stability virtuallab

8/13/2019 Stability VirtualLab

1/95

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2/95

Annual Stability Conference11 Sessions35+ Papers

Rm. Texas 3-4

Stability Fun!


3/95

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4/95

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5/95

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T-=2


6/95

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7/95

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8/95

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10/95

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11/95

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12/95

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13/95

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" !$H-.",2$H 6-=2


14/95

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15/95

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16/95

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18/95

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19/95

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21/95

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22/95


23/95


24/95


25/95


26/95

L-"#%$ 68 ,=- >#.-7, L$248"#" G-,=(H


27/95


28/95

5GAb U42",#7 '(4+)$ T+7J4#$%

2$H ,=- U00-7, (0 U$H 9-",.2#$,5-2.$#$% ;6l-7,#


29/95

Buckled shape ofcolumn is shown bydashed line

(a) (b) (c) (d) (e) (f)

Theoretical K value 0.5 0.7 1.0 1.0 2.0 2.0

)a(

)b( )c(

)d( )e(

)f (

delkcuBinmuloc

esa

f oepahsybnwohss

en

er oe

ac K ea .0

.0 01

0.1 02

02

TABLE C-A-7.1Approximate Values of Effective

Length Factor, K


30/95

Compute 10 modes

P = 1 k


31/95

. . .


(a) (b) (c) (d) (e) (f)


. . . . . .

)

) )c(

)d( )e(

f

delcuimuoldeha

f oeasybwoss

eni

ter eT

lac eulav 5.0

.

7.0 .1

. .

0.1 0.2

. .

.2

.


Length Factor, K

Mode 1:

Pcr

= 273.6

K = ! L

EI P

cr

= 2.0


32/95

Mode 2:

Pcr

= 273.6

K = ! L

EI P

cr

= 2.0. . .


(a) (b) (c) (d) (e) (f)


. . . . . .

)

) )c(

)d( )e(

f

delcuimuoldeha

f oeasybwoss

eni

ter eT

lac eulav 5.0

.

7.0 .1

. .

0.1 0.2

. .

.2

.


Length Factor, K


33/95

Mode 3:

Pcr

= 1094.5

K = ! L

EI P

cr

= 1.0. . .


(a) (b) (c) (d) (e) (f)


. . . . . .

)

) )c(

)d( )e(

f

delcuimuoldeha

f oeasybwoss

eni

ter eT

lac eulav 5.0

.

7.0 .1

. .

0.1 0.2

. .

.2

.


Length Factor, K


34/95

Mode 4:

Pcr

= 1094.5

K = ! L

EI P

cr

= 1.0. . .


(a) (b) (c) (d) (e) (f)


. . . . . .

)

) )c(

)d( )e(

f

delcuimuoldeha

f oeasybwoss

eni

ter eT

lac eulav 5.0

.

7.0 .1

. .

0.1 0.2

. .

.2

.


Length Factor, K


35/95

. . .


(a) (b) (c) (d) (e) (f)


. . . . . .

)a(

)b( )(

d )

)f (

delkcuBnmuloc

ldehsd

f opahybnwohss

enil

iteohT

la eua 5.

.

7. 0.1

. .

.1 .2

. .

0.2

.


Length Factor, K

Mode 5:

Pcr

= 2239.2

K = ! L

EI P

cr

= 0.7


36/95

. . .


(a) (b) (c) (d) (e) (f)


. . . . . .

)

) )c(

)d( )e(

f

delcuimuoldeha

f oeasybwoss

eni

ter eT

lac eulav 5.0

.

7.0 .1

. .

0.1 0.2

. .

.2

.


Length Factor, K


37/95

. . .


(a) (b) (c) (d) (e) (f)


. . . . . .

)

) )c(

)d( )e(

f

delcuimuoldeha

f oeasybwoss

eni

ter eT

lac eulav 5.0

.

7.0 .1

. .

0.1 0.2

. .

.2

.


Length Factor, K


38/95

. . .


(a) (b) (c) (d) (e) (f)


. . . . . .

