Why does an axially loaded column break along a 45 degrees plane? In this video, at 7:57, the speaker mentions that columns under compression roughly break along a plane that is at 45 degrees to the axis of loading. If this is true, can someone explain why this happens in terms of inter-molecular forces between the column molecules.
 A: The model assumes the material is isotropic, so inter-molecular forces are (on average) the same in all directions. Under this assumption, there is nothing special about inter-molecular forces along the 45 degree plane. The column breaks along that plane because it has the greatest shear stress, as the presenter states. 
Most materials, even those with microscopic structure which is directional, are isotropic on a macroscopic scale. There might be lattice grains in which the material is stronger in some directions than in others. However, the grains have usually grown independently with different preferred directions, so there is no long range order.
If the material is not isotropic then the plane along which it breaks will not necessarily be the 45 degree plane. It will depend in a complex manner on the interplay between the strength and the applied stress along different planes.
See also Why ductile materials fail in shear when subjected to torsion
A: Experimental measurements have shown that the mode of failure of many materials is along a plane of maximum shear stress.  For the rod loading that you have described, the maximum shear stress occurs on a plane oriented at an angle of 45 degrees to the load direction.
