طراحی سازه های بتونی مسلح
Abstract
۱٫ Introduction
۲٫ Towards a new design philosophy
۳٫ Computational framework
۴٫ Verification and calibration
۵٫ Applications
۶٫ Conclusions
Acknowledgements
References
Abstract
The design of complex reinforced concrete structures or elements of structures can be a challenging task for practitioner structural engineers in some specific non-conventional projects. For these specific cases, the use of well-established and standard design methods such as sectional methods or strut-and-tie methods can result into complex and sometimes inappropriate designs. On the other hand, the use of sophisticated numerical methods such as nonlinear finite element methods is not common in these situations because of their complexity and the lack of consensus on their validity within the engineering community. This work presents an innovative new design approach for complex reinforced concrete structures. The approach is inspired from the strength reduction numerical method, well-established in the field of slope stability in geotechnical engineering. It can be considered as an intermediate approach between the conservative and universally well accepted strut-and-tie method, and the powerful nonlinear finite element method. A new simple constitutive law for concrete has been developed for that purpose as a user subroutine under the software ABAQUS-Explicit. It allows for the degradation of concrete by gradually reducing its tensile strength during the analysis. This law is presented within an overall new framework for the design of reinforced concrete structure based on two steps. The structure is loaded in a first linear elastic step and then degradation of the tensile postpic occurs in a second nonlinear step. At the end of this second step, a re-organisation of the internal stresses occurs within the structure. A resisting pattern and failure modes similar to those in the strut and tie models occur as well. Two application examples are presented at the end of the study and demonstrate the potential and the feasibility of the new approach.
Introduction
The design of reinforced concrete structures is a well-established field in the civil engineering practice. For conventional structures/elements of structures, the predictive equations of the codes can generally be used to design the geometry of concrete and to detail adequate reinforcement to withstand sectional forces already computed by a structural analysis, generally a linear elastic one. The sectional design method based on beam theory can be used to design flexural and shear reinforcement in the so-called B-regions where the Bernoulli’s principle remains valid (Fig. 1a & b). However, this method fails in the regions where loading and boundary conditions are applied or near a change of geometry. Those disturbed regions, also called D-regions due to a nonlinear strain distribution as shown in Fig. 1c, are designed using more advanced methods. The strut and tie method, or S&T method, presented by Schlaich et al. [15] is widely used to design D-regions. It is based on the truss analogy where compression is taken by concrete struts and tension by reinforcement ties. The nodal zones are defined as the intersection between struts and ties (Fig. 1d). This method falls into the plastic design philosophy as a lower bound static method where only strength and equilibrium are satisfied. It therefore provides a conservative design for the D-regions when well used. However, the more complex the structure, the more difficult it becomes to develop S& T models.