STEEL-BEAM-COLUMN_2.xls

Pehitungan Struktur Baja Dengan Microsoft Excel

PERHITUNGAN BALOK KOLOM (BEAM COLUMN ) PADA ELEMEN STRUKTUR RAFTER TANPA ANPA PENGAKU BADAN *+,2011 : M& oer !lha#

A. DATA BAHAN

f 5 = f r = E= υ =

T&-a-a l&l&/ aa 'iel( stress T&-a-a 6i6a resi(ual stress Mo8l86 &la6'i9 aa #o(ulus of elasticit'   A-9a Poi66o Poisson)s ratio

240 70 200000 0.3

MPa MPa MPa

B. DATA PROFIL BAJA Profil :

' f '(

/ /2

/'

r

/1 0f

B&ra' :

[C]2011 : M!

Balok "olo# $Bea# Colu#n%

F 400.200.!.13 /' = 400 f = 200 '( = ! 'f = 13 r= 1# A = !410 ; = 237000000 5 = 17400000 r ; = 1#! r 5 = 4$.4 S; = 11%0000 S5 = 174000 (= #47

"" "" "" "" "" ""2 ""4 ""4 "" "" ""3 ""3 N)"

1


BEAM +
C. DATA BALOK KOLOM (RAFTER)

L; = L5 = M8 = M A = MB = M+ = N8 = 8 = φ = φ = φf =

12000 4000 %$000000 !2000000 %$000000 !1000000 42$000 2$#000 0.!$ 0.%0 0.7$

"" "" N"" N"" N"" N"" N N

G = E ) * 2  1 > υ  , = /1 = 'f > r = /2 = /' @ 2  /1 = / = /' @ 'f = ? = Σ *   '3)3 , = 2  1)3   f  'f 3 > 1)3  /' @ 2  ' f   '(3 = ( = 5  /2 ) 4 = C1 = π ) S;  * E  G  ?  A ) 2 , = C2 = 4  * S; ) G  ? ,2  ( ) 5 = ; = '(  /'2 ) 4 >  f @ '(    /' @ 'f   'f = 5 = 'f  f 2 ) 2 >  /' @ 2  'f   '(2 ) 4 =

7#%23 2%.00 342.00 3!7.00 3$#7#2.7 #.$1$E>11 12#!2.% 0.0002!1# 12!$%$2.0 2#$%!4.0

MPa "" "" "" ""4 ""# MPa ""2)N2 ""3 ""3

Paa- &l&"& '/.6. ; Paa- &l&"& '/.6. 5  ara9 898-a la'&ral  Mo"& "a96i"8" a9ia' &a '&rfa9'or '&rfa9'or Mo"& aa 1)4 &'a- Mo"& i '&-a/ &'a- Mo"& aa 3)4 &'a- Ga5a a96ial a9ia' &a '&rfa9'or Ga5a -&6&r a9ia' &a '&rfa9'or Fa9'or r&896i 9&98a'a 8'89 a96ial '&9a Fa9'or r&896i 9&98a'a 8'89 l&'8r Fa9'or r&896i 9&98a'a 8'89 -&6&r

D. SECTION PROPERTIES

G = "o8l86 -&6&r ? = Ko6'a'a 8'ir 'or6i ( = 9o6'a'a 8'ir l&-98- C1 = 9o&fi6i& "o"& '&989 'or6i la'&ral @ 1 C2 = 9o&fi6i& "o"& '&989 'or6i la'&ral @ 2 ; = "o8l86 &a"a- la6'i6 '/. 6. ;

[C]2011 : M!


'f '(

/ /2

/'

r

/1 0f

2


BEAM +

L; = L5 = M8 = M A = MB = M+ = N8 = 8 = φ = φ = φf =

12000 4000 %$000000 !2000000 %$000000 !1000000 42$000 2$#000 0.!$ 0.%0 0.7$

"" "" N"" N"" N"" N"" N N

G = E ) * 2  1 > υ  , = /1 = 'f > r = /2 = /' @ 2  /1 = / = /' @ 'f = ? = Σ *   '3)3 , = 2  1)3   f  'f 3 > 1)3  /' @ 2  ' f   '(3 = ( = 5  /2 ) 4 = C1 = π ) S;  * E  G  ?  A ) 2 , = C2 = 4  * S; ) G  ? ,2  ( ) 5 = ; = '(  /'2 ) 4 >  f @ '(    /' @ 'f   'f = 5 = 'f  f 2 ) 2 >  /' @ 2  'f   '(2 ) 4 =

7#%23 2%.00 342.00 3!7.00 3$#7#2.7 #.$1$E>11 12#!2.% 0.0002!1# 12!$%$2.0 2#$%!4.0

MPa "" "" "" ""4 ""# MPa ""2)N2 ""3 ""3

Paa- &l&"& '/.6. ; Paa- &l&"& '/.6. 5  ara9 898-a la'&ral  Mo"& "a96i"8" a9ia' &a '&rfa9'or '&rfa9'or Mo"& aa 1)4 &'a- Mo"& i '&-a/ &'a- Mo"& aa 3)4 &'a- Ga5a a96ial a9ia' &a '&rfa9'or Ga5a -&6&r a9ia' &a '&rfa9'or Fa9'or r&896i 9&98a'a 8'89 a96ial '&9a Fa9'or r&896i 9&98a'a 8'89 l&'8r Fa9'or r&896i 9&98a'a 8'89 -&6&r


G = "o8l86 -&6&r ? = Ko6'a'a 8'ir 'or6i ( = 9o6'a'a 8'ir l&-98- C1 = 9o&fi6i& "o"& '&989 'or6i la'&ral @ 1 C2 = 9o&fi6i& "o"& '&989 'or6i la'&ral @ 2 ; = "o8l86 &a"a- la6'i6 '/. 6. ;

[C]2011 : M!


'f '(

/ /2

/'

r

/1 0f

2


5 = "o8l86 &a"a- la6'i6 '/. 6. 5 E. PERHITUNGAN KEKUATAN 1. MOMEN NOMINAL PENGARUH LOCAL BUCKLING

λ = f ) 'f = K&la-6i-a &a"a- 6a5a Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act 

1$.3!$

λ = 170 ) f 5 =

10.%73

Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non+co#*act  Mo"& la6'i6 Mo"& a'a6 '&989 Mo"& o"ial &a"a- 8'89 : a. P&a"a- compact : : →

. P&a"a- non-compact : →

. P&a"a- langsing : →

λ

λr = 370 )  f 5 @ f r  = 2!.37! M = f 5  ; = 30!#2!4!0 N"" Mr = S;   f 5 @ f r  = 202300000 N"" λ ≤ λ M = M λ  λ ≤ λr M = M @ M @ Mr    λ @ λ )  λr @ λ λ H λr M = Mr   λr ) λ 2

λ

λ < a B&ra6ar9a ilai 9&la-6i-a 6a5a "a9a '&r"a689 &a"aMo"& o"ial &a"a- i/i'8- 6&a-ai &ri98' : >

λr non-compact

M = M = @ M = M @ M @ Mr    λ @ λ )  λr @ λ = 2!1#7%1%1 non+co#*act : M = Mr   λr ) λ 2 = @ langsing : M = 2!1#7%1%1 Mo"& o"ial 8'89 &a"a- : non-compact co#*act :

[C]2011 : M!


