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8/13/2019 Stability VirtualLab
1/95
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Annual Stability Conference11 Sessions35+ Papers
Rm. Texas 3-4
Stability Fun!
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'=244-$%- (0 >-"#%$#$%
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'=244-$%- (0 >-"#%$#$%
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/()- ?#",(.8@ABCDE"F! G7O+#.-E" /,--4 >-"#%$ '(+."-"
" !$H-.",2$H 6-=2
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3#.,+24 526(.2,(.8! M2", 0(.12.H ,( ,=- 42,- BDE"
" O!P 0(. 2$248"#" "(0,12.- #" ,=- $(.)" M27+4,8 H-
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3#.,+24 526(.2,(.8! P$ -2.48 mDDD@
" $109'; /09-70-91.
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3#.,+24 526(.2,(.8! mDDD`mDAD@
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" ;,=-. -H+72,#($24[.-"-2.7= 2$248"#" "(0,12.- #"H-
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AmXBeC G2,426 3-."#($ABXmeg N'`
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3#.,+24 526(.2,(.8!
f--H" 0(. "#)+42,#$% ",.+7,+.24 ",26#4#,8 *.(64-)"" N2.,#24 8#-4H#$% 277-$,+2,-H 68 .-"#H+24 ",.-""-"" M+44 7.(""`"-7,#($ 8#-4H#$%X *42",#7 =#$%-" 5(724 6+7J4#$%X -42",#7[#$-42",#7"
M4-^+.24 6+7J4#$%X -42",#7[#$-42",#7" I(."#($24 6+7J4#$%X -42",#7[#$-42",#7" 52,-.24`,(."#($24 6+7J4#$%X -42",#7[#$-42",#7" M4-^+.24`,(."#($24 6+7J4#$%X -42",#7[#$-42",#7" L6(
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3#.,+24 526(.2,(.8! /#)+42,#$% /,.+7,+.24 /,26#4#,8
" "-PfLX Lf/c/X NU9M;9Gj>X 5L9/Le>X@
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! '($"#H-.2,#($" 0(. )2J#$% ,=- 7=(#7-" N.#7- 2$H 2
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3#.,+24 526(.2,(.8
Q=2, #0kAb H#00-.-$, +$6.27-H 4-$%,= : 2Smb H#00-.-$, Q`"=2*- #" -)*4(8-HSjb H#00-.-$, 4(2H#$% 7($H#,#($"Seb H#00-.-$, "+**(., 7($H#,#($"Sgb #$-42",#7 -00-7," -^[#$74+H-HSnb #)*-.0-7,#($ -^[#$74+H-HShb 12.*#$% -^[#$74+H-HS
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L-"#%$ 68 ,=- >#.-7, L$248"#" G-,=(H
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5GAb U42",#7 '(4+)$ T+7J4#$%
2$H ,=- U00-7, (0 U$H 9-",.2#$,5-2.$#$% ;6l-7,#
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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
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Compute 10 modes
P = 1 k
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. . .
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
. . . . . .
)
) )c(
)d( )e(
f
delcuimuoldeha
f oeasybwoss
eni
ter eT
lac eulav 5.0
.
7.0 .1
. .
0.1 0.2
. .
.2
.
TABLE C-A-7.1Approximate Values of Effective
Length Factor, K
Mode 1:
Pcr
= 273.6
K = ! L
EI P
cr
= 2.0
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Mode 2:
Pcr
= 273.6
K = ! L
EI P
cr
= 2.0. . .
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
. . . . . .
)
) )c(
)d( )e(
f
delcuimuoldeha
f oeasybwoss
eni
ter eT
lac eulav 5.0
.
7.0 .1
. .
0.1 0.2
. .
.2
.
TABLE C-A-7.1Approximate Values of Effective
Length Factor, K
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Mode 3:
Pcr
= 1094.5
K = ! L
EI P
cr
= 1.0. . .
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
. . . . . .
)
) )c(
)d( )e(
f
delcuimuoldeha
f oeasybwoss
eni
ter eT
lac eulav 5.0
.
7.0 .1
. .
0.1 0.2
. .
.2
.
TABLE C-A-7.1Approximate Values of Effective
Length Factor, K
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Mode 4:
Pcr
= 1094.5
K = ! L
EI P
cr
= 1.0. . .
