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Unformatted text preview: CALCULATION OF STATICALLY INDETERMINATE COMPOSITE BEAM ELEMENTS BY USING REFINED BOUND ARY CON DI TIONS AND WITH AC COUNT OF THEIR STATE DI A GRAMS O. V. Goryk,* A. M. Pavlikov,** and V. A. Kyrychenko** Keywords : composite beam, statically indeterminate system, initial conditions, extreme criterion The ef fect of com pli ance of sup port units on the cal cu la tion of strength of com pos ite beams with ac count of the nonlinear deformation diagram of the composite is examined. The basic equilibrium equations of the mechan- ics of de form able solid bod ies are used to solve the prob lems of strength, ri gid ity, and dis place ments, with in - troduction into them extreme criteria for the parameters to be calculated. The procedure developed allows one to find the fi nal so lu tions by us ing it er a tive pro cesses. Introduction The deformation mechanics of heterogeneous systems and the simulation of problems on bending, vibrations, and sta- bil ity of com pos ite struc tural el e ments are of par tic u lar in ter est to re search ers in view of the ef fi cient and wide use of such el e - ments in dif fer ent en gi neer ing ap pli ca tions. The re sults ob tained in this line of sci en tific re search have been sum ma rized in many re views (see, for ex am ple, [1-5]), mono graphs (e.g., [6-10]), and other sci en tific pa pers. These stud ies are pre dom i nantly dedicated to statically determinate systems, mainly with standard classical boundary conditions, which provide the necessary accuracy of calculation results. In studying statically indeterminate beams, the physicomechanical processes occurring in the ma te rial of con straint sup port units must be taken into ac count. The prob lem pri mar ily con cerns the com pli ance, whose ef fect on dis place ments, and some times on the strength, can be sig nif i cant and can change in the course of load ing. In ad di tion, the character of operation of some composite materials, for example, reinforced concrete, makes it necessary to take into account the nonlinear deformation diagram [11]. In the pres ent study, some ways are shown to take into ac count the ef fect of com pli ance of sup port units on the strength of a composite statically indeterminate beam calculated by using a nonlinear dependence between the bending mo- ment and cur va ture of the beam. This makes it pos si ble to de ter mine the re serves of the load-car ry ing ca pac ity and dis place - ments of clamped beams com pa ra ble to ex per i ments at the ex pense of re fine ment of bound ary con di tions of the bend ing prob - lem. In fact, even at a known com pli ance of the ma te rial of sup port units, the bound ary con di tions in stat i cally in de ter mi nate beams re main un known, since the set tle ment and ro ta tion of the sup port (ini tial) cross sec tion lead to the re dis tri bu tion of bending moments along the entire beam length, including the other support....
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This note was uploaded on 02/24/2011 for the course AERO 520 taught by Professor Rs during the Spring '11 term at Istanbul Technical University.

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