# Doubt Regarding Shearing Stresses In a Beam

Lets say we have a beam which is simply supported at the two extreme ends(support conditions dont matter in my question). A concentrated transverse load is applied at the halfway point. Now lets say we take a section at x= L/3 where is L the length of the beam. Now we know that transverse shear stress at that section is max at the neutral axis and minimum(0) at the top. Now I define the axes
x- along the axis of the beam
y- along towards top
z- coming out of the plane of paper
let y vary from t/2 to -t/2. Now take a very small element at the top of the section at y = t/2. Now at this element tau(xY) (shear stress on this face(perpendicular to x axis) in the Y direction) is zero according to " transverse shear stress is minimum(0) at the top". But how is this possible because apparently even at the top the material will tend to be sheared due to the transverse load. How am I wrong? I would really appreciate is someone could help me out.

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the surface at top and bottom are free and hence inorder to have forces balanced, on taking a small element at top of the beam ; since there are no shear stresses towards atmosphere there cannot be any shear stress inside.

SO basically its right when i say that the shear stresses in the xy(towards the downward portion) is actually zero. Which means maybe the material out there does not tend to get sheared?
Maybe true but hard to digest. I am having problems as to how to visualize it physically that the material wont be/tend to be sheared.

AlephZero