'Calculating concrete structures becomes simple and straightforward'

Every concrete structure has details that interrupt its continuity. Think of brackets, beams, walls with openings, anchors and the like. Despite the fact that this discontinuity is often present, there is no standard solution for the construction of walls or, for example, storey floors. However, specialized software is available (often in the form of Excel files), which can help determine the interplay of forces in concrete structures around openings and other irregularities. Science-based software can also be used, but then there is no linkage to specific nationally applicable standards and regulations. Moreover, it does not include the design and optimization of reinforcement. This method either leads to oversimplification or, at the other end of the spectrum, a complicated attempt to simulate reality. 

A new method and software tool is now available that enables engineers to efficiently determine the correct concrete dimensions, which also applies to the location and quantity of reinforcement. With this, safe and economical designs are obtained based on applicable standards. The program is based on a computer-aided implementation of the stress field model. It works with simplified assumptions similar to those used in manual calculations, but in an improved version to allow deformability and SLS verifications (based on material properties). Stress fields can be considered as a triangular force-play calculation in which parts or components are considered as stresses rather than force results. The verification of this software package was performed using independent applications and with existing regulations and material properties. 

Compatible Stress Field Method (CFSM).

The interest of structural engineers to design and calculate concrete structures in a reliable and fast way has led to the development of a new calculation model: the Compatible Stress Field Method (hereafter referred to as CSFM). This is a method in which stress fields are calculated with the help of software, and with this one can automatically design and calculate concrete structures. Structural elements, think of beams, walls and various other irregular elements, can then be virtually subjected to loads and stresses. This includes issues such as irregularities of the applied material, compression weakening and concrete reinforcement. This advanced calculation method is suitable for checking for building codes, maximum span lengths, stress limitations, and for determining short- and long-term effects. 

The design and analysis of concrete structural elements often involves looking from a cross section (1D element) or point (2D element). This method is described in all structural design standards (EN 1992-1-1, ACI) and is used daily by many structural engineers. However, this method has its limitations, and is really only applicable in areas where Bernoulli's hypothesis of stress planes and stress distributions applies (also called B areas). The elements where this hypothesis cannot be applied are called D areas. These are elements with discontinuities. Examples of B- and D-areas are shown in Figure 1. For example, these are areas where there are irregular loads or where cross-sections are interrupted (or where there are other forms of openings). 

Excellent for engineering and design of concrete structures

The Compatible Stress Field Method is a continuous FE-based stress field analysis where classical stress field solutions are combined with kinematic aspects. The degree of stress in the concrete is calculated for the entire structure. As a result, the effective compression strength of concrete can be automatically calculated from the state of transverse stress in the same way that compression field analysis is used for compression attenuation (Vecchio and Collins 1986; Kaufmann and Marti 1998) and the EPSF method (Fernández Ruiz and Muttoni 2007). On top of that, the CSFM method incorporates such things as stress stiffness, thus representing realistic stiffnesses of structural elements. This satisfies design requirements, including deformation capacity, that were not done in previous calculation methods. The CSFM model uses structural laws prescribed in design standards for concrete and reinforcement structures. These factors are already known at the design stage, allowing the partial safety factor method to be applied. This eliminates the need for structural engineers to communicate additional and often-discussed material properties required for FE analysis. This makes this CFSM method ideally suited for the engineering and design of concrete structures. (Kaufmann and Mata-Falcón 2017; Mata-Falcón et al. 2018).

The CSFM makes assumptions in terms of imaginary, rotating, stress-free cracks that open without sliding (Figure 2) and also considers the equilibrium at the level of the cracks along with the average elongation of the reinforcement. As a result, the model includes things like maximum concrete strength (σc3r) and reinforcement stresses (σsr) at cracks while the concrete tensile strength (σc1r = 0) can be neglected. The latter is only considered in the reinforcement stiffness calculations. The inclusion of tension stiffening has the effect of simulating the average reinforcement strain (εm).

Practical examples:

Design and prescription verification of concrete walls (Figure 3), beams with openings (Figure 4 and 5), calculations at structural connections, brackets, holes and other concrete details using the innovative and safe CSFM method, as applied in the IDEA StatiCa application.