Why stress always flows through the shorter/stiffer path? Why load has a preference at which way to act? What is the reason behind this preference?  
Any link or comment would be welcome
 A: The majority of the load tends to be carried by a stiffer member.  Stress is load per area, so if the stiffer member has a larger cross-sectional area then the stress is not necessarily higher.
As to why... imagine two springs hanging in parallel from the ceiling.  Both have an unloaded length of 1 meter.  Both are attached to the same point on the handle of a 25kg suitcase.
One spring is stiff.  It takes a 20kg mass to extend it 10cm.
The other spring is weak.  It only takes a 5kg mass to extend it 10cm.
The 25kg mass will extend the two springs by 10cm.  The stiff spring takes 4 times more load than the weak spring.
In summary, stiffness reflects the ratio of load over deflection.  If the deflection of two members is the same, then the stiffer one takes a higher load by definition.
A: I think stress does not choose the path.Because stress is the resistance or reaction offered by the member or path.Stiffer paths tend to resist more than the other paths.So it is the path that chooses to offer more resistence.
