spacing Maximum longitudinal spacing of shear studs along the beam.

Min Tran Spacing Minimum transverse spacing of shear studs across the beamflange.

Max Conn in a Row Maximum number of shear studs in a single row across the

beam flange.Stud qrs This item is “Prog Calc” if the allowable horizontal load for a

single shear stud is determined by the program, or it is a user-defined allowable horizontal load for a single shear stud.

User-Defined Shear Stud PatternUniform Spacing The uniform spacing of single shear studs along the length of

the beam.

User-Defined Uniform Stud Sections

The heading of the uniform stud sections data table specifies whether the distances usedto define the extent of the stud sections (Start, End and Length items) are absolute (ac-tual) distances or relative distances. A relative distance is the distance divided by thelength of the beam.

Note: User-defined shear stud patterns are described in Composite Beam Design TechnicalNote User-Defined Shear Stud Patterns.











Start This is the distance from the I-end of the beam to the startingpoint of the uniform stud section. As described previously, itmay be an absolute or a relative distance.

End This is the distance from the I-end of the beam to the endingpoint of the uniform stud section. As described previously, itmay be an absolute or a relative distance.

Length This is the length of the uniform stud section. As described pre-viously, it may be an absolute or a relative distance.

Number The number of uniformly spaced shear studs in the uniform

stud section. Deflection, Camber and Vibration

Deflection Absolute If the live load and total load deflection limits are specified asabsolute (actual) distances, this item is Yes. If they are speci-fied as a divisor of beam length (relative), this item is No.

Live Load Limit The live load deflection limit for the beam.

Total Load Limit The total load deflection limit for the beam.

Calculate Camber If this item is Yes, the program calculates the camber for thebeam. If it is No, the program does not calculate a camber, butif desired, the user can specify the camber.

Specified Camber User-specified camber when the program does not calculatethe beam camber.

Vibration CriterionExcitation types to estimate the peak acceleration or vibrationalvelocities.


Occupancy CategoryToggle to consider the occupancy category to be used for de-termining if a beam section is acceptable.

Damping Ratio Damping ratio, which depends on occupancy category.

Bay Frequency

Acceleration Limit,ao/g

Acceleration limits for a specific occupancy.

Additional Dead Load Additional Dead load acting on floor system.

Live Load Live load for computing the beam frequency.

Colateral load Colateral load for computing beam frequency.Preference Applicable to Rhythmic Excitation









Bay Frequency

Rhythmic Activity Type Type of rhythmic activity due to occupants activity.

Affected OccupancyCategory

Type of occupancy in the area adjacent to the Rhythmic activ-ity.

Acceleration Limit,ao/g

Acceleration limits for a specific occupancy.

Upper Step FrequencyEstimated loading during rhythmic event in accordance withDG11 Table 5.2.

Lower Step FrequencyEstimated loading during rhythmic event in accordance withDG11 Table 5.2. Maximum three harmonic frequencies for

jumping exercise. Additional Dead Load Additional Dead load acting on floor system.

Live Load Live load for computing the beam frequency.

Colateral load Colateral load for computing beam frequency.




Bay Frequency

Equipment or UseCategory


Vibrational Velocity

LimitVibrational velocity limits for a specific occupancy.

Footfall Impulse fo(Fast)

Values of footfall impulse parameters from DG11 Table 6.2.

Footfall Impulse fo(Moderate)


Footfall Impulse fo(Slow)


Footfall Impulse Fm(Fast)


Footfall Impulse Fm(Moderate)


Footfall ImpulseFm(Slow)


Additional Dead Load Additional Dead load acting on floor system.Live Load Live load for computing the beam frequency.

Colateral load Colateral load for computing beam frequency.



Output Details Page 1 of 14



Technical Note

Output Details

This Technical Note describes the composite beam output for AISC-LRFD 360-

05 that can be printed to a printer or to a text file in short form or long form.

See Composite Beam Design Technical Note Output Data for information

about using the Print Composite Beam Design Tables Form, as well as the

Summary of Composite Beam Output.

The program provides the output data in a series of tables. The column head-ings for output data and a description of what is included in the columns of

the tables are provided in Tables 1 and 2 of this Technical Note.

Short Form Output Details

This output is printed when you click the File menu > Print Tables > Com-

posite Beam Design command and select Short Form in the Output Details

area of the resulting form. Similar output also appears on screen if you click

the Details button in the Show Details area of the Interactive Composite

Beam Design and Review form. See Composite Beam Design Technical Note

Interactive Composite Beam Design for more details on the interactive design.

Table 1 Output Details - Short Form


Basic Beam Information

Beam Label Label associated with the line object that represents the beam. A typical beam label would appear as "B23." Do not confusethis with the Section Label, which would be identified as"W610X82."

