RF-CONCRETE Surfaces Version 5

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RF-CONCRETE Surfaces 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 needed for the deformation analysis, the program requires the cross-section properties dependant on the cracked state that are available in every direction of reinforcement. These are the following:

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

The mean strain εΦ and the mean curvature ΚΦ are interpolated between a cracked and an 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 

Thus, the influence of shrinkage is considered by using the factor ksh,φ,c.

If no axial forces nΦ act (e.g. in the type of model 2D - XY (uZ / φX / φY), only those ideal cross-section properties are relevant that relate to the ideal center of the cross-section:

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 

Equation 2.88 (2.88)

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

ν = 1 - maxϕ{1,2} ζϕ · νinit 

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