# Calculation of required reinforcement in case of RC surface structures based on sandwich model

## Description#

The AXISVM software determines the required reinforcement of surface structures with the help of a three layered sandwich model, in case of applying SIA or DIN EN standard. Also this method is applied when the software calculates skew reinforcement, regardless of the applied standard.

## Orthogonal reinforcement#

The principal of this method is to divide the surface element into three parallel layers. The bending moments acting on the surface element are decomposed and these are equilibrated the membrane forces, in the bottom and top layers. The bottom and top layers are calculated as a 2D in-plane stress state membrane.

The membrane forces in the top and bottom layers are determined in the following way in case of orthogonal reinforcement.

## Calculation of skew reinforcement#

The same decomposition is done in the following way in case of skew reinforcement. Before the decomposition, the internal forces are transferred from x/y coordinate system into an orthogonal x’/y’ coordinate system where x’ direction is identical with ξ reinforcement direction.

## Design#

The program uses the following membrane forces, from which the required reinforcement can be determined:

• top layer: nt,x, nt,xy, nt,y nt,yx,
• bottom layer: nb,x, nb,xy, nb,y nb,yx.

Tension forces awakening in the membrane are absorbed with reinforcement, meanwhile the software checks the adequateness of the concrete. The forces and stresses used in design are calculated according to the guidelines of Annex F of EN 1992-1-1. If significant shear membrane forces awaken, then at the check of concrete strut in compression the program considers the effect of transverse tension. The effect of transverse tensile stresses on strength can be taken into account with a ν coefficient according to EN 1992-1-1 standard’s 6.5 correlation. At the same time, in case of SIA standard the following cases can be distinguished, in which cases the appropriate reducing factors can be set as parameters:

(1) tension in two directions and shear,

(2) tension in one direction, compression in one direction and shear,

(3) compression in two directions and shear.

## Error message#

The error message “The section cannot be reinforced” can appear in the following cases:

• the concrete strut in compression is not adequate for shear,
• the compressional principal stress of the concrete strut exceeds the strength design value of concrete,
• the cross sectional area of the reinforcement in bottom and top layers exceeds the maximal value according to the standard’s detailing rule.

## Notes, conclusions#

Actually the layer thicknesses are optimized to reach the ideal amount of reinforcement. In that case, when the layer thickness has maximal value, but the concrete strut in compression is still not adequate, compression reinforcement should be applied.