Steel Ch3 - Columns Movie

8/17/2019 Steel Ch3 - Columns Movie

1/60

68402 Slide # 1

esign of Compression Members

Monther waikat

Assistant Professor

epartment of Building Engineering

An-Najah National Uniersit!

"#$%&' (tru)tural Design of Buildings **

"+$&%' Design of (teel (tru)tures"&,&,' Ar)hite)tural (tru)tures **


2/60

68402 Slide # 2

Short and long columns

Buckling load and buckling failure modes

Elastic and Inelastic buckling

Local buckling

Design of om!ression "embers

Effectie Length for $igid %rames

&orsional and %le'ural(&orsional Buckling

Design of Singl) S)mmetric ross Sections

Design of Compression

Members


3/60

68402 Slide # *

Aiall! .oaded Compression Members

olumns

Struts

&o! chords of trusses Diagonal members of trusses

Column and Compression member are often used

interchangeabl)


4/60

68402 Slide # 4

Aiall! .oaded Compression Members

ommonl) +sed Sections,

- ./ sha!es

- S1uare and $ectangular or round SS

- &ees and Double &ees

- ngles and double angles

-hannel sections


5/60

68402 Slide # 3

Columns

Failure modes (limit states):

- Crushing for short column5

- Flexural or Euler Buckling unstable under bending5

- Local Buckling thin local cross section5


6/60

68402 Slide # 6

(hort Columns

om!ression "embers, Structural elements that aresubected to a'ial com!ressie forces onl) are called

columns7 olumns are subected to a'ial loads thru the

centroid7

Stress, &he stress in the column cross(section can becalculated as

f - assumed to be uniform over the entire cross-section.

Short columns ( crushing

A

P= f


7/60 68402 Slide #

.ong Columns

&his ideal state is neer reached7 &he stress(state 9ill benon(uniform due to,

- ccidental eccentricit) of loading 9ith res!ect to the centroid- "ember out(of :straightness crookedness5; or

- $esidual stresses in the member cross(section due to fabrication!rocesses7 ccidental eccentricit) and member out(of(straightness

can cause bending moments in the member7 o9eer;

these are secondar) and are usuall) ignored7

Bending moments cannot be neglected if the) are acting

on the member7 "embers 9ith a'ial com!ression and

bending moment are called beam-columns7


8/60 68402 Slide # 8

.ong Columns

&he larger the slenderness ratio L/r 5; the greater thetendenc) to buckle under smaller load

%actors affecting tendenc) to buckle,

- end conditions

- unkno9n eccentricit) concentric > eccentric loads5- im!erfections in material- initial crookedness- out of !lumbness

- residual stress- buckling can be on one or both a'es maor or minor a'is5


9/60 68402 Slide # ?

Column Bu)kling

onsider a long slender

com!ression member7 If

an a'ial load @ is a!!lied

and increased slo9l); it

9ill ultimatel) reach aalue @cr that 9ill cause

buckling of the column7

@cr is called the critical

buckling load of thecolumn7

Pcr

Pcr

P

P

(a) (b)Pcr

Pcr

P

P

P

P

(a) (b)

Figure 1. Buckling of a'iall) loaded com!ression members


10/60

68402 Slide # A0

Bu)kling .oad

δ P M −=

- o9 assume 9e hae a !in connected column7 If 9e a!!l) a similarconce!t to that before here 9e findPcr

P

- &he internal resisting moment " in the columnis

P

Pcr

M

- .e can 9rite the relationshi! bet9een thedeflected sha!e and the "oment "

EI

P

EI

M

dx

d cr δ δ −==2

2

02

2

=+ EI

P

dx

d cr δ δ

x

x

cr P - The load at which bucking starts to happen(Critical buckling load)

2

2

L

EI

P cr π

=


11/60

68402 Slide # AA

Column Bu)kling

What is buckling?

Buckling occurs when a straight column subjected

to axial compression suddenl undergoes bending

as shown in the Figure 1(b). Buckling is identi!ied

as a !ailure limit"state !or columns.

- &he critical buckling load @cr for columns is theoreticall) gien b)E1uation *7A5,

- C*7A

I - moment of inertia about axis of buckling.

K - effective length factor based on end boundar conditions.

( )2

2

L K

I E P cr

π =


12/60

68402 Slide # A2

Effe)tie .ength

K!- "istance between inflection points in column.