Group Name of the design group (if any) to which the beam has been

assigned.

Beam Beam section label (name).









Composite Beam Design AISC-LRFD 360-05 Output Details




Fy Beam yield stress, Fy.

Fu Beam minimum tensile strength, Fu.

Stud Layout Number of studs in each composite beam segment separatedby commas. They are listed starting with the composite beamsegment at the I-end of the beam and working toward the J-endof the beam.

Seg. Length Length of each composite beam segment separated by com-mas. The lengths are listed starting with the composite beamsegment at the I-end of the beam and working toward the J-endof the beam.

Stud Ratio This item has a slightly different meaning, depending onwhether the shear studs are user-defined or calculated by theprogram.

When the number of shear studs is calculated by the program,a stud ratio is reported for each composite beam segment. It isequal to the number of shear studs required in the segmentdivided by the maximum number of studs that fit in the seg-ment.

When the shear studs are user-defined, a single stud ratio isreported for the entire beam. At each output station considered(i.e., at each maximum moment or point load location), the pro-gram calculates the number of shear studs required betweenthe output station and adjacent points of zero moment, end ofthe beam top flange, or end of the concrete slab. The programthen divides this number of required shear studs by the speci-fied number of shear studs to obtain a ratio. The maximum ratioobtained at any considered output station for any design loadcase is reported as the stud ratio.

Story Story level associated with the beam.

Length Length of the beam.

Loc X Global X coordinate of the center of the beam.







Loc Y Global Y coordinate of the center of the beam.

RLLF A reducible live load is multiplied by this factor to obtain the re-duced live load.

Shored This item is Yes if the beam is shored and No if it is unshored.

Camber The camber for the beam. This item may be calculated by theprogram or it may be user-specified.

Comparative Price of the beam using the input price parameters for steel,shear studs and camber. This price is intended for comparisonof alternative designs only. It is not intended to be used for costestimating purposes.

Stud Diam Diameter of shear studs.

Overwrites If this item is Yes, one or more items have been overwritten forthis beam. If it is No, nothing has been overwritten. The valuesfor all overwrite items are included in the long form output.Thus, if this item is "Yes," you may want to print the long formoutput.

b-cp Width of the cover plate. If no cover plate is specified by theuser, N/A is reported for this item.

t-cp Thickness of the cover plate. If no cover plate is specified bythe user, N/A is reported for this item.

Fy-cp Yield stress for the cover plate. If no cover plate is specified bythe user, N/A is reported for this item.

Consider-cp This item is Yes if the specified cover plate is considered in thedesign. Otherwise, it is No.

Deck Left and Deck

Right

The deck section labels (names) on the left and right sides of

the beam.







Dir. Left and Dir. Right The deck directions on the left and right sides of the beam.Perpendclr means that the deck span is perpendicular to thebeam span. Parallel means that the deck span is parallel to thebeam span.

beff Left and beff Right The slab effective widths on the left and right sides of the beam.

Ctop Left and CtopRight

The program calculated cope of the beam top flange at the leftand right ends of the beam. Do not confuse the left and rightends of the beam with the left and right sides of the beam. Theleft end of the beam is the I-end and the right end of the beamis the J-end.

Cbot Left and CbotRight

The program calculated cope of the beam bottom flange at theleft and right ends of the beam. Do not confuse the left and rightends of the beam with the left and right sides of the beam. Theleft end of the beam is the I-end and the right end of the beamis the J-end.

Itrans Transformed section moment of inertia for full (100%) compos-ite connection for positive bending, Itr .

Ibare Moment of inertia of the steel beam, including cover plate, if itexists.

Is Moment of inertia of the steel beam alone, not including coverplate, even if it exists.

Ieff Effective moment of inertia for partial composite connection.

PCC Percent composite connection.

ytrans Distance from the bottom of the beam bottom flange (not bot-tom of cover plate, even if it exists) to the elastic neutral axis

(ENA) of the beam, with full (100%) composite connection, y .

ybare Distance from the bottom of the beam bottom flange (not bot-tom of cover plate, even if it exists) to the ENA of the beam,plus cover plate alone (if it exists).







yeff Distance from the bottom of the beam bottom flange (not bot-tom of cover plate, even if it exists) to the ENA of the beam,with partial composite connection.

Moment Design

This table of output data reports the controlling moments for both construction loads and

final loads.

Pmax The largest axial load in the beam for any design load combina-

tion.

Important note: This value is not used in the Composite BeamDesign postprocessor design. It is reported to give you a senseof how much axial load, if any, is in the beam. If there is a sig-nificant amount of axial load in the beam, you may want to de-sign it noncompositely using the Steel Frame Design postpro-cessor. The Steel Frame Design postprocessor does consideraxial load.

