English
Русский 76-82 p.
The problem of bending a strip by a force applied at the end is not of practical interest. Such method of loading and securing the ends is interesting only because it is most convenient to implement it on experience, which makes it possible to verify the Prandtl theory. When conducting experiments, there is a need for two corrections: it is necessary to evaluate the influence of the self-weight of the strip and the effect of increasing or decreasing the point of force application. As we are talking about small corrections, it is quite enough to use only the first approximation for calculations. An effective version of the energy method is recommended. It is used to calculate rectangular cantilever strips for stability of a flat bending shape, taking into account its own weight. The essence of this variant of the method is to use the Lagrange variational principle instead of the condition for equality of the potential strain energy and the work of external forces. The proposed approach allows us to perform machine implementation of calculations and take into account an arbitrary number of members of the series. The presented solution of the problem for the cantilever beam takes into account its own weight and the action of concentrated force.
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11. Pengcheng J. Analytical Evaluations of Buckling Behavior of Wood Composite I-Joist with Sinusoi-dal Web. Morgantown: West Wirginia University, 2012. 106 p.
12. Galishnikova V.V., Tesfaldet H. Gebre. A comparative study of beam design curves against lateral torsional buckling using AISC, EC and SP. Stroitel'naya mekhanika inzhenernyh konstrukcij i sooru-zhenij. 2019. 15 (1). P. 25 – 32.
13. Ascione L., Giordano A., Spadea S. Lateral buckling of pultruded FRP beams. Composites Part B: Engineering. 2011. 42 (4). P. 819 – 824.
14. Anapayan T, Mahedran M. Numerical modelling and design of LiteSteel Beams subject to lateral buckling. Journal of Constructional Steel Research. 2012. 70. P. 51 – 64.
15. Asgarian B., Soltani M., Mohri F. Lateral-torsional buckling of tapered thin-walled beams with arbi-trary cross-sections. Thin-walled structures. 2013. 62. P. 96 – 108.
2. Timoshenko S.P. Ustojchivost' uprugih sistem. L., M.: Gostekhizdat, 1946. 532 p. (rus.)
3. Ishchenko A.V., Zotov I.M. Energeticheskij metod v raschetah balok pryamougol'nogo poperechnogo secheniya pri bokovom vypuchivanii. Inzhenernyj vestnik Dona. 2019. 1. URL: ivdon.ru/ru/magazine/archive/n1y2019/5583 (rus.)
4. Karamysheva A.A. Sovershenstvovanie rascheta na ustojchivost' ploskoj formy izgiba derevyan-nyh balok peremennogo secheniya i ih optimizaciya: dis. ... kand. tekhn. nauk: 05.23.17. Rostov-na-Donu, 2016. 124 p. (rus.)
5. Lapina A.P., Zotov I.M., CHepurnenko A.S., YAzyev B.M. Sovershenstvovanie energeticheskogo metoda v raschetah balok na ustojchivost' ploskoj formy izgiba. Vestnik Volgogradskogo gosudar-stvennogo arhitekturno-stroitel'nogo universiteta. Seriya: Stroitel'stvo i arhitektura. 2019. 77. P. 5 – 16. (rus.)
6. Yazyev S.B., Karamisheva A.A., Avakov A.A. Calculation of plane bending stability of beams with variable stiffness. Procedia Engineering. 2016. 150. P. 1872 – 1877.
7. Yazyev S.B., Karamysheva A.A., Dudnik A.E. Vypuchivanie dvuhskatnoj balki pri chistom izgibe. Aktual'nye problemy tekhnicheskih nauk v Rossii i za rubezhom: Materialy mezhdunarodnoj nauch-no-prakticheskoj konferencii. Ufa, 2015. P. 35 – 37. (rus.)
8. Yazyev S.B., Karamysheva A.A., Nikora N.I., Raschet na ustojchivost' ploskoj formy deformi-rovaniya odnoskatnoj balki. Aktual'nye problemy tekhnicheskih nauk v Rossii i za rubezhom: Mate-rialy mezhdunarodnoj nauchno-prakticheskoj konferencii. Ufa, 2015. P. 32 – 35. (rus.)
9. Wang C.M. Beam-Buckling Analysis via Automated Rayleigh-Ritz Method. Journal Structure Engineering. 1994. 120 (1). P. 200 – 211.
10. Tong G.A., Zhang L. General Theory for the Flexural-Torsional Buckling of Thin-Walled Members I: Fictitious Load Method. Advance in Structure Engineering. 2003. 6(4). P. 299 – 308.
11. Pengcheng J. Analytical Evaluations of Buckling Behavior of Wood Composite I-Joist with Sinusoi-dal Web. Morgantown: West Wirginia University, 2012. 106 p.
12. Galishnikova V.V., Tesfaldet H. Gebre. A comparative study of beam design curves against lateral torsional buckling using AISC, EC and SP. Stroitel'naya mekhanika inzhenernyh konstrukcij i sooru-zhenij. 2019. 15 (1). P. 25 – 32.
13. Ascione L., Giordano A., Spadea S. Lateral buckling of pultruded FRP beams. Composites Part B: Engineering. 2011. 42 (4). P. 819 – 824.
14. Anapayan T, Mahedran M. Numerical modelling and design of LiteSteel Beams subject to lateral buckling. Journal of Constructional Steel Research. 2012. 70. P. 51 – 64.
15. Asgarian B., Soltani M., Mohri F. Lateral-torsional buckling of tapered thin-walled beams with arbi-trary cross-sections. Thin-walled structures. 2013. 62. P. 96 – 108.
Yazyev S.B. Energy method based on the stability of the flat shape of the cantilever strip bend taking into account its own weight. Construction Materials and Products. 2020. 3 (1). P. 76 – 82. https://doi.org/10.34031/2618-7183-2020-3-1-76-82