Bending analysis of beams under various loads and determination of the appropriate cross section

Engineering and economics have played a significant role in today's world. Together, these two disciplines have contributed to the construction of more sustainable, safe, and resilient structures. With technological advancements, structural analyses have become more accessible, allowing for rapid architectural design and implementation of desired geometries. Previous studies have examined the vibration analyses of beams with varying cross-sections under different support conditions. Additionally, the flexural and buckling behaviors of steel beams with various geometries have also been investigated. Within the scope of this thesis, appropriate cross-sections and displacement values for cantilever beams subjected to bending under four different loading conditions were investigated for both square and circular cross-sectional shapes. Analytical solutions based on the Euler-Bernoulli beam theory were obtained by considering a constant strength criterion throughout the analyses. Displacement values were calculated for cases where the cross-section remained constant along the beam length, as well as cases where the width or height varied. These results were computed using MATLAB software package and presented in the form of figures and tables. Threedimensional models of the cross-sections were generated using SolidWorks software package. Furthermore, reductions in total volume due to cross-sectional variations and the resulting material savings were also examined.