I have been looking at the location of shear flow centers for profiles for my mechanics of materials course.

I am trying to figure out how to determine the direction of the shear flow in a given beam section with a shear force which is either directed up or down (aligned with y-axis). In my lectures it has been said that 'the shear flow in the web of the beam section must always follow the same direction as the shear force'.

I have found some examples where it appears this rule does not work though:

  1. https://www.youtube.com/watch?v=zs_dEtwgxSM

  2. Interpretation of shear flow/shear center of L-profile

In these 2 examples the shear flow direction in the web of the beam section is drawn in opposite direction of the shear force. I do not know why the aforementioned rule does not apply to these examples. Is this rule (shear flow direction in web must follow shear force direction) correct?

How do I determine the direction of shear flow for these 2 examples/in general?


Yes, shear flow in a cross sectional element will always be in the same direction as the shear force in that same cross sectional element because the shear flow is essentially the distribution of the shear force.

Confusion may arise due to the distinction between the "shear force" in an element and the externally applied load that is producing said shear. The net shear force in the cross section will be in the opposite direction of the applied shear-producing load. (At least, that's the sign convention I use, and that appears to be what is happening in the two examples you provided.)

A couple sketches based on the video example you provided:

shear flow

Note that the net horizontal shear force will be zero and the net vertical shear force will be equal and opposite to the applied force. (Congruent with basic statics)


Propably the confusion comes from different conventions used for the internal forces. If we make a cut at any section of a member, two internal actions are defined, at opposite directions, each applied to one of the two faces of the cut. Consider as an example the following cantilever beam problem, with two cuts:

cantilever beam

The shear force, and the shear stresses have alternate directions, depending on the cut face you look at.

So, one may consider the following convention, where shear stresses match the direction of internal shear force:

enter image description here

Or this convention, where shear stresses have opposite direction to external shear force:

opposite direction

Shear flow is just shear stress multiplied by section thickness and therefore both shear flow and shear stresses (and internal shear force) have the same direction on the same face.


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