# shear formula confusion

In the notes, the author stated that the shear stress is constant over the bottom face of the segment ... why in figure 7-4 , we can see that the shear stress varies ?

Which is correct ? The red circled part or the figure ?

If you look at the 3D view of Figure 7.4c, it explains this quite clearly. The shear stress varies along the beam's height. Along its width (such as along the bottom face), the stress is indeed constant.

• ok , can you explain why the shear stress is varied linearly over the part ? if the stress varies linearly over a section , then it's normal stress, right ? from my book , shear stress only varies parabolically over a section , where the shear stress is max at the neutral axis , 0 at the top and the bottom part Nov 26 '16 at 11:18
• In Eq. (7-2), $A'$ is not a constant - it depends on the value of $\bar y'$. You are almost correct - the shear varies parabolically for a section with constant width. For an arbitrary shaped section (e.g. a circular rod, or an I-beam) the variation is not parabolic, but it does satisfy Eq. (7-2). Nov 26 '16 at 23:17