# Optimizing the concrete load-bearing structure of high-rise buildings

### Combining the ground structure method with a recursive resizing algorithm on a case study

##
More Info
expand_more

## Abstract

Theshortage in housing and office spaces, combined with the desire of people tolive in densely populated cities results in a lack of space. A proposedsolution can be found in the usage of high-rise buildings. Nowadays there ismore awareness for the environment, thus this research tries to reduce theenvironmental impact of a high-rise building by optimizing the material used inload-bearing structures. This research aims to give designers and engineersmore insight into the added value of structural optimization; in particular forthe material usage in the load-bearing structure of high-rise buildings. Theresearch objective is formulated as follows: What is the optimal topology for a reinforced concrete load-bearingstructure, situated at the perimeter of a high-rise building when optimizingthe material use? A building isclassified as high-rise building when its roof is 70 m or more above groundlevel and accommodates work and/or living space. In literature the distinctionis made between three sorts of optimization: size, shape and topologyoptimization. Topology optimization has the most freedom, therefore it is morelikely to find a novel structure which minimizes the material use as much aspossible. In specific the Ground Structure Method (GSM) is used. The initialground structure is constructed by creating members between all nodes (fullconnectivity) which are located in the design space. The cross-sectional areasof the bars are the design variables in the optimization. An option is that thevariables turn to zero, thus elements are deleted resulting in less material.The conventional GSM starts with the full connectivity as initial groundstructure, deletes elements and calculates the new load distribution until athreshold is reached. In the end the load-bearing structure will consist ofcolumns, braces and beams, which are located at the perimeter of the floorplan. Literature indicates that (high-rise) buildings which are mainly loadedby horizontal loads would be optimal if they contain arches in the load-bearingstructure, or resemble the so-called Michell truss. However, the influence ofthe vertical load is often not taken into account, therefore this isinvestigated with the help of a parametric study. To compare the results withreality, a case study (Boston & Seattle, Rotterdam) is investigated. The core of the research is the furtherdevelopment of the optimization code, based on the GSM, written by He et al.,where multiple load cases and demands for the material strengths are implemented.In contrast to deleting elements, the code uses an adaptive ‘member adding’scheme, which is firstly proposed by Gilbert and Tyas. This scheme solvesproblems faster than the conventional GSM, up to 8 times, and is able to solvelarge problems. This code is extended during this research with new functionswhich implement demands for fire, second-order, buildability, flexural bucklingand stiffness. Also it is possible to add self-weight to the optimization. Thestiffness is implemented by adding a constraint to the displacement of the topof the building, wherefore a recursive resizing algorithm is written based onthe article of Chan. Thus the extended code exists of two optimizations, firsta strength optimization and afterwards a stiffness optimization. The code iswritten in Python and for the purpose of post-processing exporting the data toExcel and Abaqus is possible. With thehelp of the extended code, two design spaces are investigated. One design spaceis smaller, such that the computational time is low and many variations can beexamined during the parametric study on the total vertical to total horizontalload ratio (v/h-ratio). The other is based on a case study for comparison witha realistic situation. The verification of the code shows that the extrafunctions work properly for the investigated problems. If the functionsconcerning the stiffness optimization, inclusion of self-weight, fire,buildability and second-order are used, the extended code becomes unstable andthe computation time increases enormously when optimizing the case study.Therefore it is chosen not to include during obtaining the results. The resultsof the parametric study shows an expected pattern for the load-bearingstructure, for a v/h-ratio below 4. The pattern consist of arches, originatingfrom the Michell truss. The optimization of the case study, subjected to onerealistic load combination, showed no clear pattern for the load-bearingstructure. Post-processing steps, based on engineering judgement, are taken toclarify the solutions, which showed that the columns above the supports shouldbe large in comparison to the other elements and that the arches are the mostoptimal structure. Therefore an “optimized” load-bearing structure consistingof arches is proposed. The analysis of the “optimized” load-bearing structureshows us that most of the elements meet the strength requirements. To find theoptimal solution an iterative process would be needed, because increasing thecross-section of an element will decrease the stress but increase thestiffness, thus attracting more load. Thedifference between the optimized load-bearing structure and the originalload-bearing structure of the case study is that the optimized uses archesinstead of (punched) structural walls and uses less material (±3%). From thepost-processing of the results it is concluded that increasing the strengthratio (compression to tensile) to 1.0, decreasing the total v/h-ratio orignoring the rigid-diaphragm working of the floor help clarify the results ofthe optimization. This research extendsthe current literature with extra insights in the use of the Ground StructureMethod in an optimization code. Also, it confirms that the arches (originatingfrom Michel Truss) is an efficient manner to transfer the loads to thesupports. However, more research in the influence of the supports, the designspace and the material type on the clearness of the optimal solution is needed. The advice for designers and engineersis to see what the possibilities are for arches to use in their load-bearingstructure, because these are efficient in transferring the loads so materialcan be saved. The current version of the code needs to be made more userfriendly, stabler and faster before it is recommended to be used by designersand engineers. The extended code is a first attempt to implement multiple rulesfrom the Eurocode in a optimization code.