N"" N"" N"" N""

3


2. MOMEN NOMINAL BALOK PLAT BERDINDING PENUH

K&la-6i-a &a"a- aa U'89 &a"a- 5a- "&"85ai 898ra : "a9a "o"& o"ial 9o"o& 6'r89'8r

λ = / ) '( = / ) '( harus

>

4!.37$

λr

i/i'8- &-a r8"86 :

M = K-  S  f r K- = 1 @ * a r ) 1200 > 300  ar  ,  * / ) ' ( @ 2$$0 ) f r , &-a λG ≤ λ f r = f 5 a. U'89 9&la-6i-a : ≤   G r . U'89 9&la-6i-a : f r = +  f 5  * 1 @  λG @ λ  )  2   λr @ λ   , λG H λr f r = f    λr ) λG 2 . U'89 9&la-6i-a : ≤ f f  = +  f 5 ) 2 U'89 '&989 'or6i la'&ral : 5 f  = f 5 ) 2 U'89 '&989 lo9al : →

→

→

≤ ≤

f 5 f 5

→ →

Ko&fi6i& "o"& '&989 'or6i la'&ral

+ = 12.$  M8 )  2.$  M8 > 3  M A > 4  MB > 3  M+  = + = → ia"il

1.07 1.07

< 2.3

P&rai-a l8a6 la' aa '&r/aa l8a6 la' 6a5a

ar = /  '( )  f  'f  = 1 = 5 ) 2 @ 1)12  ' (3  1)3  /2 = A1 = A ) 2 @ 1)3  ' (  /2 =

1.1%1 Mo"& i&r6ia !#%$13# ""4 L8a6 &a"a- 32%3 ""2 ?ari@ari -ira6i a&ra/ la' 6a5a i'a"a/ 6&&r'i-a a-ia la' aa 5a- "&-ala"i r 1 =  1 ) A1  = '&9a $1 "" 2.1. Mom! !om"!#$ %&'##&#! *+ *o&" $#*&#$

L = L5 = ?ara9 a'ara &-&9a- la'&ral λG = L ) r 1 = A-9a 9&la-6i-a Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act 

4000 77.!43

λ = 1.7#   E ) f 5  =

$0.!07

""

Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non+co#*act 

λr = 4.40   E ) f 5  =

[C]2011 : M!


127.017

4


T&-a-a a8a 8'89 "o"& 9ri'i6 '&989 'or6i la'&ral

f 

λG

<

f  = +  f 5 ) 2 = f  = "a9a ia"il

f 5

λG a T&-a-a 9ri'i6 &a"a- i/i'8- 6&a-ai &ri98' : >

λ

12!.7! 12!.7!

MPa MPa

λr

<

λG ≤ λ λ ≤ λG λG H λr

f r = f 5 = ≤ λ f r = + f 5 * 1 @  λG @ λ )  2 λr @ λ  , = r f r = f    λr ) λG 2 = f r = f r < f 5 f r = "a9a ia"il S = S; = Mo8l86 &a"a- &la6'i6

@ 211.!! @ 211.!! 211.!! 11%0000

MPa MPa MPa MPa MPa ""3

Ko&fi6i& alo9 la' &rii- &8/

K- = 1 @ * a r ) 1200 > 300  ar  ,  * / ) ' ( @ 2$$0 ) f r , = 1.0%7 M = K-  S  f r = 27#$!!%7% N"" Mo"& o"ial &a"a- 2.2. Mom! !om"!#$ %&'##&#! $o,#$ %+,$"!- #'# #/#

Fa9'or 9&la-6i-a la' aa

9& = 4 )  / ) '(  = 9& = ia"il λG = f )  2  'f  =

K&la-6i-a &a"a- 6a5a Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act 

λ = 0.3! 

 E ) f 5  =

0.$7$ 0.$7$ 7.#%

< 0.3

10.%7


λr = 1.3$   9&  E ) f 5  = f  = f 5 ) 2 = T&-a-a a8a 8'89 "o"& 9ri'i6 '&989 lo9al λG λ λG < < a B&ra6ar9a ilai 9&la-6i-a 6a5a "a9a '&r"a689 &a"aT&-a-a 9ri'i6 &a"a- i/i'8- 6&a-ai &ri98' :


f r = f 5 = ≤ λ f r = + f 5 * 1 @  λG @ λ )  2 λr @ λ  , = r f r = f    λr ) λG 2 = f r = T&-a-a 9ri'i6 &a"a- f r < f 5 f r = "a9a ia"il

[C]2011 : M!


2%.$$ 120.00

MPa

λr compact

240.00 @ @ 240.00 240.00

MPa MPa MPa MPa MPa

$


S = S; =

Mo8l86 &a"a- &la6'i6 Ko&fi6i& alo9 la' &rii- &8/

11%0000

""3

K- = 1 @ * a r ) 1200 > 300  ar  ,  * / ) ' ( @ 2$$0 ) f r , = 1.0!% M = K-  S  f r = 310%!2774 N"" Mo"& o"ial &a"a- 3. MOMEN NOMINAL PENGARUH LAE!AL BUCKLING

Mo"& o"ial 9o"o& 6'r89'8r &-a &-ar8/ '&989 la'&ral 8'89 : L ≤ L a. B&'a- !' :

M = M = f 5  ; L  L ≤ Lr . B&'a- '#!- : M = +  * Mr >  M @ Mr    L r @ L  )  L r @ L  , L H Lr . B&'a- #!#!- : M = +  π ) L * E  5  G  ? >  π  E ) L  2  5  ( , →

→

≤ M

→

≤ M

Paa- &'a- "a96i"8" alo9 5a- "a"8 "&a/a "o"& la6'i6

L = 1.7#  r 5   E ) f 5  = f L = f 5 @ f r =

2307 170 Paa- &'a- "ii"8" alo9 5a- 'a/aa5a i'&'89a ol&/ "o"& 9ri'i6 '&989 Lr = r 5  C1 ) f L  * 1 >  1 > C2  f L2  , = 'or6i la'&ral #7%4 Ko&fi6i& "o"& '&989 'or6i la'&ral + = 12.$  M8 )  2.$M8 > 3M A > 4MB > 3M+  = 1.07 M = f 5  ; = 30!#2!4!0 Mo"& la6'i6 Mr = S;   f 5 @ f r  = 202300000 Mo"& a'a6 '&989 L = L5 = Paa- &'a- '/.6. 5 ara9 898-a la'&ral 4000 L Lr > < L a L

"" MPa ""

N"" N"" ""

T&r"a689 9a'&-ori : bentang sedang Mo"& o"ial i/i'8- 6&a-ai &ri98' :

M = M = f 5  ; = @ N"" M = +  * Mr >  M @ Mr    L r @ L  )  L r @ L  , = 2!!1$$#!1 N"" M = +  π ) L * E  5  G  ? >  π  E ) L  2  5  ( , = @ N"" M = 2!!1$$#!1 N"" Mo"& o"ial 8'89 9a'&-ori : bentang sedang M M < M = 2!!1$$#!1 N"" → Mo"& o"ial 5a- i-8a9a

[C]2011 : M!


