From Theory of Beam Columns: In-Plane Behavior and Design, Volume 1


Columns subjected to lateral loads or end moments in addition to axial compression are categorized as beam-columns. The lateral loads or end moments cause deflection which is further amplified by the axial compression. The main result of the above discussion is the elastic beam-column equation (3.19). The general solutions are given by Eq. (3.22), The problem here is to find the function f( x) which depends only on the lateral loading and the constants A, B, C, D that satisfy the boundary conditions at the clamped, free, or simply supported ends.

Beam-Column with Uniform Load

As an example. consider a beam-column which is subjected to uniform load q as well as an axial compression P as shown in Fig. 3.9(a). The beam-column has length l and bending rigidity EI which is assumed to be constant along the length.

Figure 3.9: Beam-column with uniform load

The governing equation (3.19) is


and the general solution is


The four constants A, B, C and D are determined from the four boundary conditions,


Actual calculation of Eq. (3.22) gives


Thus the deflection equation (3.24) yields


It is known from the above expression that the deflection is linear to the lateral load q but not to the axial compression P (or ). The deflection pattern also changes as the axial force changes.

The maximum deflection ? occurs...

Copyright Wai-Fah Chen 2008 under license agreement with Books24x7

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Topics of Interest

3.4 GENERAL SOLUTION OF ELASTIC BEAM-COLUMN (DEFLECTION PROBLEM) Consider a member which is subjected to a thrust P, end moments M A and M B, and partly distributed uniform load q within x 1 ? x ? x...

3.8 SUMMARY The governing differential equation of a column or a beam-column is (3.155) The general solution has the form (3.156) in which represents the axial force P and f( x) is a particular...

3.9 PROBLEMS 3.1 Show that a simply supported column is in a stable equilibrium at the bifurcation point of P E = ? 2 EI/ l 2. Assuming the length of the column is inextensible, show that the column...

CHAPTER 3 3.1 Show that a simply supported column is in a stable equilibrium at the bifurcation point of P E = ? 2 EI/ l 2. Assuming the length of the column is inextensible, show that the column is...

12.1 INTRODUCTION In the previous chapters, the behavior of elastic and plastic beam-columns was investigated by formulating the governing differential equation in terms of either the deflection or...