Solving Shear Stress on a Bar - Mechanics of Materials

[Feeh]

I'm trying to understand a problem found on Mechanics of Materials and did not completely understood the problem. I can solve problems like this but I still don't know why I'm solving this way.

It is a simple question: Why the shearing force V does not cause shear stress ([itex]\tau_2[/itex]) on the point A as it does on point B? (page 575 pictures c and d for reference)

Yes, I've searched on the book but did not find why

Thanks

 

[SteamKing]

The shearing force V produced by the wind blowing on the sign runs parallel to the line AC. If we calculate the shear stress at point A using the standard formula tau = VQ/(It), then at point A, the first moment of area Q = 0 about the axis B-C, thus the shear stress = 0. We can also argue from symmetry, that if a non zero shear stress exists at point A, unless an equal and opposite shear force is present on the other side of the pole, there will be a side force introduced which is perpendicular to the shear force V, and the wind produced no such force.

It's not clear from your text if you have been introduced to calculating shear stress using the formula tau = VQ/(It). This article derives the formula for calculating shear stresses in beams:

http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?topic=me&chap_sec=04.3&page=theory

At point B, the first moment of area Q about the axis B-C will be a maximum, and the shear stress at this point is also a maximum.