Notes
The AISC-ASD89 Composite Beam Design series of Technical Notes describes in detail the various aspects of the composite beam design procedure that is used by the program when the user selects the AISC-ASD89 Design Code.
The various notations used in this series are listed herein.
The design is based on loading combinations specified by the user. To facili-tate the design process, the program provides a set of default load combina-tions that should satisfy requirements for the design of most building type structures. See Composite Beam Design Technical Note 10 Design Load Com-binations for more information.
The program also performs the following check, calculation, or analysis pro-cedures in accordance with AISC-LRFD93 requirements:
Checks the width-to-thickness ratios of the beam flanges and web, and, if it exists, the cover plate as specified for compact and noncompact sections in AISC-ASD89 Specification Chapter B, Table B5.1; see Composite Beam De-sign AISC-LRFD93 Technical Note 19 Width to Thickness Checks.
Calculates the transformed moment of inertia for a composite section, Itr; see Composite Beam Design AICS-ASD89 Technical Note 20 Transformed Section Moment of Inertia.
Calculates elastic stresses for positive bending in the steel section and the concrete slab when there is partial composite connection; see Composite Beam Design AISC-ASD89 Technical Note 21 Elastic Stresses with Partial Composite Connection.
Technical Note 16 - 2 General and Notation
Determines the allowable bending stresses using the AISC-ASD89 specifi-cation for composite beams; see Composite Beam Design AISC-ASD89 Technical Note 22 Allowable Bending Stresses.
Checks the bending stress for AISC-ASD89 design for cases with and with-out composite action; see Composite Beam Design AISC-ASD89 Technical Note 23 Bending Stress Checks.
Check the beam and reaction for shear for AISC-ASD89 composite beam design; see Composite Beam Design AISC-ASD89 Technical Note 24 Beam Shear.
Defines the program fault allowable shear stud horizontal loads for AISC-ASD89 composite beam design and provides basic equations used to de-termine the number of shear studs on the beam; see Composite Beam De-sign AISC-ASD89 Technical Note 25 Shear Studs.
Determines the placement of shear studs on a composite beam, including three example problems; see Composite Beam Design AISC-LRFD93 Tech-nical Note 26 Calculations for Number of Shear Studs . Also see Composite Beam Design Technical Note 13 Distribution of Shear Studs on a Composite Beam, Technical Note 14 The Number of Shear Studs that Fit in a Compos-ite Beam Segment ComposCompos-ite Beam Design, and Technical Note 15 User-Defined Shear Stud Patterns Composite Beam Design for more information about shear stud distribution.
The program also provides input and output data summaries, which are de-scribed in Composite Beam Design AISC-LRFD93 Technical Note 27 Input Data and Technical Note 28 Output Details Composite Beam Design AISC-LRFD93.
Notation
Abare Area of steel beam (plus cover plate if one exists), in2. This area does not include any contribution from the concrete slab.
Ac Area of the concrete slab, in2. When the deck span is per-pendicular to the beam span, this is the area of concrete in the slab above the metal deck that is above the elastic
Composite Beam Design AISC-ASD89 General and Notation
General and Notation Technical Note 16 - 3
neutral axis (ENA) of the fully composite beam. When the deck span is parallel to the beam span, this is the area of concrete in the slab, including the concrete in the metal deck ribs, that is above the ENA of the fully composite beam. This item may be different on the left and right sides of the beam.
Aelement Area of an element in the composite section, ignoring any
area of concrete that is in tension and ignoring any con-crete in the metal deck ribs when the metal deck span is perpendicular to the beam span, in2.
Af Area of compression flange (not including the cover plate, even if it exists), in2
Agt Gross area along the tension plane of a bolted connection, in2.
Ans Net area along the shear plane of a bolted connection, in2. As Area of rolled steel section alone (without the cover plate,
even it one exists), in2
Asb Initial displacement amplitude of a single beam resulting from a heel drop impact, in.
Asc Cross-sectional area of a shear stud, in2.
Atr Area of an element of the composite beam section, in2. Cb Bending coefficient dependent on moment gradient,
unitless.
