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The nonlinear system analysis makes it possible to determine the
internal forces and deformation values of shell structures made of
reinforced concrete and steel. For solid elements the stress state
is calculated based on the bilinear constitutive model under
consideration of geometric and physical nonlinearities. The results
can be used to perform a check of the ultimate state limit and
serviceability for the entire system.
The following nonlinear effects can also be taken into
consideration:
- Equilibrium on the deformed system, also according to the
deflection theory
- Areas of reinforced concrete according to DIN 1045, DIN
1045-1, ÖNorm B4700, SIA 262 and
EN 1992-1-1
- Areas of steel with bilinear stress-strain curves under
consideration of the Huber-von Mises yield criterion
- Areas and volumes with bilinear stress-strain curves and
separately definable compressive and tensile strength
Nonlinear Layer Elements
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So-called layer elements are used
to enable the integration of nonlinear stresses across the area
section. This is done by determining the stresses in each layer
according to the plain stress theory, two-dimensional stress
state, under consideration of the physical nonlinearities. The
stresses are integrated to determine the internal forces. |
Structures Made of Reinforced Concrete
The biaxial concrete behavior is realized under consideration of
the strengths according to Kupfer/Hilsdorf/Rüsch and the concept of
equivalent one-axis strain:
The required material parameters and partial safety factors are
taken from the corresponding standard. The concrete tensile strength
can be considered with softening or bilinear behavior.
This
calculation is based on previous results of an evaluation of
reinforcing steel. Alternatively, the user can also directly specify
the reinforcement level.
The following example is taken from the chapter 'Grundlagen der
Bemessung nach DIN 1045-1 in Beispielen' (Basics of Design According
to DIN 1045-1 in Examples), Betonkalender 2001.
For the slab
shown the deformations at the serviceability limit state are to be
determined.
First a linear-elastic calculation followed by
design according to DIN 1045-1 is carried out. The reinforcement
determined is then taken into account during nonlinear system
analysis. The deformations calculated in the individual analyses are
listed below.
Color gradient of the deformation at the
serviceability limit state
|
max Uz [mm] |
| Elastic
calculation |
12.6 |
| Serviceability |
22.9 |
|
Serviceability and Creeping (eff. phi
= 2,0) |
48.8 |
Structures made of steel and bilinear material
The calculation is carried out according to the theory of
plasticity. The check guarantees that, under the consideration of
the internal force interaction, the full-plastic internal force
limits are not exceeded and that the system is in a stable state of
equilibrium. In addition to the internal forces and deformations,
the nonlinear stress and strain distribution in the complete
structure is made available.
The following is a representation of the yield
surface according to Raghava for the two-dimensional stress state as
used for layer elements with bilinear material characteristics.
The plasticized areas can be seen clearly on the
tube joint illustrated below. The load capacity has almost been
reached the existing load.
Color gradient representation of the
comparison stresses
See also: Nonlinear system
analysis for beam structures
Documentation:
Nonlinear
finite elements
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