Statically indeterminate
The Static determination is a measure of static systems ( body structures, trusses ) and describes how many bearing forces to face the possible directions of motion of a system.
A system is statically determined when the number of support reactions ( " Boundary Conditions " ) equal to the number of possible directions of movement ( " degrees of freedom " ) and each direction of movement counteracts only one bearing reaction. Statically determinate systems are the simplest systems and can be calculated using the equilibrium conditions alone. This applies both to the reaction forces as well as for all internal forces at any subsystems.
A system is statically indeterminate if the number of support reactions exceeds the number of possible directions of movement. At least one movement direction to counteract more than one layer of reaction. The calculation of such systems is done using methods that go beyond the basic force equilibrium conditions.
A kinematic system is statically determined or when the number of the bearing reaction is smaller than the number of possible directions of movement. At least one direction of movement counteracts no bearing reaction and the system can move or rotate freely in this direction. Kinematic systems are therefore not usable baustatischer view.
Equilibrium conditions
Suffice to calculate all statically determinate systems as aids the equilibrium conditions: When the three planar static equilibrium conditions:
In spatial statics result analogous six equilibrium conditions:
Degree of static indeterminacy
To check the static determination of a system of rigid bodies, which are interconnected via connecting elements, a necessary condition can be evaluated.
For this, the weights are ( that is, the respective number of support reactions ) to determine all the connection elements and the support and evaluate the following formula:
Where:
Each value corresponds to a quantity to be determined (forces or moments ), while the above three equilibrium conditions ( planar case ) can be formulated at each body.
- For n <0: in each case determined under static ( unstable, unstable )
- For n = 0: necessary for static determinacy
- For n > 0: in any case, statically indeterminate, n is the degree of static indeterminacy
For flat trusses, which are hinged rods that transmit only train or compressive forces, the following applies:
This is
In each node, only two equilibrium conditions can be formulated, since no moments occur. This equation is thus a special case of the above general formula dar. While the first formula on the cutting free of the individual's body is based, the second formula is based on the evaluation of the steady state conditions in each joint, and thus corresponds to the approach to the junction method.
-Effects resulting from forced
Deformations due to displacements and rotations of the bearings, temperature expansions, creep and shrinkage of concrete cause in statically determinate systems no constraining forces and thus no internal forces. In statically indeterminate systems, however, forces caused by these impacts. In the calculation of such systems therefore appropriate load cases are to be reported.
Internal and external static determinacy
In a series of beam structures, it is useful and clearly to distinguish between external and internal static determinacy. A system or part thereof is externally statically determined when the outer bearing reactions can be calculated solely with the equilibrium conditions of the load. A system is called internally statically determinate if the internal forces can be calculated to cut subsystems using the equilibrium conditions of the load.
Examples
Statically determinate systems are for example:
- Simply supported beam ( beam on two supports)
- Simply supported beam with cantilever
- Cantilever
- Three-hinged frame
- Three-hinged arch
- Gerber carrier
Statically indeterminate systems are for example:
- Continuous beam
Examples of specific externally, but internally indeterminate system:
- Frame truss
- Vierendeel