scholarly journals Use of strain-energy method for calculating rectangular beams in cases of lateral buckling

2019 ◽  
Vol 91 ◽  
pp. 02035
Author(s):  
Aleksandr Ishchenko ◽  
Ivan Zotov
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Iterative Method ◽  
Cross Section ◽  
Energy Method ◽  
Strain Energy ◽  
Bessel Functions ◽  
Critical Force ◽  
Lateral Buckling ◽  
Strain Energy Method

The paper deals with the lateral buckling problem of a freely supported wooden strip with a constant narrow cross section, loaded with a local force in the middle of the span. A differential equation is given for cases when the force is applied out of the gravity section center. Strain-energy method was used in the study of beam lateral buckling. In the case when the load is applied in the center of gravity, problem comes down to a generalized characteristic equation. The correlation between the magnitude of the critical force and the application point of the load was obtained. The linear approximating function was identified for the indicated dependence. The obtained results are compared with an analytical solution using the Bessel functions and a numerical iterative method.

scholarly journals Side busking of the cantilever beam with narrow rectangular cross section

2019 ◽  
Vol 97 ◽  
pp. 04066
Author(s):  
Serdar Yazyev ◽  
Ivan Zotov ◽  
Dmitriy Vysokovsky ◽  
Batyr Yazyev
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Beam Energy ◽  
Secular Equation ◽  
Rectangular Cross Section ◽  
Critical Force ◽  
Lateral Buckling ◽  
Concentrated Force ◽  
Comparison Of The Results ◽  
The Relationship

The problem of lateral buckling of a cantilever strip with a constant narrow cross section loaded with a concentrated force at the end of the span is considered. In the study of lateral buckling of beam energy method was used. For the case of load application in the center of gravity, the problem is reduced to a generalized secular equation. The relationship between the magnitude of the critical force and the position of the point of application of the load. A comparison of the results obtained by the authors with an analytical solution using infinite series and a numerical iterative method is shown.

The Behaviour of Multiple Loops in Torsion

1988 ◽  
Vol 15 (3) ◽  
pp. 149-156 ◽  
Author(s):  
R. A. Cavina ◽  
N. E. Waters
Keyword(s):  
Energy Method ◽  
Strain Energy ◽  
Vertical Axis ◽  
Experimental Measurements ◽  
Complementary Strain ◽  
Radial Axis ◽  
Strain Energy Method ◽  
Good Agreement

The angular stiffness of a multiple looped span, subject to rotation about a vertical axis (torsion) and also to rotation about a horizontal or radial axis (mesio-distal tilt), have been derived using the complementary (strain) energy method. Experimental measurements on enlarged models were in good agreement with the values calculated from the theoretical relationships obtained. The variations in angular stiffness resulting from changes in the loop height, width, and position of clinical sized loops are discussed.

Infrastructure Sustainability

2011 ◽  
pp. 186-201
Author(s):  
Hoi Wai Shih ◽  
David Thambiratnam ◽  
Tommy Chan
Keyword(s):  
Energy Method ◽  
Strain Energy ◽  
Health State ◽  
Modal Strain Energy ◽  
Structural Health ◽  
Modal Strain Energy Method ◽  
Modal Flexibility ◽  
Before And After ◽  
Composite Bridges ◽  
Strain Energy Method

Assessing the structural health state of urban infrastructure is crucial in terms of infrastructure sustainability. This chapter uses dynamic computer simulation techniques to apply a procedure using vibration-based methods for damage assessment in multiple-girder composite bridges. In addition to changes in natural frequencies, this multi-criteria procedure incorporates two methods, namely, the modal flexibility and the modal strain energy method. Using the numerically simulated modal data obtained through finite element analysis software, algorithms based on modal flexibility and modal strain energy change, before and after damage, are obtained and used as the indices for the assessment of structural health state. The feasibility and capability of the approach is demonstrated through numerical studies of a proposed structure with six damage scenarios. It is concluded that the modal strain energy method is capable of application to multiple-girder composite bridges, as evidenced through the example treated in this chapter.

Determination of Longwall Mining-Induced Stress Using the Strain Energy Method

2015 ◽  
Vol 48 (6) ◽  
pp. 2421-2433 ◽  
Author(s):  
Mohammad Rezaei ◽  
Mohammad Farouq Hossaini ◽  
Abbas Majdi
Keyword(s):  
Energy Method ◽  
Strain Energy ◽  
Longwall Mining ◽  
Induced Stress ◽  
Strain Energy Method
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