Limit of eccentricity for hollow circular section
Consider a hollow circular
column having external diameter ‘D’ and internal ‘d’ is subjected to load ‘P’
at eccentricity ‘e’ from center as shown in fig. 7.a.
Let,
)
)
%20\right)}{D/2}=\frac{\pi%20\left(D^{4}-d^{4}\right)}{32 \cdot D})
}{32 \cdot D})
}{32 \cdot D}})
}{32 \cdot D}%20\times%20\frac%20{1}{P})
}{32D%20\cdot%20A}%20=%20\frac{\pi%20 \left(D^{4}-d^{4}\right)}{32D%20\cdot%20\frac{\pi}{4}\times%20 \left(D^{2}-d^{2}\right)})
}{8D \cdot \left(D^{2}-d^{2}\right)})
 \cdot \left(D^{2}-d^{2}\right)}{8D \cdot \left(D^{2}-d^{2}\right)})
 }{8D})
σ0= Direct stress;
σb = Bending stress;
P = Applied load (compressive or tensile);
D = External diameter of circular column;
d = Internal diameter of circular column;
M = Bending Moment acting on column =P.e
e = Eccentricity w.r.t. center;
ymax = Max. centroidal distance = D/2;
Z = Section modulus;
Now, for no tension condition;
This limiting eccentricity when load ‘P’ act anywhere form center.
Kernel or Core Section: For circular section diameter of Kernel Section is
 }{8D} \times 2 = \frac{\left(D^{2}+d^{2}\right) }{4D})
as shown in fig.7.b.
as shown in fig.7.b.
0 comments