)

) )c(

)d( )e(

f

delcuimuoldeha

f oeasybwoss

eni

ter eT

lac eulav 5.0

.

7.0 .1

. .

0.1 0.2

. .

.2

.


Length Factor, K


39/95

. . .


(a) (b) (c) (d) (e) (f)


. . . . . .

)a(

)b( )

d )e

)f (

delkcBnmuloc

lesd

f opahsynwohss

enl

iter ohT

a eua 5.

.

7. 0.1

. .

.1 .2

. .

0.2

.


Length Factor, K

Mode 9:

Pcr

= 4380

K = ! L

EI P

cr

= 0.5


40/95

Dbg

Dbn

Dbh

DbC

DbB

A

D

gDD

ADDD

AgDD

mDDD

mgDD

jDDD

jgDD

eDDD

egDD

gDDD

D gDD ADDD AgDD mDDD mgDD

! ; +

& 2 $ , #

" 2 #

< 3 " = >

5,?1@$ ,+ A@1#$"&


41/95

Vary beam sizes w/

I Top Beam

! I Bottom Beam

C 027,(.

! 7.> I(*> T(,,()

> I(*

> T(,,()

AbD

Dbg

I=2$J" ,(c+- ?+2


42/95

5Gmb M27,(." P$W4+-$7#$% ,=-M4-^+.24 T+7J4#$% /,.-$%,= (0

'()*.-""#($ G-)6-."5-2.$#$% ;6l-7,#


43/95


44/95


45/95


46/95


47/95

& 8

U+4-.

LP/'

$( " ( [ $( $ .-"" ( [ $( $ .-"

$( " ( [ $ .-"" ( [ $ .-"

U'5P'5

!

!

I=2$J" ,( >2$ I2)2.J#$


48/95

I = 2 $

J " , (

T + 4 - $ ,

L 4 - )

H 2 . 2 ,

T - $ , 4 - 8

F


49/95

& 8

U+4-.

LP/'

$( " ( [ $( $ .-"" ( [ $( $ .-"

$( " ( [ $ .-"" ( [ $ .-"

U'5

P'5

I=2$J" ,( >2$ I2)2.J#$


50/95

5Gjb U00-7,#


51/95

/#H-128" 4-2$#$%X 1-"#H-128" H2.,-Hq -


52/95

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6")89&

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6")89&

;"< =,(9

="''"9 =,(9

>?@A?B

C

D @ A ? B


53/95


54/95

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34#5 -6#*%$ 789 34#5 -6#*%$ 789

: ;?@ ;


55/95

5Geb M27,(." P$W4+-$7#$% ,=-

/,.-$%,= (0 M4-^+.24 G-)6-."5-2.$#$% ;6l-7,#


56/95

5Ge! QAe^gj YLBBmZ! : 2 u Abm ,( jAbA 0,b

! M(. -27= : 2X #$


57/95


58/95

! !


59/95

M n / M p

! !

L p Lr

I=2$J" ,( >2$ I2)2.J#$

Lb


60/95

5Ggb 52,-.24`I(."#($24 T+7J4#$%

(0 T-2)" 1#,= G()-$, O.2H#-$,5-2.$#$% ;6l-7,#


61/95

5Gg


62/95

5Gg!

!!

#

"

# $

"!"#

!%#

!


63/95

G A u `ADDD #$`J

G m u ADDD #$`J

G 7. u jnDAbC #$`J

G A u `ADDD #$`J

G m u `nDD #$`J

G 7. u BhChbj #$`J

C b

MASTAN 2=

9787.3

3601.8= 2.72

C b

AISC = 2.19


64/95

I=2$J" ,( c+- ?+2


65/95

Q($% 2$H >.#


66/95

I#)- 0(. 8(+ ,( ,2J- #, 0(. 2 "*#$@

W24x68 with L = 24 ft. (288 in.)M1 = -1000 in-k

M2 = +1000 in-k

u jnDm J#*`#$u jDD J#*`0,


67/95

!!

