Basic Theory of Plates and Elastic Stability - Part 17 ppt

Effective Length Factors of•Simplified Equations to Alignment Charts 17.5 Modifications to Alignment ChartsDifferent Restraining Girder End Conditions •Different Re- straining Column End

Duan, L and Chen, W.F “Effective Length Factors of Compression Members”

Structural Engineering Handbook

Ed Chen Wai-Fah

Boca Raton: CRC Press LLC, 1999

Effective Length Factors of

•Simplified Equations to Alignment Charts

17.5 Modifications to Alignment ChartsDifferent Restraining Girder End Conditions •Different Re-

straining Column End Conditions •Column Restrained by

Tapered Rectangular Girders•Unsymmetrical Frames• fects of Axial Forces in Restraining Members in Braced Frames

Ef-•Consideration of Partial Column Base Fixity•InelasticK

-factor17.6 Framed Columns—Alternative MethodsLeMessurier Method•Lui Method•Remarks17.7 Unbraced Frames With Leaning ColumnsRigid Columns •Leaning Columns•Remarks

17.8 Cross Bracing Systems17.9 Latticed and Built-Up MembersLaced Columns• Columns with Battens •Laced-Battened Columns•Columns with Perforated Cover Plates•Built-Up Members with Bolted and Welded Connectors

17.10Tapered Columns17.11Crane Columns17.12Columns in Gable Frames17.13Summary

17.14Defining TermsReferences

Further Reading.

17.1 Introduction

The concept of the effective length factors ofcolumnshas been well established and widely used bypracticing engineers and plays an important role in compression member design The most structuraldesign codes and specifications have provisions concerning the effective length factor The aim of thischapter is to present a state-of-the-art engineering practice of the effective length factor for the design

of columns in structures In the first part of this chapter, the basic concept of the effective length

factor is discussed And then, the design implementation for isolated columns,framed columns,crossing bracing systems,latticed members,tapered columns,crane columns, as well as columns

ingable framesis presented The determination of whether a frame is braced or unbraced is alsoaddressed Several detailed examples are given to illustrate the determination of effective lengthfactors for different cases of engineering applications

in the flexural buckling plane; andL is the unsupported length of column.

Physically, theK-factor is a factor that when multiplied by actual length of the end-restrained

column (Figure17.1a) gives the length of an equivalent pin-ended column (Figure17.1b) whosebuckling load is the same as that of the end-restrained column It follows that effective length,KL,

FIGURE 17.1: Isolated columns

of an end-restrained column is the length between adjacent inflection points of its pure flexuralbuckling shape.

Specifications provide the resistance equations for pin-ended columns, while the resistance offramed columns can be estimated through theK-factor to the pin-ended columns strength equation.

TheoreticalK-factor is determined from an elastic eigenvalue analysis of the entire structural system,

while practical methods for the K-factor are based on an elastic eigenvalue analysis of selected

subassemblages The effective length concept is the only tool currently available for the design ofcompression members in engineering structures, and it is an essential part of analysis procedures

17.3 Isolated Columns

From an eigenvalue analysis, the generalK-factor equation of an end-restrained column as shown

in Figure17.1is obtained as:

det

EI

... data-page="13">

whereC and S are stability functions as defined by Equations17. 3and1 7.4;G A and< /p>

G Bare defined in Equations17. 7and1 7.8;G... class="page_container" data-page="11">

17. 5 Modifications to Alignment Charts

In using the alignment charts in Figure17. 4and Equations17. 5and1 7.6, engineers must always beaware of the assumptions... C3= 0, andobtain from Equations17.33 ,17. 34 ,17. 39, and1 7.40,

(b) If the far end of columnC1