K- #ffective length factor

!- Column unsupported length

KL=L KL=0.5L L

KL=0.7L L

K = 1.0 K = 0.5 K = 0.7


13/60

68402 Slide # A*

Column Bu)kling

Boundar)

conditions

&able (272 !!ro'imate alues of Effectie Length %actor; F


14/60

68402 Slide # A4

E/ ,/+- Bu)kling .oads

Determine the buckling strength

of a . A2 ' 30 column7 Its

length is 6 m7 %or minor a'is

buckling; it is !inned at both

ends7 %or maor buckling; is it!inned at one end and fi'ed at

the other end7

x

y


15/60

68402 Slide # A3


#tep $. isualiGe the !roblem- %or the .A2 ' 30 or an) 9ide flange section5; ' is the maora'is and ) is the minor a'is7 "aor a'is means a'is about 9hichit has greater moment of inertia I' H I)57

#tep $$. Determine the effectie lengths

- ccording to &able (272,- For pin"pin end conditions about the minor axis- % & 1.' (theoretical alue) and % & 1.' (recommended design

alue)

- For pin"!ix end conditions about the major axis- %x & '.* (theoretical alue) and %x & '.+ (recommended design

alue).

- ccording to the !roblem statement; the unsu!!orted length forbuckling about the maor '5 a'is L' 6 m7


16/60

68402 Slide # A6


- &he unsu!!orted length for buckling about the minor )5 a'is L) 6 m7- Effectie length for maor '5 a'is buckling F' L' 078 ' 6 478 m7- Effectie length for minor )5 a'is buckling F) L) A70 ' 6 6 m7

#tep $$$. Determine the releant section !ro!erties

- Elastic modulus of elasticit) E 200 J@a constant for all steels5- %or .A2 ' 30, I' A6*'A06 mm47 I) 2*'A06 mm4


17/60

68402 Slide # A


#tep $,. alculate the buckling strength

- ritical load for buckling about ' ( a'is @cr('

@cr(' A*?63 k7

ritical load for buckling about )(a'is @cr()

@cr() A26A k7

Buckling strength of the column smaller @cr('; @cr()5 @cr A26A k7

"inor )5 a'is buckling goerns7

( )

2 6

2

200 163 10

4800

π × × ×

( )22

y y

y

L K

I E π

( )

2 6

2

200 23 10

6000

π × × ×

( )2

2

x x

x

L K

I E π


18/60

68402 Slide # A8


$otes%

- Minor axis buckling usually governs for all doublysymmetric cross-sections !o"ever# for some cases#

ma$or %x& axis buckling can govern

- 'ote that the steel yield stress "as irrelevant forcalculating this buckling strength


19/60

68402 Slide # A?

Let us consider the !reious e'am!le7 ccording to ourcalculations @cr A26A k7 &his @cr 9ill cause a uniform

stress f @cr / in the cross(section7

%or .A2 ' 30; ?420 mm27 &herefore; for @cr A26A

kK f A**7? "@a7 &he calculated alue of f is 9ithin the elastic range for a

*44 "@a )ield stress material7

o9eer; if the unsu!!orted length 9as onl) * m; @cr

9ould be calculated as 3044 k; and f 3*373 "@a7 &his alue of f is ridiculous because the material 9ill

)ield at *44 "@a and neer deelo! f 3*373 k7 &he

member 9ould )ield before buckling7

*nelasti) Column Bu)kling


20/60

68402 Slide # 20

*nelasti) Column Bu)kling

-. (/.1) is alid onl when the material eerwhere in the cross"section is in the elastic region. $! the material goes inelastic then

-. (/.1) becomes useless and cannot be used.

What happens in the inelastic range?

Seeral other !roblems a!!ear in the inelastic range7

- &he member out(of(straightness has a significant influence on the bucklingstrength in the inelastic region7 It must be accounted for7

- &he residual stresses in the member due to the fabrication !rocesscauses )ielding in the cross(section much before the uniform stress f

reaches the )ield stress %)7

- &he sha!e of the cross(section .; ; etc75 also influences the bucklingstrength7

- In the inelastic range; the steel material can undergo strain hardening7 ll of these are er) adanced conce!ts and be)ond the sco!e of this

course7


21/60


22/60

68402 Slide # 22

*nelasti) Bu)kling of Columns

P F F =

- Elastic buckling assumes the material to follo9 ookes la9 and thusassumes stresses belo9 elastic !ro!ortional5 limit7

- If the stress in the column reaches the !ro!ortional limit then Eulersassum!tions are iolated7

