Abstract
Members with varying geometrical and/or material properties are commonly used in many engineering applications. Stepped columns with internal axial loads constitute a special case of such nonuniform columns. Crane columns in industrial buildings or structural columns supporting intermediate floors are important applications of stepped members in civil engineering. Since neither axial load nor stiffness is constant along the column height, the stability analysis of a stepped column is usually more complicated than that of a uniform column. Determination of exact buckling loads for stepped columns with different end conditions is not always practical. This paper shows that variational iteration method (VIM), a kind of analytical technique recently proposed for solution of nonlinear differential equations, can satisfactorily be used to obtain approximate solutions for buckling loads of stepped columns with internal axial loads. VIM solutions perfectly match with the exact solutions available in the literature for some special cases of two-segment stepped columns. For many other cases, that is, for various values of three design parameters, namely, (i) load ratio, (ii) stiffness ratio, and (iii) length ratio, approximate buckling loads for two-segment stepped columns are determined using VIM and presented in tabular form which can easily be used by design engineers.
Highlights
This paper shows that variational iteration method (VIM), a kind of analytical technique recently proposed for solution of nonlinear differential equations, can satisfactorily be used to obtain approximate solutions for buckling loads of stepped columns with internal axial loads
Members with functionally graded material distribution and/ or varying cross-sectional dimensions are commonly used in many engineering applications since use of such elements in a structural/mechanical system may reduce the weight of the system considerably, which, in turn, leads to significant cost savings in design
In a geometrically nonuniform member, variation in cross sectional dimensions may be either continuous over the entire length of the member as in tapered members or may occur at discrete points as in stepped members
Summary
Members with functionally graded material distribution and/ or varying cross-sectional dimensions are commonly used in many engineering applications since use of such elements in a structural/mechanical system may reduce the weight of the system considerably, which, in turn, leads to significant cost savings in design. Pinarbasi [7, 8] has recently applied VIM to lateral torsional buckling analysis of deep rectangular beams whose minor-axis flexural and torsional rigidities change continuously along their lengths and flexural buckling analysis of columns with elastic end restraints whose flexural rigidities vary continuously along their heights and verified that VIM can efficiently be used in these complex stability problems. In this paper, this practical and powerful technique is applied to stability problems of stepped columns. After verifying the effectiveness of VIM in stability analysis of stepped columns, buckling loads of twosegment stepped columns with different load, stiffness, and length ratios are computed and tabulated using VIM
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