Cbot Cope depth at bottom of beam, in. This item is internally calculated by the program and it may be different at each end of the beam. It is used in the shear calculations.
Ctop Cope depth at top of beam, in. This item is internally cal-culated by the program and it may be different at each end of the beam. It is used in the shear calculations.
Technical Note 16 - 4 General and Notation D Damping ratio, percent critical damping inherent in the floor system, unitless. This item is used in checking the Murray damping requirement.
DL Acronym for deal load.
Ec 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 may be different for stress calculations and deflection calculations. For stress calculations in AISC-ASD89 design Ec is always based on Equation 1 of Com-posite Beam Design Technical Note 20 Transformed Section Moment of Inertia using the f value specified in the materialc' properties for the concrete and assuming that the concrete weighs 150 pcf regardless of its actual unit weight. This is consistent with Section I2.2 of the AISC-ASD89 Specifica-tion.
Es Modulus of elasticity of steel, ksi ENA Acronym for elastic neutral axis
Fb Allowable bending stress in steel beam, ksi
Fb-bbf Allowable bending stress at the bottom of the beam
bot-tom flange, ksi
Fu Minimum specified tensile strength of the steel beam and the shear studs, ksi
Fv Allowable shear stress in steel beam, ksi
Fy Minimum specified yield stress of structural steel, ksi Fycp Minimum specified yield stress of cover plate, ksi.
G Gap distance between face of support and end of top flange of steel beam, in. The program always takes this distance as 1/2 inch.
Hs Length of shear stud connector after welding, in.
Composite Beam Design AISC-ASD89 General and Notation
General and Notation Technical Note 16 - 5
Ibare Moment of inertia for a steel beam (plus cover plate, if it exists), in4.
Ieff Effective moment of inertia for a beam about the ENA of a composite beam with partial composite connection, in4. I0 Moment of inertia of an element of a steel beam section
taken about its own ENA, in4.
Is Moment of inertia of the steel beam along (not including cover plate, even if it exists), in4.
Itr Transformed section moment of inertia about ENA of a composite beam with full (100%) composite connection, in4.
Kf A unitless coefficient typically equal to 1.57 unless the beam is the overhanging portion of a cantilever with a backspan, in which case, Kf is as defined in Figure 1 of Composite Beam Design Technical Note 12 Beam Vibration, or the beam is a cantilever that is fully fixed at one end and free at the other end, in which case Kf is 0.56.
L Center-of-support to center-of-support length of the beam, 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 end of the beam top flange, (2) another beam framing into the beam being considered, (3) physical end of concrete slab. Figure 1 of Composite Beam Design Technical Note 13 Distribution of Shear Studs on a Com-posite Beam illustrates some typical cases for LCBS.
Technical Note 16 - 6 General and Notation
L1left Distance from an output station to an adjacent point of
zero moment or physical end of the beam top flange, or physical end of the concrete slab, measured toward the left end (I-end) of the beam, in.
L1right Distance from an output station to an adjacent point of zero moment or physical end of the beam top flange, or physical end of the concrete slab, measured toward the right end (J-end) of the beam, in.
LL Acronym for live load.
M Moment, kip-in.
MAll Other Moment due to all loads except dead load, kip-in.
MDL Moment due to dead load, kip-in.
Mmax station Maximum moment at any output station for a given design load combination, kip-in.
Mstation Moment at the output station considered for the design
load combination, kip-in.
M1 Smaller bending moment at the end of the unbraced beam span, kip-in. This is used when the program calculates the Cb factor.
M2 Larger bending moment at the end of an unbraced beam span, kip-in. This is used when the program calculates the Cb factor.
MaxLS Maximum longitudinal spacing of shear studs along the length of the beam, in. This item is specified on the Shear Studs tab in the composite beam overwrites.
MLS Minimum longitudinal spacing of shear studs along the length of the beam, in. This item is specified on the Shear Studs tab in the composite beam overwrites.
Composite Beam Design AISC-ASD89 General and Notation
General and Notation Technical Note 16 - 7
MSCBS Minimum required number of shear studs in a composite beam segment, unitless.
MSPR Maximum shear studs per row across the beam top flange as specified on the Shear Studs tab in the composite beam overwrites, unitless.
