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where rm is the radius of gyration of steel section and shall not be less than 0.3 times the overall thickness of the composite cross-section in the plane of buckling, Ac is the area of concrete, Ar is the area of longitudinal reinforcing bars, As is the area of steel shape, E is the modulus of elasticity of steel, Ec is the modulus of elasticity of concrete, Fy is the specified minimum yield stress of steel shape, Fyr is the specified minimum yield stress of longitudinal reinforcing bars, fc' is the specified compressive strength of concrete, and cj, c2, c3 are the coefficients given in the table below.

Type of composite section c1 c2 c3

Concrete encased shapes 0.7 0.6 0.2

### Concrete-filled pipes and tubings 1.0 0.85 0.4

In addition to satisfying the condition fcPn > Pu, shear connectors spaced no more than 16 in. (405 mm) apart on at least two faces of the steel section in a symmetric pattern about the axes of the steel section shall be provided for concrete encased composite columns to transfer the interface shear force V'u between steel and concrete. VU is given by

Vu ( 1--—y J when the force is applied to the steel section

Vu i pY J when the force is applied to the concrete encasement where Vu is the axial force in the column, As is the area of the steel section, —y is the yield strength of the steel section, and Pn is the nominal compressive strength of the composite column without consideration of slenderness effect.

If the supporting concrete area in direct bearing is larger than the loaded area, the bearing condition for concrete must also be satisfied. Denoting fcPnc (= fcPn,composite section - fcPn,steel shape alone) as the portion of compressive strength resisted by the concrete and AB as the loaded area, the condition that needs to be satisfied is

4.13.2 Composite Beams

Composite beams used in construction can often be found in two forms: steel beams connected to a concrete slab by shear connectors and concrete encased steel beams.

### 4.13.2.1 Steel Beams with Shear Connectors

The design flexure strength for steel beams with shear connectors is f bMn. The resistance factor f b and nominal moment Mn are determined as follows:

Condition fb

Positive moment region and 0.85

Positive moment region and 0.90

Negative moment region 0.90

Determined from plastic stress distribution on the composite section Determined from elastic stress superposition considering the effects of shoring Determined for the steel section alone using equations presented in Section 4.5

### 4.13.2.2 Concrete Encased Steel Beams

For steel beams fully encased in concrete, no additional anchorage for shear transfer is required if (a) at least 1j in. (38 mm) concrete cover is provided on top of the beam and at least 2 in. (51 mm) cover is provided over the sides and at the bottom of the beam and (b) spalling of concrete is prevented by adequate mesh or other reinforcing steel. The design flexural strength f bMn can be computed using either an elastic analysis or a plastic analysis.

If an elastic analysis is used, fb shall be taken as 0.90. A linear strain distribution is assumed for the cross-section with zero strain at the neutral axis and maximum strains at the extreme fibers. The stresses are then computed by multiplying the strains by E (for steel) or Ec (for concrete). Maximum stress in steel shall be limited to Fy and maximum stress in concrete shall be limited to 0.85fC.The tensile strength of concrete shall be neglected. Mn is to be calculated by integrating the resulting stress block about the neutral axis.

If a plastic analysis is used, f b shall be taken as 0.90 and Mn shall be assumed to be equal to Mp, the plastic moment capacity of the steel section alone.

### 4.13.3 Composite Beam-Columns

Composite beam-columns shall be designed to satisfy the interaction equation of Equation 4.73 or 4.74 whichever is applicable, with fcPn calculated based on Equations 4.132 to 4.135, Pe calculated using the equation Pe = AsFmy/1;? and fbMn calculated using the following equation (Galambos and Chapuis 1980):

where Zis the plastic section modulus of the steel section, cr is the average of the distance measured from the compression face to the longitudinal reinforcement in that face and the distance measured from the tension face to the longitudinal reinforcement in that face, h1 is the width of the composite section perpendicular to the plane of bending, h2 is the width of the composite section parallel to the plane of bending, Ar is the cross-sectional area of longitudinal reinforcing bars, Aw is the web area of the encased steel shape (= 0 for concrete-filled tubes), Fy is the yield stress of the steel section, and Fyr is the yield stress of reinforcing bars.

If 0 < (Pu/f cPn) < 0.3, a linear interpolation of f bMn calculated using the above equation assuming Pu/fcPn = 0.3 and that calculated for beams with Pu/fcPn = 0 (see Section 4.13.2) should be used.

### 4.13.4 Composite Floor Slabs

Composite floor slabs (Figure 4.38) can be designed as shored or unshored. In shored construction, temporary shores are used during construction to support the dead and accidental live loads until the concrete cures. The supporting beams are designed on the basis of their ability to develop composite action to support all factored loads after the concrete cures. In unshored construction, temporary shores are not used. As a result, the steel beams alone must be designed to support the dead and accidental live loads before the concrete has attained 75% of its specified strength. After the concrete is cured, the composite section should have adequate strength to support all factored loads.

Composite action for the composite floor slabs shown in Figure 4.38 is developed as a result of the presence of shear connectors. If sufficient shear connectors are provided so that the maximum flexural strength of the composite section can be developed, the section is referred to as fully composite. Otherwise, the section is referred to as partially composite. The flexural strength of a partially composite section is governed by the shear strength of the shear connectors. The horizontal shear force Vh that should be designed for at the interface of the steel beam and the concrete slab is given by

In regions of positive moment:

In regions of negative moment:

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