Composite Beams and Columns

General ProvisionsWhen determining load effects in members and connections of a structure with composite members consider effective sections at the time each increment of load is applied.Properties of the concrete and reinforcing steel are per ACI 318Available strength of members is from either plastic stress distribution or strain compatibilityTensile strength of concrete is assumed to be zero

Plastic Stress DistributionAvailable strength assumes steel has hit yield stress in either tension or compression, and the concrete in compression is at 085 fcThis method is typically used for regular sections

Strain compatibility methodLinear strain distribution across the section is assumed.Maximum concrete compressive strain of 0.003 is usedWe use this method in Structures: Compressive

Encased composite columnsCross-sectional area of steel must be at least 1% of total cross-sectionConcrete encasement must be reinforced with continuous longitudinal bars and lateral ties/spiralsTransverse reinforcement 0.009 in2/inReinforcement ratio must be at least 0.004

Available Compressive StrengthFor axial load encased column, limit case of flexural bucklingfc = 0.75 and Wc = 2.00

P0 = nominal elastic compressive strength without length effects (kips)As = area of steel section (in2)Asr = area of continuous reinforcing bars (in2)Ac = area of concrete (in2)sy = yield strength of steel section (ksi)syr = yield strength of reinforcement (ksi)fc = concrete compressive strength (ksi)

Elastic buckling strength

EIeff = effective rigidity of composite section (kip-in2)K = effective length factorL = laterally unbraced length of the member (in)

Effective rigidity

Es = modulus of steel (ksi)Ec = modulus of concrete (ksi)Is = moment of inertia steel section (in4)Isr = moment of inertia reinforcement (in4)Ic = moment of inertia concrete (in4)

Nominal compressive strengthIf Pe 0.44 P0

Else (Pe < 0.44 P0)

Shear ConnectorsIt is necessary to ensure that load is transferred from the concrete to the steelShear connectors accomplish thisResist the shear force between the slab and beamPrevent separation of the slab from the beam

Shear ConnectorsStud connectors are the most common in U.S. Short round steel bar, welded to the beam at one end, with a head at the other end. Diameter from 12 in. to 1 in. and lengths from 2 to 8 in. The ratio of the length to diameter 4.Most commonly used sizes are 34 in. or 7/8 in. dia. Head diameter is 12 in. larger than stud and the head thickness is 3/8 in. or 12 in.

Shear studsASTM-A108, AISI Grades C1010, C1015, C1017 or C1020 cold-drawn steel with a minimum tensile strength of 60 ksi and a minimum elongation of 20%specified in the AWS Structural Welding Code D1.1-75.To prevent premature failure of studs because of tearing of base metal, the size of a stud not located over the beam web is limited to 2 12 times the flange thickness.The strength of stud connectors increases with stud length up to a length of about four diameters and remains approximately constant for greater lengths

Equivalent shear forceV = required shear forceWhen external force is applied to the steel section

When external force is applied to the concrete encasement

DistributionShear connectors that can hold the required V must be distributed along the length for at least 2.5 times the depth of the encased column above and below the applied loadMaximum spacing is 16Connectors must be on at least 2 faces, symmetrically

Shear Connectors

Additional issuesAt least four longitudinal bars must be used.Transverse reinforcement must be spaced at the lesser of16 longitudinal bar diameters48 tie bar diametersHalf of the least dimension of the composite sectionAt least 1.5 inches of clear cover is required

Built-up Composite columnsIf the steel section is built from two or more encased steel shapes, the shapes must be interconnectedLacingTie platesBatten platesEtcTo prevent buckling of individual shapes

Shear strength of a connector

Asc = cross-sectional area of stud (in2)Ec = modulus of concrete (ksi)su = tensile strength of connector (ksi)

GirderFloor beamLS

Effective widthbYctwtfbftchrd

Shear ConnectorsConcrete SlabRibbed steel deckSteel section