#


4. TAHANAN MOMEN LENTUR

a. Mo"& o"ial &ra6ar9a &-ar8/ local ,uckling  . Mo"& o"ial alo9 la' &rii- &8/ : Mo"& o"ial &ra6ar9a '&989 'or6i la'&ral Mo"& o"ial &ra6ar9a local ,uckling . 6a5a . Mo"& o"ial &ra6ar9a &-ar8/ lateral ,uckling  Mo"& o"ial '&r9&il 5a- "&&'89a Ta/aa "o"& l&'8r

M = 30!#2!4!0 N"" M = M = M = M = φ  M =

27#$!!%7% 310%!2774 2!!1$$#!1 27#$!!%7% 24!%300!1

N"" N"" N"" N"" N""

5. TAHANAN AKSIAL TEKAN

Fa9'or '&989 9olo" i/i'8- &-a r8"86 6&a-ai &ri98' : a. U'89 ilai λ ≤ 0.2$ "a9a '&r"a689 9olo" !' : →

ω = 1

. U'89 ilai 0.2$  λ ≤ 1.20 "a9a '&r"a689 9olo" '#!- : →

ω = 1.43 )  1.# @ 0.#7  λ 

. U'89 ilai λ H 1.20 "a9a '&r"a689 9olo" $#!-"!- : →

ω = 1.2$  λ2

Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 ; Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 5 Paa- '&989 &f&9'if i/i'8- 6&a-ai &ri98' : Paa- 9olo" '&r/aa 68"8 ; : Paa- '&989 &f&9'if '&r/aa 68"8 ; Paa- 9olo" '&r/aa 68"8 5 : Paa- '&989 &f&9'if '&r/aa 68"8 5

9; = 95 = L; = L9; = 9;  L; = L5 = L95 = 95  L5 =

1.00 1.00 12000 12000 4000 4000

"" "" "" ""

P#&#m*& $#!-"!-#! *&6#'# +m%+ 7 8

[C]2011 : M!


7


λ; = 1 )π  L9; ) r ;   f 5 ) E  =

0.7!7#

P#&#m*& $#!-"!-#! *&6#'# +m%+ / 8

λ5 = 1 ) π  L95 ) r 5   f 5 ) E  =

0.%71$

M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ 7 8

λ; = U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 ; ω = a. Kolo" *en(ek : ω = 1.43 )  1.# @ 0.#7  λ  = . Kolo" se(ang : ω = 1.2$  λ2 = . Kolo" langsing : ω; = Fa9'or '&989 '/.6. ;

0.7!7# @ 1.333# @ 1.333#

M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ / 8

λ5 = U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 5 ω = a. Kolo" *en(ek : ω = 1.43 )  1.# @ 0.#7  λ  = . Kolo" se(ang : ω = 1.2$  λ2 = . Kolo" langsing : ω5 = Fa9'or '&989 '/.6. 5 f r; = f 5 ) ω; = T&-a-a '&989 '/.6. ; f r5 = f 5 ) ω5 = T&-a-a '&989 '/.6. 5

0.%71$ @ 1.$0#7 @ 1.$0#7 17%.%## 1$%.2!!

MPa MPa

T#6#!#! #"#$ *#! 8

Ta/aa a96ial '&9a o"ial '/.6. ; Ta/aa a96ial '&9a o"ial '/.6. 5 Ta/aa a96ial '&9a o"ial '&r9&il Ta/aa a96ial '&9a

N; = A  f r; = 1$13$17 N N5 = A  f r5 = 133%#13 N N = 133%#13 N φ  N = 113!#71 N

. INTERAKSI AKSIAL TEKAN DAN MOMEN LENTUR

N8 = 42$000 Ga5a a96ial a9ia' &a '&rfa9'or M8 = %$000000 Mo"& a9ia' &a '&rfa9'or φ  N = 113!#71 Ta/aa a96ial '&9a φ  M = 24!%300!1 Ta/aa "o"& l&'8r El&"& 5a- "&a/a -a5a a96ial '&9a a "o"& l&'8r /ar86 "&"&8/i

[C]2011 : M!


N N"" N N""

!


&r6a"aa i'&ra96i a96ial '&9a a "o"& l&'8r 6 : N8 )  φ N  H 0.20 U'89 ilai

N8 )  φ N  > ! ) %  * M 8 )  φ  M  , N8 )  φ N  ≤ 0.20 N8 )  2  φ N  > * M8 )  φ  M  ,

→

U'89 ilai →

N8 )  φ N  =

0.3732

≤ 1.0 ≤ 1.0

>

0.2

N8 )  φ N  > ! ) %  * M 8 )  φ  M  , = N8 )  2  φ N  > * M8 )  φ  M  , =

0.712$ @ 0.712$

Nilai i'&ra96i a96ial '&9a a "o"& l&'8r = < 0.712$ 1.0 AMAN (OK) . TAHANAN GESER

Ko'rol 'a/aa -&6&r o"ial la' aa 'aa &-a98 : K&'&ala la' aa 'aa &-a98 /ar86 "&"&8/i 65ara'

/2 ) '( 42.7$

#.3#  <

E ) f 5 

1!3.#0

Ga5a -&6&r a9ia' &a '&rfa9'or L8a6 &a"a- aa Ta/aa -a5a -&6&r o"ial Ta/aa -a5a -&6&r 8 S5ara' 5- /ar86 i&8/i : 2$#000

"lat badan memenuhi s#arat $OK%

8 = A( = '(  /' =  = 0.#0  f 5  A( = φf   = φf   

8 )  φf    =

34$#00 0.7$00

2$#000 3200 4#0!00 34$#00

N ""2 N N

AMAN (OK)

< 1.0 (OK)

:. INTERAKSI GESER DAN LENTUR

El&"& 5a- "&"i98l 9o"ia6i -&6&r a l&'8r /ar86 ila989a 9o'rol 6. : S5ara' 5a- /ar86 i&8/i 8'89 i'&ra96i -&6&r a l&'8r : M8 )  φ M  > 0.#2$  8 )  φf    1.37$

[C]2011 : M!


%


M8 )  φ

M8 )  φ  M  = 8 )  φf    = M  > 0.#2$  8 )  φf    = <

[C]2011 : M!


0.3!1# 0.7407 0.!44# 1.35 AMAN (OK)

10

Perhitungan Struktur Baja Dengan Microsoft Excel

PERHITUNGAN BALOK KOLOM (BEAM COLUMN ) PADA ELEMEN STRUKTUR RAFTER DENGAN PENGAKU BADAN *+,2011 : M& oer !lha#

A. DATA BAHAN

f 5 = f r = E= υ =

T&-a-a l&l&/ aa 'iel( stress T&-a-a 6i6a resi(ual stress Mo8l86 &la6'i9 aa #o(ulus of elasticit'  A-9a Poi66o Poisson)s ratio

240 70 200000 0.3

MPa MPa MPa

B. DATA PROFIL BAJA Profil :

' f '(

/ /2

/'

r

/1 0f

[C-2011: M!


F 400.200.!.13 /' = 400 f = 200 '( = ! 'f = 13 r= 1# A = !410 ; = 237000000 5 = 17400000 r ; = 1#! r 5 = 4$.4 S; = 11%0000 S5 = 174000

"" "" "" "" "" ""2 ""4 ""4 "" "" ""3 ""3

11


BEAM +

L; = L5 = a= '6 = M8 = M A = MB = M+ = N8 = 8 = φ = φ = φf =

12000 1$00 1000 # 12#000000 122000000 14#000000 11$000000 42$000 2$#000 0.!$ 0.%0 0.7$

"" "" "" "" N"" N"" N"" N"" N N

G = E ) *21 > υ, = /1 = 'f > r = /2 = /' @ 2  /1 = / = /' @ 'f = ? = Σ *   '3)3 , = 2  1)3  f  'f 3 > 1)3  /' @ 2  'f   '(3 = ( = 5  /2 ) 4 = C1 = π ) S;  * E  G  ?  A ) 2 , = C2 = 4  * S; ) G  ? ,2  ( ) 5 = ; = '(  /'2 ) 4 >  f @ '(    /' @ 'f   'f = 5 = 'f  f 2 ) 2 >  /' @ 2  'f   '(2 ) 4 =

7#%23 2%.00 342.00 3!7.00 3$#7#2.7 #.$1$E>11 12#!2.% 0.0002!1# 12!$%$2.0 2#$%!4.0

MPa "" "" "" ""4 ""# MPa ""2)N2 ""3 ""3

Paa- &l&"& '/.6. ; Paa- &l&"& '/.6. 5 ara9 898-a la'&ral ?ara9 a'ara &-a98 I&r'i9al aa aa T&al la' &-a98 I&r'i9al aa aa Mo"& "a96i"8" a9ia' &a '&rfa9'or Mo"& aa 1)4 &'a- Mo"& i '&-a/ &'a- Mo"& aa 3)4 &'a- Ga5a a96ial a9ia' &a '&rfa9'or Ga5a -&6&r a9ia' &a '&rfa9'or Fa9'or r&896i 9&98a'a 8'89 a96ial '&9a Fa9'or r&896i 9&98a'a 8'89 l&'8r Fa9'or r&896i 9&98a'a 8'89 -&6&r


G = "o8l86 -&6&r ? = Ko6'a'a 8'ir 'or6i ( = 9o6'a'a 8'ir l&-98- / = 'i--i &r6i/ aa ; = "o8l86 &a"a- la6'i6 '/. 6. ; 5 = "o8l86 &a"a- la6'i6 '/. 6. 5

[C-2011: M!


