ANALYSIS & DESIGN OF COMPRESSION, Slides of Structures and Materials

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PREPARED BY:

ENGR. B.G GARWAGEO, MSCE

Assistant Professor

ANALYSIS & DESIGN OF COMPRESSION MEMBERS

SteelD-STEEL DESIGN

LECTURE 104

Compression members are structural elements that are subjected only to axial compressive forces; that is, the loads are applied along a longitudinal axis through the centroid of the member cross section, and the stress can be taken as f = P/A, where f is considered to be uniform over the entire cross section. Compression Members The most common type of compression member occurring in buildings and bridges is the column, a vertical member whose primary function is to support vertical loads. In many instances, these members are also subjected to bending, and in these cases, the member is a beam–column. Three general modes by which axially loaded columns can fail Flexural buckling (also called Euler buckling) is the primary type of buckling discussed in this chapter. Members are subject to flexure, or bending, when they become unstable. Local buckling occurs when some part or parts of the cross section of a column are so thin that they buckle locally in compression before the other modes of buckling can occur. The susceptibility of a column to local buckling is measured by the width–thickness ratios of the parts of its cross section Flexural torsional buckling may occur in columns that have certain cross sectional configurations. These columns fail by twisting (torsion) or by a combination of torsional and flexural buckling.

What is Steel?What is Steel?

COLUMN THEORY

critical buckling load. slender compression member stocky member critical buckling load is given by For the equation to be valid, the member must be elastic, and its ends must be free to rotate but not translate laterally. This end condition is satisfied by hinges or pins, as shown in Figure 4.2. The remarkable relationship was first formulated by Swiss mathematician Leonhard Euler and published in 1759. The critical load is sometimes referred to as the Euler load or the Euler buckling load. The

What is Steel?What is Steel?

COLUMN THEORY

critical buckling load. slender compression member stocky member critical buckling load is given by For the equation to be valid, the member must be elastic, and its ends must be free to rotate but not translate laterally. This end condition is satisfied by hinges or pins, as shown in Figure 4.2. The remarkable relationship was first formulated by Swiss mathematician Leonhard Euler and published in 1759. The critical load is sometimes referred to as the Euler load or the Euler buckling load. The

What is Steel?What is Steel? KL is the effective length K is the effective length factor

COLUMN FORMULAS

slenderness ratio KL/r, an upper limit of 200 is recommended (see user note in AISC E2). This is a practical upper limit, because compression members that are any more slender will have little strength and will not be economical.

Design of Axially Loaded Compression Members The selection of an economical rolled shape to resist a given compressive load is simple with the aid of the column load tables. Enter the table with the effective length and move horizontally until you find the desired available strength (or something slightly larger). In some cases, you must continue the search to be certain that you have found the lightest shape. Usually the category of shape (W, WT, etc.) will have been decided upon in advance. Often the overall nominal dimensions will also be known because of architectural or other requirements.

For shapes not in the column load tables, a trial-and-error approach must be used. The general procedure is to assume a shape and then compute its strength. If the strength is too small (unsafe) or too large (uneconomical), another trial must be made. A systematic approach to making the trial selection is as follows: