It is necessary to determine whether a structure is unstable, statically determinate, or redundant. For pin-joined structures, the unknown quantities are the axial force in the members and the reactions at the supports. Thus, if there are m-members and r-reactions, the total number of unknowns will be m + r.
Similarly, it is possible to resolve the forces in two directions at every joint in the system. Thus, for j-joints, a total of 2j equations can be formed relating to the unknowns.
Where,
m = number of members;
r = number of reactions and
j = number of joints
If the structure is statically determinate, it can be analysed with the equations of equilibrium outlined below.
If the structure is unstable, it may be necessary to add a new member or remove a joint to make it stable. If the structure is statically indeterminate, it can be solved using a computer system or a member or joint removed to make it statically determinate.
Note: External loads are not taken into consideration in the determination of stability or redundancy
Example
Determine the degree of determinacy of the following structural arrangements shown below
While drawing from the last three examples shown above, a structure satisfying the statical determinacy test (m + r = 2j) does not make the structure stable. There is always the need to investigate the framework of the structure carefully to ensure that;
- A triangular system of arrangement is present.
- There is no risk of sway
- There is no risk of translation.
All of the above would be avoided by providing triangular braces and pinned supports to the structure.
Thanks!