Pmax Combo The design load combination associated with Pmax.

PCC PNA Location of plastic neutral axis (PNA) for partial composite con-nection (PCC).

PCC phi Mn Factored nominal flexural resistance with partial composite con-nection.

Full PNA Location of plastic neutral axis (PNA) for full composite connec-tion.

Full phi Mn Factored nominal flexural resistance with full composite con-nection.

Type This item is either Constr Pos, Constr Neg, Final Pos or FinalNeg. Const Pos means it is a positive moment for constructionloading. Const Neg means it is a negative moment for construc-tion loading. Final Pos means it is a positive moment for final

loading. Final Neg means it is a negative moment for final load-ing.







Combo Design load combination that causes the controlling moment forthe moment type considered in the table row.

Lb Unbraced Length

Mu The controlling factored design moment for the moment typeconsidered in the table row.

phi Mn Maximum factored flexural resistance associated with this loadcombination.

Ratio This is Mu divided by Mn.

Shear Design

This table of output data reports the controlling shears for both construction loads and

final loads.

Type This item is either Constr Left, Constr Right, Final Left or FinalRight. Constr Left means it is a construction loading shear atthe left end of the beam. Constr Right means it is a constructionloading shear at the right end of the beam.

Final Left means it is a final loading shear at the left end of the

beam. Final Rght means it is a final loading shear at the rightend of the beam.

Combo Design load combination that causes the controlling shear forthe shear type considered in the table row.

Vu The controlling factored shear for the shear type considered inthe table row.

phi Vn The maximum factored shear resistance associated with thecontrolling moment.

Ratio This is Vu divided by Vn.







Deflection Design

This table of output data reports the controlling deflections for both live load and total

load.

Type This item is either Live Load or Total Load.

Consider This item is always Yes, indicating that deflection is one of thecriteria checked when determining if a beam section is consid-ered acceptable.

Combo Design load combination that causes the controlling deflectionfor the deflection type considered in the table row.

Deflection The controlling deflection for the deflection type considered inthe table row.

Note:

Deflection is described in Composite Beam Design Technical Note Beam Deflection

and Camber.

Limit The deflection limit for the deflection type considered in the ta-ble row.

Ratio This is the controlling deflection divided by the deflection limit.

DG11 Vibration Design

Neff The effective number of beams used in the vibration evalua-tions.

Type Walking, Rhytmic or Equipment.

Consider Indicates whether vibration was considered in the design.

Mode Acceleration or Upper and Lower or Fast, Moderate and Slow

Actual Calculate acceleration/vibrational velocity (in terms of g) of thebeam.













Target Minimum acceptable acceleration/vibrational velocity (in termsof g) required.

Ratio Target divided by actual.

Ok Indicates whether the member is acceptable for vibration re-quirements.

Long Form Output DetailsThis output is printed when you click the File menu > Print Tables > Com-

posite Beam Design command to open the Print Composite Beam Design

Tables form and select Long Form under Output Details. The long form output

details report provides all of the data described in Table 1 for the Short Form

Output as well as the data described in Table 2 Output Details - Long Form.

Table 2 Output Details - Long Form


Beam PropertyOverwrites

Indicates user-specified overwrite values or program calculatedvalues.

Composite Type Either composite or noncomposite (NC) with studs, or noncom-posite without studs.

Shoring Provided Yes or No.

beff Left Program calculated or user-defined effective width of concreteslab on left side of beam.

beff Right Program calculated or user-defined effective width of concreteslab on right side of beam.

Fy Yield stress of beam.

Fu Minimum tensile strength of the beam.







Beam Unbraced Length Overwrites (Construction Loading):

Bracing State User defined or program calculated.

Unbraced L22 Maximum unbraced length for buckling about the 2-2 axis of thebeam. This item is filled with "N/A" unless the unbraced lengthfor buckling about the local 2-2 axis is user defined and is asingle maximum unbraced length for the entire beam.

Absolute L22 A "Yes" for this item indicates that the unbraced lengths arespecified as absolute distances from the left end of the beam. A"No" indicates that they are specified as relative distances fromthe left end of the beam, with 0 indicating the left end of thebeam and 1 indicating the right end of the beam.

Cb Factor Unitless factor used in determining allowable bending stress.Program calculated if zero is specified.

Program Calculated Uniform Braces for Construction Loading:

Start Distance from the left end of the beam to the starting point ofthe uniform brace that braces the beam for buckling about the2-2 axis.

End Distance from the left end of the beam to the ending point of theuniform brace that braces the beam for buckling about the 2-2axis.

Type Type of uniform brace for buckling about the 2-2 axis. T = topflange only braced, B = bottom flange only braced, A = both(all) flanges braced.

