Consider a beam with a rectangular c/s subjected to some arbitrary loading. At any cross section the shear force is V. This shear force is the resultant of all the internal resistive forces which act parallel to the section.
These individual internal resistive forces (which make V) might not necessarily be directed parallel to the y axis all over the surface. For instance, it may be as shown in (a) below, where all the individual internal forces are not parallel to y axis.
The textbook that I follow, states the following -
The textbook uses the word reasonable, to explain why the shear stresses are all parallel to the y axis. However, I'm not able to figure out what is the reason. How did we conclude that shear stresses are all parallel to the y axis in a rectangular section?
When I started studying about shear stresses in beams, I went in with a preconception that no matter what is the c/s shape all the shear stresses (or the individual internal resistive forces) will be parallel to the y axis, throughout the area. Then I got to know that in circular sections near the periphery the stresses are not along y, but tangent to the boundary. That made realize, it's not necessary that shear stresses in all c/s shapes will be parallel to y axis all over the c/s. Then it struck me, that the book never proved the shear stresses in a rectangular beam are all parallel to the y axis, and just covered it in a word reasonable.
Can anyone elaborate on the reason why shear stresses in a rectangular beam direction along y?