Unified Failure Model Of Reinforced Concrete Elements Subjected To Complex Loads

Failures of reinforced concrete (RC) structures in hazards are mainly caused bydifferent combinations of axial loads, bending, shear force and torsion, and failuremechanisms are very complex. While RC elements under axial loads and bending areunderstood uniquely, different theories have been developed to demonstrate failuremechanisms of RC elements subjected to shear and torsion. During decades, dozens ofmethods have been achieved to analyze structures under one or several external loads.Some methods provide equations obtained by regression analyses of experimental results,such as "Code for design of concrete structures"(GB50010-2010). Apparently, equationsbased on empirical regressions have no theoretical basis, and few connections amongequations can be observed. For many years, researchers such as Professor Hsu have beenworking on a unified theory using compatibility conditions, equilibrium conditions, andconstitutive laws. Currently, only this approach can analyze structures subjected to axialloads, bending, shear force, and torsion at any loading stage and give out accurate results,but in practice it seems too complex and lengthy to be used. A mature theory inengineering should be very rigorous and unified in theory, convenient and simple inexpression, and also related parameters should be easily determined by traditional testmethods. Comparing with the theory used in steel structures, existing theories for RCmembers under complex external loads are still immature.A simple unified theory is proposed in this thesis for widely used rectangularreinforced concrete elements subjected to axial loads, bending, shear force and torsion.This simple-formed theory is able to demonstrate failure mechanisms of structures subjected to complex loads. By using failure criteria of steel and concrete, stressdistributions at ultimate limit state satisfying equilibrium conditions can be describedwithout violating boundary conditions. Therefore, the interaction relationship amongexternal loads can be achieved. According to the Lower-bound Theorem, the obtainedsolution is a lower-bound limit analysis. If described stress distributions are rather close tothe realist limit state, the solution would be fairly accurate.As observed in experiments, if the applied axial compression is relatively small, afterthe appearing of cracks, part of concrete can not contribute any more, reinforcing steelsand remaining concrete continue to carry more external loads after cracking until failureoccurs, and the failure mechanism is ductile failure. However, if the axial compression israther large, elements would fail instantly when stresses of concrete reach the failurecriterion and concrete is crushed, the stress development is different from the developmentof ductile failure, and the stress state at failure is called the brittle failure limit state. Whileestablishing a unified theory based on the Lower-bound Theorem, each failure mechanismare studied separately, and different interaction equations are derived.The strategy of analyzing ductile failure is established as follows. At first, the warped3-dimensional failure surface is required, then stress distributions on the failure surfaceshould be described, and finally equilibrium conditions would lead to the interactionrelationship among external loads. While analyzing the failure surface, this thesis providesa new method to calculate inclinations of significant cracks. With this new method, notonly the warped failure surface of a reinforced concrete element subjected to complexexternal loads can be described, it can also rather accurately describe the failure surfacewhen an element is only subjected to only one kind of external load. During finding stressdistributions on the failure surface, contributions of concrete and steels are analyzedseparately. Based on theories and experiments, contributions of steels exposed on the failure surface can be presumed. Since compatibility conditions are not considered duringthe process, the expression of steel contribution is simple and practical. At failure thenormal-section of concrete will be divided into two parts, a tension zone and acompression zone. Concrete in tension zone reaches the failure criterion first, cracks duringloading, and still contributes after cracking because of aggregates’ interlock. A newapproach to calculate the contribution of concrete in tension zone is proposed. Byintroducing a reduction coefficient kT, which can be easily obtained, the contribution ofconcrete in tension zone can be quantified. The complicated stress state of concrete incompression zone can be determined using the3-dimensional failure criterion. Therefore,the stress distribution of concrete at failure can be easily quantified. Different failuremechanisms are distinguished by the location of compression zone caused by differentcombinations of external loads, and after analyzing equilibrium conditions of all failuremechanisms, the interaction equation can be simply expressed and also can demonstratethe relationship among different external loads.In brittle failure analysis, concrete fails first, and failures of RC elements happen atthe same time. The stress state of concrete decides the condition of element. According tothe failure mechanism, stress distributions at this moment can be presumed based onexperimental results. When stresses of concrete reach the3-dimensional failure criterion ofconcrete, failure occurs, and then the interaction relationship can be expressed. Throughthe proposed simple and practical analysis, the main characteristic of failure mechanisms isreflected.Then, reinforced concrete elements subjected to axial loads, biaxial bending, biaxialshear, and torsion are analyzed using the same strategy. After the comparison with testresults, the preliminary theory can rather accurately predict ultimate bearing capacities.After comparing theoretical results with experimental results, a relatively good agreement has been found. After the comparison with "Code for design of concretestructures"(GB50010-2010), the proposed theory is found to be more accurate and morecapable of explaining failure mechanisms.The problem of current approaches that can explain failure mechanisms of RCelements subjected to axial load, bending, shear force, and torsion and numerical analysesis that they all require complex computation and they are not suitable for engineeringanalyses. Comparing to other methods, the proposed unified theory can be identified as thefilling of this vacancy in engineering.All in all, the proposed unified theory of rectangular reinforced concrete elementssubjected to axial loads, bending, shear, and torsion not only can explicitly explain failuremechanisms, ultimate bearing capacities can be easily calculated and the failure mode canbe quickly determined. Overall, this theory is significative for the analysis of reinforcedconcrete structures in engineering.