Applications of truss topology optimization in the design of reinforced concrete structures using „Strut and Tie” models

Karol Bołbotowski

Institute of Building Engineering; Faculty of Civil Engineering; Warsaw University of Technology (Poland)
https://orcid.org/0000-0003-3489-9221

Michał Knauff

Department of Civil Engineering; Faculty of Civil and Environmental Engineering; Warsaw University of Life Sciences - SGGW (Poland)

Tomasz Sokół

Department of Civil Engineering; Faculty of Civil and Environmental Engineering; Warsaw University of Life Sciences - SGGW (Poland)
https://orcid.org/0000-0001-7777-6171

Abstract

Although Strut and Tie models are often used in practical design due to their apparent concept based on truss analysis, the creation of a model consistent with behaviour of the real structure is not an easy task. Frame corner model considered in the paper and presented in code [7] and article [8] exemplifies the problem. The authors proposed a method of automatic generating of ST models by making use of truss topology optimization (volume minimization problem). The method is based on classical ground structure approach. The authors introduced a method of including the cost of nodes in the objective function, which allowed to obtain solutions consisting of rationally small number of bars (unlike Michell’s structures). Moreover, algorithms ensuring consistency with Eurocode requirements were developed. The method was implemented in computer program. With the use of the software the authors proposed an alternative ST model for the frame corner, which requires considerably less reinforcement steel in comparison with the model suggested by the code. The versatility of the program was well proven in several other examples of plane stress problems in reinforced concrete design.

Keywords:

Strut and Tie models, reinforced concrete structures, Eurocode 2 design, frame corner, topology optimization, Michell’s structures