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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

DYNAMICALLY LOADED BAR:STABILITY AND KINEMATIC EQUATIONS OF MOTION

Vestnik MGSU 6/2013
  • Manchenko Maksim Mikhaylovich - St.Petersburg State University of Architecture and Civil Engineering (SPbGASU) postgraduate student, Department of Theoretical Mechanics; +7 (812) 296-20-22., St.Petersburg State University of Architecture and Civil Engineering (SPbGASU), 4 2nd Krasnoarmeyskaya st., 190005, St.Petersburg; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 71-76

Differential equations of motion for a bar are provided in this paper. The bar is exposed to the applied force that intensifies as the time progresses. The condition substantiating the trans-versal inertia force is identified using the equations. On top of the emerging inertia force, brief high-speed stress increases the yield stress of the material.The external force is accompanied by the eccentricity. Therefore, linear dimensions of the bar and its eccentricity make plastic behaviour possible both in compressed and stretched areas of the rod sections. Patterns of distribution of plastic deformations (one-sided and double-sided yield) are generated using the equations of motion for each case. Cauchy problems are supple- mented by the incoming conditions according to the principle of continuity of displacement and velocity.The criterion of stability loss is a condition when the variation of the exterior torque equals to the variation of the interior torque. At the same time, the variation of a longitudinal force must be equal to zero. Having completed a series of transformations, the author obtains the stability loss functional. It is calculated simultaneously with the motion equation. When the functional is equal to zero, the bearing capacity is exhausted.Moreover, there is a simplified method of identifying the critical force. The comparison of values with the testing findings demonstrates the efficiency of employment of the approximate method.

DOI: 10.22227/1997-0935.2013.6.71-76

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