# Concrete Design

**Contents**

FEM-Design performs design calculations for reinforced concrete-, steel- and timber structures according to Eurocode. The following design considers EC2 (standard) and the National Annex (NA) for Denmark, Finland, Germany, Hungary, Romania, Norway, Sweden, Poland and United Kingdom.

# Design forces

The design forces are the forces that the reinforcements should be designed for in the reinforcement directions. The term design forces have meaning only in surface structures like plate, wall or 3D plate. In beam structures the design forces are equivalent to the internal forces. The necessary reinforcement calculations are based on the design forces.

The way of calculating the design forces is common in all modules and in all standards.

In FEM-Design the design forces calculation is based on the mechanism of optimal reinforcement calculation for skew reinforcements made by M.P. Niel- sen, Wood-Armer and Dr. Ferenc Németh, see [2]. The following description will show the way of calculation for moments but the way of the calculation is the same for normal forces too. Just substitute the m signs with n and you will have the calculation for normal forces.

For the calculation of the design forces we have given:

- ξ, η reinforcement directions,
- α, β angle of global x direction and the ξ, η reinforcement directions,
- mx, my, mxy internal forces.

The results will be the design moments:

In the first step we are taking a ξ-ϑ coordinate system and transform the internal forces into this system:

Now the design forces will be chosen from four basic cases called a), b), ξ) and η). The possible design moment pairs of the cases:

a) case:

b) case:

ξ) case:

η) case:

From the four cases the one is invalid where:

- the signs are different:
**m**_{ξ}*m_{η}< 0 - the crack tensor invariant is less than the internal forces invariant:

The valid positive pair will be the design moment for bottom reinforcement; the valid negative pair will be the design moments for the top reinforcement (positive means positive and zero values; negative means negative and zero values).

So the result will be four values in a certain point: two moment values for each reinforcement directions. It can sound strange that the reinforcements are used for both positive and negative moment in one direction at the same time, but if we are looking at a plate where the **m _{x} **is positive and the

**m**is negative and the reinforcements have an angle of 45 degree to the x direction we could imagine that the bottom reinforcement bars make equilibrium to the

_{y}**m**and the top reinforcement bars make equilibrium to the

_{x}**m**. So a certain reinforcement direction takes positive and negative loads at the same time.

_{y}# Shrinkage as load action

In the Plate and 3D Structure modules the shrinkage behaviour of reinforced concrete slabs can be taken into consideration as load action. The program add this movement effect (specific rotation) calculated from the formulas written be- low to the structure as invisible load (one load case must be defined as Shrinkage type, see User’s Guide [1]).

The effect of the shrinkage for the surface reinforcement bars in one direction (here X) (it is also valid in other bar directions):

The specific normal force causing the given shrinkage value (ε_{cs} [‰] at concrete materials) in the concrete zone of the section is (here in X direction):

N_{X} = E_{c }A_{c} ε_{cs} [kΝ/m]

The position change of centre of gravity considering reinforcement bars (here X-direction; see dashed line):

where:

n = E_{s} / E_{c }and S_{s} is the statical moment of (here) X-directional bars around the Y axis of the calculation plane.

The moment around the Y axis of the calculation plane from N_{X} because of the position change of centre of gravity:

M_{Y} = N_{X} z_{s}

The specific rotation (curvature) from M_{Y} for 1 meter wide section:

# Design calculations for surface structures

## Ultimate limit state

The design of the slab is performed with respect to the design moments described in Design forces.

In order to minimize cracking in the slab a good way is to reinforce according to the elastic moments which normally also leads to good reinforcement economy. The required bending reinforcement is designed according to EC2 3.1.7, where a rectangular stress distribution as shown below has been assumed.

λ = 0,8 for f_{ck} ≤ 50 MPa

λ = 0,8 - (f_{ck} - 50)/400 for 50 < f_{ck} ≤ 90 MPa

and:

η = 1,0 for f_{ck} ≤ 50 MPa

η = 1,0 - (f_{ck }- 50)/200 for 50 < f_{ck} ≤ 90 MPa

If the current moment is larger than the moment representing balanced design, compression reinforcement will be provided if allowed by the user otherwise an error message will be displayed. If the spacing regulations for the reinforcement are exceeded before adequate moment capacity can be reached a warning mes- sage will be displayed.

Note, that the required bending reinforcement is at design level primary not affected of the presence of user defined reinforcement. However, when user defined applied reinforcement is selected the stiffness will be effected, which in most cases will influence the moment distribution and thus secondary the required bending reinforcement.

## Shear capacity

## Punching

## Serviceability limit state

# Design calculations for bar structures

## Material properties

## Longitudinal reinforcement

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## Stirrups

### Shear

### Torsion

### Shear and torsion