Calculation Theory And Finite Element Analyse Method Of Stiffness Of Concrete Member

Bending member is the popular component of the civil engineering, deflection calculation of the bending member is one part of the structure design. Through analyses of test data and test phenomena, bringing forward the Mechanics model, the stiffness calculation formulas of the bending members of Code for Design of Concrete Structure are based on semi-theories and semi-experiments. Although the Code has sufficiently considered the characteristic of the bending members, the calculation formulas have its reasonability and applicability, and the calculation result has good precision through the full consideration, the formulas are absent of the clear mechanical concepts and are difficult to understand. For being in line with the international conventions, understanding easily and calculating easily, according to concrete mechanics principle, the paper will build up concrete stiffness formula and carry out simplification.Based on the normal section calculation assumption, based on the normal section's physical condition, geometric condition , equilibrium condition of under-reinforced beam , according to the different phase and behaviour of the bending member's bearing and deformation, the paper will get three different stages of calculation formulas of flexural rigidities by joining three different condition equations in every stage. We know, the calculatian of the deformation and crack width of the member used in a stage is built above the II stage basis. So, making use of the II stage stiffness formulas, by analysing different height, different concrete strength, different reinforcement ratio of rectangle cross section, we will find out major factors affecting stiffness formulas and get stiffness formulas according to concrete mechanical principle and be simplified, and we will carry out contrast and analysis between simplified stiffness formula and Code formula. Making use of the simplified concrete stiffness formula, on the basis of the equivalent stiffness principle, the paper reaches deflection formula of freely supported beam, and respectively uses the deflection formula and ANSYS to calculate deflection, and compares the calculation result with the experiment result and analyses. Using ANSYS finite element program, the concrete beam finite element models are established on the basis of the experiment's parameters. Based on analytical result the relationship graphics are plotted such as moment-deflection relationship graphic, and the graphics are compared with the mechanics analytical result.Four problems have been mainly solved in the paper as the following:1. Based on the some assumption, according to the physical condition and geometric condition and equilibrium condition, the three stages of stiffness calculation formulas of the single reinforcement rectangular concrete beam are established with concrete mechanical analysis method.2. Based on different height of member, different concrete strength, different reinforcement ratio of rectangle cross section beam, the stiffness calculation formulas of the II stage will be simplified.3. Making use of the simplified concrete stiffness formula, on the basis of the fewest stiffness principle, the paer reaches deflection formula of letter strutbeam, and respectively uses the deflection formula and ANSYS to calculate deflection, and compares the calculation result with the experiment result and analyses. The concrete beam' finite element model is established with ANSYS finite element program. With the analytical result the moment-deflection relationship graphics and compared with the mechanical result.4. Compare and analyse similarities and differences about the aspect of the stiffness calculation in Sino-US Code.