'f '(

/ /2

/'

r

/1 0f

12


C1 = 9o&fi6i& "o"& '&989 'or6i la'&ral C2 = 9o&fi6i& "o"& '&989 'or6i la'&ral E. PERHITUNGAN KEKUATAN S5ara' 5- /ar86 i&8/i 8'89 alo9 &-a &-a98 "a9a ilai : < a ) / = 2.$!4 3.00

a ) / ≤ 3.0

berla&u rumus balo& dengan penga&u $OK%

K&'&ala la' aa &-a &-a98 I&r'i9al 'aa &-a98 "&"aa- /ar86 "&"&@ / ) '( 7.07   E ) f 5  8/i :  4!.37$ 204.0% tebal plat badan memenuhi $OK% 1. MOMEN NOMINAL PENGARUH LOCAL BUCKLING 1.1. P!-#&+6 *+ $o#$ (local buc&ling% #'# #/#

λ = f ) 'f = K&la-6i-a &a"a- 6a5a Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act 

1$.3!$

λ = $00 ) f 5 =

32.27$

Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non+co#*act  Mo"& la6'i6 Mo"& a'a6 '&989 Mo"& o"ial &a"a- 8'89 : a. P&a"a- compact  →

. P&a"a- non-compact  →

. P&a"a- langsing  →

λ

λr = #2$ ) f 5 = 40.344 M = f 5  ; = 30!#2!4!0 N"" Mr = S;   f 5 @ f r  = 202300000 N"" λ ≤ λ M = M λ  λ ≤ λr M = M @ M @ Mr    λ @ λ )  λr @ λ λ H λr M = Mr   λr ) λ 2

λ

λ < a B&ra6ar9a ilai 9&la-6i-a 6a5a "a9a '&r"a689 &a"aMo"& o"ial &a"a- i/i'8- 6&a-ai &ri98' : <

compact

M = M = 30!#2!4!0 N""

co#*act :

[C-2011: M!

λr


13


M = M @ M @ Mr    λ @ λ )  λr @ λ = @ N"" M = Mr   λr ) λ 2 = @ N"" langsing : M = 30!#2!4!0 N"" compact Mo"& o"ial 8'89 &a"a- : non+co#*act :

1.2. P!-#&+6 *+ $o#$ (local buc&ling% #'# %#'#!

λ = / ) '( = K&la-6i-a &a"a- aa Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act 

4!.37$

λ = 1#!0 ) f 5 =

10!.444


λ

λr = 2$$0 ) f 5 = λ <

λ

a B&ra6ar9a ilai 9&la-6i-a aa "a9a '&r"a689 &a"aMo"& o"ial &a"a- i/i'8- 6&a-ai &ri98' : <

1#4.#02

λr compact

M = M = 30!#2!4!0 N"" M = M @ M @ Mr    λ @ λ )  λr @ λ = @ N"" non+co#*act : 2 M = Mr   λr ) λ  = @ N"" langsing : M = 30!#2!4!0 N"" Mo"& o"ial 8'89 &a"a- : compact co#*act :

2. MOMEN NOMINAL BALOK PLAT BERDINDING PENUH

λ = / ) '( = 4!.37$ λr / ) '( H

K&la-6i-a &a"a- aa U'89 &a"a- 5a- "&"85ai 898ra :

4!.37$ "a9a "o"& o"ial 9o"o& 6'r89'8r

harus

40.344 i/i'8- &-a r8"86 : >

M = K-  S  f r K- = 1 @ * a r ) 1200 > 300  ar  ,  * / ) ' ( @ 2$$0 ) f r , &-a λG ≤ λ f r = f 5 a. U'89 9&la-6i-a :   G ≤ r . U'89 9&la-6i-a : f r = +  f 5  * 1 @  λG @ λ  )  2   λr @ λ   , λG H λr f r = f    λr ) λG 2 . U'89 9&la-6i-a : ≤ f f  = +  f 5 ) 2 U'89 '&989 'or6i la'&ral : 5 f  = f 5 ) 2 U'89 '&989 lo9al : →

→

→

≤ ≤

f 5 f 5

→ →

Ko&fi6i& "o"& '&989 'or6i la'&ral

+ = 12.$  M8 )  2.$M8 > 3M A > 4MB > 3M+  =

[C-2011: M!


0.%!

< 2.3

14


ia"il P&rai-a l8a6 la' aa '&r/aa l8a6 la' 6a5a

+ =

0.%!

ar = /  '( )  f  'f  = 1 = 5 ) 2 @ 1)12  ' (3  1)3  /2 = A1 = A ) 2 @ 1)3  ' (  /2 =

1.1%1 Mo"& i&r6ia !#%$13# ""4 L8a6 &a"a- 32%3 ""2 ?ari@ari -ira6i a&ra/ la' 6a5a i'a"a/ 6&&r'i-a a-ia la' aa 5a- "&-ala"i r 1 =  1 ) A1  = '&9a $1 "" 2.1. Mom! !om"!#$ %&'##&#! *+ *o&" $#*&#$

L = L5 = ?ara9 a'ara &-&9a- la'&ral λG = L ) r 1 = A-9a 9&la-6i-a Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act 

1$00 2%.1%1

λ = 1.7#   E ) f 5  =

$0.!07

""


λr = 4.40   E ) f 5  =

127.017

T&-a-a a8a 8'89 "o"& 9ri'i6 '&989 'or6i la'&ral

f 

λG

<

f 5

λ

<

f  = +  f 5 ) 2 = f  = "a9a ia"il λG < a

117.3% 117.3%

MPa MPa

λr

T&-a-a 9ri'i6 &a"a- i/i'8- 6&a-ai &ri98' :


f r = f 5 = ≤ λ f r = + f 5* 1 @  λG @ λ )  2 λr @ λ , = r f r = f    λr ) λG 2 = f r = T&-a-a 9ri'i6 &a"a- f r < f 5 f r = "a9a ia"il S = S; = Mo8l86 &a"a- &la6'i6

240.00 @ @ 240.00 240.00 11%0000


Ko&fi6i& alo9 la' &rii- &8/

K- = 1 @ * a r ) 1200 > 300  ar  ,  * / ) ' ( @ 2$$0 ) f r , = 1.0!% M = K-  S  f r = 310%!2774 N"" Mo"& o"ial &a"a- 2.2. Mom! !om"!#$ %&'##&#! local buc&ling #'# #/#

K&la-6i-a &a"a- 6a5a

[C-2011: M!

