P_1.1.1 spatial_construct

Both in traditional and modern constructive timber engineering carried out by engineers, spatial skeletal supporting structures by far account for the greatest share of all realised building elements and constructions when compared to plane-like supporting structures. As far as the latter are concerned, it is only recently that they have become more frequent both from a technological and mechanical understanding of bearing effects. The pressure-transmitting components of skeletal support constructions as an ensemble, so to speak, as well as all compression elements individually of which such structures are composed are, due to their slim build, subject to stability effects. Such effects have been tackled since the beginning of skeletal timber construction by means of suitable constructive measures, and through prescribed suitable numeric proof by standards, and the meeting the required bearing strength and safety has to be demonstrated in all cases.

Important technological developments in the last few decades (glulam building style, mixed and compound systems, connection technology, quality classification of timber, and so on) have made it possible to enter areas of widths and narrownesses that used to be exclusively reserved to other building materials (such as steel or reinforced concrete). This fact, together with the rapid development, at the same time, in the theory of the non-linear mechanics of supporting constructions make it seem advisable to undertake the experiment of bringing together the two so far separate lines of development in an organic manner, and to unite them according to the rational slogan of the German philosopher G.W. Leibniz in his "Theory and Practice“ treatise.

The term “stability“ has, in the course of the last century, slowly but gradually developed into its present matured form, finds its place in the uniform term of bearing capacity and is, in this way, available for a future beneficial and targeted application and integration in disciplines of constructive engineering carried out by engineers. The term bearing capacity is based on the strictly theoretical and practical differentiation of effects that significantly influences the complex systems of simple single components as well as:

• the kinetic barmodel,
• geometric non-linearity,
• material non-linearity,
• connections and flexible composite joint with non-linear characteristics, as well as
• geometric imperfections and equivalent imperfections.

Each of these mentioned problem areas requires to be worked at in a detailed and profound scientific way. In bringing together all these problem fields that have so far been dealt with separately, new ground can be broken for the theory and practice of constructive engineering carried out by engineers. Additionally, conceptual gaps can be closed to neighbouring disciplines, such as steel construction or working in reinforced concrete. These latter two disciplines did, in fact, a long time ago deal with the term bearing capacity and started then to use it for themselves. This is yet another argument in favour of a conceptional unification and further development regarding the technical building implementation and future standard treatment of mixed systems with building components from differing materials or compound systems, various compound systems, etc.

In the course of the predecessor projects, during the last two years crucial preparation work was undertaken regarding some of the mentioned problem areas, such as

• the examination of stability of the single rod with a view to bending and buckling and lateral torsional buckling on the basis of the bearing strength capacity, a comparison of these results with existing standard rules, as well as the thus derived mechanical explanation of some characteristics of these standard rules and
• deriving the theoretical principles for the geometric non-linear rod as a basis for all further work to be built on it. These scientific elaborations are documented in separate reports.

The envisaged project part is thought to continue the started work and bring it to completion. In order to do so, the following working steps have been mainly focused on:

• Looking into geometric imperfections for single rods and even or spatial rod systems; on the basis of the development and consequential application of thinking tools of spectral partitioning and modal superpositions of eigenshapes; based on these, a relation concerning the “Model Column Method” can be established regarding the calculation according to theory 2. Order and demonstration of a seamless integration of the Model Column Method as a special case in applying theory 2. Order for an approximation calculation of the ultimate buckling load of systems; proposal for a systematic selection and assumption of geometric imperfections for bearing strength calculations to be carried out in the course of construction drafts or demanded standard bearing capacity proofs.
• Theoretical treatment and computer realisation of the non-linear curved beam as well as of rod systems (the question of imperfections shall be answered in the course of the former mentioned Eigenshape concept).
• Examination of the role of shear stresses following shear-warping and torsional-warping in rod cross sections, in particular of various compound systems; general kinematic treatment of the warping and cross section formation; interplay of these shear mechanisms (Q_y + Q_z + M_t) with longitudinal standard bearing mechanisms (N + M_y + M_z) in the context of an extended three-dimensional material non-linearity.