Concepto de CT y marcos de referencia

Some subsequent studies (Hall, 1981; Fukumoto et al., 1983), however, have utilized the availability of computerized databases that contain a number of the column tests reported in the literature. The reader is referred to the paper by Hall (1981) for numerous plots that include accumulated test data from the literature for a variety of column types. Empirical factors can account approximately for initial imperfections of geometry and loading, but the for- mulas do not consider the inelastic basis of general column behavior, nor can they rationally account for end restraint.

2. Formulas based on the yield limit state. These formulas define the strength of a column as the axial load that gives an elastic stress for an initially imperfect column equal to the yield stress. Such column formulas have a long history, also dating back to the middle of the nineteenth century, and they continue to enjoy popularity to the present, for example, the use of the Perry–Robertson (Robertson, 1925) formula.

3. Formulas based on the tangent-modulus theory. Such formulas can account rationally for the bifurcation load, but not the maximum strength, of per- fectly straight columns. If the effects of imperfections are such that they just reduce the maximum strength to the tangent-modulus strength, these formu- las have empirical justification. On the other hand, if the perfect column can be thought of as an anchor point in an interaction surface, initial imperfec- tions of geometry and loading can be represented as flexural effects in the interaction equation.

The “CRC Column Strength Curve,” named after the acronym of the for- mer name of the Structural Stability Research Council (i.e, Column Research Council), was recommended in the first edition of this guide (1960) and has been used for many steel design specifications in North America and else- where. It is based on the average critical stress for small- and medium-sized hot-rolled wide-flange shapes of mild structural steel, with a symmetrical residual stress distribution typical of such members. The column curves based on the tangent-modulus theory can also accurately account for end restraints (Yura, 1971).

4. Formulas based on maximum strength. State-of-the-art column design for- mulas are based on extensive studies of the maximum strength of repre- sentative geometrically imperfect columns containing residual stresses. The analyses have incorporated comprehensive numerical data, as well as eval- uations of test results and how well these compare. Reliability analyses have been performed, leading to the resistance factors that are given in state-of-the-art design standards. The third edition of this guide presented new column curves based on this principle (Bjorhovde, 1972). Subsequently, SSRC published Technical Memorandum No. 5, stating the principle that design of metal structures should be based on the maximum strength, includ- ing the effects of geometric imperfections.

It was also suggested that the strength of columns might be represented better by more than one column curve, thus introducing the concept of

INFLUENCE OF IMPERFECTIONS 29 multiple column curves (Bjorhovde and Tall, 1971, Bjorhovde, 1972). SSRC curves 1, 2, and 3 and curves 1P, 2P, and 3P are two sets of such curves; another example is the set of five curves in Eurocode 3 [European Commit- tee for Standardization (CEN, 2005)]. The Canadian Standards Association (CSA, 2009) provides two column curves that are based on SSRC curves 1 and 2. The column curve of the American Institute of Steel Construction (AISC) specifications (AISC, 2005a) is the same as SSRC curve 2P, although the equation takes a different form. Finally, end-restraint effects are readily incorporated with the maximum-strength approach.

3.2.4 Local Buckling

When structural members composed of slender elements, such as the flanges and webs of many steel shapes, are loaded axially, the overall column capacity can be limited by the capacity of the individual cross-sectional elements. This phenomenon is known as local buckling and is closely related to classical plate-bucking theory. This topic is covered in Chapter 4.

3.2.5 Bracing

The strength of a compression member can be influenced greatly by the method with which it is braced. Although brace locations between the member ends influence the effective length of the member, as discussed in Section 3.4, the type, strength, and stiffness of the braces, as well as the means of connecting them to the column, can affect the behavior significantly. Torsional buckling modes can only be restrained using braces that restrain twisting deformations. Bracing of members is a complex topic that is largely beyond the scope of this chapter. Column bracing topics are covered in Section 3.4.2 and Chapter 12.

3.3 INFLUENCE OF IMPERFECTIONS 3.3.1 Residual Stresses

Structural steel shapes and plates contain residual stresses that result primarily from nonuniform cooling after rolling. Welded built-up members also exhibit tensile residual stresses in the vicinity of the welds due to the cooling of the weld metal. These are generally equal to the yield stress of the weld metal, which will normally be somewhat greater than the yield stress of the base metal (Tall, 1966; Alpsten and Tall, 1970; Bjorhovde et al., 1972). Flame cutting (also called oxygen cutting) intro- duces intense heat in a narrow region close to the flame-cut edge. As a result, the material in this region acquires properties that are significantly different from those of the base metal, and residual stresses develop that are often much higher than the yield stress of the parent material (McFalls and Tall, 1970; Alpsten and Tall, 1970; Bjorhovde et al., 1972). Finally, cold forming and cold straightening introduce residual stresses, especially in regions with the most severe bending effects, such as in corners of cold-formed shapes (Alpsten, 1972b; Sherman, 1976; Yu, 1992).