## 4 Finite Element Analysis
### Verification of Finite Element Models  
The midspan vertical deflections under different load levels obtained from the finite element analysis (FEA) of each specimen were compared with the corresponding test results, as shown in Figure 16a-d for the specimens T-HW, T-HN, TS-AS, and TS-FC, respectively. It is shown in Figure 16 that the initial stiffness of all specimens and the change trends in the load-midspan vertical deflection curves showed good agreement. Furthermore, the load carrying capacity of the test for specimen T-HW, T-HN, and TS-AS are 110 kN, 90 kN, and 150 kN, respectively, whereas the load carrying capacity of the FEA for the corresponding specimens are 116 kN, 94 kN, and 158 kN, respectively. For specimen TS-FC, since it did not reach failure, the complete load-midspan vertical deflection curve was not obtained and it was basically in the elastic stage. The load-midspan vertical deflection curve is basically consistent with the corresponding FEA result in the elastic stage, as shown in Figure 16d. Overall, the load carrying capacities of the FEA are slightly higher than those of the experimental test, and the highest difference value between the test and FEA is 5.4%, which meets the requirements of practical engineering. Furthermore, the axial strains of all specimens from the test and FEA were compared in Figure 17, in which the vertical axis represents the axial strain (\(\epsilon\)) of chord and brace members at the end of the experimental loading. It can be seen from Figure 17 that the axial strains of the FEA are slightly smaller than the corresponding test, but the difference values between them are relatively small (the largest difference value is 6.1%). It is shown from the comparison that the FEA results of specimens agreed well with the corresponding test results. Figure 15: Weld modelling. Figure 16: Comparison of experimental and finite element analysis vertical load–midspan vertical deflection curves. (**a**) T-HW; (**b**) T-HN; (**c**) TS-AS; (**d**) TS-FC. Figure 17: Comparison of experimental and finite element analysis axial strains. (**a**) Top chord ’hj’; (**b**)Top chord ’fh’; (**c**) Diagonal brace ’jp’; (**d**) Diagonal brace ’jo’. 2. The TS-FC specimen did not fail until reaching the maximum load the test setup could produce, and there was no visible change in appearance. Furthermore, the load carrying capacity and integral rigidity of specimen TS-FC are larger than for specimen TS-AS, which illustrated that the reinforcing method of filling concrete into the top and bottom chord members can improve the mechanical behavior and integral stiffness of trusses better than adding a half outer sleeve on each joint. 3. Compared with the load carrying capacity of specimen T-HW, the load carrying capacity of specimen T-HN decreased by 18%, and the load carrying capacity of specimen TS-AS increased by 36%, whereas the load carrying capacity of specimen TS-FC increased by more than 60%. The deflections of the specimens TS-AS, T-HN, and T-HW are in descending order, meaning that specimen TS-AS has the best deformability, while specimen T-HN has better deformability than specimen T-HW. 4. The axial strains of the top chord members in compression are much smaller than the yield strain of the steel material, whereas the axial strains of the bottom chord members in tension are smaller than the yield strain of steel materials, and the axial strains of diagonal brace members are close to the yield strain of the steel materials. In addition, the strains at the crown positions on joints of the T-HW and T-HN specimens vary greatly, which means there is a case of stress concentration, whereas the strains at the same position of specimens TS-AS and TS-FC vary uniformly. It is shown that the reinforcing methods of adding a half outer sleeve on each joint and filling concrete into the top and bottom chord members could help to improve the force condition of joints of warren CHS tubular trusses. 5.