λG = f )  2  'f  =


7.#%

1$


9& = 4 )  / ) '(  = 9& = ia"il

Fa9'or 9&la-6i-a la' aa

0.$7$ 0.$7$

< 0.3

Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act 

λ = 0.3! 

 E ) f 5  =

10.%7


λr = 1.3$   9&  E ) f 5  = f  = f 5 ) 2 = T&-a-a a8a 8'89 "o"& 9ri'i6 '&989 lo9al λG λ λG < < a

2%.$$ 120.00

MPa

λr

T&-a-a 9ri'i6 &a"a- i/i'8- 6&a-ai &ri98' :


f r = f 5 = ≤ λ f r = + f 5* 1 @  λG @ λ )  2 λr @ λ , = r f r = f    λr ) λG 2 = f r = T&-a-a 9ri'i6 &a"a- f r < f 5 f r = "a9a ia"il S = S; = Mo8l86 &a"a- &la6'i6

240.00 @ @ 240.00 240.00 11%0000


Ko&fi6i& alo9 la' &rii- &8/

K- = 1 @ * a r ) 1200 > 300  ar  ,  * / ) ' ( @ 2$$0 ) f r , = 1.0!% M = K-  S  f r = 310%!2774 N"" Mo"& o"ial &a"a- 3. MOMEN NOMINAL PENGARUH LAE!AL BUCKLING

Mo"& o"ial 9o"o& 6'r89'8r &-a &-ar8/ '&989 la'&ral 8'89 : L ≤ L a. B&'a- !' :

M = M = f 5  ; L ≤ L ≤ Lr . B&'a- '#!- : M = +  * Mr >  M @ Mr    L r @ L  )  L r @ L  , L H Lr . B&'a- #!#!- : M = +  π ) L * E  5  G  ? >  π  E ) L  2  5  ( , →

→

≤ M

→

≤ M

Paa- &'a- "a96i"8" alo9 5a- "a"8 "&a/a "o"& la6'i6

L = 1.7#  r 5   E ) f 5  = f L = f 5 @ f r = T&-a-a l&l&/ i98ra-i '&-a-a 6i6a

2307 "" 170 MPa Paa- &'a- "ii"8" alo9 5a- 'a/aa5a i'&'89a ol&/ "o"& 9ri'i6 '&989 Lr = r 5  C1 ) f L  * 1 >  1 > C2  f L2  , = 'or6i la'&ral #7%4 "" Ko&fi6i& "o"& '&989 'or6i la'&ral

[C-2011: M!


1#


+ = 12.$  M8 )  2.$M8 > 3M A > 4MB > 3M+  = 0.%! M = f 5  ; = 30!#2!4!0 N"" Mo"& la6'i6 Mr = S;   f 5 @ f r  = 202300000 N"" Mo"& a'a6 '&989 L = L5 = Paa- &'a- '/.6. 5 ara9 898-a la'&ral 1$00 "" L Lr < < L a L T&r"a689 9a'&-ori : bentang pende& Mo"& o"ial i/i'8- 6&a-ai &ri98' :

M = M = f 5  ; = 30!#2!4!0 N"" M = +  * Mr >  M @ Mr    L r @ L  )  L r @ L  , = @ N"" 2 M = +  π ) L * E  5  G  ? >  π  E ) L   5  ( , = @ N"" M = 30!#2!4!0 N"" Mo"& o"ial alo9 8'89 9a'&-ori : bentang pende& M M H M = 30!#2!4!0 N"" Mo"& o"ial 5a- i-8a9a 4. MOMEN NOMINAL PENGARUH LOCAL BUKLING PADA BADAN

K&la-6i-a &a"a- aa Ga5a a96ial l&l&/

λ = / ) '( = N5 = A  f 5 = N8 )  φ  N5  =

4!.37$ 201!400 0.234

N N

a. Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- compact : N8 )  φ  N5  ≤ 0.12$ U'89 ilai →

U'89 ilai →

λ = 1#!0 ) f 5  *  1 @ 2.7$  N 8 )  φ  N5  , N8 )  φ  N5  H 0.12$ λ = $00 ) f 5  *  2.33 @ N8 )  φ  N5  , ≥ ##$ )

f 5

. Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non-compact : →

λr = 2$$0 )

f 5  *  1 @ 0.74  N 8 )  φ  N5  ,

N8 )  φ  N5  > λ = 1#!0 ) f 5  *  1 @ 2.7$  N 8 )  φ  N5  , = λ = $00 ) f 5  *  2.33 @ N 8 )  φ  N5  , = λ = ##$ ) f 5 = λ = Ba'a6 9&la-6i-a "a96i"8" &a"a- co#*act  U'89 ilai :

0.125

@ #7.#4% 42.%2# #7.#4%

Ba'a6 9&la-6i-a "a96i"8" &a"a- non+co#*act 

λr = 2$$0 )

[C-2011: M!

f 5  *  1 @ 0.74  N8 )  φ  N5  , =


13#.104

17


λ

λ

λ < a B&ra6ar9a ilai 9&la-6i-a aa "a9a '&r"a689 &a"aMo"& o"ial i/i'8- 6&a-ai &ri98' : <

λr compact

M = M = 30!#2!4!0 N"" M = M @ M @ Mr    λ @ λ )  λr @ λ = @ N"" non+co#*act : M = Mr   λr ) λ 2 = langsing : @ N"" M = 30!#2!4!0 N"" Mo"& o"ial 8'89 &a"a- : compact co#*act :


a. Mo"& o"ial &-ar8/ local ,uckling : Mo"& o"ial &-ar8/ local ,uckling aa 6a5a Mo"& o"ial &-ar8/ local ,uckling aa aa . Mo"& o"ial alo9 la' &rii- &8/ : Mo"& o"ial &-ar8/ '&989 'or6i la'&ral Mo"& o"ial &-ar8/ local ,uckling . 6a5a . Mo"& o"ial &-ar8/ lateral ,uckling  . Mo"& o"ial &-ar8/ local ,uckling aa aa Mo"& o"ial '&r9&il 5a- "&&'89a Ta/aa "o"& l&'8r

M = 30!#2!4!0 N"" M = 30!#2!4!0 N"" M = M = M = M = M = φ  M =

310%!2774 310%!2774 30!#2!4!0 30!#2!4!0 30!#2!4!0 2777#$#32

N"" N"" N"" N"" N"" N""

. TAHANAN AKSIAL TEKAN

Fa9'or '&989 9olo" i/i'8- &-a r8"86 6&a-ai &ri98' : a. U'89 ilai λ ≤ 0.2$ "a9a '&r"a689 9olo" !' : →

ω = 1

. U'89 ilai 0.2$  λ ≤ 1.20 "a9a '&r"a689 9olo" '#!- : →

ω = 1.43 )  1.# @ 0.#7  λ 

. U'89 ilai λ H 1.20 "a9a '&r"a689 9olo" $#!-"!- : →

ω = 1.2$  λ2

Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 ; Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 5 Paa- '&989 &f&9'if i/i'8- 6&a-ai &ri98' : Paa- 9olo" '&r/aa 68"8 ; :

[C-2011: M!


9; = 95 =

1.00 1.00

L; =

12000

""

1!


