@article{Bilyk_Nuzhniy_Dzhanov_Perestiuk_2020, title={Features of the analytical solution of the problem of displacement cantilever steel beams with variable flange depth}, url={http://bctp.knuba.edu.ua/article/view/218014}, DOI={10.32347/2522-4182.7.2020.85-92}, abstractNote={<span class="fontstyle0">The article is devoted to the problem of generalization of the influence of the variability of stiffness of elastic steel elements on the<br />displacement and angles of rotation in the Cartesian coordinate system when placing the origin of<br />the coordinates in the center of gravity of the largest cross section. Cantilever elastic I-beam steel<br />beam with variable flange depth is considered.<br />The obtained formulas are shows the influence<br />of the variability of the I-beam cross-section on the<br />moment of inertia in two main axis. This made it<br />possible to write the differential equation of beam<br />bending as a linear equation with variable coefficients.<br />The solution of the differential equation makes<br />it possible to obtain analytical formulae for determining the displacements and angles of rotation of<br />the cross section of cantilever I-beams with variable flange depth. To confirm the obtained analytical expressions in the transition to the definition of<br />deflections and angles of rotation of the I-beams<br />with a constant cross-section, the Lopital-Bernoulli<br />rule was used. A variant of the formula for the<br />consequences of the second remarkable (special)<br />boundary in the disclosure of uncertainty is obtained.<br />This makes it possible to prove by an analytical<br />approach the coincidence of the obtained solutions<br />with the solutions for constant cross-section Ibeams. Numerical studies also confirmed the obtained result. This approach can be applied to Ibeams with variable flange depth under different<br />support conditions.<br />The obtained displacement formulas make it<br />possible to check the stiffness of cantilever steel Ibeams with a linear change in their stiffness of the<br />beams according to the deflection limits. The obtained results can also be used for research of Ibeams with variable flange depth under different<br />support conditions. The obtained displacement<br />formulas make it possible to check the stiffness of<br />cantilever steel I-beams with a linear change in<br />their stiffness of the beams according to the deflection limits. The obtained results can also be used<br />for research of I-beams at linear change of stiffness, including a change of the modulus of deformation of steel at limited plastic work deformations on different sections of a beam.</span> <br /><br />}, number={7}, journal={Будівельні конструкції. Теорія і практика}, author={Bilyk, Artem and Nuzhniy, Valeriy and Dzhanov, Liubomyr and Perestiuk, Vadim}, year={2020}, month={Груд}, pages={85–92} }