!#

!"#

W24x68

Mcr (kip-in) Case 1 Case 2

M1/M2 = -1

M1/M2 = +1

Case 1: Braces at endsCase 2: Braces at ends

and mid-span

Observations :

L =24 ft. (288 in.)


68/95

!!

!#

!"#

W24x68

Mcr (kip-in) Case 1 Case 2

M1/M2 = -1 3,602 12,120

M1/M2 = +1 9,838 27,414

Case 1: Braces at endsCase 2: Braces at ends

and mid-span

Observations :

L =24 ft. (288 in.)

3.36

Mcr increases as L b is reduced

2.73

Mcr increases as moment gradient increases An inflection point is not a brace point!

2.79


69/95

5Gnb T-2) >-"#%$ 68 U42",#7

2$H P$-42",#7 L$248"-"5-2.$#$% ;6l-7,#


70/95

]N.-H#7,#($ #" 2$#"= N=8"#7#",

YACCg ` ABnmZ


71/95

5Gnk U42",#7 -"#%$!

"

"#$%&' ($%&' "#$%&' )$%&'

* + , -

B /&414CAb L44 )-)6-." W16x31, P u = SmbW27x84, W16x31, W18x35, P u= Sjb L44 )-)6-." "2)- "#R-X P u = 200k X )#$b 1-#%=,S

eb G-)6-." "#R-" )28


72/95

W27x84 W16x31 W18x35

100 kip

Case 2: Inelastic Analysis

P u = 101.3 kip Wt = 1.881 kip P u / Wt = 53.84

!"

"#$%&' ($%&' "#$%&' )$%&'

* + , -


73/95

!"#$ !% %$ $& ! " '()*+ ,-*./) '()*+&-0*.1 3-)/+4 56789: 5;789: 0 ! " ?! "#$%&'()*$+ =*>0 ! " ? ,*

(@ AB(0)*C ,5DEF5 ,5DEF5 ,5DEF5 ;G@6F 9@;H5 5@69< I9@G9J@ AB(0)*C


74/95

5Ghb /-7($H`(.H-. U00-7,"Y! `s 2$H ! `tZ U00-7,"

5-2.$#$% ;6l-7,#


75/95

%&''( )'*+,- . /0' /1(' 23 /425+&+'*

P, 12" ,=- 6-", (0 ,#)-"Y*4+%E$ 7=+% ,=- -V+2,#($" 2$H

6-#$% 264- 1#,= ,=- ,264-Z#, 12" ,=- 1(.", (0 ,#)-"

Y6-#$% .-"*($"#64- 0(. .-2448+$H-.",2$H#$% ,=- 6-=2


76/95

A", (.H-.


77/95

M max1st

= 200 k-in

M max2nd= 391 k-in

B1Computation

=

391200

= 1.96

M 1

1st= ! 150 k-in

M 21st = + 200 k-in = M max1st( )C

m = 0.6 ! 0.4 ! 150 + 200( )= 0.9

P Pe

= 0.5 B1

AISC=

0.9

1 ! 0.5= 1.8

M max

2nd= B

1

AISC M max

1st

M max

2nd= 1.8 " 200 =360 k-in


78/95

!

#

$

%

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#-./01.21 234567 89:;


79/95


80/95

5GCb /,.-$%,= (0 T-2)`'(4+)$"5-2.$#$% ;6l-7,#


81/95


82/95

5GC

! QAe^gj YLBBmZX: 2 u Ag 0,b! P$


83/95

!"!!

!"$!

!"%!

!"&!

!"'!

!"(!

!")!

!"!! !"%! !"'! !")! !"*! $"!!

+,-.

/+-0+1%

+2,1+

P / P y

M / M px

P + M major


84/95

!"!!

!"$!

!"%!

!"&!

!"'!

!"(!

!")!

!"!! !"%! !"'! !")! !"*! $"!!

+,-.