L9; = 9;  L; = L5 = L95 = 95  L5 =

12000 1$00 1$00

λ; = 1 )π  L9; ) r ;   f 5 ) E  =

0.7!7#

Paa- '&989 &f&9'if '&r/aa 68"8 ; Paa- 9olo" '&r/aa 68"8 5 : Paa- '&989 &f&9'if '&r/aa 68"8 5

"" "" ""

P#&#m*& $#!-"!-#! *&6#'# +m%+ 7 8

P#&#m*& $#!-"!-#! *&6#'# +m%+ / 8

λ5 = 1 ) π  L95 ) r 5   f 5 ) E  =

0.3#43

M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ 7 8

λ; = U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 ; ω = a. Kolo" *en(ek : ω = 1.43 )  1.# @ 0.#7  λ  = . Kolo" se(ang : ω = 1.2$  λ2 = . Kolo" langsing : ω; = Fa9'or '&989 '/.6. ;

0.7!7# @ 1.333# @ 1.333#

M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ / 8

λ5 = U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 5 ω = a. Kolo" *en(ek : ω = 1.43 )  1.# @ 0.#7  λ  = . Kolo" se(ang : ω = 1.2$  λ2 = . Kolo" langsing : ω5 = Fa9'or '&989 '/.6. 5 f r; = f 5 ) ω; = T&-a-a '&989 '/.6. ; f r5 = f 5 ) ω5 = T&-a-a '&989 '/.6. 5

0.3#43 @ 1.0$4# @ 1.0$4# 17%.%## 227.$#$

MPa MPa

1$13$17 1%13!24 1$13$17 12!#4!%

N N N N

T#6#!#! #"#$ *#! 8


N; = A  f r; = N5 = A  f r5 = N = φ  N =

. INTERAKSI AKSIAL TEKAN DAN MOMEN LENTUR

Ga5a a96ial a9ia' &a '&rfa9'or Mo"& a9ia' &a '&rfa9'or Ta/aa a96ial '&9a Ta/aa "o"& l&'8r

[C-2011: M!


N8 = 42$000 N M8 = 12#000000 N"" φ  N = 12!#4!% N φ  M = 2777#$#32 N""

1%


El&"& 5a- "&a/a -a5a a96ial '&9a a "o"& l&'8r /ar86 "&"&8/i &r6a"aa i'&ra96i a96ial '&9a a "o"& l&'8r 6 : N8 )  φ N  H 0.20 U'89 ilai

N8 )  φ N  > ! ) %  * M 8 )  φ  M  , N8 )  φ N  ≤ 0.20 N8 )  2  φ N  > * M8 )  φ  M  ,

→

U'89 ilai →

N8 )  φ N  =

0.3304

≤ 1.0 ≤ 1.0

>

N8 )  φ N  > ! ) %  * M8 )  φ  M  , = N8 )  2  φ N  > * M8 )  φ  M  , =

0.2

0.733# @ 0.733#

Nilai i'&ra96i a96ial '&9a a "o"& l&'8r = < 0.733# 1.0 AMAN (OK) :. TAHANAN GESER

Ta/aa -&6&r o"ial la' aa &-a &-a98 i/i'8- 6&a-ai &ri98' : / ) '( ≤ 1.10   9  E ) f 5  U'89 ilai Ta/aa -&6&r $#*" : →

 = 0.#0  f 5  A( 1.10   9  E ) f 5 

U'89 ilai Ta/aa -&6&r $#*o $#*" : →

≤

/ ) '(

≤

1.37   9  E ) f 5 

 = 0.#0  f 5  A(  * 1.10  9  E ) f 5  , )  / ) ' (  / ) '( > 1.37   9  E ) f 5 

U'89 ilai Ta/aa -&6&r $#*" : →

 = 0.%0  A(  9  E )  / ) ' ( 2

A( = '(  /' = 3200 ""2 9 = $ > $ )  a ) /  2 = $.74!! / ) '( = P&rai-a 'i--i '&r/aa '&al aa 4!.37$ 1.10   9  E ) f 5  = 7#.13# 1.37   9  E ) f 5  = %4.!24 / ) '( 1.10  9E ) f 5  / ) '( 1.37  9E ) f 5  < < a L8a6 &a"a- aa

Ta/aa -&6&r plastis

[C-2011: M!


20


Ta/aa -&6&r o"ial i/i'8- 6&a-ai &ri98' :

 = 0.#0  f 5  A( = 4#0!00  = 0.#0  f 5  A(  * 1.10  9  E ) f 5  , )  / ) ' (  = @ 2  = 0.%0  A(  9  E )  / ) ' (  = @  = 4#0!00 Ta/aa -&6&r o"ial 8'89 -&6&r : plastis φf   = 34$#00 Ta/aa -a5a -&6&r 8 = 2$#000 Ga5a -&6&r a9ia' &a '&rfa9'or φf   8 S5ara' 5- /ar86 i&8/i :  AMAN (OK) 2$#000 34$#00 8 )  φf    = 0.7407 < 1.0 (OK)

N N N N N N

;. INTERAKSI GESER DAN LENTUR

El&"& 5a- "&"i98l 9o"ia6i -&6&r a l&'8r /ar86 ila989a 9o'rol 6. : S5ara' 5a- /ar86 i&8/i 8'89 i'&ra9a6i -&6&r a l&'8r : M8 )  φ M  > 0.#2$  8 )  φf    1.37$ M8 )  φ  M  = 0.4$3# 8 )  φf    = 0.7407 M8 )  φ M  > 0.#2$  8 )  φf    = 0.%1## < 1.35 AMAN (OK) 0.%1## 10. PENGAKU ERTIKAL PADA BADAN

L8a6 &a"a- la' &-a98 I&r'i9al /ar86 "&"&8/i

A6

1 > a ) /2  , '6 = T&al la' &-a98 I&r'i9al aa aa stiffner  # "" /6 = /' @ 2  'f = Ti--i la' &-a98 374 "" A6 = /6  '6 = L8a6 &a"a- la' &-a98 2244 ""2 D= U'89 6&a6a- &-a98 1 +I = 1.$  9  E ) f 5  1 )  / )' ( 2 = 3.070! 0.$  D  A(  1 > +I  * a ) / @ a ) / 2 ) 1 > a ) /2  , = 1134 ""2 ≥

0.$  D  A(  1 > +I  * a ) / @ a ) / 2 )

S5ara' 5a- /ar86 i&8/i :

A6

≥

0.$  D  A(  1 > +I  * a ) / @ a ) / 2 ) 2244

[C-2011: M!

>

1134


1 > a ) /2  , (OK)

21


P&-a98 I&r'i9al aa la' aa /ar86 "&"85ai "o"& i&r6ia : 6 ≥ 0.7$  /  '(3 a ) / ≤ √2 8'89 6 ≥ 1.$  /3  '(3 ) a2 a ) / > √2 8'89

6 = 2)3  /6  '63 =

H a)/= 2.$!4 Ba'a6a "o"& i&r6ia &-a98 I&r'i9al i/i'8- 6&a-ai &ri98' : 0.7$  /  '(3 = 1.$  /3  '(3 ) a2 = Ko'rol "o"& i&r6ia la' &-a98 6 = $3!$#

[C-2011: M!

$3!$# √ 2

""4

@ 44$14 44$14

""4 ""4 ""4

Mo"& i&r6ia "ii"8" = H 44$14 AMAN (OK)


22


PERHITUNGAN KOLOM LENTUR DUA ARAH (BIA'IAL) K
A. DATA BAHAN

f 5 = f r = E= υ =

T&-a-a l&l&/ aa 'iel( stress T&-a-a 6i6a resi(ual stress Mo8l86 &la6'i9 aa #o(ulus of elasticit'  A-9a Poi66o Poisson)s ratio

240 70 200000 0.3

MPa MPa MPa

B. DATA PROFIL BAJA Profil : ' f '(

/ /2

/'

r

/1 0f

F 400.200.!.13 /' = 400 f = 200 '( = ! 'f = 13 r= 1# A = !410 ; = 237000000 5 = 17400000 r ; = 1#! r 5 = 4$.4 S; = 11%0000 S5 = 174000

"" "" "" "" "" ""2 ""4 ""4 "" "" ""3 ""3

C. DATA KOLOM Paa- &l&"& '/.6. ; Paa- &l&"& '/.6. 5 Ga5a a96ial a9ia' &a '&rfa9'or Mo"& a9ia' &a '&rfa9'or '/.6. ; Mo"& a9ia' &a '&rfa9'or '/.6. 5 Ga5a -&6&r a9ia' &a '&rfa9'or Fa9'or r&896i 9&98a'a 8'89 a96ial '&9a Fa9'or r&896i 9&98a'a 8'89 l&'8r

[C]:2011 : M!