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
. . . . . .
)
) )c(
)d( )e(
f
delcuimuoldeha
f oeasybwoss
eni
ter eT
lac eulav 5.0
.
7.0 .1
. .
0.1 0.2
. .
.2
.
TABLE C-A-7.1Approximate Values of Effective
Length Factor, K
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. . .
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( )(
d )
)f (
delkcuBnmuloc
ldehsd
f opahybnwohss
enil
iteohT
la eua 5.
.
7. 0.1
. .
.1 .2
. .
0.2
.
TABLE C-A-7.1Approximate Values of Effective
Length Factor, K
Mode 5:
Pcr
= 2239.2
K = ! L
EI P
cr
= 0.7
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. . .
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
. . . . . .
)
) )c(
)d( )e(
f
delcuimuoldeha
f oeasybwoss
eni
ter eT
lac eulav 5.0
.
7.0 .1
. .
0.1 0.2
. .
.2
.
TABLE C-A-7.1Approximate Values of Effective
Length Factor, K
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. . .
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
. . . . . .
)
) )c(
)d( )e(
f
delcuimuoldeha
f oeasybwoss
eni
ter eT
lac eulav 5.0
.
7.0 .1
. .
0.1 0.2
. .
.2
.
TABLE C-A-7.1Approximate Values of Effective
Length Factor, K
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. . .
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
. . . . . .
)
) )c(
)d( )e(
f
delcuimuoldeha
f oeasybwoss
eni
ter eT
lac eulav 5.0
.
7.0 .1
. .
0.1 0.2
. .
.2
.
TABLE C-A-7.1Approximate Values of Effective
Length Factor, K
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. . .
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( )
d )e
)f (
delkcBnmuloc
lesd
f opahsynwohss
enl
iter ohT
a eua 5.
.
7. 0.1
. .
.1 .2
. .
0.2
.
TABLE C-A-7.1Approximate Values of Effective
Length Factor, K
Mode 9:
Pcr
= 4380
K = ! L
EI P
cr
= 0.5
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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#$"&
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Vary beam sizes w/
I Top Beam
! I Bottom Beam
C 027,(.
! 7.> I(*> T(,,()
> I(*
> T(,,()
AbD
Dbg
I=2$J" ,(c+- ?+2
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5Gmb M27,(." P$W4+-$7#$% ,=-M4-^+.24 T+7J4#$% /,.-$%,= (0
'()*.-""#($ G-)6-."5-2.$#$% ;6l-7,#
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& 8
U+4-.
LP/'
$( " ( [ $( $ .-"" ( [ $( $ .-"
$( " ( [ $ .-"" ( [ $ .-"
U'5P'5
!
!
I=2$J" ,( >2$ I2)2.J#$
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I = 2 $
J " , (
T + 4 - $ ,
L 4 - )
H 2 . 2 ,
T - $ , 4 - 8
F
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& 8
U+4-.
LP/'
$( " ( [ $( $ .-"" ( [ $( $ .-"
$( " ( [ $ .-"" ( [ $ .-"
U'5
P'5
I=2$J" ,( >2$ I2)2.J#$
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5Gjb U00-7,#
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/#H-128" 4-2$#$%X 1-"#H-128" H2.,-Hq -
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!"#$%"&'()+,-'#($&'
"&). /"# 0$1,-2(.3&4$5$',1 6(-,-
7,/'
6")89&
+$:4'
6")89&
;"< =,(9
="''"9 =,(9
>?@A?B
C
D @ A ? B
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!" #$%&' !"#$%&' ()*')+% ,+)" #$%&' ,+)"#$%&' ()*')+%
-*&%&'#" ."&/+0)+% 1&22)*)+') -*&%&'#" ."&/+0)+% 1&22)*)+')
34#5 -6#*%$ 789 34#5 -6#*%$ 789
: ;?@ ;
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5Geb M27,(." P$W4+-$7#$% ,=-
/,.-$%,= (0 M4-^+.24 G-)6-."5-2.$#$% ;6l-7,#
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5Ge! QAe^gj YLBBmZ! : 2 u Abm ,( jAbA 0,b
! M(. -27= : 2X #$
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! !
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M n / M p
! !
