compression members1

7/23/2019 Compression Members1

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Compression Members

(Column)


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Introduction

Compression members are usually

given names which identify them as

particular members in a structure.

The vertical compression members

in a building frames are called

columns.

Other names are posts struts etc.


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!uc"ling

Buckling occurs whena straight column

subjected to axial

compression suddenly

undergoes bending


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!uc"ling

Major Axis Minor Axis


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#ocal !uc"ling


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!uc"ling


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Table C$C%.&


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'adius of yration

In structural engineering, the two-dimensional radius of

gyration is used to describe the distribution of

cross sectionalarea in a column around its centroidal axis.

The radius of gyration is given by the following formula
http://en.wikipedia.org/wiki/Structural_engineeringhttp://en.wikipedia.org/wiki/Cross_section_(geometry)http://en.wikipedia.org/wiki/Cross_section_(geometry)http://en.wikipedia.org/wiki/Structural_engineering


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'adius of yration

where I is the second moment of area and A is the totalcross-sectional area. The gyration radius is useful in

estimating the stiffness of a column. owever, if the

principal moments of the two-dimensional gyration tensor

are not e!ual, the column will tend to buckle around theaxis with the smaller principal moment. "or example, a

column with an ellipticalcross-section will tend to buckle

in the direction of the smaller semiaxis.

It also can be referred to as the radial distance from agiven axis at which the mass of a body could be

concentrated without altering the rotational inertia of the

body about that axis.
http://en.wikipedia.org/wiki/Second_moment_of_areahttp://en.wikipedia.org/wiki/Gyration_tensorhttp://en.wikipedia.org/wiki/Bucklinghttp://en.wikipedia.org/wiki/Ellipsehttp://en.wikipedia.org/wiki/Ellipsehttp://en.wikipedia.org/wiki/Bucklinghttp://en.wikipedia.org/wiki/Gyration_tensorhttp://en.wikipedia.org/wiki/Second_moment_of_area


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esign of Columns $ *teps #iven are the loads or forces, $teel strength

%emember& The 'llowable compressive stress Fa is a

function of slenderness ratio ( ), which can be

determined only once *r+ is known. "or that we need to

select a section , shape and sie.

'ssume a suitable allowable stress Fa.

For A36 steel, Fa = 12 16 ksi for columns and 9

12 ksi for struts.

Determine area reuired !" usin# t$e formula%


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esign of Columns $ *teps $elect suitable shape and sie which gives area,

approximately e!ual to or greater than re!uired in theprevious step.

"or section selected, compute actual ( ) and calculate

allowable stress by using formulae manual.

If allowable stress is greater than actual grosscompressive stress, then section selected is /, otherwise

revise and select another section.


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Calculate +llowable *tress n the gross section of axially loaded compression

members whose cross section meet the re!uirements ofTable B0.1, when , the largest effective slenderness

ratio of any unbraced segment is less than &c , the

allowable stress is


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Calculate +llowable *tress n the gross section of axially loaded compression

members whose , exceeds &c, the allowable stress is


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,-ample & 2ata

3oad 4 566 kips

3ength of 7olumn 4 10 feet

$teel 4 '85

9nd condition Top 4 "ixed

9nd condition Bottom 4 "ixed 'ssumption

7ompact $ection : "or checking refer to ;age 0-85 Table B0.1

(3imiting ow 7alculating the #ross area re!uired


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,-ample & $ Contd $election of Trial $ection

$ection < 1? x 16@ < 1A x 165

'rea *'+ 8A.66 81.A6 ;age 1-A5 to 1-A=

rmin 8.8 8.11 ;age 1-A5 to 1-A=

Calue of / from Table 7-7A.1 is 6.50 so

4 81.8 8.5A D A66 / This is checked for A66 because in Table 7-85 and 7-06 value are given

only up to A66.

"rom Table 7-85, ;age 8-15, 8141@.= , 8A41@.=6, 841@.?A, [email protected]

By interpolating 1@.=8 ksi [email protected]@ ksi

7alculating the 'llowable load

'a = Fax A# 58?.05 kips 56?.@ kips

7heck E 566 kips / /

>ow /3 values 4 @.0 @.0 >ow cross check the

value of 'afrom tables on ;age 8-A8 and 8-A. The values

calculated are good.


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,-ample % 2ata

3oad 4 866 kips

3ength of 7olumn 4 1A feet

$teel 4 '85

9nd condition Top 4 inge

9nd condition Bottom 4 inge 'ssumption

7ompact $ection : "or checking refer to ;age 0-85 Table B0.1

(3imiting ow 7alculating the #ross area re!uired


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,-ample % $ Contd $election of Trial $ection

$ection < 15 x 0 < = x 5 'rea *'+ 15.=6 [email protected] ;age 1-AA and 1-8A

rmin 1.56 A.1A ;age 1-A8 and 1-88

Calue of / from Table 7-7A.1 is 1.66 so

4 @6.66 5.@A D A66 / This is checked for A66 because in Table 7-85 and 7-06

value are given only up to A66.

"rom Table 7-85, ;age 8-15, @641?.A6, 5415.?,

5=415.5? By interpolating 1?.A6 ksi 15.50 ksi


;a 4 "ax 'g A8=.05 kips 8A=.66 kips

7heck E 866 kips > /


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,-ample / 2ata

3oad 4 F kips

3ength of 7olumn 4 1= feet

$teel 4 '85

9nd condition Top 4 inge

9nd condition Bottom 4 inge

'ssumption

7ompact $ection : "or checking refer to ;age 0-85

Table B0.1 (3imiting ow 7alculating the #ross area

< 1A x 86

7 10 x 06


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,-ample / $ Contd


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,-ample / $ Contd

1A.8? in

5.1 in

18.605 in

F in


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,-ample / $ Contd 2epth of $ection 4 1A.8? H 6.15 4 18.605 in


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,-ample / $ Contd Iyy 4 F

Iyy 4 $ince it is not shifting owing to the configuration

Ixx 4 G A6.86 H G ?6?

Ixx 4 ?A?.86

rmin 4 F

rmin 4 ?.A0 in


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,-ample / $ Contd

$o /

"rom Table 7-85, ;age 8-15, 06 4 1=.80, 01 4 1=.A5

By interpolating the 'llowable $tress 4 "a4 1=.A5 ksi


;a 4 "ax 'g 4 1=.A5 x A8.?@ 4 [email protected] kips


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,-ample 0

2ata

3oad 4 F kips

3ength of 7olumn 4 A? feet

$teel 4 '85

9nd condition Top 4 %oller

9nd condition Bot 4 "ixed

'ssumption

7ompact $ection : "or checking refer to ;age 0-85

Table B0.1 (3imiting ow 7alculating the #ross area

;late 1A x 8?

? 3s @x?x1A


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,-ample 0 $ Contd


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,-ample 0 $ Contd

5+

6.=1+

8.81+

1A+

8?+

1A+


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,-ample 0 $ Contd Ixx 4 F

Ixx 4 16= H ? x ( 5.@A H 15=.80 )

Ixx 4 16= H 61.6=

Ixx 4 [email protected]=


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,-ample 0 $ Contd

Iyy 4 F

Iyy 4 6.?AA H 00A.A=

Iyy 4 00A.6

rmin 4 F

rmin 4 ?.68 in


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,-ample 0 $ Contd

$o /

"rom Table 7-85, ;age 8-15, 1 4 15.88, A 4 15.AA

By interpolating the 'llowable $tress 4 "a

4 15.A@ ksi


;a 4 "ax 'g 4 15.A@ x 8? 4 008.?@@ kips

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