"olo# .entur Dua /rah $Biaxial%

L; = 4$00 "" L5 = 4$00 "" N8 = 30$000 N M8; = %4$00000 N"" M85 = 1$100000 N"" 8 = 207000 N φ = 0.!$ φ = 0.%0

23


Fa9'or r&896i 9&98a'a 8'89 -&6&r

φf =

0.7$


G = E ) *21 > υ, = 7#%23.07#% MPa /1 = 'f > r = 2%.00 "" /2 = /' @ 2  / 1 = 342.00 "" / = /' @ 'f = 3!7.00 "" ? = Σ *   '3)3 , = 2  1)3  f  'f 3 > 1)3  /' @ 2  'f   '(3 = 3$#7#2.7 ""4 ( = 5  /2 ) 4 = #.$1$E>11 ""# C1 = π ) S;  * E  G  ?  A ) 2 , = 12#!2.% MPa C2 = 4  * S; ) G  ? ,2  ( ) 5 = 0.0002!1# ""2)N2 ; = '(  /'2 ) 4 >  f @ '(    /' @ 'f   'f = 12!$%$2.0 ""3 5 = 'f  f 2 ) 2 >  /' @ 2  'f   '(2 ) 4 = 2#$%!4.0 ""3 ; = "o8l86 &a"a- la6'i6 '/. 6. ; G = "o8l86 -&6&r 5 = "o8l86 &a"a- la6'i6 '/. 6. 5 ? = Ko6'a'a 8'ir 'or6i ( = 9o6'a'a 8'ir l&-98- C1 = 9o&fi6i& "o"& '&989 'or6i la'&ral C2 = 9o&fi6i& "o"& '&989 'or6i la'&ral / = 'i--i &r6i/ aa

[C]:2011 : M!


24


K
3 = L3 =

3 = L3 =

4$00

34!00000 7000

2 = L2 = 1 = L1 =

237000000

B 237000000

GB; = Σ

4$00

34!00000 7000

1 = L1 =

4 = L4 =

A 237000000

2 = L2 = G A; = Σ

4$00

34!00000

?oi' B : Σ   ) L = 10$333 Σ   ) L = %%43  ) L  ) Σ   ) L  = 10.# 7000

34!00000

?oi' A : Σ   ) L = 10$333 Σ   ) L = %%43  ) L  ) Σ   ) L  = 10.# Fa9'or aa- '&989 &f&9'if '/.6. ; 7000

9; = * 3G A;GB; > 1.4G A;> GB; > 0.#4 , ) * 3G A;GB; > 2.0G A;> GB; > 1.2! ,

→

'/.6. J :

3 = L3 =

3 = L3 =

1 = L1 =

4$00

$000

B 17400000

$000

[C]:2011 : M!

A 17400000 4$00

4 = L4 = GB5 = Σ

4$00

12$0000

1 = L1 =

0.%#4!%

17400000

12$00000

2 = L2 =

9; =

2 = L2 = G A5 = Σ

12$00000

?oi' B : Σ   ) L = 7733 Σ   ) L = $000  ) L  ) Σ   ) L  = 1.$ $000

12$00000

?oi' A : Σ   ) L = 7733 Σ   ) L = 27$0  ) L  ) Σ   ) L  = 2.! $000


2$


Fa9'or aa- '&989 &f&9'if '/.6. 5

95 = * 3G A5GB5 > 1.4G A5> GB5 > 0.#4 , ) * 3G A5GB5 > 2.0G A5> GB5 > 1.2! ,

→

9J =

0.!$!7$

E. PERHITUNGAN KEKUATAN 1. TAHANAN AKSIAL TEKAN

Fa9'or '&989 9olo" i/i'8- &-a r8"86 6&a-ai &ri98' : a. U'89 ilai λ ≤ 0.2$ "a9a '&r"a689 9olo" pende& : →

ω = 1

. U'89 ilai 0.2$  λ ≤ 1.20 "a9a '&r"a689 9olo" sedang : →

ω = 1.43 )  1.# @ 0.#7  λ 

. U'89 ilai λ H 1.20 "a9a '&r"a689 9olo" langsing : →

ω = 1.2$  λ2

M!!*+#! #&#m*& $#!-"!-#! 8

Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 ; Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 5 Paa- 9olo" '&r/aa 68"8 ; : Paa- '&989 &f&9'if '&r/aa 68"8 ; Paa- 9olo" '&r/aa 68"8 5 : Paa- '&989 &f&9'if '&r/aa 68"8 5 Para"&'&r 9&la-6i-a '&r/aa 68"8 ;

9; = 95 = L; = L9; = 9;  L; = L5 = L95 = 95  L5 =

λ; = 1 ) π  L9; ) r ;   f 5 ) E  =

0.%# 0.!# 4$00 4342 4$00 3!#4

"" "" "" ""

0.2!$0

Para"&'&r 9&la-6i-a '&r/aa 68"8 J

λ5 = 1 ) π  L95 ) r 5   f 5 ) E  =

0.%3!#

M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ 7 8

λ; = U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 ; ω = a. Kolo" *en(ek : ω = 1.43 )  1.# @ 0.#7  λ  = . Kolo" se(ang : ω = 1.2$  λ2 = . Kolo" langsing : ω; = → Fa9'or '&989 '&r/aa 68"8 ;

0.2!$0 @ 1.014% @ 1.014%

M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ / 8

U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 5 a. Kolo" *en(ek :

[C]:2011 : M!


λ5 = ω =

0.%3!# @

2#


. Kolo" se(ang : . Kolo" langsing : Fa9'or '&989 '&r/aa 68"8 5

ω = 1.43 )  1.# @ 0.#7  λ  = ω = 1.2$  λ2 = ω5 = →

1.472$ @ 1.472$

f r; = f 5 ) ω; = f r5 = f 5 ) ω5 =

23#.4!# 1#2.%%2

MPa MPa

N; = A  f r; = N5 = A  f r5 = N = φ  N =

1%!!!43 13707#7 13707#7 11#$1$2

N N N N

T-#!-#! *+ 8

T&-a-a '&989 '&r/aa 68"8 ; T&-a-a '&989 '&r/aa 68"8 5 T#6#!#! #"#$ *#! 8


2. MOMEN NOMINAL PENGARUH LOCAL BUCKLING PADA SA=AP

Mo"& o"ial &a"a- a9ia' &-ar8/ loal 89li- aa 6a5a 8'89 : λ ≤ λ a. P&a"a- compact : →

. P&a"a- non-compact : →

. P&a"a- langsing : →

M = M λ  λ ≤ λr M = M @ M @ Mr    λ @ λ )  λr @ λ λ H λr M = Mr   λr ) λ 2

M; = f 5  ; = Mo"& la6'i6 '/.6. ; Mr; = S;   f 5 @ f r  = Mo"& a'a6 '&989 '/.6. ; M5 = f 5  5 = Mo"& la6'i6 '/.6. 5 Mr5 = S5   f 5 @ f r  = Mo"& a'a6 '&989 '/.6. 5 λ = f ) 'f = K&la-6i-a &a"a- 6a5a Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act 

λ = 170 ) f 5 =

30!#2!4!0 202300000 #3!3#1#0 2%$!0000 1$.3!$

N"" N"" N"" N""

10.%73


λ

>

λ

λr = 370 )  f 5 @ f r  = λ < a

B&ra6ar9a ilai 9&la-6i-a 6a5a "a9a '&r"a689 &a"a-

[C]:2011 : M!