L p Lr
I=2$J" ,( >2$ I2)2.J#$
Lb
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5Ggb 52,-.24`I(."#($24 T+7J4#$%
(0 T-2)" 1#,= G()-$, O.2H#-$,5-2.$#$% ;6l-7,#
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5Gg
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5Gg!
!!
#
"
# $
"!"#
!%#
!
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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
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I=2$J" ,( c+- ?+2
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Q($% 2$H >.#
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I#)- 0(. 8(+ ,( ,2J- #, 0(. 2 "*#$@
W24x68 with L = 24 ft. (288 in.)M1 = -1000 in-k
M2 = +1000 in-k
u jnDm J#*`#$u jDD J#*`0,
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!!
!#
!"#
W24x68
Mcr (kip-in) Case 1 Case 2
M1/M2 = -1
M1/M2 = +1
Case 1: Braces at endsCase 2: Braces at ends
and mid-span
Observations :
L =24 ft. (288 in.)
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!!
!#
!"#
W24x68
Mcr (kip-in) Case 1 Case 2
M1/M2 = -1 3,602 12,120
M1/M2 = +1 9,838 27,414
Case 1: Braces at endsCase 2: Braces at ends
and mid-span
Observations :
L =24 ft. (288 in.)
3.36
Mcr increases as L b is reduced
2.73
Mcr increases as moment gradient increases An inflection point is not a brace point!
2.79
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5Gnb T-2) >-"#%$ 68 U42",#7
2$H P$-42",#7 L$248"-"5-2.$#$% ;6l-7,#
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]N.-H#7,#($ #" 2$#"= N=8"#7#",
YACCg ` ABnmZ
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5Gnk U42",#7 -"#%$!
"
"#$%&' ($%&' "#$%&' )$%&'
* + , -
B /&414CAb L44 )-)6-." W16x31, P u = SmbW27x84, W16x31, W18x35, P u= Sjb L44 )-)6-." "2)- "#R-X P u = 200k X )#$b 1-#%=,S
eb G-)6-." "#R-" )28
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W27x84 W16x31 W18x35
100 kip
Case 2: Inelastic Analysis
P u = 101.3 kip Wt = 1.881 kip P u / Wt = 53.84
!"
"#$%&' ($%&' "#$%&' )$%&'
* + , -
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!"#$ !% %$ $& ! " '()*+ ,-*./) '()*+&-0*.1 3-)/+4 56789: 5;789: 0 ! " ?! "#$%&'()*$+ =*>0 ! " ? ,*
(@ AB(0)*C ,5DEF5 ,5DEF5 ,5DEF5 ;G@6F 9@;H5 5@69< I9@G9J@ AB(0)*C
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5Ghb /-7($H`(.H-. U00-7,"Y! `s 2$H ! `tZ U00-7,"
5-2.$#$% ;6l-7,#
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%&''( )'*+,- . /0' /1(' 23 /425+&+'*
P, 12" ,=- 6-", (0 ,#)-"Y*4+%E$ 7=+% ,=- -V+2,#($" 2$H
6-#$% 264- 1#,= ,=- ,264-Z#, 12" ,=- 1(.", (0 ,#)-"
Y6-#$% .-"*($"#64- 0(. .-2448+$H-.",2$H#$% ,=- 6-=2
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A", (.H-.
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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
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!
#
$
%
&
'!
'#
! !(' !(# !() !($ !(* !(% !(+ !(& !(, '
! " # $ % &
( ) )
* + , - . + & " %
/ 0 1
232$
#-./01.21 234567 89:;
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5GCb /,.-$%,= (0 T-2)`'(4+)$"5-2.$#$% ;6l-7,#
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5GC
! QAe^gj YLBBmZX: 2 u Ag 0,b! P$
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!"!!
!"$!
!"%!
!"&!
!"'!
!"(!
!")!
!"!! !"%! !"'! !")! !"*! $"!!
+,-.
/+-0+1%
+2,1+
P / P y
M / M px
P + M major
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!"!!
!"$!
!"%!
!"&!
!"'!
!"(!
!")!
!"!! !"%! !"'! !")! !"*! $"!!
+,-.
/+-0+1%
P / P y
M /M py
P + M minor
5GBb "#%$ 68
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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 $H` ,( A ", (.H-. H.#0," 2" 2$
#$H#72,(. (0 2 "8",-)E" "-$"#,#
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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,+.-
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