MTS Minimum transverse spacing of shear studs across the beam top flange as specified on the Shear Studs tab in the composite beam overwrites, in.
N The number of shear studs required between an output station and adjacent points of zero moment or physical end of the beam top flange, or physical end of the concrete slab, unitless. This number is based on Equation 6, Equa-tion 7, or EquaEqua-tion 9 of Composite Beam Design AISC-ASD89 Technical Note 25 Shear Studs.
NCBS The number of uniformly distributed shear studs that the program requires for a composite beam segment, unitless.
Neff The effective number of beams resisting a heel drop im-pact, unitless. This item is used in the vibration calcula-tions.
Nr Number of shear stud connectors in one metal deck rib, but not more than 3 in the calculations even if more than 3 studs exist in the rib, unitless. The program uses whatever value is specified for the Max Studs per Row item on the Shear Studs tab in the composite beam overwrites for Nr, unless that value exceeds 3, in which case the program uses 3.
N1 Number of shear connectors required between the point of maximum positive moment and adjacent points of zero moment for the design load combination, unitless.
N2 Number of shear connectors required between a point load and the nearest point of zero moment for the design load combination, unitless.
Technical Note 16 - 8 General and Notation NR Number of metal deck ribs within a composite beam seg-ment that are available to receive shear studs when the metal deck span is oriented perpendicular to the beam span, unitless.
NSmax Maximum number of shear studs that fit in a composite beam segment, unitless.
PO Heel drop force, kips. This force is taken as 600 pounds converted to the appropriate units.
PCC Percent composite connection, unitless.
RF Reduction factor for the allowable horizontal load for a shear stud based on the metal deck and shear stud ge-ometry, unitless.
RLL Acronym for reduced live load.
RLLF The reduced live load factor for an element, unitless. The RLLF is multiplied times the unreduced live load to get the reduced live load.
RSmax Maximum number of rows of shear studs that can fit in a composite beam segment when there is a solid slab or when the metal deck span is oriented parallel to the beam span, unitless.
S Support distance. This is the assumed distance from the center of the support to the face of the support used to calculate the available length of the beam top flange.
Sbare Section modulus of the steel beam alone (plus cover plate, if it exists) referred to the extreme tension fiber, in3.
Seff Effective section modulus of a partially composite beam referred to the extreme tension fiber of the steel beam section (including cover plate, if it exists), in3.
Composite Beam Design AISC-ASD89 General and Notation
General and Notation Technical Note 16 - 9
Sr Center-to-center spacing of metal deck ribs, in. This item may be different on the left and the right sides of the beam.
Ss Section modulus of the steel beam alone (not including cover plate even if it exists), in3.
St-eff The section modulus for the partial composite section
re-ferred to the top of the effective transformed section, in3. This item may be different on the left and the right sides of the beam.
Str Section modulus for the fully (100%) composite trans-formed section referred to the extreme tension fiber of the steel section (including cover plate, if it exists), in3. Refer-ring to Figure 1 of Composite Beam Design AISC-ASD89 Technical Note 21 Elastic Stresses with Partial Composite Connection, Str is calculated using Equation 3 of Composite Beam Design AISC-ASD89 Technical Note 21 Elastic Stresses with Partial Composite Connection.
SDL Acronym for superimposed dead load.
SPRmax Maximum number of shear studs that can fit in one row across the top flange of a composite beam, unitless.
V Shear force, kips.
Vall Allowable beam shear (end reaction), kips.
Vh Total horizontal shear to be resisted by shear studs be-tween the point of maximum moment and points of zero moment for full (100%) composite connection, kips.
V'h Total horizontal shear to be resisted by shear studs be-tween the point of maximum moment and points of zero moment for partial composite connection, kips.
Technical Note 16 - 10 General and Notation W Total load supported by the beam that is considered when calculating the first natural frequency of the beam, kips.
