# Study on Bending Performance of Tightly Spliced Truss-Reinforced Plate-Honeycomb Flat Beam
## 4 Theoretical Analysis and Design Method
### Calculate the Ultimate Bending Capacity by Using Double T-Section Method  
#### 4.2.1 Cross-Section Type  
In this paper, the equivalent rectangular stress method is used to equate the height of the theoretical compression zone of the concrete flange plate to the actual compression height of the concrete flange plate, so that it can better calculate the location of the plastic neutral axis of the cross-section of the honeycomb composite flat beam specimen. Since the honeycomb composite flat beam specimen is weakest at the honeycomb hole section, the ultimate flexural load capacity of the composite flat beam is calculated mainly by using the honeycomb hole section as the control section in this section. The combined flat beam is divided into two T-shaped sections above and below the honeycomb hole and the concrete flange plate for calculation, referred to as the double T-shaped steel method. Referring to the classification standard of the cross-section in a T-shaped reinforced concrete beam, the combined flat beam can be divided into two categories according to the position of the neutral axis: the first category of cross-section when the neutral axis is located within the thickness of concrete flange plate; the second category of cross-section when the neutral axis is located below the bottom surface of concrete flange plate. One type of cross-section can be distinguished according to the position of the plastic neutral axis relative to the honeycomb hole, \(l_{a}\) cross-section when the plastic neutral axis is located at the web above the honeycomb hole, and \(l_{b}\) cross-section when the plastic neutral axis is located within the height of the honeycomb hole opening, as shown in Figure 19.  
When the plastic neutral axis is located at the web above the honeycomb aperture when the section belongs to the \(I_{a}\) class of sections:  
\[b_{1}h_{1}f_{y}+b_{w}\bigg{(}\frac{h-h_{e}}{2}-h_{1}\bigg{)}f_{y}+\alpha f_{c }\beta b_{f}\bigg{(}\frac{h-h_{e}}{2}-c\bigg{)}\geq b_{2}h_{2}f_{y}+b_{w} \bigg{(}\frac{h-h_{e}}{2}-h_{2}\bigg{)}f_{y} \tag{4}\]  
when the plastic neutral axis is located below the concrete flange slab, the section is a Class II section:  
\[b_{1}h_{1}f_{y}+\bigg{(}\frac{h-h_{e}}{2}-h_{1}\bigg{)}b_{w}f_{y}+\alpha_{1}f_ {c}\beta b_{f}h_{f}\leq b_{2}h_{2}f_{y}+\bigg{(}\frac{h-h_{e}}{2}-h_{2}\bigg{)} b_{w}f_{y} \tag{5}\]  
Among them:  
Figure 19: Hollow honeycomb composite flat beam section. (**a**) Section information and plastic neutralization axis; (**b**) analysis of force characteristics.  
\(b_{1}\), \(b_{2}\), \(b_{w}\), \(b_{f}\)--The widths of the plates of the upper flange, lower flange, and web of the steel beam as well as the concrete flange plate;  
\(h_{1}\), \(h_{2}\), \(h_{w}\), \(h_{f}\)--Plate thicknesses of the upper flange, lower flange, and web of the steel beam as well as the concrete flange plate;  
\(h\)--Height of the cross-section of the honeycomb combined flat beam;  
\(h_{e}\)--Honeycomb hole diameter;  
\(f_{y}\)--The yield stress of the steel section;  
\(f_{c}\)--Peak concrete stress.  
When none of the specimen sections satisfy Equations (4) and (5), the plastic neutral axis of the combined flat beam section is located within the opening of the honeycomb hole and is a \(l_{b}\) type section.