In the link at 12:35 , the author show the equation of the displacement of the beam without explaining , can someone try to explain why we need to use 3 Φ , 2EI / L , 2θa and 2θB ? I have no idea at all .
The slope deflection method is a structural analysis technique used to determine the bending moments and rotations at various points along an indeterminate beam. It takes into account the flexibility of the structure and uses equilibrium equations to calculate the unknown forces and displacements.
The slope deflection method is typically used for analyzing continuous beams, frames, and other indeterminate structures. It is most effective when the number of unknowns is less than or equal to the number of equilibrium equations.
The slope deflection method differs from other structural analysis methods, such as the moment distribution method, in that it considers the rotation at each joint in addition to the bending moments. This allows for a more accurate analysis of indeterminate structures.
One advantage of using the slope deflection method is that it can handle structures with multiple supports and varying stiffness. It also takes into account the actual geometry of the structure, rather than assuming a fixed end rotation. Additionally, it can be used to analyze structures with both fixed and pinned supports.
Some limitations of the slope deflection method include the assumption of small displacements and rotations, neglecting shear deformations, and the need for manual calculations which can be time-consuming for complex structures. It is also not suitable for structures with changing cross-sections or for structures with large displacements or rotations.