# Geometric Nonlinear Analysis of the Catenary Cable Element Based on UPFs of ANSYS
## 4 Verification and Numerical Examples
### Engineering Example Validation and Analysis  
The Shatuo Bridge in Guizhou Province, China, is a reinforced concrete cantilevered arch bridge with a net span of 240 m, a net vector height of \(f=40\) m, a net vector-to-span ratio of \(f/L=1/6\), and an arch axis factor of \(m=1.85\). The arch ring section form is a single-box double-chamber structure, box width 10 m, height 4.5 m, where the thickness of the top plate from the foot of the arch is 80 cm to \(L/4\) section of 35 cm, and then to the top of the arch \(L/2\) section of 50 cm gradual; bottom plate thickness from the foot of the arch is 80 cm to \(L/4\) section of 35 cm gradual, \(L/4\) section to the top of the arch bottom plate thickness; web thickness from the foot of the arch 65 cm to \(L/4\) section of 40 cm at the foot of the arch and then tapered to 50 cm at the \(L/2\) section of the top plate, as shown in Figure 8. The main arch circle is divided longitudinally into 37 sections and is constructed by hanging basket cantilever casting. The site layout of the buckling anchor cables for the Shatuo Special Bridge is shown in Figure 9. 4-8 and 8-9 in the figure indicate No. 4-5 piers and No. 8-9 piers. 6-7 in the figure indicate No. 6-9 archs. The Scene picture of Shatuo Bridge is shown in Figure 10a. In order to verify the correctness and practicality of the developed elements, this paper uses the measured data from the Shatuo Special Bridge for comparison with the ANSYS theoretical model data. APDL parametric modeling is used for the Shatuo Bridge; as shown in Figure 10b, the whole bridge is divided into 1808 elements and 1011 nodes, of which the 3D beam element Beam188 simulates the central arch circle, abutment pier, and buckling tower, the buckling anchor cables are simulated by the development element user101 and truss element link10 respectively. The buckling anchor cables are simulated by the virtual rigid beam Beam44 between the main arch circle and the abutment pier. Boundary conditions: Solidified form at the foot of both arches, anchor cable anchorage position is solidified. Loads: 90 t for the hanging baskets plus formwork and 40 t for the hangers plus formwork. Both were acting as concentrated loads on the arch ring. In order to verify the correctness of the development element user101, the finite element model was corrected by reference [55], and the updated values of each material parameter are shown  
Figure 8: Diagram of the cross-sectional form of the arch ring: (**a**) section of arch foot; (**b**) \(L/4\) cross section; (**c**) vault cross section. Units in cm. Figure 9: Site layout of the Shatuo Bridge buckling anchor cable. Units in cm. For verifying the advancement and accuracy of the development element user101, the measured values of the maximum vertical downward deflection, the measured values of the maximum cable force, and the measured values of the maximum tensile stress in the top and bottom slab of the arch were compared with the calculated values simulated by element user101 and element link10 respectively. The following data and graphs were obtained. The bridge was divided into 63 construction phases. The newly developed element user101 was used to simulate the buckled anchor cables in just 37 min, while the ANSYS element link10 was used to simulate a total of 43 min, an improvement of 6 min in calculation efficiency. Table 7 and Figure 11 show that the cable structure simulated by the user101 element can be matched well with the experimental results. And the relative error of the newly developed element user101 in calculating the main arch deflection of each casting section is 8.4% at most, while the maximum relative error of element link10 is 13.6%. This is because the link10 element, as a two-node truss element, does not take into account the sag effect of the cable, while the sag effect of the buckled anchor cable will cause the main arch to deflect more.