# Study on Bending Performance of Tightly Spliced Truss-Reinforced Plate-Honeycomb Flat Beam
## 4 Theoretical Analysis and Design Method
### Simplified Calculation of Ultimate Bending Capacity  
Using the equivalent rectangular stress method of double T-beams in the above section, the calculation is based on the section where the honeycomb hole is located. Although the flexural load capacity of the weakest section can be calculated, the calculation decomposes the cross-section of the combined flat beam into the upper and lower parts of unconnected T-beams and concrete flange plate and does not consider the role of the web at the longitudinal solid web of the honeycomb beam, which leads to conservative calculation results. This method also requires the identification of the relative relationship between the plastic neutral axis of the combined beam and the honeycomb hole before calculation, which makes the calculation process a bit tedious. Therefore, this section simplifies the formula for calculating the flexural load capacity of the honeycomb composite flat beam specimen on the basis of the equivalent rectangular stress method. Under the condition that the previous assumptions hold, the effect of honeycomb holes on the calculation is ignored first, the formula for calculating the flexural load capacity of the solid web combination flat beam is derived, and the fitting function of the honeycomb hole-height ratio and the load capacity reduction coefficient fitted by the integrated finite element calculation results are derived for the flexural load capacity of the honeycomb combination beam. In Figure 20, a\({}^{\prime}\), b\({}^{\prime}\), and c\({}^{\prime}\) represent the plastic neutral axis positions at different positions. When the neutral axis of the composite specimen is located at position a\({}^{\prime}\) and the plastic neutral axis of the honeycomb steel beam is located at position c\({}^{\prime}\), the section stress distribution of the first type of solid web composite beam is shown in Figure 20b. Similarly, when the neutral axis of the composite specimen is located at position b\({}^{\prime}\) and the plastic neutral axis of the honeycomb steel beam is located at position c\({}^{\prime}\), the section stress distribution of the second type of solid web composite beam is shown in Figure 20c. According to the cross-sectional tensile equilibrium equation of the combined flat beam specimen, i.e., Equation (15), the distance of the cross-sectional plastic neutral axis from the top of the combined flat beam can be found at \(y_{c}\). \[\alpha_{1}f_{c}\beta b_{f}(y_{c}-c)+b_{1}h_{1}f_{y}+b_{w}(y_{c}-h_{1})f_{y}=b_ {2}h_{2}f_{y}+b_{w}(h-y_{c}-h_{2})f_{y} \tag{15}\]  
The cross-sectional equivalent method decomposes the cross-sectional bending moment of the combined flat beam into two parts: the bending capacity of the steel beam around its own plastic neutral axis and the concrete equivalent compression zone combined force on the equivalent steel beam tension zone combined force after taking distance. Substitute Equations (7) and (15) into Equation (8) to find out the flexural load-carrying capacity of solid web type combined flat beam. Where y is the distance from the concrete compressive zone combined force to the steel beam tensile zone combined force, which can be found by the following formula:\[y=\frac{y_{s}-y_{c}}{2}+y_{c}-c-\frac{x}{2} \tag{16}\]  
The bending capacity of the solid web combined flat beam is calculated as shown in Equation (17):  
\[M=M_{s}+b_{f}\alpha f_{c}\beta(y_{c}-c)\bigg{(}\frac{y_{s}-y_{c}}{2}+y_{c}-c- \frac{x}{2}\bigg{)} \tag{17}\]  
When the plastic neutral axis is located below the bottom plate of the concrete flange plate, the stress diagram shown in Figure 20c is used. According to the cross-sectional tensile equilibrium equation of the combined flat beam specimen, i.e., Equation (18), the distance between the plastic neutral axis of the cross-section and the top of the combined flat beam can be found at \(y_{c}\). \[\alpha_{1}f_{c}\beta b_{f}h_{f}+b_{1}h_{1}f_{y}+b_{w}(y_{c}-h_{1})f_{y}=b_{2} h_{2}f_{y}+b_{w}(h-y_{c}-h_{2})f_{y} \tag{18}\]  
Figure 20: Stress analysis of solid web composite beam section.