/+-0+1%

P / P y

M /M py

P + M minor

5GBb "#%$ 68


85/95

5GBb >-"#%$ 68 ,=-

>#.-7, L$248"#" G-,=(H5-2.$#$% ;6l-7,##.-7, L$248"#" G-,=(Hb"

m$H

`(.H-. 2$248"-" ,( H-,-.)#$- ! - E" 2$H$ - E"" !,#4#R- $(,#($24 4(2H" #$ *427- (0 H#.-7,

)(H-4#$% (0 ! ( 2$H %6" N.27,#7- 1#,= #$,-.27,#($ -V+2,#($" !"- ,=- .2,#( (0 m $H` ,( A ", (.H-. H.#0," 2" 2$

#$H#72,(. (0 2 "8",-)E" "-$"#,#


86/95

LP/' /*-7#W#72,#($/0G /9GDjb LHl+",)-$," ,( /,#00$-""I=- 2$248"#" (0 ,=- ",.+7,+.-,( H-,-.)#$- ,=- .-V+#.-H",.-$%,=" (0 7()*($-$,""=244 +"- .-H+7-H ",#00$-""-"X2" 0(44(1"kYAZ L 027,(. (0 DbCD "=244 6-2**4#-H ,( 244 ",#00$-""-" ,=2,2.- 7($"#H-.-H ,( 7($,.#6+,-,( ,=- ",26#4#,8 (0 ,=-",.+7,+.-


87/95

LP/' /*-7#W#72,#($/0G /9GDjb LHl+",)-$," ,( /,#00$-""I=- 2$248"#" (0 ,=- ",.+7,+.-,( H-,-.)#$- ,=- .-V+#.-H",.-$%,=" (0 7()*($-$,""=244 +"- .-H+7-H ",#00$-""-"X2" 0(44(1"kYAZ L 027,(. (0 DbCD "=244 6-2**4#-H ,( 244 ",#00$-""-" ,=2,2.- 7($"#H-.-H ,( 7($,.#6+,-,( ,=- ",26#4#,8 (0 ,=-",.+7,+.-

N-.=2*" P"=(+4H =2


88/95

! " # $ % &

( ) * +

,

-./ 012)34"5 !6)7 ! " 8 "99 :6+3; " F

F5 AB .6)7 =GH6I1C=@) @/J/@1CC/1>3

#5 A=)=2D6@= D1$6DHD ! " )71) 31J3K=3LMNO N+= " F

!#P$QR

#9ST9U

" # S T 9 U

! " ! " 95"! "


89/95

)5H O+#H-" ",+H-$, ,=.(+%= 2 H-"#%$ 7=-7J (0 2 "#)*4-

"8",-) +"#$% ,=- >#.-7, L$248"#" G-,=(H


90/95

5GB! L4"( #$74+H-" )2J#$% 2 7()*2.#"($ 1#,= m $H`

(.H-. #$-42",#7 2$248"#" 277(.H#$% ,( LP/'L**-$H#^ A *.(


91/95

5-""($" 5-2.$-H! L44 )(H+4-" 0+448 ,-",-H #$ )8 'UfOeDg`>-"#%$ (0 /,--4 /,.+7,+.-" 7(+."-! /,+H-$,"k

" 5-2.$ ,( .-2H 2$H 0(44(1 #$",.+7,#($"" M#$H G/ U^7-4 5G "*.-2H"=--," J-8 ,( V+#7J48

*.-*2.- 7()*2.2,#


92/95

M+,+.- G(H+4-"! c(+. "+%%-",#($"F

" -`)2#4 )- 2, R#-)#2$v6+7J$-44b-H+! c+.2E" &'() *+),-. /012'.'03 4567)80+

" 4-2$#$% 7(4+)$" 6.27#$% Y$-2.48 7()*4-,-FZ" "()- 24.-2H8 #$74+H-H #$ 5GE"@

! /,26#4#,8 (0 "4-$H-. 7.(""`"-7,#($"" '!`M/G


93/95

'!`M/G

=,,*k[[111b7-bl=+b-H+[6"7=20-.[7+0")[


94/95

/+))2.8! 3#.,+24 526(.2,(.8! 9-


95/95

i+-",#($"S

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