1. Determinacy relates to the analysis of how fully a structure's internal forces and reactions can be determined using equations of equilibrium. A structure is considered determinate if all the internal forces and support reactions can be precisely calculated using static equilibrium equations.
2. Stability refers to the ability to maintain equilibrium and resist failure or collapse. A stable structure is able to maintain equilibrium when subjected to external loads or forces, without undergoing excessive deformation or displacement. Statically Unstable occurs when the state of balance is disrupted, typically due to an inadequate number of supporting elements within a structure.

Formulations for Stability and Determinacy of Beams, Truss and Frames

Where:
r = Total number of reactions
c = Equations of condition (c = 1 for a hinge; c = 2 for a roller; c = 0 for a beam with internal pin connection)
b = Number of members
j = Number of joints

Beam Stability and Determinacy Examples
Given	Computation	Condition	Result
R = 5, m = 1	5 > 3(1)	r > 3 + c	Indeterminate
R = 5, C = 0	5 > 3 + 0	r > 3 + c	Beam is stable and indeterminate
Given	Computation	Condition	Result
R = 7, m = 2	7 > 3(2)	r > 3 + c	Indeterminate
R = 5, C = 1	5 > 3 + 1	r > 3 + c	Beam is stable and indeterminate
Given	Computation	Condition	Result
R = 6, m = 2	6 = 3(2)	r = 3 + c	Determinate
R = 4, C = 1	4 = 3 + 1	r = 3 + c	Stable and determinate
Given	Computation	Condition	Result
R = 11, m = 4	11 < 3(4)	r < 3 + c	Unstable
R = 7, C = 2	7 > 3 + 2	r > 3 + c	Unstable internally
Given	Computation	Condition	Result
R = 7, m = 4	7 < 3(4)	r < 3 + c	Unstable
R = 4, c = 3	4 < 6	r < 3 + c	Unstable