Method 1

Begin with a free-body diagram. With Method 1, the bridge is (in essence) supported at each end by pin supports. Thus, each support exerts two components of force; one parallel and one perpendicular to the moat wall. There are four unknowns,

     F_Ax     F_Ay     F_Bx     F_By

There are only three independent equilibrium equations for a 2-D system. Since the number of unknowns is one greater than the total number of equilibrium equations, this method of laying the bridge leads to a statically indeterminate system with a degree of redundancy of one.

The engineer is unable to solve for the reaction forces using only the equilibrium equations.

Begin with a free-body diagram. With Method 2, each support exerts a force that is perpendicular to the moat wall. These reactions are concurrent, as the lines of action of each reaction force intersect at point P.

The weight of the cow creates an unbalanced moment about point P. Thus, the bridge is unstable due to improper supports and will not remain in equilibrium under the weight of the cow. There are only two unknowns,

     F_Ay     F_Bx  

Even thought there are three independent equilibrium equations, there are infinite solutions for the two unknowns. The engineer is unable to determine a unique solution for the reactions using the equilibrium equations.

Begin with a free-body diagram. With Method 3, there are three unknowns,

     F_Ay     F_Bx     F_By

There are three independent equilibrium equations. The reaction forces are neither parallel nor concurrent, and this system is statically determinate. The engineer can solve for the reactions using the equilibrium equations.