# 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.

• What is the time mark in the video at which the remark is made?What explanation does the presenter give for why this happens? Jun 16 '18 at 16:12
• @sammygerbil The time mark is 7:57. The presenter says that the column breaks due to mechanical stresses along an imaginary inclined plane in the column. But, I want an explanation based on inter-molecular forces, therefore, the question.
– user198167
Jun 16 '18 at 16:22

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.

• First of all, thanks for the answer. But, I have a doubt. If shear stress is not inter-molecular in origin, then, what is the cause of the shear stress. Also, I will look into the link that you have posted. Many thanks!
– user198167
Jun 16 '18 at 17:21
• Yes the shear stress is an applied stress, the result of external forces. How the material responds to applied stress - ie whether the internal stresses which are generated are strong enough to resist or whether the material breaks - does depend on the inter-molecular forces. Jun 16 '18 at 17:26
• In the video, the presenter resolves F along two directions, one along the normal to the imaginary plane and one along the imaginary plane. I can, in a similar manner, choose to resolve the force into two forces, kF and -(k-1)F, acting along the normal to the imaginary plane and I can say that the material will break along a plane along the normal for a value of k, where, kF > maximum stress the material can bear. By this argument, the material can break at any value of F since we can always choose some value of k such that kF > maximum stress the material can bear.
– user198167
Jun 16 '18 at 19:06
• Also, please check this link. They have given an explanation of Hooke's law based on inter-atomic forces: animations.physics.unsw.edu.au/jw/elasticity.htm
– user198167
Jun 16 '18 at 19:31
• Sorry I do not understand what you mean about resolving into 2 forces along the same normal. And I don't understand how the link about Hooke's law relates to this question. Jun 16 '18 at 19:34

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.

• Thanks! Can you explain why this occurs in terms of inter-molecular / inter-atomic interactions similar to how this guy derives stress on Page 56-60: link
– user198167
Jun 19 '18 at 5:04
• Sorry. Can't help you there. I'm a continuum mechanics guy. Jun 19 '18 at 10:33