The Static Correction Method Based On Probability Model Of The Beam Structure

Along with the engineering of our country appears more complex structures such aslong-span and high-rise buildings, everyone concerns about the safety is becoming morewidespread when the applicability, economy have a certain guarantee. Therefore, todetection and analysis the major engineering structures with stochastic finite elementmethod have become gradually important. Because of the errors of building model,dimension variations in the construction process and the changes of the stiffness for thestructure’s damage in use process, the influence of such factors as the theoreticalcalculation results of the finite element model and the actual structure of the measuringresults will be difference. Theoretical computation results of the finite element modeland the actual structure measurement results will have difference. To ensure thetheoretical computation results of the finite element model after correction are consistentwith the actual structure measurement results, the initial model must be continuallymodified. Depending on this background, the paper briefly introduced the studies ofstatic correction. And by the results of other research, the static correction for beamstructure is investigated. Then combined with the measurement situation of practicalengineering and the influence of the measuring errors on the static correction, the paper ismainly studied the following contents:1. Introduce the static correction method based on probability model of the beamstructure. Without the measuring error, the finite element method and static condensationtechnique are used to static correction with measurement data of each node. Then gainthe correction factors and their statistical properties to evaluate the every element of thebeam structure. It shows that vertical displacements of the theoretical calculation areconsistent with the node displacement of the actual measurement.2. Consider the number of nodes in practical engineering. Without the measuring error,use the finite element method and model curtailing technique to correct each elementwith numbered data in practical measurement. Then gain the correction factors and theirstatistical properties to evaluate the every element of the beam structure. From theexample of simple supported beam and continuous beam, as the station is less, the errorof correction factor becomes greater. Contrast and judge the correction of each element toimprove the static correction with limited node measurement data. It shows that thesearch area of element to be corrected partially becomes narrow. And to some extent itoptimizes the correction’s precision. 3．Consider the influence of various factors on the measurement data. Measuringerror which is beta distributed is considered in the static correction. Expand thecorrection factors according to the orthogonal polynomial for fourth order and gaintheir statistical properties. And consider the effect that the variation of coefficient hason the results. From the example of continuous beam, its result is consistent with theresult of Monte-Carlo method and the method of this paper is effective.