Beam Unbraced Length Overwrites (Final Loading):

Bracing State User defined or program calculated.

Unbraced L22 Maximum unbraced length for buckling about the 2-2 axis of thebeam. This item is filled with "N/A" unless the unbraced lengthfor buckling about the local 2-2 axis is user-defined and is asingle maximum unbraced length for the entire beam.







Absolute L22 A "Yes" for this item indicates that the unbraced lengths arespecified as absolute distances from the left end of the beam. A"No" indicates that they are specified as relative distances fromthe left end of the beam, with 0 indicating the left end of thebeam and 1 indicating the right end of the beam.

Cb Factor Unitless factor used in determining allowable bending stress.Program calculated if zero is specified.

Program Calculated Uniform Braces for Final Loading:

Start Distance from the left end of the beam to the starting point ofthe uniform brace that braces the beam for buckling about the2-2 axis.

End Distance from the left end of the beam to the ending point of theuniform brace that braces the beam for buckling about the 2-2axis.

Type Type of uniform brace for buckling about the 2-2 axis. T = topflange only braced, B = bottom flange only braced, A = both(all) flanges braced.

Deck Property Overwrites:

Beam Side Left and right.

Deck Label User defined or program calculated.

Deck Width User defined or program calculated.

Deck Direction User defined or program calculated.

Shear Stud Property Overwrites:

Min. Long Spacing Minimum allowed longitudinal spacing of the shear stud con-

nectors.

Max. Long Spacing Maximum allowed longitudinal spacing of the shear stud con-nectors.







Min. Tran Spacing Minimum allowed transverse spacing of shear stud connectors.

Max. Conn. in a Row Maximum allowed number of shear stud connectors in a singlerow across the beam flange.

Qn Allowable horizontal shear load for a single shear stud.

Deflection, Camber and Vibration Overwrites:

Deflection Absolute A "Yes" for this item indicates that the deflection limits are

specified as absolute distances. A "No" indicates that they arespecified as the length of the beam, L, divided by some num-ber, e.g., L/360

Precomp DL Limit Limiting precomposite Dead load deflection used when deflec-tion limitations are considered in selecting the optimum beam.

Super Load Limit Limiting super dead load deflection used when deflection limita-tions are considered in selecting the optimum beam.

Live Load Limit Limiting live load deflection used when deflection limitations areconsidered in selecting the optimum beam.

Total Load Limit Limiting total load deflection used when deflection limitationsare considered in selecting the optimum beam.

Calculated Camber Yes or No.

Specified Camber Specified value or N/A if not specified.

Neff Beam Effective number of beams used in the vibration calculations.

Other Restriction Overwrites:

Limit Beam Depth Yes if user inputs depth limit.

Minimum Depth Minimum shown if specified. Zero is not specified.

Maximum Depth Maximum shown, if specified; 1100 mm is not specified.







Maximum PCC Maximum percent composite connection considered by theprogram

Minimum PCC Minimum percent composite connection considered by the pro-gram

RLLF A reducible live load is multiplied by this factor to obtain the re-duced live load.

Reduction Factor The reported reaction forces are multiplied by this factor. Speci-fying 1 in the overwrites means that the program calculatedload-factored end reaction forces is to be reported.

Consider similarity Yes or No.

DG11 Vibration Design

Element Identification of Beam, Girder or Slab

Delta Deflection of Beam, Girder or Slab used to determine the fre-quency.

fn Beam, Girder or Slab frequency in Hz.

Output for Walking Excitation

fn Frequency of a panel in Hz.

Beta Modal damping ratio.

W Effective Weight of the floor.

Po Constant force causing vibration.

ap/g Estimated Peak Acceleration (in units of g).

ao/g Acceleration Limit (in units of g).







Output for Rhythmic Excitation



wt Effective total weight per unit area distributed over the floorpanel.

wp Effective weight per unit area distributed over the floor panel.

wp/wt Ratio of wp/wt.

Harmonic Number of Harmonic cycles.

Alpha Dynamic coefficient from DG11 Table 5.1.

Lower f Lower frequency in Hz.

ao/g (L) Lower acceleration limit (in units of g).

Upper f Upper frequency in Hz.

ao/g (U) Upper acceleration limit (in units of g).

Output for Sensitive Equipment Excitation



Neff Number of effective beams.

Deltaoj Maximum deflection of beam.

DeltagP Maximum deflection of girder.

DeltaP Maximum deflection of panel.

Pace Walking pace, i.e. Slow/Moderate/Fast.






fo Frequency caused by walking pace in Hz.

Fm Maximum Force causing impulse loading.

Am Maximum dynamic deflection caused by Fm.

Xmax Maximum displacement caused by impulse loading.

Vmax Maximum velocity caused by impulse loading.

Documents

Composit Beam