# Concrete Design

Version 32.1 by IwonaBudny on 2018/12/04 15:28

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: mξ*mη < 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 mx is positive and the my 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 mx and the top reinforcement bars make equilibrium to the my. So a certain reinforcement direction takes positive and negative loads at the same time.

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]).

Note: The shrinkage effect has to be used together with applied reinforcement.

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 (εcs [‰] at concrete materials) in the concrete zone of the section is (here in X direction):

NX = EAc εcs [k&Nu;/m]

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

where:

n = Es / Eand Ss 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 NX because of the position change of centre of gravity:

MY = NX zs

The specific rotation (curvature) from MY 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  fck ≤ 50 MPa

λ = 0,8 - (fck - 50)/400                     for  50 < fck ≤ 90 MPa

and:

η = 1,0                                              for  fck ≤ 50 MPa

η = 1,0 - (fck - 50)/200                     for  50 < fck ≤ 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

The shear capacity is calculated according to EC2 6.2.2 and 6.2.3 considering applied bending reinforcement when the option Checking has been selected. Otherwise, the required bending reinforcement according to this chapter. The design criteria for the shear capacity is:

VSd < VRd1

where:

VSd is the design shear force;

VSd = Q, which is calculated as

VRd is the shear capacity.

If the section in which the shear force is acting has an angle with respect to the reinforcement directions the shear capacity is calculated as:

## Punching

The punching capacity is calculated according to EC2 6.4.3 - 6.4.5.

### Checking

Punching without shear reinforcement

A concrete compression check on u0 is made according to 6.4.5 (6.53). A concrete shear check on u1  is made for a capacity calculated according to 6.4.4 (6.47).

Punching with shear reinforcement

A concrete compression check on u0 is made according to 6.4.5 (6.53). Reinforcement is calculated with regard to critical perimeters u1, u2, ... unReinf  according to 6.4.5 (6.52 ).

(ui are control perimeters above the reinforced region, distance between them is ”Perimeter distance”, defined in the calculation parameter).

A concrete shear check on uout is made for a capacity calculated according to 6.4.4 (6.47)

(uout is either the first perimeter that does not need reinforcement, or if it is not found, the perimeter that is k deff distance from the outer perimeter of the reinforcement).

Warnings

A warning message is shown, if reinforcement does not comply with the detailing rules in 9.4.3.

# Design calculations for bar structures

## Longitudinal reinforcement

Analysis of second order effects with axial load

Tags: Shrinkage