Formulas: Composite Beams with Steel Headed Stud or Steel Channel Anchors

Equation C-I3-1

where

• $A_{s}=\text { area of steel cross section, in. }^{2}\left(\mathrm{~mm}^{2}\right)$
• $d_{1}=$ distance from the compression force in the concrete to the top of the steel section, in. (mm)
• $\begin{aligned} d_{3} & =\text { distance from the resultant steel tension force for full section tension yield } \\ & \text { to the top of the steel, in. (mm) }\end{aligned}$
• $I_{L B}=$ lower-bound moment of inertia, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$
• $I_{s}$ = moment of inertia for the structural steel section, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$

$\begin{aligned} \Sigma Q_{n} & =\text { sum of the nominal strengths of steel anchors between the point of maximum positive moment and the point of zero moment, kips (kN) } \\ & \text { }\end{aligned}$

Equation C-I3-2

Equation C-I3-3

where

• $\begin{aligned} C_{f} & =\text { compression force in concrete slab for fully composite beam; smaller of } F_{y} A_{s} \\ & \text { and } 0.85 f_{c}^{\prime} A_{c} \text {, kips (N) }\end{aligned}$

$A_{c}=$ area of concrete slab within the effective width, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

$\begin{aligned} I_{t r} & =\text { moment of inertia for the fully composite uncracked transformed section, in. }^{4} \\ & \left(\mathrm{mm}^{4}\right)\end{aligned}$

Equation C-I3-4

where

• $\begin{aligned} S_{s} & =\text { section modulus for the structural steel section, referred to the tension flange, } \\ & \text { in. }^{3}\left(\mathrm{~mm}^{3}\right)\end{aligned}$
• $S_{t r}=$ section modulus for the fully composite uncracked transformed section, referred to the tension flange of the steel section, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

Equation C-I3-5

The use of a constant stiffness in elastic analyses of continuous beams is analogous to the practice in reinforced concrete design. The stiffness calculated using a weighted average of moments of inertia in the positive moment region and negative moment regions may take the following form:

where

$I_{p o s}=$ effective moment of inertia for positive moment, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$

$I_{n e g}=$ effective moment of inertia for negative moment, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$

Formula 6

Governing Equation: $C'_{r3} = T_r - C'_{r1} - C'_{r2}$ (defines the balance of longitudinal forces.

Found in

• FLEXURE