Statically Determinate Truss
In structural engineering, a truss is a framework consisting of straight members connected at their ends by joints. Trusses are commonly used in the construction of bridges, roofs, and other structures to provide support and stability. The analysis of trusses involves determining the forces and stresses within the members to ensure that the structure is capable of carrying the applied loads.

Definition of Statically Determinate Truss
A truss is said to be statically determinate if the forces in all of its members can be determined using the equations of static equilibrium alone, without the need for additional compatibility or deformation equations. In other words, the truss can be analyzed by applying the principles of statics to solve for the unknown forces in the structure.

Analysis of the Given Truss
In the given problem, the truss has three members labeled as B, R, and J. The values provided for these members are B=6, R=6, and J=4. To determine whether the truss is statically determinate, we need to analyze the forces in its members.

Applying Equilibrium Conditions
To analyze the truss, we can start by applying the equilibrium conditions at the joints. The equilibrium equations state that the sum of the forces in the x-direction and y-direction must be equal to zero.

Joint B
At joint B, there are two unknown forces: the horizontal force in member B and the vertical force in member R. Applying the equilibrium conditions:
Sum of horizontal forces = 0: B = 0
Sum of vertical forces = 0: R = 0

Joint R
At joint R, there are two unknown forces: the horizontal force in member B and the vertical force in member J. Applying the equilibrium conditions:
Sum of horizontal forces = 0: B = 0
Sum of vertical forces = 0: J = 0

Joint J
At joint J, there are two unknown forces: the horizontal force in member R and the vertical force in member J. Applying the equilibrium conditions:
Sum of horizontal forces = 0: R = 0
Sum of vertical forces = 0: J = 0

Conclusion
From the analysis above, we can see that all the unknown forces in the truss can be determined using the equations of static equilibrium alone. Therefore, the truss is statically determinate.

Explanation
A truss is considered statically determinate when the forces in all of its members can be determined solely by applying the equations of static equilibrium. In the given problem, the forces in all the members of the truss can be determined by applying the equilibrium conditions at each joint. The values provided for the members (B=6, R=6, and J=4) do not affect the analysis because these values are used to represent the forces in the members, not the actual lengths or dimensions of the truss. The fact that all the unknown forces can be determined using the equations of static equilibrium indicates that the truss is statically determinate.