L/rL/r

#tress F2#tress F2

-uler assumptions-uler assumptions

2

2

)/( r L

E F cr

π =

Elastic Buckling

%Long Columns&

(nelastic Buckling

%)hort columns&

0roportional0roportional

limitlimit


23/60

68402 Slide # 2*

A*(C (pe)ifi)ations for Column

(trength

@u ≤ φ @n

@n g %cr CE*(A

CE*(4

& e- #lastic critical #uler buckling load 'g - gross member area

K - effective length factor

! - unbraced length of the member

r - governing radius of gration

&he 078 factor in E1 E*(*5 tries to account for initial crookedness7

( ) 2

2

r KL

E F e

π =

>

≤

=

ye

y ye F y F

cr

F E r KL F

F E r KL F F

71.4877.0

71.4658.0

Inelastic CE*(2

Elastic CE*(*


24/60

68402 Slide # 24

A*(C (pe)ifi)ations 0or Column

(trength

λc =

E

F

r

LK y

π

Fcr /Fy

1.0

1.5

0.39 Fcr

= Fy

λ2c

877.0

Fcr

= Fy( )2c658.0 λ

λc =

E

F

r

LK y

πλ

c =

E

F

r

LK y

π

Fcr /Fy

1.0

1.5

0.39 Fcr

= Fy

λ2c

877.0F

cr = F

y

λ2c

877.0

Fcr

= Fy( )2c658.0 λFcr = Fy( )2c658.0 λ

r

KL

y F

E 71.4

ye F y F

cr F F

= 658.0

ecr F F 877.0=

Inelastic Buckling

Short columns5

Elastic BucklingLong columns5


25/60

68402 Slide # 23

A*(C (pe)ifi)ations 0or Column

(trength

%or a gien column section,

- alculate I; g; r

-Determine effectie length * L based on end boundar) conditions7

- alculate FL/r- If FL/r is greater than ; elastic buckling occurs and use

E1uation E*745

- If FL/r is less than or e1ual to ; inelastic buckling

occurs and use E17 E*7*5 ote that the column can deelo! its )ield strength %) as

FL/r a!!roaches Gero7

y F

E 71.4

y F

E 71.4


26/60

68402 Slide # 26

E/ ,/& - Column (trength

alculate the design strength of .A4 ' 4 9ith length of 6m and !inned ends7 *6 steel is used7

- #tep $. alculate the effectie length and slenderness ratio for the

!roblemF' F) A70

L' L) 6 m

"aor a'is slenderness ratio F'L'/r ' 6000/A3*74 *?7A

"inor a'is slenderness ratio F)L)/r ) 6000/6* ?372

- #tep $$. alculate the buckling strength for goerning slendernessratio

&he goerning slenderness ratio is the larger of F'L'/r '; F)L)/r )5


27/60


28/60

68402 Slide # 28

.o)al Bu)kling .imit (tate

Figure 3. Local buckling of columns

&he ISs!ecifications for

column strength

assume that column

buckling is the

goerning limit state7

o9eer; if the

column section is

made of thin slender5

!late elements; thenfailure can occur due

to local buckling of the

flanges or the 9ebs7


29/60

68402 Slide # 2?


- Local buckling is another limitationthat re!resents the instabilit) of thecross section itself7

- If local buckling occurs; the fullstrength of the cross section can

not be deelo!ed7


30/60

68402 Slide # *0

If local buckling of the indiidual !late elements occurs; thenthe column ma) not be able to deelo! its buckling strength7

&herefore; the local buckling limit state must be !reented

from controlling the column strength7

Local buckling de!ends on the slenderness 9idth(to(thickness b/t ratio5 of the !late element and the )ield stress

%)5 of the material7

Each !late element must be stock) enough; i7e7; hae a b/t

ratio that !reents local buckling from goerning the column

strength7

&he IS s!ecification !roides the slenderness b/t5 limits

that the indiidual !late elements must satisf) so that local

buckling does not control7



31/60

68402 Slide # *A


- Local buckling can be !reented b) limiting the 9idth to thickness ratiokno9n as


32/60

68402 Slide # *2

&he IS s!ecification !roides t9o slenderness limits λ! and λr 5 for the local buckling of !late elements7


