In the Serreria bridge there are three points of resistance including two rollers at the ends of the bridge. At the junction of the deck and the pylon the connection is a fixed connection, hence the deck and pylon are monolithic.
The analysis of real cable-stay bridge from a system point of view requires a number of material science considerations in addition to the load path. These factors include creep(in the case of concrete) and temperature deformations.
As a result the final deformed state can be unpredictable and markedly different than the predictions based on mechanics alone. The structural engineer seeks an analysis method and sets of assumptions which will predict a "naturally/energetically" stable state of force distribution and deformations. This "stable state" is one that can "absorb" the effects of the elements on the material and overcome the material's degradation without redistributing the forces and deformations in an unpredictable manner.
Force Equilibrium method
The cable-stay bridge model(Fig. 1) in which the cable-deck junctions are modeled as simple vertical supports is considered both extremely stable and practical. In this manner the deck/girder is modeled as a continuous beam with rollers at the cable-deck junctions and a pin at the pylon-deck junction(Fig. 2). As such the bending moment profile of the continuous deck/girder can be used as a target to optimize the cable forces. Fig. 3 shows the tension forces acting on the deck and pylon at their respective junctions.(All drawings 1,2,3 are Autodesk Revit structure line models)
Fig.1 Revit Line drawing: cable-stay
Fig. 2. Equivalent continuous beam model of cable stay
Fig. 3. Tension forces at interface of deck and pylon
The practicality of modeling this behavior is where structural engineering struggled with. However, several approaches are now available.
The assumption of Fig. 2 is adequate for optimizing the cable forces from a strictly mechanics point of view. To account for creep and environmental deformations, appropriate pre-stressing and creep loading can be added to the model. Using Chen's method(referenced above) a Matrix equation can be set to iteratively find the optimum cable forces that will satisfy the Target bending moments in the deck/main girder which stabilize the system.
If {M0} is the matrix of target Moments at the Cable/deck junctions, and [m] is a matrix of moment coefficients due to unit vertical point loads at the joints, {T} is a vector of optimum cable forces and {Md} is a vector of extra moments due to creep and prestressing and other environmental factors;
{M0} = [m]{T} + {Md} can be solved to find {T}.
The iteration comes into play if one chooses to additively account for the different factors that cause bending moments in the deck/girder.
In the simplified academic exercise, {Md} is {0} and {T} can be found easily.
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