Did you know that To calculate masonry structures, a nonlinear material model has been implemented in RFEM. It is based on the approach of Lourenco, a composite yield surface according to Rankine and Hill. This model allows you to describe and model the structural behavior of masonry and the different failure mechanisms.
The limit parameters were selected in such a way that the design curves used correspond to a normative design curve.
RFEM allows you to use a special line hinge to model the special properties of the connection between the reinforced concrete slab and masonry wall. This limits the transferable forces of the connection depending on the specified geometry. You guess right: This means that the material cannot be overloaded.
The program develops interaction diagrams that are applied automatically. They represent the various geometric situations and you can use them to determine the correct stiffness.
The calculation of masonry is carried out in compliance with the nonlinear-plastic material law. If the load at any point is higher than the possible load to be resisted, redistribution takes place within the system. This have the simple purpose of restoring the equilibrium of forces. With the successful completion of the calculation, the stability analysis is provided.
Are you familiar with the Tsai-Wu material model? It combines plastic and orthotropic properties, which allows for special modeling of materials with anisotropic characteristics, such as fiber-reinforced plastics or timber.
If the material is plastified, the stresses remain constant. The redistribution is carried out according to the stiffnesses available in the individual directions. The elastic area corresponds to the Orthotropic | Linear Elastic (Solids) material model. For the plastic area, the yielding according to Tsai-Wu applies:
All strengths are defined positively. You can imagine the stress criterion as an elliptical surface within a six-dimensional space of stresses. If one of the three stress components is applied as a constant value, the surface can be projected onto a three-dimensional stress space.
If the value for fy(σ), according to the Tsai-Wu equation, plane stress condition, is smaller than 1, the stresses are in the elastic zone. The plastic area is reached as soon as fy (σ) = 1; values greater than 1 are not allowed. The model behavior is ideal-plastic, which means there is no stiffening.
Did you know? In contrast to other material models, the stress-strain diagram for this material model is not antimetric to the origin. You can use this material model to simulate the behavior of steel fiber-reinforced concrete, for example. Find detailed information about modeling steel fiber-reinforced concrete in the technical article about Determining the material properties of steel-fiber-reinforced concrete.
In this material model, the isotropic stiffness is reduced with a scalar damage parameter. This damage parameter is determined from the stress curve defined in the Diagram. The direction of the principal stresses is not taken into account. Rather, the damage occurs in the direction of the equivalent strain, which also covers the third direction perpendicular to the plane. The tension and compression area of the stress tensor is treated separately. In this case, different damage parameters apply.
The "Reference element size" controls how the strain in the crack area is scaled to the length of the element. With the default value zero, no scaling is performed. Thus, the material behavior of the steel fiber concrete is modeled realistically.
Find more information about the theoretical background of the "Isotropic Damage" material model in the technical article describing the Nonlinear Material Model Damage.
Stress determination using an elastic-plastic material model
Design of masonry disc structures for compression and shear on the building model or single model
Automatic determination of stiffness of a wall-slab hinge
An extensive material database for almost all stone-mortar combinations available on the Austrian market (the product range is continuously being expanded, for other countries as well)
Automatic determination of material values according to Eurocode 6 (ÖN EN 1996‑X)
You enter and model the structure directly in RFEM. You can combine the masonry material model with all common RFEM add-ons. This enables you to design the entire building models in connection with masonry.
The program automatically determines for you all parameters required for the calculation by using the material data that you have entered. Then, it finally generates the stress-strain curves for each FE element.
Was your design successful? Then just sit back and relax. You benefit from the numerous functions in RFEM also here. The program gives you the maximum stresses of the masonry surfaces, whereby you can display the results in detail at each FE mesh point.
Moreover, you can insert sections in order to carry out a detailed evaluation of the individual areas. Use the display of the yield areas to estimate the cracks in the masonry.
Did you know? When unloading the structural component with a plastic material model, in contrast to the Isotropic | Nonlinear Elastic material model, the strain remains after it has been completely unloaded.
You can select three different definition types:
Standard (definition of the equivalent stress under which the material plastifies)
Bilinear (definition of the equivalent stress and strain hardening modulus)
Stress-strain diagram: definition of polygonal stress-strain diagram
If you release a structural component with a nonlinear elastic material again, the strain goes back on the same path. In contrast to the Isotropic|Plastic material model, there is no strain left when completely unloaded.
You can select three different definition types:
Standard (definition of the equivalent stress under which the material plastifies)
Bilinear (definition of the equivalent stress and strain hardening modulus)
If you are working with nonlinearities, this feature is suited very well to support you. For example, you can specify nonlinearities of member end releases (yielding, tearing, slippage, and so on) and supports (including friction). Furthermore, you can use special dialog boxes to determine the spring stiffnesses of columns and walls based on the geometry specifications.
Due to the integration of RF‑/DYNAM Pro in RFEM or RSTAB, you can incorporate numeric and graphic results from RF‑/DYNAM Pro - Nonlinear Time History to the global printout report. Also, all RFEM and RSTAB options are available for a graphical visualization. The results of the time history analysis are displayed in a time history diagram.
The results are displayed as a function of time and the numerical values can be exported to MS Excel. Result combinations can be exported, either as a result of a single time step or the most unfavorable results of all time steps are filtered out.
Calculation in RFEM The nonlinear time history analysis is performed with the implicit Newmark analysis or the explicit analysis. Both are direct time integration methods. The implicit analysis requires small time steps to provide precise results. The explicit analysis determines the required time step automatically to provide the stability to the solution. The explicit analysis is suitable for the analysis of short excitations, such as impulse excitation, or an explosion.
