Preliminary Exploration The Theories Of Post-cracking Stiffness Of Rectangular Reinforced Concrete Pier

The earthquake is one of the most serious natural disasters in the world. And the highway network, as a lifeline of relief work, plays a very important role in the transportation of materials and equipments. The highway bridge is critical position among the network as well as the part that is easily broken when the earthquake comes. Therefore, the seismic design of bridge is important for the highway network especially.The seismic design of the pier governs the whole bridge's seismic performance. Under the action of seismic load, the reinforced concrete works in the state of cracks, and its stiffness distribution has influenced the stress and deformation of the bridge. In this paper, based on the concrete column members, the flexural stiffness distribution of them and the algorithmic method of cracked section stiffness by the action of the earthquake were analyzed. Hence, this paper can provide a reference for the seismic ductile design and relative researches.Based on the concepts of the mechanics and the dimensionless analysis, this paper, targeting at the bi-reinforced rectangular concrete column, discusses the depth of compression zone and properties of the rigidity distribution in the elastic range. And then, an analogue method called "three-phase method" which is studied on the post-cracking flexural stiffness of concrete flexural members, is theoretically presented forward in the paper for the first time, as well as its algorithmic method and procedure are introduced.With the analysis of the"three-phase method", conclusions are in this paper as follows:1. For the bending members without axial force, the cracking stiffness is only relative to the materials and sectional characteristics, but has nothing to do with the external force degree. To increase the ratio of longitudinal reinforcement or the axial pressure properly to the compression-bending member, the cracking stiffness will also increase; on the contrary, it will decrease.2. For the compression-bending member, its neutral axis distribution curve c = f (z) includes two asymptotes: z = 0 and c = c0. Based on the neutral axis distribution and properties of flexural stiffness, the concept of"three-phase method"is proposed in this paper. That is, the compression-bending member is separated to three parts: full section stiffness, cracked section stiffness and minimum stiffness, and, by the"three-phase method", which are calculated respectively.3. The three segment of algorithmic method of flexural stiffness are as following: I: the flexural stiffness of total cross section; II: to use one or more than one secants as the distribution curve of the neutral axis, then to calculate the flexural stiffness by deciding the position of neutral axises of these sections; III: regarding the different sections'flexural rigidity as a constant. To take the depth of compression of the different sections should be twice as high as it is pressed without axial force. that is , c = 2c0, and then to calculate the cracked section stiffness according to the sectional types.4. The demarcation section of the three parts: it is indeed easy to define the demarcation point section of I and II part. However, the demarcation point section between II and III seems a little difficult to find. The paper recommends the section of c = 2c0 is section z1.5. for the low reinforcement ratio or high axial compression ratio pier column, when section reaches a certain yield moment My, the II and III part is divided by c = 2c0 (it is also possible that the minimums part won't be presented).6. The computational procedure of force-displacement curve can efficiently reflect the changing process of stiffness of pier column members with loading steps.The proposition and study of the "three-phase method" provide a totally new calculation idea of the analysis of mechanical behavior and ductile capacity, and compensate for the disadvantages of theory of stiffness calculation. Meanwhile, it is of a great reference value in the study of effective stiffness of reinforced concrete column members.