2!.37!

λr non-compact

27


Mom! !om"!#$ *6'.%. 7 8

M; = M; = @ N"" M; = M; @ M; @ Mr;   λ @ λ )  λr @ λ = 2!1#7%1%1 N"" non+co#*act : M; = Mr;   λr ) λ 2 = @ N"" langsing : M; = 2!1#7%1%1 N"" Mo"& o"ial 8'89 &a"a- : non-compact co#*act :

Mom! !om"!#$ *6'.%. / 8

M5 = M5 = @ N"" M5 = M5 @ M5 @ Mr5   λ @ λ )  λr @ λ = $$1$3!2! N"" non+co#*act : M5 = Mr5   λr ) λ 2 = langsing : @ N"" M5 = $$1$3!2! N"" Mo"& o"ial 8'89 &a"a- : non-compact co#*act :

3. MOMEN NOMINAL PENGARUH LOCAL BUKLING PADA BADAN

K&la-6i-a &a"a- aa Ga5a a96ial l&l&/

λ = / ) '( = 4!.37$ N5 = A  f 5 = 201!400 N N8 )  φ  N5  = 0.1#! N

a. Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- compact : N8 )  φ  N5  ≤ 0.12$ U'89 ilai →

U'89 ilai →

λ = 1#!0 ) f 5  *  1 @ 2.7$  N 8 )  φ  N5  , N8 )  φ  N5  H 0.12$ λ = $00 ) f 5  *  2.33 @ N8 )  φ  N5  , ≥ ##$ )

f 5

. Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non-compact : →

λr = 2$$0 )

f 5  *  1 @ 0.74  N 8 )  φ  N5  ,

N8 )  φ  N5  > λ = 1#!0 ) f 5  *  1 @ 2.7$  N 8 )  φ  N5  , = λ = $00 ) f 5  *  2.33 @ N 8 )  φ  N5  , = λ = ##$ ) f 5 = λ = Ba'a6 9&la-6i-a "a96i"8" &a"a- co#*act  U'89 ilai :

0.125

@ #%.7!1 42.%2# #%.7!1

Ba'a6 9&la-6i-a "a96i"8" &a"a- non+co#*act 

λr = 2$$0 ) λ

<

f 5  *  1 @ 0.74  N8 )  φ  N5  , = λ λ < a

B&ra6ar9a ilai 9&la-6i-a aa "a9a '&r"a689 &a"a-

144.1$1

λr compact

Mom! !om"!#$ *6'.%. 7 8

[C]:2011 : M!


2!


M; = M; = 30!#2!4!0 N"" M; = M; @ M; @ Mr;   λ @ λ )  λr @ λ = @ N"" non+co#*act : M; = Mr;   λr ) λ 2 = langsing : @ N"" M; = 30!#2!4!0 N"" Mo"& o"ial '/.6. ; : &a"a- compact co#*act :

Mom! !om"!#$ *6'.%. / 8

M5 = M5 = #3!3#1#0 N"" M5 = M5 @ M5 @ Mr5   λ @ λ )  λr @ λ = non+co#*act : @ N"" 2 M5 = Mr5   λr ) λ  = @ N"" langsing : M5 = #3!3#1#0 N"" Mo"& o"ial '/.6. 5 : &a"a- compact co#*act :


Mo"& o"ial &ra6ar9a &-ar8/ local ,uckling aa 6a5a M; = Mo"& o"ial '/.6. ; M5 = Mo"& o"ial '/.6. 5 Mo"& o"ial &ra6ar9a &-ar8/ local ,uckling aa aa M; = Mo"& o"ial '/.6. ; M5 = Mo"& o"ial '/.6. 5 Mo"& o"ial '&r9&il 5a- "&&'89a → M; = Mo"& o"ial '/.6. ; → M5 = Mo"& o"ial '/.6. 5 Ta/aa "o"& l&'8r '/.6. ; Ta/aa "o"& l&'8r '/.6. 5

2!1#7%1%1 N"" $$1$3!2! N"" 30!#2!4!0 N"" #3!3#1#0 N""

2!1#7%1%1 $$1$3!2! φ  M; = 2$3$11272 φ  M5 = 4%#3!44$

N"" N"" N"" N""

5. INTERAKSI AKSIAL TEKAN DAN MOMEN LENTUR

Ga5a a96ial a9ia' &a '&rfa9'or Mo"& a9ia' &a '&rfa9'or '/.6. ; Mo"& a9ia' &a '&rfa9'or '/.6. 5 Ta/aa a96ial '&9a Ta/aa "o"& l&'8r '/.6. ; Ta/aa "o"& l&'8r '/.6. 5

[C]:2011 : M!


N8 = M8; = M85 = φ  N = φ  M; = φ  M5 =

30$000 %4$00000 1$100000 11#$1$2 2$3$11272 4%#3!44$

N N"" N"" N N"" N""

2%


Kolo" 5a- "&a/a -a5a a96ial '&9a a "o"& l&'8r /ar86 "&"&8/i &r6a"aa i'&ra96i a96ial '&9a a "o"& l&'8r 6 : N8 )  φ N  H 0.20 U'89 ilai

N8 )  φ N  > ! ) %  * M 8; )  φ  M;  > M85 )  φ  M5  , N8 )  φ N  ≤ 0.20 U'89 ilai N8 )  2  φ N  > * M8; )  φ  M;  > M85 )  φ  M5  , →

≤ 1.0

→

≤ 1.0

N8 )  φ N  = 0.2#1! > N8 )  φ N  > !)%* M8; )  φ  M;  > M85 )  φ  M5  , = N8 )  2  φ N  > * M8; )  φ  M;  > M85 )  φ  M5  , =

U'89 ilai :

0.20

0.!#3$ @ 0.!#3$

Nilai i'&ra96i a96ial '&9a a "o"& l&'8r = < 0.!#3$ 1.0 AMAN (OK) . TAHANAN GESER

K&'&ala la' aa 'aa &-a98 /ar86 "&"&8/i 65ara'

/2 ) '( 42.7$

#.3#  <

E ) f 5 

1!3.#0

"lat badan memenuhi s#arat $OK%

Ko'rol 'a/aa -&6&r o"ial la' aa 'aa &-a98 : 8 = 207000 Ga5a -&6&r a9ia' &a '&rfa9'or A( = '(  /' = L8a6 &a"a- aa 3200  = 0.#0  f 5  A( = 4#0!00 Ta/aa -a5a -&6&r o"ial φf   = 34$#00 → Ta/aa -a5a -&6&r φf   8 S5ara' 5- /ar86 i&8/i : < 207000 34$#00 AMAN (OK)

8 )  φf    =

0.$%%0

N ""2 N N

< 1.0 (OK)

. INTERAKSI GESER DAN LENTUR

El&"& 5a- "&"i98l 9o"ia6i -&6&r a l&'8r /ar86 ila989a 9o'rol 6. : Sa5ara' 5a- /ar86 i&8/i 8'89 i'&ra9a6i -&6&r a l&'8r :

M8; )  φ M;  > M85 )  φ  M5  > 0.#2$  8 )  φf   

[C]:2011 : M!


1.37$

30

STEEL-BEAM-COLUMN_2.xls

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