Authors :
Ibearugbulem O. M., Ezeh J. C., Ibarugbulem C. N., Onyechere I. C.
Volume/Issue :
Volume 5 - 2020, Issue 3 - March
Google Scholar :
https://goo.gl/DF9R4u
Scribd :
https://bit.ly/39SN6g6
Abstract :
This paper presents the closed form stability
analysis of solid non-prismatic columns. Using
fundamental kinematics and Hooke’s law, the total
potential energy functional of a non-prismatic column was
obtained. This was minimized with respect to deflection
and the non-linear Euler-Bernoulli equation of
equilibrium of a non-prismatic column was obtained. Two
mathematical axioms were employed to completely
integrate the non-linear governing equation. Individual
deflection equations for four columns of various boundary
conditions were obtained. Substituting the deflection
equation into the non-linear governing equation and
rearranging it gave the closed form formula for
calculating buckling loads of non-prismatic columns. This
formula was used to determine buckling loads for eight
example problems. Results from four of the example
problems were compared with results from earlier study
that used an approximate method called weighted moment
of inertia. The highest percentage difference recorded is
9.59%, which validates the present method since the result
from earlier study is based on approximate method.
Keywords :
Closed form; non-prismatic; deflection; governing equations; buckling.
This paper presents the closed form stability
analysis of solid non-prismatic columns. Using
fundamental kinematics and Hooke’s law, the total
potential energy functional of a non-prismatic column was
obtained. This was minimized with respect to deflection
and the non-linear Euler-Bernoulli equation of
equilibrium of a non-prismatic column was obtained. Two
mathematical axioms were employed to completely
integrate the non-linear governing equation. Individual
deflection equations for four columns of various boundary
conditions were obtained. Substituting the deflection
equation into the non-linear governing equation and
rearranging it gave the closed form formula for
calculating buckling loads of non-prismatic columns. This
formula was used to determine buckling loads for eight
example problems. Results from four of the example
problems were compared with results from earlier study
that used an approximate method called weighted moment
of inertia. The highest percentage difference recorded is
9.59%, which validates the present method since the result
from earlier study is based on approximate method.
Keywords :
Closed form; non-prismatic; deflection; governing equations; buckling.
