Design strategy structural concrete in 3D focusing on uniform force results and sequential analysis

Introduction (chapter 1) In analysis software models the infrastructural constructions are often reduced to geometrical linear and surface models (plane stress and shell models). The selection of a model much depends on the speed of the analysis process and the total processing time. The increased computer power has boosted the visualisation of pre-designs since the end of the nineties. The multi-disciplinary nature of a (pre-)design has also placed more focus on the Building Information Model (BIM). This concept may be regarded as a continuation of the product models of the eighties. Modelling of structures (chapter 2) Our aim is to (re)use the geometrical data from the visualisation software, presented as solid models, in the design software. We also want other (even non-technical) disciplines to gain an insight into the structural designs. This makes the use of solid models in the analysis software obvious, especially in the case of structural concrete designs that have more volume if compared to steel designs. In steel we express thickness in millimetres, whereas in concrete these quickly become centimetres. As far as overall processing time is concerned, the analysis of solid models (total analysis time including time for input and output) is no longer a problem for the current computers. However, the analysis software generally does not connect with the structural design in concrete, especially when it comes to calculating the amount of reinforcement. After all, solid models present the stresses, strains and deflections as the result of an analysis, whereas the calculation of the amount of reinforcement is based on forces and moments. Transparent results for the differences in analysis models (chapters 3, 4 and 5) In the first part of this PhD research we have developed a procedure to obtain forces and moments from the solid models. The forces and moments are calculated and presented on reference lines or reference planes by integrating stresses along heights or widths of a section. These reference lines and reference planes may be compared to the ‘old’ system lines or system planes of the linear and surface models. This means that there is full transparency(uniformity) in the results regarding the possible analysis models. The same procedure is suitable for geometrical orthotropic models such as structures. In the past the box structures in the analysis process were mostly calculated using orthotropic surface models due to the desired reduction of the overall processing time of the analysis itself. The results of the 3D geometrical surface models and reference planes in this study may be compared to the results based on the ‘old’ orthotropic analysis models. At the result level the analysis models are now transparent. The course of stresses and/or strains has now been made more clear. This especially applies to structural areas that cannot be related directly to pure bending, but which are still disturbed areas. This is therefore an important step towards improved acceptance of solid models in structural design. The speed of the computer and the developments in the field of internal equation solutions in analysis software have produced so much gain in time in recent years that the overall processing time has become minimal. Although the analysis time of a solid model will still remain longer than with other models, the time required to schematise a structure has been reduced. The schematisations are necessary in linear and surface models, while still leading to a number of limitations for the result. The improved clarity and the possible checks on the design mean that the quality of the analysis model has strongly improved. This may lead to a reduction of the overall failure cost in construction, estimated to amount to 7-12% of the total building sum. Sequential analysis (chapter 6) The second part of this PhD research deals with the consistent checking of a (pre-)design. In practice, the checks on the designs of concrete structures are done on the basis of regulations, including safety factors. Earlier, there was only a single general structural safety factor, but this has now been split up into partial safety factors for both the material and the load. In concrete structures the checks mainly take place in various cross sections. When checking the cross section, the designer can start from cracked concrete, but not when determining the course of the forces of the entire structure. This is not consistent. A crack pattern leads to a redistribution of forces, and by allowing a crack pattern to a limited extent and by using partial safety factors, the safety of the entire structure is still guaranteed. The fully non-linear analyses that include the integral crack pattern may then be applied to demonstrate the safety. The regulations indicate how such a check should take place, but this is not an accepted procedure in current engineering practice. It is also not mandatory. A fully non-linear analysis of a structure is time-consuming, and is considered to be a highly specialist analysis. Also, it is not guaranteed in advance that it leads to the saving of costs. Perhaps this non-linear analysis process should be used for the assessment of the integral life cycle cost rather just the building cost. The assessment of safety and risk has become increasingly important in the design of a structure. That is why it is desirable in the analysis to assess the actual stresses in steel and concrete during the serviceability limit state of a structure in connection with the chance that it will occur. The eventual cracked state must be analysed using a non-linear analysis up to the serviceability limit state. This still causes practical problems. Although the crack pattern is still limited in this state, it may interfere to the extent that the non-linear process does not reach this desired load level through the instability of the software. This is often caused by the redistribution of forces or stresses. To obtain a stable analysis process we have developed a calculating method that will supply a robust redistribution of forces and moments. This method also serves to check the ultimate limit state of a structure. This defines the aim of the second part of this PhD research. We have selected a quasi nonlinear method, consisting of a series of linear elastic calculations. We call this a sequential analysis. The solution routine should remain robust throughout the crack pattern, allowing redistribution by the crack pattern. Through iterative reduction of the material properties (stiffness and tensile strength) of concrete within an always robust linear analysis, this method can be used for an entire structure. The total processing time can be estimated after one iteration. Up to the level of the ultimate limit state a maximum of 60 iterations is needed, 4 iterations per load increment. This has reduced the processing time from days to hours. Verification and validation of sequential method (chapters 7, 8 and 9) The sequential method has been tested against three experiments conducted in Toronto, Canada, that were also subjected to a fully non-linear analysis. The results are equal for both the experiments and the fully non-linear analysis. The crack widths can be determined directly from the analyses and be compared to the admissible values. Sensitivity assessments in analyses of the same experiments indicate how the partial safety factors are influenced. Sensitivity analyses (chapter 10) The real results from this analysis form the basis of a safety assessment through partial safety factors or a probabilistic analysis, resulting in the probability of a fault or failure. If the design does not comply with the required level, it can be adjusted. In this manner the design chain has been closed in the sense that a check has taken place on the basis of consistent results in a closed analysis process. The assumption is that through a regulation specific aspects are covered by partial safety factors. This assumption has gained more ground as a result of this research. Also, the integral method offers possibilities for optimisations in the design of concrete structures. This closed analysis process has created the possibility to start an automated design process. The acceptance of the new process is also in line with the present focus on integral design costs based on life cycle, environment and durability. Apart from the design of new structures, the tool developed here is also very suitable for the assessment of the condition of existing structures. Important in this respect are changes in the material properties or in the load. On the basis of the archived geometry and the reinforcement that is present we can now quickly assess the influence on the safety factors