Nonlinear analysis - Introduction

 

Physical non-linear calculation represents very powerful tools for analysing any kind of structure in civil engineering build-up not only from steel fibre reinforced concrete but also from the other materials. Generally, there could be significant differences of results towards to linear analysis, especially in case of hyper-static structures. In case of linear analysis, just E-modulus of material is taken into account for preparation of stiffness matrix. There is no stress distribution based on increasing of strain in component. On the other side the non-linear calculation provides stress distribution and increasing of bearing capacity after reaching of the ultimate strain until the collapse mechanism based on different values of stress and strain dependent on predefined nonlinear stress-strain relationship in material diagram.

Especially for steel fibre reinforced concrete this analysis can provide real behaviour of the structure with different results towards to linear analysis only. This behaviour is very influenced by the crack formation very typical for fibre concrete. The toughness of fibre concrete is significantly increased by steel fibre existence up to values very close to standard reinforcement.

A typical shape of stress-strain diagram is visible on the following figure, where parabolic behaviour is used in compression as in standard concrete. Tensile behaviour represents the narrow peak expressed as mean tensile strength. From the point of strain, this peak works very well as a crack localizator. After the crack formation, the toughness of SFRC allows to keep certain level of tensile stress with increasing of strain up to failure which is fixed as 25‰. Generally, there are two types of tensile branch based on selected fibre type with softening or hardening post-cracking behaviour (5D and 4D with ascending branch and 3D with descending branch in tension). The diagram for nonlinear analysis are prepared based on user defined dosage and points are generated according to requirements in [1] DAfStb Guideline "Steel fibre reinforced concrete" see figure R.1 .

The nonlinear behaviour of reinforcement is also considered if the reinforcement is defined. The real stress train diagram is used for nonlinear calculation (see following figure). There are also two options for diagram (with and without hardening).