Within the scope of AXISVM certain tools are available to improve finite element modeling, without compromising the modeling accuracy. Diaphragms mean such a practical opportunity, which will be introduced through this article.
The diaphragm #
Diaphragms are substituting elements, which are infinitely rigid in their own plane of operation, so they act like a real rigid body. The relative spatial positions of nodes are fixed. This makes diaphragms suitable for substituting slabs, which have negligible rotation components in vibration analysis.
The upcoming figure shows the first vibration mode, on the left side the slab is modeled as a diaphragm, on the right side as a classical domain.
Diaphragm properties #
Diaphragms have the following properties:
- The contour of the diaphragm stay undeformed in its plane of operation.
- The horizontal projection of nodes are always permanent relative to the contour line.
- The value of rotation about axis perpendicular to the plane of operation is identical in every point of the diaphragm.
- Diaphragms transfer normal and shear forces.
- Bending and torsional moments do not transfer through diaphragms, this results that diaphragms are not suitable to model the interaction of the substituted slab with other structural elements, or to provide the structural continuity. This property can be avoided by defining simultaneously the slab as a domain and after it defining on it a diaphragm.
- Diaphragms reduce the dimension of equation system, consequently the computing time as well.
- Diaphragms also reduce the masses’ degree of freedoms (the maximal number of modal shapes).
The experience shows that diaphragms – based on the previously seen statements – can reduce the computing time efficiently in case of skeletal structures (building models containing mostly columns, or maybe a small number of walls). In case of other structures diaphragms are less commonly used. Inconsiderate usage of them can lead to the increase of computing time.
Defining diaphragms #
Diaphragms can be defined directly, by giving the contour of it (as can be seen on the right side of the next figure) with the help of “Diaphragm” button (in the “Elements” menu), or by modifying previously defined domains (as can be seen on the left side of the upcoming figure).
It has to be noted that directly defined diaphragms are not considered as domains in the model, they actually substitute domains. In this case – since these are not structural elements – directly defined diaphragms will contain the following shortcomings:
- It is not possible to recieve and transfer inner forces to connecting structural elements (e. g. rib, column, or generally every elements which does not connect to any other supported structural part).
- It is not possible to define surface loads/domain loads on a pure diaphragm (except by inserting a load panel).
- The displacements of the structure can vary, because the “clamping” effect of the slab will not appear on column ends.
Due to these properties diaphragms practically can be handled as chain of nodes with constrained number of degree of freedoms. This is the reason why these all should be modeled systematically to gain realistic results.
To form the system of diaphragms is a sensitive modeling question. In the upcoming figure it can be properly seen that the vibrational behavior of each storey is not identical (the stiffening core vibrates separately from the adjacent building parts).
In the following picture there is a linked system of diaphragms. This behavior is consequent, so the whole structure can vibrate identically.
Hence this, the following considerations should be taken into account during the preparation of a model containing diaphragms:
- The diaphragms have to form a connecting system.
- In accordance with previously mentioned facts, when defining a diaphragm it must not connect to an unsupported structural element.
- It is not possible to define loads directly on diaphragms.
- It is not possible to define a hinged connection to diaphragms.
Vibration analysis #
It is optionable to convert slabs defined previously as ordinary domains to diaphragms during the vibration analysis, before launching the analysis with the following switch button.
By applying this automatic conversion the loads acting on the slab (if the mentioned setting is applied) get to the edge of the diaphragm. The following conditions are available for this adjustment:
- Only horizontal domains are converted to diaphragms.
- Loads acting on converted domains are redistributed on the edges of adjacent elements.
- Domains supported directly (with defined support) are not converted.
Selection possibilities in case of defined domain #
Important to note the different possibilities of selection when one makes diaphragm of a predefined domain. The following two options are available for this:
- Beside the selection of domain contour, the whole finite element mesh is also selected. The diaphragm is defined in this way:
- Only the domain contour is selected before the definition of diaphragm:
The basic difference manifests in local effects on the domain. The less the slab stiffness is, the difference is as more emphatic, e. g. the effect of a concentrated load acting on the middle of the domain. The next figures show the difference (these discrepancies could be proportionally significant):
The hereby shown two domains are in top view. In both case a horizontal concentrated load is acting in the middle of the domain (in the plane of the diaphragm). Next figures show the translations in the direction of the force:
Although the difference is numerically tiny, the reason is high slab stiffness. In despite of it, the importance of definition method is spectacular in the case of a predefined domain’s conversion into a diaphragm.
Source http://www.ingware.com