Calculation in RSTAB The nonlinear time history analysis is performed with the explicit analysis. This is a direct time integration method and determines the required time step automatically in order to provide the solution stability.
The nonlinear calculation is activated by selecting the design method of the serviceability limit state. You can individually select the analyses to be performed as well as the stress-strain diagrams for concrete and reinforcing steel. The iteration process can be influenced by these control parameters: convergence accuracy, maximum number of iterations, arrangement of layers over cross-section depth, and damping factor.
You can set the limit values in the serviceability limit state individually for each surface or surface group. Allowable limit values are defined by the maximum deformation, the maximum stresses, or the maximum crack widths. The definition of the maximum deformation requires additional specification as to whether the non-deformed or the deformed system should be used for the design.
RF-CONCRETE Members
The nonlinear calculation can be applied to the ultimate and the serviceability limit state designs. In addition, you can specify the concrete tensile strength or the tension stiffening between the cracks. The iteration process can be influenced by these control parameters: convergence accuracy, maximum number of iterations, and damping factor.
The following material models are available in RF − MAT NL:
Isotropic Plastic 1D/2D/3D and Isotropic Nonlinear Elastic 1D/2D/3D
You can select three different definition types here:
Basic (definition of the equivalent stress under which the material plastifies)
Bilinear (definition of the equivalent stress and strain hardening modulus)
Diagram:
Definition of polygonal stress-strain diagram
Option to save / import the diagram
Interface with MS Excel
Orthotropic Plastic 2D/3D (Tsai-Wu 2D/3D)
This material model allows the definition of material properties (modulus of elasticity, shear modulus, Poisson's ratio) and ultimate strengths (tension, compression, shear) in two or three axes.
Isotropic Masonry 2D
It is possible to specify the limit tension stresses σx,limit and σy,limit as well as the hardening factor CH.
Orthotropic Masonry 2D
The material model Orthotropic Masonry 2D is an elastoplastic model that additionally allows softening of the material, which can be different in the local x- and y-directions of a surface. The material model is suitable for (unreinforced) masonry walls with in-plane loads.
Isotropic Damage 2D/3D
Here, you can define antimetric stress-strain diagrams. The modulus of elasticity is calculated in each step of the stress-strain diagram using Ei = (σi -σi-1 )/(εi -εi-1 ).
It is possible to specify nonlinearities of member end releases (yielding, tearing, slippage, and so on) and supports (including friction). There are special dialog boxes available for determining the spring stiffnesses of columns and walls based on the geometry specifications.
The nonlinear deformation analysis is performed by an iterative process considering the stiffness in cracked and non-cracked sections. The nonlinear reinforced concrete modeling requires definition of material properties varying across the surface thickness. Therefore, a finite element is divided into a certain number of steel and concrete layers in order to determine the cross-section depth.
The mean steel strengths used in the calculation are based on the 'Probabilistic Model Code' published by the JCSS technical committee. It is up to the user whether the steel strength is applied up to the ultimate tensile strength (increasing branch in the plastic area). Regarding material properties, it is possible to control the stress-strain diagram of the compressive and tensile strength. For the concrete compressive strength, you can select a parabolic or a parabolic-rectangular stress-strain diagram. On the tension side of the concrete, it is possible to deactivate the tensile strength as well as to apply a linear-elastic diagram, a diagram according to the CEB-FIB model code 90:1993, and concrete residual tensile strength considering the tension stiffening between the cracks.
Furthermore, you can specify which result values should be displayed after the nonlinear calculation at the serviceability limit state:
Deformations (global, local based on non-/deformed system)
Crack widths, depths, and spacing of the top and bottom sides in principal directions I and II
Stresses of the concrete (stress and strain in principal direction I and II) and of the reinforcement (strain, area, profile, cover, and direction in each reinforcement direction)
RF-CONCRETE Members:
The nonlinear deformation analysis of beam structures is performed by an iterative process considering the stiffness in cracked and non-cracked sections. The material properties of concrete and reinforcing steel used in the nonlinear calculation are selected according to a limit state. The contribution of the concrete tensile strength between the cracks (tension stiffening) can be applied either by means of a modified stress-strain diagram of the reinforcing steel, or by applying a residual concrete tensile strength.
Iterative nonlinear calculation of deformations for beam and plate structures consisting of reinforced concrete by determining the respective element stiffness subjected to the defined loads
Deformation analyses of cracked reinforced concrete surfaces (state II)
General nonlinear stability analysis of compression members made of reinforced concrete; for example, according to EN 1992-1-1, 5.8.6
Tension stiffening of concrete applied between cracks
Numerous National Annexes available for the design according to Eurocode 2 (EN 1992-1-1:2004 + A1:2014, see EC2 for RFEM)
Optional consideration of long-term influences such as creep or shrinkage
Nonlinear calculation of stresses in reinforcing steel and concrete
Nonlinear calculation of crack widths
Flexibility due to detailed setting options for basis and extent of calculations
Graphical representation of results integrated in RFEM; for example, deformation or sag of a flat slab made of reinforced concrete
Numerical results clearly arranged in tables and graphical display of the results in the model
Complete integration of results in the RFEM printout report
After the calculation, the module shows clearly arranged tables listing the results of the nonlinear calculation. All intermediate values are included in a comprehensible manner. Graphical representation of design ratios, deformations, concrete and reinforcing steel stresses, crack widths, crack depths, and crack spacing in RFEM facilitates a quick overview of critical or cracked areas.
Error messages or remarks concerning the calculation help you find design problems. Since the design results are displayed by surface or by point including all intermediate results, you can retrace all details of the calculation.
Due to the optional export of input or result tables to MS Excel, the data remain available for further use in other programs. The complete integration of results in the RFEM printout report guarantees verifiable structural design.