Stress Distribution for Different Eccentrically Loaded Sections Circular Section:
We have seen that for no tension,
e ≤ ( 2k 2 /d)
For a solid circular section,
I = π d 4/64 ;
A = (π/4) d 2
∴ k 2 = I / A = d2 /16
∴ e ≤ (2/d) ×(d2)/16≤ (d/8)
Figure
Therefore, in order that tension is not to be produced, the load line should fall within middle fourth of the section. The core in this case is a circle within the same centre and diameter d/4 as illustrated in Figure.