Concrete Design
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.