The non-linear spring model picks up where current standards and guidelines on designing fastenings under tension loading in concrete based on the Concrete Capacity method (CC method) reach their limits. The limitations of applying these concepts become apparent when it comes to the base plate geometry, for instance. The European EN 1992-4 standard and its American equivalent, the ACI 318, only cover rectangular groups of up to nine anchors with a maximum 3x3 configuration, for example. These regulations also require a sufficiently stiff base plate. This is a prerequisite in order to determine the internal force distribution of an anchor group with a linear strain distribution approach, which additionally takes leverage forces into account. Definitions and regulations to determine sufficiently stiff base plates are not covered by current regulations and guidelines, however.
 
In practical construction, the requirements and suitable fixings solutions often deviate from designs covered by current guidelines. The non-linear spring model is a potential solution that allows the overall non-linear behaviour of fastenings to be taken into account. The new calculation method allows deformations and stresses within the base plate to be calculated under the influence of force. It also allows the load distribution or load transfer between individual fastenings of a group to be determined. Examining sufficient base plate stiffness is therefore no longer required, as the model automatically determines the resistance of the group while taking into account the existing base plate and anchor stiffness. 

In addition to the transferable forces, the performance-based (displacement-based) concept thereby also includes displacements and deformations of an anchorage under the influence of force in the calculation. The method realistically takes into account design rules in terms of anchor configuration, base plate thickness as well as load. As a result, the spring model enables a better assessment of the overall system than calculations based solely on load-bearing capacity.

The concept is based on the assumption that within an anchor group, the anchors resist the tension forces, while the compression forces are transferred directly into the concrete by the base plate. The spring model approach is combined with the FEM (Finite Element Method) for design purposes. The base plate and the connecting profile are divided into finite elements. Tension-only springs can be used to model the fastening points and the contact between the base plate and the concrete. The calculation is carried out by applying the FEM. The projected area system is applied to individual anchors of a group while its individual resistance is considered. 

The influence of the component corner and neighbouring fastenings is also taken into consideration. Displacement-controlled non-linear analysis is performed to model the precise force distribution between the anchors of the group and the displacement of the base plate. This results in the realistic calculation of the anchor group resistance in the form of a load-displacement curve. The non-linear spring modelling approach was developed and verified as part of a dissertation at the University of Stuttgart (to be published in 2021) by Boglárka Bokor, who works at the fischer Group of Companies as Senior Expert Technology Transfer and International Standardisation. 
 
The “Spring models for realistic anchor designs in concrete” white paper is available to download from the fischer website: https://www.fischer.de/de-de/service/federmodell. It provides planners and structural engineers with further details on the new approach. Models and examples illustrate the potential applications of the innovative design method. It examines the differences between the linear and non-linear spring model as well as the CC method in regard to the possibilities and limitations of the approaches when designing tension loaded anchorages in concrete.