# Composite Beams with Steel Stud Design

**Symbols**

* A_{sa}* = Cross-sectional area of steel headed stud anchor, in.

^{2}(mm

^{2})

*Modulus of elasticity of Asa = cross-sectional area of steel headed stud anchor, in.*

**E**_{c}=^{2}(mm

^{2})

*Specified minimum tensile strength of a steel headed stud anchor, ksi (MPa)*

**F**_{u}=*= Area of steel cross-section, in.*

**A**_{s}^{2}(mm

^{2})

*= Distance from the resultant steel tension force for full section tension yield to the top of the steel, in.*

**d**_{3}*= Lower bound moment of inertia, in.*

**ILB**^{4}(mm

^{4})

*= Moment of inertia for the structural steel section, in.*

**I**_{s}^{4}(mm

^{4})

*= Sum of the nominal strengths of steel anchors between the point of the maximum positive moment and the point of zero moment to either side, kips (kN)*

**ΣQ**_{n}*= Area of concrete slab within effective width, in.*

**A**_{c}^{2}(mm

^{2})

*= Specified minimum yield stress of steel, ksi (MPa)*

**F**_{y}*=Specified compressive strength of concrete, ksi (MPa)*

**f**_{c}′*= Distance from the centroid of the compression force, C, in the concrete to the top of the steel section, in. (mm)*

**d**_{1}*= Distance from the centroid of the compression force in the steel section to the top of the steel section, in. (mm). For the case of no compression in the steel section, d*

**d**_{2}_{2}= 0.

*= Tensile strength of the steel section;*

**P**_{y}### Flexural Moment Strength

#### Concrete Slab Effective Width, b_{eff}

According to AISC 360-16 I3.1a, the effective width of the concrete slab is determined the sum of the effective widths for each side of the beam centerline, each of which does not exceed:

(a) 1/8 of the beam span, center-to-center of supports;

(b) one-half the distance to the centerline of the adjacent beam

(c) the distance to the edge of the slab

#### Plastic Stress Dissipation

Characteristic bending moment strength, M_{n}, is determined according to AISC 360-16 I3.2a by plastic stress distribution method in the composite section.

#### Compressive Strength of Reinforced Concrete Slab

Compressive strength, C value in reinforced concrete slab should be calculated by considering 3 conditions according to AISC 360-16.

#### Shear Strength of Studs

The characteristic shear strength of a steel anchor embedded in concrete is calculated as follows according to AISC 360-16.

#### Composite Ratio, PCC

It is the ratio of the sum of the shear strengths of the anchoring elements between the points where the positive bending moment is maximum and zero, ΣQ_{n}, to the compressive force in the reinforced concrete slab, C.

#### Depth of Concrete Compression Block

### Design Bending Moment Strength

* *Design bending moment strength for composite beams according to ASD (GKT) and LRFD (YDKT),

** ** M_{c} = M_{n} / Ω (ASD) M_{c} = ϕM_{n} (LRFD)

### Construction Phase Account

During the construction phase, loads are considered in the design. When temporary supports are not used during the construction phase, since all loads are borne only by the steel cross-section, the bending moment strength is determined without considering the composite cross-section.

### Deflection - Moment of Inertia,

Deflection is calculated in AISC 360-16 using the lower bound moment of inertia value according to the formula C-I3-1.

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