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Symmetrical bending of beams is the basis of the linear flexure equation or bending theory for a beam supported (simple or cantilever ) subjected to a pure moment and the beam with cross section of at least one axis of symmetry such as a square and in this case for an external moment applied in the same plane the neutral axis with zero shear stress is in the geometric centre so either half would be in compression ir in tension so the section would be in equilibrium. If the same beam is subjected to different types of loading say in 2 axes then this would result in asymmetric bending. This type of bending also occurs when you have a non symmetric cross section. Have a look at this https://m.youtube.com/watch?v=vzzGbLRAFqM In engineering complex bending situations are usually reduced or broken down into simple bending sub-components and in design symmetry as in nature is the preference and makes the analysis / calculations easier.