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I am a little confused with some concepts in elastostatics regarding shear stresses inside thin profiles.

Please see the first picture:

P1

Question #1: I know that the direction of the shear stresses in the upper and lower parts in picture 1 are wrong. But I don't understand why the shear stresses in a profile with a shear force are like it is shown in the second picture? Why are the shear stresses "rotated"?

Picture 2:

P2

Question #2: (about the shear center)

In my understanding, the red force F is meant to act on a point, where it is able to compensate the moment of the shear stresses inside the profile's cross section. But why is this point (SC) located on the left of the profile and not on the right? In my understanding, both moments will act in the same direction and, therefore, reinforce the torsion of the profile. Often this is explained with an "equivalence" of the two moments rather than an equilibrium of the moments. But I do not understand why an equivalence is necessary to compensate the moment...

Thanks!

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1 Answer 1

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I do not understand these issues, but I can offer a 3D model of an elastic beam with a one sealed end. A vertical force is applied to the free end. As a result of elastic deformation, the beam bends down and twists. Figure 1 shows the initial shape of the beam (green) and in the deformed state (red).The distribution of the stress tensor component $\sigma _{zz}$ in 6 beam sections is shown on the right. Figure 1

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  • $\begingroup$ thank you. but unfortunately, this doesn't help me. $\endgroup$
    – user195973
    Sep 30, 2019 at 7:18
  • $\begingroup$ What will help you? $\endgroup$ Sep 30, 2019 at 10:29
  • $\begingroup$ An explanation why the force F and the shear stresses act in the same direction. Why is there an equivalency of the moments important and not an equilibrium? $\endgroup$
    – user195973
    Sep 30, 2019 at 12:09
  • $\begingroup$ We have a numerical 3D model of the beam. We know the strain tensor and stress tensor. How to describe what you want? $\endgroup$ Sep 30, 2019 at 12:56
  • $\begingroup$ Can you provide a vector-plot instead of a color coded representation of the stresses? $\endgroup$
    – user195973
    Sep 30, 2019 at 13:25

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