Compact

No!Compact

"#eder

Compact

No!Compact

"#eder

b

t

F

Axial shr!"#i#$% ∆

A x i a l F r c " %

F

Fy

Compact

No!Compact

"#eder

Compact

No!Compact

"#eder

b

t

F

Axial shr!"#i#$% ∆

A x i a l F r c " %

F

Fy


33/60

68402 Slide # **

- If the slenderness ratio b/t5 of the !late element is greater than λr then it is slender 7 It 9ill locall) buckle in the elastic range before reaching %)

- If the slenderness ratio b/t5 of the !late element is less than λr butgreater than λ!; then it is non-compact 7 It 9ill locall) buckle

immediately after reaching %)

- If the slenderness ratio b/t5 of the !late element is less than λ!; thenthe element is compact 7 It 9ill locall) buckle much after reaching %)

If all the !late elements of a cross(section are com!act;

then the section is compact 7- If an) one !late element is non(com!act; then the cross(section isnon(com!act

- If an) one !late element is slender; then the cross(section isslender7



34/60

68402 Slide # *4


-ross section can be classified as


35/60

68402 Slide # *3

&he slenderness limits λ! and λr for arious !late elements 9ithdifferent boundar) conditions are gien in the IS "anual7

ote that the slenderness limits λ! and λr 5 and the definition of !late

slenderness b/t5 ratio de!end u!on the boundar) conditions for the

!late7

- If the !late is su!!orted along t"o edges !arallel to the direction ofcom!ression force; then it is a stiffened element7 %or e'am!le; the 9ebs of

. sha!es

- If the !late is su!!orted along onl) one edge !arallel to the direction of thecom!ression force; then it is an unstiffened element7 E'7; the flanges of .

sha!es7 &he local buckling limit state can be !reented from controlling the

column strength b) using sections that are com!act and non(com!act7

oid slender sections



36/60


37/60

68402 Slide # *

E/ ,/, 1 .o)al Bu)kling

2000001.49 1.49 42.3

248r

y

E

F λ = × = × =

Determine the local buckling slenderness limits and ealuatethe .A4 ' 4 section used in E'am!le *727 Does local

buckling limit the column strengthM - Ste! I7 alculate the slenderness limits

See &ables in !reious slide7%or the flanges of I(sha!e sections in !ure com!ression

%or the 9ebs of I(sha!es section in !ure com!ression

+se E 200000 "@a

2000000.56 0.56 15.9

248r

y

E

F λ = × = × =


38/60

68402 Slide # *8

E/ ,/, 1 .o)al Bu)kling

- #tep $$. alculate the slenderness ratios for the flanges and 9ebs of.A4 ' 4- %or the flanges of I(sha!e member; b bf /2 flange 9idth / 2

&herefore; b/t bf /2tf 7

%or . A4 ' 4; bf /2tf 674A See Section @ro!ert) &able5

- %or the 9ebs of I sha!ed member; b hh is the clear distance bet9een flanges less the fillet / corner radius ofeach flange

%or .A4 ' 4; h/t9 2374 See Section @ro!ert) &able57

- #tep $$$. "ake the com!arisons and comment%or the flanges; b/t N λr 7 &herefore; the flange is non(com!act

%or the 9ebs; h/t9 N λr 7 &herefore the 9eb is non(com!act

&herefore; the section is non(com!act

&herefore; local buckling 9ill not limit the column strength7


39/60

68402 Slide # *?

Design of Compression Members

-Ste!s for design of com!ression members

- alculate the factored loads @u

- ssume a cross section5 or *L/r ratio bet"een +, to ,&

- alculate the slenderness ratio *L/r and the ratio F e

- alculate φc %cr based on alue of F e

- alculate the rea re1uired g

- hoose a cross section and get * x L/r x 5and * y L/r y 5 *L/r 5 ma'

-$ecalculate φc %cr and thus check

-

cr c

$re%$&red

F

P '

φ =

$cr c ( c P F ' P ≥= φ φ

( )2

2

r KL

E F e

π =


40/60

68402 Slide # 40

E/ ,/$ 1 Design (trength

Determine the design strength of an S&" ??2 .A4 'A*2 that is !art of a braced frame7 ssume that the

!h)sical length L ? m; the ends are !inned and the

column is braced at the ends onl) for the O(O a'is and

braced at the ends and mid(height for the P(P a'is7

- #tep $. alculate the effective lengths7%rom Section @ro!ert) &able

%or .A4 ' A*2, r ' A3?73 mmK r ) ?373 mmK g 230*0 mm2

F' A70 and F) A70

L' ? m and L) 473 m

F'L' ? m and F)L) 473 m


41/60

68402 Slide # 4A


( )344 620.50.658 344 272.8cr F = × =

- #tep $$. Determine the goerning slenderness ratioF'L'/r ' ?000/A3?73 3674F)L)/r ) 4300/?373 47A

