Equilibrium Equations:
We know that structures remain at rest, and since they are at rest they have to maintaining the state of equilibrium in between actions and reactions. We can define the geometry of the structure in three dimensional spaces. Since structure is at rest we can say that the actions which are acting on the structure; are in the equilibrium with reactions provided to it. This can be written in the form of equations which are also known as 'Equilibrium Equations' and are as follows:
We know that structures remain at rest, and since they are at rest they have to maintaining the state of equilibrium in between actions and reactions. We can define the geometry of the structure in three dimensional spaces. Since structure is at rest we can say that the actions which are acting on the structure; are in the equilibrium with reactions provided to it. This can be written in the form of equations which are also known as 'Equilibrium Equations' and are as follows:
These are six in numbers. If the structure is built with more than one part, the equilibrium equations will be the six times the number of parts.
If the structure is two dimensional; for example in x y plane, these equations will reduced as follows:
These equations are in three in numbers for each member.
Moreover, for uni-axial members (trusses and cables), the number of equilibrium equations will reduced to just one for each part.
Support Reactions:
Structure is supported with various types of supports.
Each support provide a set of support reaction and the magnitude of these
reactions itself is the function of loading conditions. For illustration of support reactions click here.
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