This is calculated by the program as the sum of all of the dead load and superimposed dead load supported by the beam plus a percentage of all of the live load and reducible live load supported by the beam. The percentage of live load is specified in the composite beam preferences. The percentage is intended to estimate the sustained portion of the live load (about 10% to 25% of the total design live load).
a3 Whichever is smaller of the distance from the top of the concrete slab to the ENA or the thickness of the concrete above the metal deck (or the thickness of a solid slab), tc, in. This item may be different on the left and right sides of the beam.
a4 Whichever is smaller of the distance from the top of the metal deck to the ENA or the height of the metal deck, hr, in. This item applies when there is metal deck (not a solid slab) and the ENA falls below the top of the metal deck.
This item may be different on the left and right sides of the beam.
b Width, in.
bcp Width of cover plate, in.
beff Effective width of concrete flange of composite beam, in.
This item may be different on the left and the right sides of the beam.
beff par Effective width of concrete flange of composite beam,
when there is partial composite connection, transformed to an equivalent width of steel (that is, multiplied by Ec / Es), in. This item may be different on the left and the right sides of the beam.
bf Width of flange of a rolled steel beam, in.
Composite Beam Design AISC-ASD89 General and Notation
General and Notation Technical Note 16 - 11
bf-bot Width of steel beam bottom flange, in.
bf-top Width of steel beam top flange, in.
b1 Smaller of the width of the beam bottom flange and the width of the cover plate, in.
b2 Projection of the cover plate beyond the edge of the beam bottom flange, in. See Figure 1 of Composite Beam Design AISC-ASD89 Technical Note 19 Width to Thickness Checks.
d Depth of steel beam from the top of the beam top flange to the bottom of the beam bottom flange, in.
davg Average depth of concrete slab, including the concrete in the metal deck ribs, in.
delement Distance from the ENA of the element considered to the
ENA of the steel beam alone (including cover plate if it ex-ists), in. Signs are considered for this distance. Elements located below the ENA of the steel beam alone (including cover plate if it exists) have a negative distance and those above have a positive distance.
ds Diameter of a shear stud, in.
f First natural frequency of the beam in cycles per second.
fb Bending stress, ksi.
fbot-bm The maximum tensile stress at the bottom of the bottom
flange of the steel beam, ksi.
fbot-st The maximum tensile stress at the bottom of the steel
section (including cover plate, if it exists), ksi.
fc The maximum concrete compressive stress, ksi.
ftop-st The maximum stress at the top of the steel beam (may be
tension or compression depending on the location of the ENA), ksi.
Technical Note 16 - 12 General and Notation
fv Shear stress, ksi.
f'c Specified compressive strength of concrete, ksi.
g Acceleration of gravity, in/seconds2.
h Clear distance between flanges less the fillet of corner ra-dius for rolled shapes and clear distance between flanges for other shapes, in.
hr Height of metal deck rib, in.
*
hr Height of the metal deck ribs above the elastic neutral axis (i.e., that is in compression) used for calculating the transformed section properties, in. Note that this could be different on the left and right sides of the beam.
If the deck ribs are oriented perpendicular to the beam span, h*r = 0.
If the deck ribs are oriented parallel to the beam span, one of the following three items applies:
1. If the ENA is below the metal deck, h*r = hr.
2. If the ENA is within the metal deck, h*r equals the height of the metal deck above the ENA.
3. If the ENA is above the metal deck, h*r = 0.
kc Unitless factor used in AISC-ASD89 specification Equation F1-4.
l Laterally unbraced length of the compression flange, in.
lh The distance from the center of a bolt hole to the end of the beam web, in. The program assumes this distance to be 1.5 inches as shown in Figure 2 of Composite Beam De-sign AISC-ASD89 Technical Note 24 Beam Shear Checks.
Composite Beam Design AISC-ASD89 General and Notation
General and Notation Technical Note 16 - 13
lv The distance from the center of the top bolt hole to the top edge of the beam web (at the cope), in. The program as-sumes this distance to be 1.5 inches as shown in Figure 2 of Composite Beam Design AISC-ASD89 Technical Note 24 Beam Shear Checks.
n The number of bolts as determined from Table 1 of Com-posite Beam Design AISC-ASD89 Technical Note 24 Beam Shear Checks, unitless.
q Allowable shear load for one shear stud, kips.
q Allowable shear load for one shear stud, kips.