&he larger slenderness ratio; therefore; buckling about the maor

a'is 9ill goern the column strength7

- #tep $$$. alculate the column strength

( )

2 2

2 2

200000620.5

56.4e

x x x

E F

K L r

π π ×= = = "@a

200000/ 4.71 4.71 113.6

344 x x x

y

E K L r

F < = =

"@a


42/60

68402 Slide # 42


5.1356.0 =×= y

r F

E λ

- #tep $,. heck the local buckling limits

%or the flanges; bf /2tf 7A3 N

%or the 9eb; h/t9 A7N

&herefore; the section is non(com!act7 QF7

5.1356.0 =×=

yr F

E

λ

0.9 25030 272.8 1000 6145 P )N Φ = × × =


43/60

68402 Slide # 4*

E/ ,/2 1 Column Design

com!ression member is subected to serice loads of 00 k DL and 2400 kof LL7 &he member is 78 m long > !inned at each end7 +se ??2 steel andselect a . sha!e7

- #tep $. alculate the factored design load @u

@u A72 @D R A76 @L A72 ' 00 R A76 ' 2400 4680 k7

- #tep $$. alculate %cr b) assuming FL/r 80

( )

2 2

2 2

200000308.4

80e

E F

KL r

π π ×= = = "@a"@a

( )344 308.40.658 344 215.3cr F = × =

200000/ 4.71 4.71 113.6

344 y

E KL r

F < = =

"@a"@a


44/60


45/60

68402 Slide # 43

Effe)tie .ength

S!ecific alues of * shall be kno9n

%or com!ression elements connected as rigid frames the effectie

length is a function of the relatie stiffness of the element com!ared to

the oerall stiffness of the oint7 &his 9ill be discussed later in this

cha!ter

alues for * for different end conditions range from 073 for

theoreticall) fi'ed ends to A70 for !inned ends and are gien b),

Table C-C2.2 AISC Manual

End conditions *

.in-.in ,

.in-Fixed ,0

Fixed-Fixed ,1+ Fixed-Free 2

$ecommended

design alues not

theoretical alues5


46/60


47/60

68402 Slide # 4

Effe)tie .ength of Columns in

0rames

So far; 9e hae looked at the buckling strength of indiidualcolumns7 &hese columns had arious boundar) conditionsat the ends; but the) 9ere not connected to other members9ith moment fi'5 connections7

&he effectie length factor F for the buckling of anindiidual column can be obtained for the a!!ro!riate endconditions from &able (272 of the IS "anual 7

o9eer; 9hen these indiidual columns are !art of aframe; their ends are connected to other members beams

etc757- &heir effectie length factor F 9ill de!end on the restraint offered b)

the other members connected at the ends7

- &herefore; the effectie length factor F 9ill de!end on the relatierigidit) stiffness5 of the members connected at the ends7


48/60

68402 Slide # 48


0rames

&he effectie length factor for columns in frames must becalculated as follo9s,

- %irst; )ou hae to determine 9hether the column is !art of a bracedframe or an unbraced moment resisting5 frame7

- If the column is !art of a braced frame then its effectie length factor 0

N F T A- If the column is !art of an unbraced frame then A N F T U

- &hen; )ou hae to determine the relatie rigidit) factor J for bothends of the column

- J is defined as the ratio of the summation of the rigidit) EI/L5 of allcolumns coming together at an end to the summation of the rigidit)EI/L5 of all beams coming together at the same end7

It must be calculated for both ends of the column

∑∑

=

b

b

c

c

L

I E

L

I E

*

c, for columns

b, for beams


49/60

68402 Slide # 4?


0rames

-&hen; )ou can determine the effectie length factor F for the

column using the calculated alue of J at both ends; i7e7; J and

JB and the a!!ro!riate alignment chart

- &here are t9o alignment charts !roided b) the IS manual;

- Qne is for columns in braced sides9a) inhibited5 frames7 0 N F T A- &he second is for columns in unbraced sides9a) uninhibited5 frames7A N F T U

- &he !rocedure for calculating J is the same for both cases7


50/60

68402 Slide # 30

Effe)tie .ength

"onogra!h or

Vackson and "oreland

lignment hart

for +nbraced %rame


51/60

68402 Slide # 3A

Effe)tie .ength

"onogra!h or

Vackson and "oreland

lignment hart

for braced %rame


52/60

68402 Slide # 32

E/ ,/" 1 Effe)tie .ength 0a)tor

alculate the effectielength factor for the W14

x 5/ column B of the

frame sho9n7 ssume

that the column is

oriented in such a 9a)

that maor a'is bendingoccurs in the !lane of

the frame7 ssume that

the columns are braced

at each stor) leel for

out(of(!lane buckling7 ssume that the same

column section is used

for the stories aboe and

belo97

10 '!.

