Limit of eccentricity for circular section

Consider a circular column having diameter ‘D’ subjected to load ‘P’ at eccentricity ‘e’ from center as shown in fig. 5.a.

Let,

σ₀= Direct stress;

σ_b = Bending stress;

P = Applied load (compressive or tensile);
D = Diameter of circular column;

$A = Cross\:sectional\: area = \frac{\pi}{4}\times D^{2}$
M = Bending Moment acting on column =P.e
e = Eccentricity w.r.t. center;
$I = Moment \:of\: inertia\: of\: column\: section = \frac{\pi}{64}\times D^{4}$
y_max = Max. centroidal distance = D/2;
Z = Section modulus;
$Z = \frac{I}{y_{max}}=\frac{\left( \frac{\pi}{64}\times D^{4} \right)}{D/2}=\frac{\pi D^{3}}{32}$

Now, for no tension condition;

$\sigma_{0}=\sigma_{b}$

$\frac{P}{A}=\frac{M}{Z}=\frac{P\cdot e}{\frac{\pi D^{3}}{32}}$

$e=\frac{P}{A} \times \frac{\pi D^{3}}{32} \times \frac {1}{P}$

$e=\frac{\pi D^{3}}{32 \cdot A} = \frac{\pi D^{3}}{32 \cdot \frac{\pi}{4}\times D^{2}}=\frac{D}{8}$

This limiting eccentricity when load ‘P’ act anywhere form center.

Kernel or Core Section: For circular section diameter of Kernel Section is (D/8)+ (D/8) = D/4.as shown in fig.5.b.

Vinayak Hulwane

I share my knowledge in civil engineering and try to makes it helpful to all studying and practicing civil engineers. Help to improve it.

Search in this blog

Limit of eccentricity for circular section

Vinayak Hulwane

0 comments

MSBTE

University

Flickr Images

Search in this blog

Limit of eccentricity for circular section

Vinayak Hulwane

You Might Also Like

0 comments

MSBTE

University

Flickr Images