3.3.2: Shell Cross Sections

In Karamba3D there are four different kinds of shell cross sections:

"Shell Const”	For shells with constant thickness and material over all mesh faces.
“Shell Var”	Lets one specify the thickness and material of each face of the shell-mesh individually.
“ShellRC Std Const”	This allows to specify a standard (Std) reinforced concrete(RC) cross section which is constant over the shell.
"ShellRC Std Var”	The same as above but lets one choose the reinforced concrete properties differently for each element.

Constant and Variable Shell Cross Sections

The components “Shell Const” and “Shell Var” only differ in the data structures expected at the inputs “Material(s)” and “Height(s)”. In case of “Shell Const” these are data items. The “Shell Var”-variant expects two lists. The descriptions below refer to the “Shell Var”-component.

Fig. 3.3.2.1 shows a shell consisting of two elements. Triangular meshes form the basis for defining a shell geometry (see section 3.1.9) and specify the sequence of faces (i.e. shell elements). The list of element thicknesses in fig. 3.3.2.1 corresponds to that order. Be aware of the fact that meshes containing quads will be automatically triangulated. In case that there are more mesh faces than thickness specifications, the last item ($6cm$ in this case) acts as the default value. The same holds for the supplied list of materials. Make sure to graft the “Materials”- and “Heights”-input when you want to define a list of shell cross sections. Otherwise one cross section results where one would expect several. For the “Shell Const” definition no data tree manipulation is necessary in such a case.

Fig. 3.3.2.1: Shell made up of two elements with different thicknesses

When rendering the shell cross sections (see fig. 3.3.2.1) thicknesses get linearly interpolated between the nodes. The cross section height at each node results from the mean thickness of shell elements attached to it.

The input-plugs “Family”, “Name”, “Color” and “Materials” have the same meaning as described in section 3.3.1.

Constant and Variable Reinforced Concrete Shell Cross Sections

The design of reinforced concrete cross sections in Karamba3D is based on linear elastic cross section forces. The “Optimize Reinforcement”-component takes these and computes the necessary reinforcement assuming cracked concrete cross sections. Thus defining reinforced concrete cross sections does not alter the mechanical behavior of the structure. They rather serve as input to the reinforcement design procedure.

Similar to shell cross sections there exist two variants of components for reinforced cross sections:

“ShellRC Std Const”	For shells with constant height, material and reinforcement. It saves the user thoughts about data trees.
“ShellRC Std Var”	This component allows to specify different heights, materials and reinforcement for each face of a shell mesh.

Further below variant two will be explained. The “ShellRC Std Const”-component works similar to the variable-variant. The only difference are the data structures expected at the inputs.

Fig. 3.3.2.2: Shell made up of two elements with different properties

Fig. 3.3.2.2 shows the definition for a reinforced concrete shell with two faces with different thicknesses, materials and reinforcement definitions. The geometry corresponds to that of fig. 3.3.2.1. A standard reinforced concrete cross sections consists of five layers: Layer zero is the concrete cross section. The layers one to four correspond to reinforcement. The top layer (with respect to where the local z-axis points to) comes first, the bottom layer last. Their orientation with respect to layer zero is 0°, 90°, 90° and 0°.

Besides the standard inputs of cross sections (“Family”, “Name”, “Elem|Id” and “Color”) the “ShellRC Std Var”-component offers these:

“Materials-Concr”	Expects a list of materials to be used for the concrete cross section. The items of this list get mapped to the shell elements according to the longest list principle. “C30/37” according to Eurocode 2 represents the default concrete.
“Heights”	Heights of the concrete cross sections for each shell face. The longest list principle applies. The default height is$20cm$.
“Materials-Reinf”	List of materials to be used as reinforcement for each element – by default “BSt 500” according to Eurocode 2 with a characteristic strength of $50 kN/cm^2$. Again the longest list principle applies.
“Areas”	Expects a data-tree with a maximum of four entries per branch. The values define the minimum reinforcement for each layer. The physical unit is centimeter. Thus the areas of the reinforcement bars need to be divided by their mutual distance in order to arrive at an equivalent plate thickness. The layer thicknesses default to $0cm$.
“Covers”	Input here a data-tree with four values per branch. These specify the position of the reinforcement layers with respect to the upper and lower side of the concrete cross sections. Positive values give the distance from the upper, negative values the distance from the lower side towards the interior. Without any input the covers default to $3.5cm$, $4.5cm$, $-4.5cm$ and $-3.5cm$.
“Dirs”	Reinforcement layers can be given an angle with respect to the local shell coordinate system. A positive value rotates in anti-clockwise direction about the local z-axis. A value of zero – which is the default – aligns the first and last layer with the local x-axis. The angle of rotation can be specified for each shell face individually.

With the input-plug “LayerInd” of the “ShellView”-component one can select specific layers for visual inspection and results retrieval.