# Study on Bending Performance of Tightly Spliced Truss-Reinforced Plate-Honeycomb Flat Beam
## 3 Test Results and Discussions
### Strain Characteristics
#### 3.3.4 Stress Distribution of Honeycomb Holes in Shear Section  
Four three-way strain flowers were arranged around the first hole in the bending and shearing section of the combined flat beam specimen. The values of the strain flowers should be converted into equivalent forces according to the Mises yield criterion, and the yielding of the steel at this test point occurs when the equivalent force reaches the yield strength, calculated as follows:  
\[\sigma_{1}^{3}=\frac{E_{s}}{2}\bigg{[}\frac{\varepsilon_{1}+\varepsilon_{3}}{1- v}\pm\frac{1}{1+v}\sqrt{2(\varepsilon_{1}-\varepsilon_{2})^{2}+2(\varepsilon_{2}- \varepsilon_{3})^{3}}\bigg{]} \tag{1}\]  
\[\theta=\frac{1}{2}arctg\bigg{(}\frac{2\varepsilon_{2}-\varepsilon_{1}- \varepsilon_{3}}{\varepsilon_{1}-\varepsilon_{3}}\bigg{)} \tag{2}\]  
Among them:  
\(\varepsilon_{1}\), \(\varepsilon_{2}\), \(\varepsilon_{3}\)--\(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\) directional strain values;  
\(v\)--Poisson's ratio of the steel;  
\(\theta\)--The angle between the direction of the principal stress at the strain flower collection point and the positive direction of the \(x\)-axis;  
\(\sigma_{1}\), \(\sigma_{2}\), \(\sigma_{3}\)--The three principal stresses at the location of the measurement point, where \(\sigma_{1}\) is the maximum principal stress, \(\sigma_{2}\) = 0, and \(\sigma_{3}\) is the minimum principal stress.  
According to the fourth strength theory of material mechanics, it is known that:  
\[\sigma_{y}=\sqrt{\frac{1}{2}\Big{[}\big{(}\sigma_{1}-\sigma_{2}\big{)}^{2}+ \big{(}\sigma_{2}-\sigma_{3}\big{)}^{2}+\big{(}\sigma_{3}-\sigma_{1}\big{)}^{2 }\Big{]}} \tag{3}\]  
Figure 16 shows the load-stress trends around the first honeycomb hole in the bending and shearing section of the composite flat beam specimen near the centralized force loading point. After the strains measured by the strain flowers around the first honeycomb hole  
Figure 15: Longitudinal strain of reinforcement at joint position of composite slab. (**a**) DTCB1; (**b**) DTCB2; (**c**) DTCB3; (**d**) DTCB4; (**e**) DTCB5.  
in the bending and shearing section of the composite flat beam are converted into Mises stresses, it can be seen that the stresses at the locations of the No.6 and No.9 strain flowers are the largest, i.e., the stress changes are more obvious near the loading end of the concentrated force. The stress in the No.9 strain pattern, which is in the tension zone in the middle of the beam and below the axis, is the highest, and the area around the honeycomb hole in the web of the beam near the loading end of the concentrated force is the first to yield during loading. The equivalent stresses at the locations of strain pattern No.6 and No.7 in the specimen are smaller than those at the locations of strain pattern No.8 and No.9, and the stresses in the honeycomb holes in the tensile zone are larger than the stresses in the honeycomb holes in the compressive zone in the composite flat beam specimen. All specimens except DTCB4 started to yield after the combined flat beam started to yield, and the equivalent force at strain pattern No.6 and No.9 started to increase rapidly, and the yielding around the honeycomb holes was slightly later than the yielding of the upper and lower flange parts. After yielding the holes near the concentration side, the stresses at the locations of strain blossoms No.7 and No.8 slowed down due to the redistribution of stresses around the specimens and the honeycomb holes, and none of them exceeded the yield stress value of the steel.