# Study on Bending Performance of Tightly Spliced Truss-Reinforced Plate-Honeycomb Flat Beam
## 4 Theoretical Analysis and Design Method
### Design Suggestion Method of Honeycomb Composite Flat Beam  
(1) In the process of bending, the steel components may have local buckling of the cross-sectional plates, which may cause early damage to the specimens and reduce the strength and stiffness of the combined flat beam specimens, thus affecting the bearing capacity and deformation capacity of the combined flat beam. It is recommended to fill the honeycomb holes and set up supporting stiffening ribs at the support and upper flange of the beam where the load is concentrated by a large, fixed load. When the web width-to-thickness ratio of the honeycomb beam is greater than 80 \(\varepsilon_{k}\), transverse stiffening ribs should be provided at places with high local stress. (2) The load location has a certain influence on the critical load of the steel beam. The floor load of the honeycomb composite flat beam proposed in this paper is transferred to the lower flange of the steel beam through the floor slab and to the H-beam anti-kinematic connection key, and this load transfer path can reduce the beam torsion as well as prevent beam instability. At the same time, since the concrete flange plate is located on both sides of the honeycomb beam web and basically fills the honeycomb holes, it provides effective lateral support to the honeycomb steel beam, so it is not necessary to verify the overall stability of the honeycomb composite beam when the overall stability of the honeycomb steel beam meets the requirements. The overall stability of the honeycomb beam element can be calculated by discounting the overall stability of the solid web flexural element by the corresponding formula, and the discount factor is related to the span-to-height ratio,the opening rate, and the hole density of the beam [29]. Therefore, the honeycomb steel beam can be subjected to the overall stability test according to the following equation:  
\[KMb_{0 max} \tag{21}\]  
where:  
\(M_{max}\)--The maximum bending moment acting around the strong axis;  
\(\varphi_{b}\)--The overall stability coefficient of the beam;  
\(W_{0}\)--Section modulus of the bridge section of the cellular beam;  
\(f\)--Standard values of steel strength;  
\(K\)--Cellular hole discount factor, \(K=0.24e^{0.16\varphi+2.33+0.01D}\), which can be approximated as 1.1;  
\(D\)--The span-to-height ratio of the beam;  
\(\lambda\)--Opening rate;  
\(\rho\)--Hole density. (3) The component strength of the honeycomb combination flat beam and other load-bearing limit states are generally designed using the plastic design method, that is, using Equations (7), (14), (15) or Equation (20) ultimate flexural load-bearing capacity calculation formula proposed in this chapter, with a certain safety factor. The honeycomb combined flat beam directly subjected to power should adopt the elastic design method, and the load should be combined according to the short-term effect. (4) The calculation of the deflection of cellular combination beams is mainly divided into the estimation method, comparison method, and finite element method, where the estimation method is based on the calculation of the deflection of web-type combination flat beams by introducing an increase factor for the corresponding calculation. The calculation of deflection of solid web combination beams in China's steel structure code is based on the standard combination of loads and the larger calculated deflection of quasi-permanent combination, and the combination beam subject to positive moment only should have its stiffness discounted accordingly:  
\[B=\frac{EI_{eq}}{1+\xi} \tag{22}\]  
where:  
\(E\)--Modulus of elasticity of the steel;  
\(l_{eq}\)--Composite beam commutation section moment of inertia;  
\(\xi\)--Stiffness reduction factor. According to the relevant literature, the deflection calculation value of the cellular composite flat beam is obtained by appropriately scaling up the deflection calculation value on the basis of the solid web composite flat beam.