Research On Criterion Of Ultimate Bearing Capacity Of Two-way Slab Reinforced Concrete Based On Mathematical And Statistical Analysis

The design of the building structure should use different levels of safety depending on the severity of the possible consequences of structural damage(endangering human life,causing economic losses,having a social impact,etc.).Safety is also an important indicator of the reliability of building structures in the engineering field.As one of the most widely forms of building structure,reinforced concrete structure has the advantages of being strong,durable,good fire resistance,steel saving and low cost,etc.How to assess the safety of reinforced concrete members is an important research topic.The ultimate load capacity,as the maximum capacity of a structure to withstand external loads before complete collapse,is the most fundamental and critical characteristic load,and is of great importance to the evaluation of structural safety.The current methods of numerically calculating the ultimate load carrying capacity of reinforced concrete members are mainly numerical non-convergence,displacement abruptness and plastic zone penetration,but the results obtained by these three methods are not objective.In order to judge the ultimate bearing capacity of reinforced concrete members more comprehensively,this paper proposes to explore the ultimate bearing capacity criterion of reinforced concrete members based on mathematical and statistical analysis,and to analyse the objective law inherent in the members from the perspective of statistics.This paper takes the reinforced concrete two-way slab as the research object.First carry out finite element simulation analysis.Then extracts each physical quantity(strain energy,etc.)under different loading conditions in the slab.Studies the variation law between each physical quantity,so as to propose the ultimate load carrying capacity criterion for reinforced concrete members.Finally uses the existing test to verify.The specific research content is as follows:(1)A strain energy criterion for the ultimate load capacity of reinforced concrete two-way slabs is proposed.The strain energy of the reinforced concrete two-way slab is extracted and its variation law is investigated.The analysis results show that the strain energy under each working condition obeys the log-normal distribution.Based on the variation of the parameters of the log-normal distribution,the ultimate load carrying capacity of the member is proposed.At the same time,the existing tests are used as examples to verify the criterion,and it is found that the ultimate load derived using the method proposed in this paper is stable within a reasonable interval,and the method has some engineering application value.(2)By extracting the first principal strain of the concrete unit and its first principal strain change amount,the law of its change under different working conditions is explored.It is found that when the first principal strain occupies a large proportion of the larger interval,the histogram of the frequency of the first principals train changes becomes more and more concentrated,and the cumulative frequency of positive and negative changes becomes closer to 0.5,the member approaches the ultimate state,thus proposing the ultimate load capacity criterion of reinforced concrete slabs based on the first principal strain.(3)The first principal strains at particular points in the span in the transverse and longitudinal directions at the bottom of the slab are investigated and it is found that the first principal strains at different points show significant abrupt changes at the later stages of loading,and the load corresponding to the abrupt changes is the ultimate load.Points in the span in the transverse and longitudinal directions of the bottom surface of the slab are investigated and it is found that the first principal strains at different points show obvious abrupt changes at the later stages of loading.The load at the point of abrupt strain change is the ultimate load.The accuracy and applicability of the abrupt strain change theory is also verified by using the existing test slab as an example.