10 '!.

12 '!.

15 '!.

20 '!.18 '!.18 '!.

W14 x 68

W14 x 68

W14 x 68

B

A

W 1 2 x 7

9

W 1 2 x 7 9

W 1 2 x 7

9

10 '!.

10 '!.

12 '!.

15 '!.

20 '!.18 '!.18 '!.

W14 x 68

W14 x 68

W14 x 68

B

A

W 1 2 x 7

9

W 1 2 x 7 9

W 1 2 x 7

9

374 m 374 m 6 m

473 m

*76 m

*70 m

*70 m


53/60

68402 Slide # 3*

E/ ,/" 1 Effe)tie .ength 0a)tor

-#tep $. Identif) the frame t)!e and calculate L'; L); F'; and F) if

!ossible7

It is an unbraced sides9a) uninhibited5 frame7

L' L) *76 m

F) A70

F' de!ends on boundar) conditions; 9hich inole restraints due tobeams and columns connected to the ends of column B7

eed to calculate F' using alignment charts7

- #tep $$. alculate F'I'' of . A2 ' 3* 423 in4 I'' of .A4'68 3* in4

021.1360.6

493.6

1220

723

1218

7231212

425

1210

425

L

(

L

(

)

*

*

c

c

A ==

×+

×

×+

×=

∑

∑

=


54/60


55/60

68402 Slide # 33

E/ ,/# 1 Column esign

Design olumn B of the frame sho9n belo9 for a designload of 2*00 k7

ssume that the column is oriented in such a 9a) that

maor a'is bending occurs in the !lane of the frame7

ssume that the columns are braced at each stor) leelfor out(of(!lane buckling7

ssume that the same column section is used for the

stories aboe and belo97

+se ??2 steel7


56/60

68402 Slide # 36


10 '!.

10 '!.

12 '!.

15 '!.

20 '!.18 '!.18 '!.

W14 x 68

W14 x 68

W14 x 68

B

A

W 1 2 x

7 9

W 1 2 x

7 9

W 1 2 x

7 9

10 '!.

10 '!.

12 '!.

15 '!.

20 '!.18 '!.18 '!.

W14 x 68

W14 x 68

W14 x 68

B

A

W 1 2 x

7 9

W 1 2 x

7 9

W 1 2 x

7 9

374 m 374 m 6 m

473 m

*76 m

*70 m

*70 m


57/60

68402 Slide # 3


- #tep $ ( Determine the design load and assume the steel material7Design Load @u 2*00 k7

Steel )ield stress *44 "@a ??2 material57

- #tep $$. Identif) the frame t)!e and calculate L'; L); F'; and F) if!ossible7It is an unbraced sides9a) uninhibited5 frame7

L' L) *76 m

F) A70

F' de!ends on boundar) conditions; 9hich inole restraints dueto beams and columns connected to the ends of column B7

eed to calculate F' using alignment charts7

eed to select a section to calculate F'


58/60

68402 Slide # 38


- #tep $$$ ( Select a column section 3ssume minor axis buckling governs

F) L) *76 m

Select section .A2'3*

F)L)/r ) 372 %e 60474 %cr 2A7A

φ c@n for )(a'is buckling 243374 k

- #tep $, ( alculate F'I'' of . A2 ' 3* A'A06 mm4

I'' of .A4'68 *0A'A06 mm4


59/60


60/60


#tep , ( heck the selected section for O(a'is bucklingF' L' A7* ' *76 4768 m

F' L'/r ' *372 %e A3?074 %cr *A472

%or this column; φc@n for O(a'is buckling 28467*

#tep ,$ ( heck the local buckling limits

%or the flanges; bf /2tf 876? N

%or the 9eb; h/t9 287A N

&herefore; the section is non(com!act7 QF; local buckling is not a

!roblem

5.1356.0 =×=

yr

F

E λ

9.3549.1 =×=

yr

F

E λ

Steel Ch3 - Columns Movie

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