What is the direction of shear couple acting,on planes carrying sigma(x) stresses? Is it positive or negative what's the criteria to determine the signs of shear couples?
1 Answer
First, note that you've drawn normal stresses ($\sigma_x=\sigma_{xx}$ and $\sigma_y=\sigma_{yy}$), not shear stresses. Shear stresses are drawn parallel to the adjacent edge.
Second, a common convention is for a shear force applied in the positive direction (e.g., of the x axis) and acting on a surface with a normal pointing in the positive direction (e.g., of the y axis) to correspond to one component of a positive shear stress $\sigma_{xy}$. Note that this rule also works for the normal stresses $\sigma_{xx}$ and $\sigma_{yy}$, except in this case the force is parallel to the surface normal.
For an object in static equilibrium, there is also an equal shear force pointing in the negative direction and acting on the opposite surface (this would also be denoted $\sigma_{xy}$) and two more forces corresponding to $\sigma_{yx}=\sigma_{xy}$. In this way, all horizontal and vertical forces and all moments are balanced.
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$\begingroup$ Yes I know that I've drawn the normal stresses but can you tell in terms of rotation.is clockwise shear positive or anticlockwise shear?? $\endgroup$– McGucketCommented May 1, 2017 at 16:07
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$\begingroup$ Please read my comment. "Clockwise" is meaningless; one shear couple is clockwise, and the other is counterclockwise (for an object in static equilibrium: efunda.com/formulae/solid_mechanics/mat_mechanics/images/…). Both couples are needed to make up $\sigma_{xy}=\tau_{xy}$. $\endgroup$ Commented May 1, 2017 at 16:45
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$\begingroup$ I'm dealing with problems that say "shear couple acting on plane is clockwise" this is making me 😕 confused.. I'm attaching the problem of the image in question.. thanks till now $\endgroup$– McGucketCommented May 1, 2017 at 16:48