| Summary: Determining the initial cable forces in cable-stayed bridges is a critical step in ensuring the structural integrity and stability of these magnificent engineering marvels. This article explains the methods and techniques engineers employ to calculate and set the initial cable forces accurately. It's showing how Midas Civil aids in the effortless analysis of cable-stayed bridges. |
A cable-stayed bridge is a structural system that effectively combines cables, girders, and the pylon into an esthetically pleasing structure.The pre-tensioned cables reduce the moments coming onto the girders acting like intermediate supports, and thus, engineers can go for longer spans that balanced cantilever bridges cannot afford.
The concept seems simple, but calculating the cable forces becomes complicated, and in the past, the initial pretension was determined by experimental values, trial-and-error methods etc.
Are you curious about how these elegant structures are structurally analyzed? Keep reading.
As mentioned above, the dominant issue of the design and build of a cable-stayed bridge is to compute and achieve the initial equilibrium configuration at the completed state. Let’s check out different methods for calculating the initial cable forces for obtaining the desired behavior.
The initial equilibrium configuration of cable-stayed bridges is the equilibrium position due to dead load and tension forces in the stay cables. The cable pretension should be optimized to reduce the moments in the tower and girders.
Figure 1: Russky Island Bridge in Russia; World's tallest cable stayed bridge (Analysed using Midas)
This method is valid when there is no large inclination in the longitudinal girder, and the horizontal component of cable force's effect on the beam is less. In this method, vertical displacement is restrained at the cable anchorage position so that the girder can be idealized as a continuous beam.
Figure 2: Zero Displacement Method
This method is valid when there is a considerable inclination in the longitudinal girder and the horizontal component of cable force's effect on the beam is large. Thus, the effect of horizontal cable force is considered while calculating the initial cable forces.
Figure 3: Force Equilibrium Method
In the force method, we can assume the member force by converting the structure as determinate structure. Using the member forces due to live loads to obtain member forces due to dead loads. Member force can be efficiently determined considering the material properties.
In this method, to determine the unknown loads for each stay cable and to achieve an ideal state, a unit pretension load is applied for each cable. Performing a linear analysis - the method determines the influence on the structure due to each unit's tension load. Furthermore, the structural restrictions for e.g., moment or displacement values, which are realized through the load factors in the combined load case, must be defined.
Figure 4: Influence Matrix Method
Engineers across the globe have realized the Midas touch of Midas Civil in solving complicated bridges, such as the Russky Island Bridge in Russia, the tallest cable-stayed bridge in the world, the Sutong Bridge in China, the second-longest cable-stayed bridge in the world, and many other wonders around the world.
Let's see how initial cable forces are calculated in Midas Civil and how the software helps the engineers optimize the cable forces efficiently in the nick of time.
Figure 5: Sutong Bridge, China; World's second longest cable stayed bridge (Analysed using Midas)
Using the Influence Matrix Method, this function optimizes cables' tensions at a cable structure's initial equilibrium position. The program can calculate the initial cable force by inputting restrictions such as displacement, moment, etc. and satisfying the constraints.
Figure 6: Before & After Cable Force Tuning
The 'Unknown Load Factor' function in Midas Civil calculates the initial pretension that needs to be applied to the cables for a cable-stayed bridge. However, with the 'Unknown Load Factor,' the designer cannot achieve the desired initial pretension in a single attempt. The designer should perform multiple iterations, fine-tuning the pre tension using the influence matrix to obtain the initial pre tension that results in the desired bending moments and deformations.
Cable Force Tuning' in Midas Civil is a function that makes the iteration process required for bridge design easy. The feature allows the user to adjust the cable force and check the girders' displacements or the pylon in real time without reanalyzing. Click here to learn more about cable tuning in Midas Civil.
Figure 7: Cable Force Tuning in Midas Civil
Now, bridges are longer and more complex than ever before, and the world is moving faster. We cannot afford to waste time solving the indeterminacies of cable-stayed bridges through trial-and-error methods.
With Midas Civil at their disposal, engineers can confidently begin designing and building cable-stayed bridges since the software simplifies the most complex indeterminate structures time-bound.
As we look to the future, Midas Civil continues to play a pivotal role in shaping the skylines with safer, more efficient, and truly iconic cable-stayed bridges worldwide.
Stay tuned for more exciting bridges in the upcoming blogs.