chapter 5 - compression members

7/26/2019 Chapter 5 - Compression Members

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Compression Members: Structural elements that

are subjected only to axial compressive forces. Thestress can be taken as

= P/A,

where F a is considered to be uniform over the

entire cross section.

This ideal state is never achieved in reality, becausesome eccentricity of the load is inevitable.

The column: Is the most common type ofcompression member occurring in buildings andbridges.

The strength of steel compression members isusually limited by their tendency to buckle.

The load at which a compression member

becomes unstable is the buckling load .

The buckling load depends on the length,cross-section, and end conditions of the columnand the stiffness of the material.

Pcr is the load at which the compressionmember becomes unstable

E is modulus of elasticity of steel = 29,000 ksi

I is moment of inertia of the cross section L is the length of the compression member

K is the effective length factor

EI P cr

Eqn 5.1

Knowing that I = A r 2 and that thecompression stress on any member is

F c = P/A,we can express the Euler criticalbuckling load in terms of stress as

)/( r KL

Eqn 5.2

Where KL/r is called the slenderness ratio,and the AISC specification recommendslimiting the column slenderness ratio such

200/ r KL Eqn 5.3

Braced frames exist in buildings where the lateralloads are resisted by diagonal bracing or shearwalls

In unbraced or moment frames, the lateral loads areresisted through bending of the beams, girders, andcolumns, and thus the girder-to-column and beam-to-column connections are designed as moment

connections

Determine the effective length factor for the groundfloor columns in the following frames:

Braced FrameSince the building is bracedby diagonal braces andshear walls, the K -valuefor all columns in thebuilding is assumed to be1.0.

Unbraced Frames

(Moment Frame withPinned Column Bases)Since the bottom ends ofthe ground floor columnsare pinned, the effective

length factor, K , for eachcolumn at this level in themoment frame is 2.4.

Unbraced Frames(Moment Frame with

Fixed Column Bases)Since the bottom ends ofthe ground floorcolumns are fixed, the

effective length factor, K ,for each column at thislevel in the momentframe is 1.2.

The AISC specification defines thedesign compressive strength of a column asfollows:

g cr n A F P *nu P P

Φ = 0.90,Pn = Nominal compressive strength, kips,Pu = Ultimate Load. kipsF cr = Flexural buckling stress (see below), ksi, and

Ag = Gross cross-sectional area of the column, in.2.

Eqn 5.4

Eqn 5.5

Ag Fcr P n * Eqn 5.6

The flexural buckling stress, F cr, isdetermined as follows:

Case where inelastic buckling dominates the columnbehavior because of the presence of residual stresses in themember.

Eqn 5.7

The flexural buckling stress, F cr, isdetermined as follows:

Accounts for elastic buckling in long or slendercolumns.

Eqn 5.8

44.0or

71.4658.0

otherwise F

KLif F

To avoid or prevent local buckling, theAISC specification prescribes limits to thewidth-to-thickness ratios of the platecomponents that make up the structural

member.

There are three possible localstability parameters :

compact, non-compact, or slender .

A compact section reaches its cross-sectional material strength, or capacity,before local buckling occurs.

A non-compact section, only a portionof the cross-section reaches its yieldstrength before local buckling occurs.

A slender section, the cross-section

does not yield and the strength of themember is governed by local buckling.

Local buckling ofcolumn under

axial compressionload

Stiffened and unstiffened elements

Limiting width–thickness ratios for compression elements

It is sometimes necessary to determine thestrength of an existing structural member for whichthe size is known; this process is called analysis, as

opposed to design, where the size of the member isunknown and has to be determined.

The first step is to determine the effective

length, KL, and the slenderness ratio, KL/r , for eachaxis of the column. For many shapes, both KL and r are different for each axis

A compression member 10ft long consists oftwo angles 6in x 4in x 3/8” with long legs back toback and strutting 3/8in gusset plates at eachend. E = 29,000ksi and Fy =50ksi. Use AISCMspecifications.

a) What is the minimum radius of gyration?b) What is the allowable axial stress?

c) what is the safe axial load capacity of thecompression member?

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