written by Achraf Ben Afia
Cable structures are distinguished by their remarkable capacity to withstand significant tensile stresses. This advantage allows architects and engineers to design structures that are not only resilient but also lightweight, cost effective, and visually striking. Additionally, owing to their light weight, assemblage of cable elements is simple and effortless. Structures involving cables have a rich history, spanning various types. Notable examples include suspension bridges, cable-stayed bridges, and footbridges, as well as mast structures, suspension roof systems, cable-net structures, and tensegrity structures.
Cable structural elements are geometrically nonlinear, and hence we need a nonlinear solver in order to analyze this kind of structure. Advance Design, the structural simulation software by Graitec, implements a nonlinear solver that enables engineers to easily incorporate cables into their projects.
In this article, we will take a look at how to model a cable structure in GRAITEC Advance Design, including analysis and FEM results.
1 – Example of Cable Structure
Our working example is inspired by the structure shown in the following figure, which is a cantilever car parking shade.
Figure 1: Cantilever car parking shade structure
In this structure, we notice that the cantilever beams carry a lightweight roof with its self-weight. The roof might be subject to wind and snow loads. A bright idea would be to use cables linking columns and cantilever beams. These cables work in tension and have an important role in supporting the cantilever beams.
2 – Modeling in Advance Design
To simplify the study, we will consider only one frame, including one column fixed at the bottom end, one major cantilever beam, one small cantilever beam, and three cables. The structure is modeled in Advance Design. Illustration of the structure, dimensions and cross-sections are shown in the following figure. We can see that variable cross section W beams are used, and this choice is made to minimize the self-weight of beams at both ends, making the project more aesthetic as well.
Figure 2: Example of frame of cantilever car parking shade structure
After modeling the structure, we can apply different loads. However, for this example we will consider only the self-weight and a uniform linear dead load of 0.5 kN/m applied on the major beam (see figure 3). This load is an estimation of the roof dead load.
Figure 3: Linear load applied on the cantilever beam
Once we apply the load, we can generate a load combination following a specific code. For this example, the Canadian CNB 2015 code is selected (see figure 4).
Figure 4: Creating combinations
As mentioned in the introduction, cables are nonlinear structures, and hence we need to activate nonlinear analysis in Advance Design. To do so, we need to right-click on settings and click on nonlinear static.
Figure 5: Activate nonlinear analysis
For more details about geometrical nonlinear analysis in Advance Design, please consult this blog: Geometrical Non-linear Analysis In Advance Design.
Next, we click on NL that we created. First, we enable Large displacement. Then we click on the icon indicated by the arrow in the figure below.
Figure 6: Setting nonlinear parameters
Then we need to select a load or a combination load by clicking on Add/Remove analysis in the bottom left of the window. In this example, we selected the combination 1.4 D1+1.4D2.
Figure 7: Add combination for nonlinear analysis
Once done, we can keep the following parameters by default and run the FE analysis.
Figure 8: Nonlinear analysis parameters
3 – Analysis and Results
After launching the analysis, we can dispose of several results, for example the displacement of the structure subject to the applied load (figure 9).
Figure 9: Displacement of the analyzed structure
It is important to also verify the axial force of the structure. In Advance Design, the normal force Fx is positive in the case of tension and negative in the case of compression, regardless of the orientation of local x. As shown in Figure 10, all three cables are subject to tensional forces; the maximum tensional force is Fx=15.8 kN and occurs for the bottom cable linking the foot of the column with the small beam.
Figure 10: Display of axial forces
In summary, cable structures offer remarkable tensile strength, enabling architects and engineers to create lightweight, cost effective, and visually appealing structural projects. GRAITEC Advance Design, with its nonlinear solver, is the perfect software for analyzing cable structures. Using a simple example, we have covered the modeling process, load application, and nonlinear analysis activation. The results highlight the crucial role of cables in supporting the structure, owing to their high tensile strength.
TRY IT FOR YOURSELF! Discover the all-in-one FEM software for structural engineers: GRAITEC Advance Design.