The images below are from "Strength of materials" book by Timoshenko. As evident from the text, the author states that stress on the cross section pq can be resolved into normal stress and shear stress since the force P can be resolved into two components, one of which is parallel to the cross section pq, while the other one normal to pq. What confuses me is why are we resolving P at all? Why do we have a stress which is not in the direction of loading? What is the physical cause behind this stress?

I think there is something missing in my understanding of what causes shear stress while axial loading. So basically I want an explanation of what causes shear stress generally and in this specific case. (Equations, references and an intuitive explanation will help. Explanation in terms of molecular interactions will be much appreciated.)

TL;DR -> Okay, please provide explanation of what causes shear stress while axial loading.

Figure 1

Figure 2

  • $\begingroup$ "What bugs me is why resolve P along these specific directions." - Those specific directions are used because those correspond to the "principal stress axes" of the system. Along these directions there are just normal forces and no shearing forces, so the state of stress becomes relatively simple and easy to describe when using these directions. Look up "principal stress axes". If you choose to work with other directions such as the direction shown by the n-vector, things get more complicated. For that direction you have both a tensile stress and a shear stress acting simultaneously. $\endgroup$ – Samuel Weir Jun 12 '18 at 21:08
  • $\begingroup$ @SamuelWeir Can you please share some links where I can learn about "principal stress axes"? Also, I was looking for a more intuitive explanation of the concept. Can you maybe elaborate the concept that you are talking about as an answer? $\endgroup$ – ahamshubham Jun 13 '18 at 4:21
  • $\begingroup$ You can simply google "principal stress axes" yourself or find out about it in just about any basic book on materials science or mechanical stresses. You're in the best position to judge what particular reading material is a best fit to your own level of reading and background knowledge. $\endgroup$ – Samuel Weir Jun 13 '18 at 5:35
  • $\begingroup$ @SamuelWeir I looked into what "principal stress axes" are but reading about them did not answer my question. I want to know why does an axial load cause a shear, which is not in the direction of loading? $\endgroup$ – ahamshubham Jun 13 '18 at 8:07
  • $\begingroup$ @SamuelWeir I have updated my question accordingly $\endgroup$ – ahamshubham Jun 13 '18 at 8:23

if you draw a square on a rubber band with one side parallel to the axis of loading, it will stretch into a rectangle, but all angles remain perpendicular, indicating no shear.

If you rotate the square 45° such that corner to corner is along the axis, you end up with a stretched diamond, with the angles of the corners along the axis of loading getting smaller, and the others getting larger, indicating that there is shear.

It is a little more complicated than this, in that the non-loading direction will shrink with Poison's ratio, but it is a way to visualize why you get shear in one direction, and no shear in another direction.

  • $\begingroup$ Thanks! Can you please point me to a reference where I can read more about this, if possible, it should be mathematical. $\endgroup$ – ahamshubham Jun 19 '18 at 5:09

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