Postbuckling of elastic beam subjected to a concentrated moment within the span length of beam |
| |
Authors: | Boonchai Phungpaingam Somchai Chucheepsakul |
| |
Institution: | (1) Department of Civil Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Pracha-utid Rd, Bangmod, Toongkru, Bangkok, 10140, Thailand |
| |
Abstract: | This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment
within the span length of beam. Two approaches are used in this paper. The nonlinear governing differential equations based
on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of
the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations
and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set
of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated
by using Runge–Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized
within prescribed tolerance (10−5). The results from both approaches are in good agreement. From the results, it is found that the stability of this type of
beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the
hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam. |
| |
Keywords: | Postbuckling Elastica Concentrated moment Elliptic integral Shooting method |
本文献已被 维普 SpringerLink 等数据库收录! |
|