An Improved Higher-Order Shear Deformation Theory for Flexural Analysis of Simply Supported Deep Beam Subjected to Parabolic Load
摘要
The research paper presents novel improved seventh order shear deformation theory to study the deep beam's bending behavior. The shear deformation effects are represented by displacement field in depth or thickness coordinate. The displacement field take into accounts transverse as well as in plane displacement. By using constitutive relations, transverse shear stresses can be computed which ensure the no shear stress state on the beam's upper and lower surfaces, hence shear correction coefficient is eliminated. Virtual work principle applied to get the boundary condition and governing expressions. The isotropic, homogeneous simply supported deep beam impacted by parabolic loading is contemplated for illustration, to showcase the present theory’s efficacy. The analysis is carried out and the expressions are obtained pertaining to transverse displacements, normal displacement, transverse shear stress, normal bending-stress. For the various beam's aspect ratio, numerical results are obtained. Tables and graphs are employed to present the results. The results achieved are evaluated against with results documented in the in the published literature viz elementary theory, Timoshenko theory and different higher-order hypotheses to substantiate the effectiveness of bestowed theory.