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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_engineering7/23/2019 Compression Members1
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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_area7/23/2019 Compression Members1
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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
7alculating the 'llowable load
;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
7alculating the 'llowable load
;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
7alculating the 'llowable load
;a 4 "ax 'g 4 15.A@ x 8? 4 008.?@@ kips