Question

Stress distribution in rectangular section

Answer 1

Shearing stress distribution in typical cross-sections:

Let us consider few examples to determaine the sheer stress distribution in a given X- sections

Rectangular x-section:

Consider a rectangular x-section of dimension b and d



A is the area of the x-section cut off by a line parallel to the neutral axis.



is the distance of the centroid of A from the neutral axis



This shows that there is a parabolic distribution of shear stress with y.

The maximum value of shear stress would obviously beat the location y = 0.



Therefore the shear stress distribution is shown as below.



It may be noted that the shear stress is distributed parabolically over a rectangular cross-section, it is maximum at y = 0 and is zero at the extreme ends.

I - section :

Consider an I - section of the dimension shown below.



The shear stress distribution for any arbitrary shape is given as



Let us evaluate the quantity



, the



quantity for this case comprise the contribution due to flange area and web area