RF-CONCRETE Surfaces – Online Manual Version 5

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RF-CONCRETE Surfaces – Online Manual Version 5

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2.7.7 Cross-Section Properties for Deformation Analysis

Cross-Section Properties for Deformation Analysis

For the material stiffness matrix D for the deformation analysis, the program requires the cross-section properties dependant on the cracked state that are available in every reinforcement direction. These are in detail

  • the moment of inertia to the ideal center of gravity IΦ,
  • the moment of inertia to the geometric center of the cross-section I0,Φ,
  • the cross-section area AΦ,
  • the eccentricity of the ideal center eΦ to the geometric center.

The mean strain εΦ and mean curvature ΚΦ are interpolated from the cracked and uncracked state according to EN 1992-1-1, Equation (7.18):

εϕ = ζϕ · εϕ,II + 1 - ζϕ · εϕ,1κϕ = ζϕ · κϕ,II + 1 - ζϕ · κϕ,1 

The strains in the cracked state c (state I and II) are calculated according to the following equations:

εϕ,c = nϕE · Aϕ,cκϕ,c = κsh,ϕ,c · mϕ - nϕ · eϕ,cE · Iϕ,c 

The influence of shrinkage is therefore considered with the factor ksh,φ,c.

When no axial forces nΦ act, like in the model type 2D - XY (uZ / φX / φY), for example, only the ideal cross-section properties that relate to the ideal center of the cross-section are relevant:

Aϕ = Aϕ,I · Aϕ,IIζϕ · Aϕ,I · ksh, ϕ,II + 1 - ζϕ · Aϕ,II · ksh,ϕ,IIϕ = Iϕ,I · Iϕ,IIζϕ · Iϕ,I · ksh,ϕ,II + 1 - ζϕ · Iϕ,II · ksh,ϕ,l 

If axial forces are available, the cross-section properties are related to the geometric center of the cross-section:

Aϕ = nϕA · εϕ                     mit εϕ = mϕ - κϕ · E · IϕnϕIϕ,0 = Iϕ + Aϕ · eϕ2            mit Iϕ nach Gleichung 2.87 

In the course of the calculation of the cross-section properties, the initial value of poisson's ratio νinit is reduced according to the following equation:

ν = 1 - maxϕ{1,2} ζϕ · νinit 

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