**The heart of structure behavior: LOAD PATH**
** **The load path is a term that describes the distribution of the loads within the structure to the reservoir of resistance(the ground). By the principle of conservation of energy, the load path is the path that minimizes the total potential energy of the system.

The brute analysis of a cable-stay bridge assumes that there is minimum(or zero) bending in the deck span. For analysis purposes this means that the cable-stay can be analyzed as a truss(i.e. all loading are transferred as point loads at the intersection of the cable and the deck/pylon.

I want to examine the natural load path with and without the assumption of truss behavior.

A cable-stayed bridge analysis is complex because

(i) it is 3D

(ii) non-linearity is possible.

To understand it at the fundamental level, I will use Staad.Pro models and Midas Civil 2011. My goal is to analyze and interpret the results of a structural model of the Serreria bridge by Calatrava. To accomplish this I modeled the bridge in Midas Civil(shown below). I then proceed to break down the behavior of the model from first principles.

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*Fig 1. My Midas Civil 2011 model of Calatrava's Serreria cable-stayed bridge*
The load path of suspended structures, when fully understood, can help one to iterate between "form follows function" and "function follows form".

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Fig. 2 Frame model of a suspension bridge system(modeled in Staad.pro)

*Natural Load Effects*
In the figure below(Fig. 2), a series of joint loads are supported by a system modeled as a frame. Without releasing end moments in the inclined members or specifying those members as tension members,the load effects show all the possibilities of structural deformation. That is, the effect of the load on members include shear, axial, moment and torsion.

*Fig 3: A highlighted suspension member(in red) without end moment releases exhibits moment and axial load effects. *

*Load effects under constraints*
When the inclined members are connected to the rest of the system by pin connections,those members behave like trusses(that is, there are no moment due to shear or torsion). Still, the beam and column continue to behave as beam-columns, exhibiting all the load effects due to the point loads imparted by the inclined members

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*Fig. 4 Far left suspension member in compression under conditions of end moment release. There is no constraint that the member can only carry tension.*
It is instructive that at the location of the support(pin connection), the internal force in the suspension member is compression. That is, for linear analysis of a determinate truss, the member force at the support of a cable will be compression(this is valid under conditions where there is only gravity load as in the case of a cable-stayed bridge loaded under its own weight).

As shown in Fig. 5 below, when the suspension member is specified as 'tension-only' it is deactivated in the stiffness matrix of the system if it undergoes compression. The load transfer is iterated until the all tension members are either zero force members or are in tension. To avoid this iteration, a back-stay cable can be used to stabilize the system as shown in figure 6 below.

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*Fig. 5 Tension only member on left is deactivated in Staad because in the first iteration it experiences compression. (NB: all the cables are pre-tensioned with 1-kip force)*
*Fig. 6 Support back-stay cable ensures that all designated cable members(tension-only and pre-tensioned with 1-kip) are in tension in equilibrium. The main vertical member(pylon or tower) is connected to the main girder by a fixed connection. Rollers at the ends of the main girder allow horizontal movement.*
Fig 6. is the basic structural skeleton of Calatrava's cable-stayed bridge motifs. In the Serreria bridge, he ammends this motif by creating a curved pylon in place of the vertical to give it some dramatic feel.
**Assumption of Minimal bending in deck span**
In practical cable design, for optimal serviceability, bending in the deck is undesirable. This constraint can simplify analysis because the cables, deck and pylon(s) can be assumed to behave as trusses. Using this assumption increases the axial forces however, as shown in fig 7.
*Fig. 7 The deck spans are modeled as truss members. The cables are also modeled as truss members. The pylon is left as a beam-column. The results of axial forces shows relative thickness of the axial force 'fills' . In this model, there is no pre-tension in the cables.*