# Flexural Capacity of a New Composite Beam with Concrete-Infilled Tubular Lower Flange
## 3 Flexural Strength Estimation  
### Non-Composite Specimens  
In this section, the nominal flexural strength equations of the non-composite specimens at construction stage are derived for two different cases, depending on the existence of openings in the web. If no openings exist in the web, it is suggested that the smaller of the plastic moment (\(M_{p}\)) and lateral torsional moment (\(M_{LTR}\)) of the given construction stage section is taken as the nominal flexural strength (\(M_{n}\)), as in the design of conventional wide flange sections. However, if openings exist in the web, its yield moment (\(M_{y}\)) is taken as the nominal flexural strength. This is mainly because the ultimate failure mode of the non-composite specimens is generally the local web buckling, as discussed in Section 4.1. Similarly to this case, the Load and Resistance Factors Design (LRFD) of the American Institute of Steel Construction (AASC) [16] recommends that the nominal flexural strength of the composite beam section with noncompact web shape should be estimated based on its yield moment. The test results in Section 4.1 confirm that this approach can accurately predict the flexural strengths of the non-composite beams with web openings. It is assumed that the non-composite specimens considered in this study satisfy the width/thickness ratio criteria provided in the LRFD design specification for its upper flange and web components. Figure 9 illustrates the three representative locations of the plastic neutral axis (PNA) for the non-composite beam sections without web openings. The plastic moment estimation for these three cases can be straightforwardly done as follows. Figure 8: Photo of the actual test setup. Figure 9: Locations of plastic neutral axis for the non-composite specimen without web openings. In case the plastic neutral axis exists at the web  
The internal axial force for each component of the section can be computed as shown in Table 4. In the equations of the table, \(F_{y}\) and \(F_{y,re}\) represent the yield strengths of steel plate components and rebars, respectively. In addition, \(n\) and \(A_{re}\) denote the number of rebars used and the area of a single rebar, respectively. It is assumed that the contribution of concrete components subjected to tension force is ignored. The location of the PNA (\(y_{PNA}\)) for this case can be determined from the axial force equilibrium condition expressed below:  
\[C_{Af}+C_{Aw}=T_{Aw}+T_{twf}+T_{tw}+T_{tbf}+T_{re}. \tag{2}\]  
By using the PNA location determined from the above equation, the plastic moment of the given composite section can be calculated by:  
\[ \begin{array}{ll}M_{p}=&C_{Af}\times(y_{PNA}-\frac{t_{f}}{2})+C_{Aw}\times \frac{(y_{PNA}-t_{f})}{2}+T_{Aw}\times\frac{(h_{A}-y_{PNA})}{2}+T_{twf}\times(h _{A}-y_{PNA}+\frac{t_{w}}{2})\\ &+T_{tw}\times(h_{A}-y_{PNA}+\frac{h_{w}}{2})+T_{tbf}\times(H-y_{PNA}-\frac{t_ {w}}{2})+T_{re}\times(H-y_{PNA}-h_{re})\end{array} . \tag{3}\]  
In case the plastic neutral axis exists at the upper flange of the tube  
The internal axial force for each component of the section can be computed as shown in Table 5. The location of the PNA for this case can be determined from the axial force equilibrium condition expressed below:  
\[C_{Af}+C_{Aw}+C_{twf}=T_{twf}+T_{tw}+T_{tbf}+T_{re}. \tag{4}\]  
By using the PNA location determined from the above equation, the plastic moment of the given composite section can be calculated by:  
\[ \begin{array}{ll}M_{p}=&C_{Af}\times(y_{PNA}-\frac{t_{f}}{2})+C_{Aw}\times(y _{PNA}-t_{f}-\frac{(h_{A}-t_{f})}{2})+C_{twf}\times\frac{(y_{PNA}-h_{A})}{2} +T_{twf}\times(\frac{h_{A}+t_{w}-y_{PNA}}{2})\\ &+T_{tw}\times(h_{A}-y_{PNA}+\frac{h_{w}}{2})+T_{tbf}\times(H-y_{PNA}-\frac{t _{w}}{2})+T_{re}\times(H-y_{PNA}-h_{re})\end{array} . \tag{5}\]