Statics of Rigid Bodies
Calculated are support forces and reaction forces at hinges between parts of the system or structure.
Only static equilibrium equations are used here, so the investigated system must be statically determinate (isostatic).
The necessary condition is that the number of equilibrium equations equals the number of unknown reaction forces.
In case of a statically indeterminate system only the degree of statical indeterminacy will be calculated.
Steps to set up a new model:
- define coordinates of all relevant points (bearings, hinges and load locations).
The mouse can be used: double click to create new points, click drag to move existing points
- define each part of the structure by a list of points, a part with only 2 points is a truss.
The mouse can be used: click the points, double click to finish a list
- define for points with bearings, which direction is supported
- define loads (forces and/or moments)
If a point belongs to 2 parts of the structure, it will automatically become a hinge connecting them.
If a part is defined by only 2 points it will be interpreted as a truss in the results.
About how it works
A body is in equilibrium under the action of a general plane system of forces,
when no resulting force or moment acts on it. That gives 3 scalar equilibrium equations for each body.
Therefore, all bodies and pendulum rods are cut free and 3 equilibrium conditions are created in each case,
in which, in addition to the known loads, the hinge forces are also included as unknowns, 2 per hinge.
The bodies are connected to one another via the hinges. There is a central system of forces in each case.
Therefore, 2 equilibrium conditions are created for each coupling hinge.
An equation is also created for each floating bearing, which, depending on its orientation, sets one of the two bearing forces to 0.
With b bodies, j hinges and f floating supports, this results in a system of equations with 3·b+2·j+f equations for the unknown hinge forces and support reactions.
The unknowns of this system of equations are the 2 reaction forces per hinge that are independently introduced for each body and bearing.
When it comes to "hand calculations", the procedure is slightly different, e.g. pendulum rods are not treated as bodies,
but only as single-value power transmitters.
This significantly reduces the number of equations required, especially for truss frameworks.
About the results
The system is statically determinate if the system of unknowns can be solved from the system of available equations.
A necessary condition is that the number of equations equals the number of unknowns.
All reaction forces will be calculated in this case.
The system is statically indeterminate if the number of unknowns is larger than the number of available equations.
In this case only the degree of statical indeterminacy will be calculated and displayed.
Reaction forces cannot be calculated without information about the deformation behavior of the components of the system.
The system is kinematically indeterminate if the number of unknowns is smaller than the number of available equations.
Kinematical indeterminacy means that parts of the system or the system as a whole can move.
In this case the degree of kinematical indeterminacy will be calculated and displayed, and if equilibrium is possible, the reaction forces are also calculated.
more JavaScript applications