3.6.11: Optimize Reinforcement

The “Optimize Reinforcement”-component calculates reinforcement quantities for arbitrary shells. The algorithm is based on the sandwich model approach of Marti (see [6] or [4]). Each load-case is considered separately and the maximum reinforcement of all load-cases is chosen.

Fig. 3.6.11.1: Calculation of reinforcement quantities for a 1mx1m plate and an in-plane tensile 50kN load.

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Fig. 3.6.11.1 shows a rectangular plate of size $1m$ by $1m$ with a uniform tensile line-load of $50kN/m$ which translates to two point-loads of $25kN$each. The first step consists of defining a reinforced concrete cross section via a “Cross Section”-component (see section 3.3.2). The definition of reinforcement layers does not impact the displacements or cross section forces of the model. It merely forms the basis for calculating reinforcement quantities using linear elastic cross section forces. For reinforcement design it is assumed that the material in layer zero (usually concrete) has no tensile and infinite compressive strength. Since the latter is a simplification, one should assure a sufficient height of the concrete cross section by using the “Optimize Cross Section”-component first.

The input-plugs of the “Optimize Reinforcement”-component are similar to those of the “Optimize Cross Section”-component:

"Model"	Structure for doing reinforcement design
"ElemIds"	Identifiers of elements for which reinforcement quantities should be calculated. If not specified, optimization is carried out for all reinforced concrete cross sections.
"GroupdIds"	List of identifiers of groups of elements that take part in reinforced cross section design and shall have uniform reinforcement.
"MaxUtil"	Target value of the reinforcement utilization where 1.0 means full utilization - the default.

Under the submenu “Settings” reside two plugs which let you specify the partial safety factors for concrete (“gammaMc”) and steel (“gammaMs”). The former exists for future use, since currently concrete is assumed to be infinitely strong in compression. The latter is set to 1.15 which constitutes the standard value according to Eurocode 2 (see [3]). The output of “Optimize Reinforcement” comprises these plugs:

"Model"	Structure with optimized reinforcement
"Info"	Warnings regarding the reinforcement design process
"Mass"	Total mass of reinforcement after optimization in kilograms
"Disp"	Maximum displacement of the structure for each load-case
"Energy"	Elastic deformation energy of the structure for each load-case

The “ShellView”-component lets one display the thickness of the reinforcement layers and the stresses there (see fig. 3.6.11.1). The input-plug “LayerInd” sets the index of the layer to be displayed. The concrete cross section has index zero, index one corresponds to the top-, index four to the bottom-most reinforcement layer. The Z-direction of the local coordinate system points to the top of the cross section. The entry “Local layer axes” under “Display Scales” in the component “ModelView” lets one enable, disable and scale the arrows of the local coordinate system.

In the example of fig. 3.6.11.1 the default reinforcement material BSt500 with a characteristic yield strength of $f_{y,k}=50kN/cm^2$ leads to a necessary amount of reinforcement of $a_s = \frac{50kN \cdot 1.15}{2 \cdot 50kN/cm^2}$. This is equivalent to a layer thickness of 0.00575 cm. The “2” in the denominator results from the fact that there are two reinforcement layers (of index one and four) which point in the direction of the tensile force.

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