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&/ aa 'iel( stress T&-a-a 6i6a resi(ual stress Mo8l86 &la6'i9 aa #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
Pehitungan Struktur Baja Dengan Microsoft Excel
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
Paa- &l&"& '/.6. ; Paa- &l&"& '/.6. 5 ara9 898-a la'&ral Mo"& "a96i"8" a9ia' &a '&rfa9'or '&rfa9'or Mo"& aa 1)4 &'a- Mo"& i '&-a/ &'a- Mo"& aa 3)4 &'a- Ga5a a96ial a9ia' &a '&rfa9'or Ga5a -&6&r a9ia' &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 = "o8l86 -&6&r ? = Ko6'a'a 8'ir 'or6i ( = 9o6'a'a 8'ir l&-98- C1 = 9o&fi6i& "o"& '&989 'or6i la'&ral @ 1 C2 = 9o&fi6i& "o"& '&989 'or6i la'&ral @ 2 ; = "o8l86 &a"a- la6'i6 '/. 6. ;
[C]2011 : M!
Balok "olo# $Bea# Colu#n%
'f '(
/ /2
/'
r
/1 0f
2
Pehitungan Struktur Baja Dengan Microsoft Excel
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
Paa- &l&"& '/.6. ; Paa- &l&"& '/.6. 5 ara9 898-a la'&ral Mo"& "a96i"8" a9ia' &a '&rfa9'or '&rfa9'or Mo"& aa 1)4 &'a- Mo"& i '&-a/ &'a- Mo"& aa 3)4 &'a- Ga5a a96ial a9ia' &a '&rfa9'or Ga5a -&6&r a9ia' &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 = "o8l86 -&6&r ? = Ko6'a'a 8'ir 'or6i ( = 9o6'a'a 8'ir l&-98- C1 = 9o&fi6i& "o"& '&989 'or6i la'&ral @ 1 C2 = 9o&fi6i& "o"& '&989 'or6i la'&ral @ 2 ; = "o8l86 &a"a- la6'i6 '/. 6. ;
[C]2011 : M!
Balok "olo# $Bea# Colu#n%
'f '(
/ /2
/'
r
/1 0f
2
Pehitungan Struktur Baja Dengan Microsoft Excel
5 = "o8l86 &a"a- la6'i6 '/. 6. 5 E. PERHITUNGAN KEKUATAN 1. MOMEN NOMINAL PENGARUH LOCAL BUCKLING
λ = f ) 'f = K&la-6i-a &a"a- 6a5a Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act
1$.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"ial &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&ra6ar9a ilai 9&la-6i-a 6a5a "a9a '&r"a689 &a"aMo"& o"ial &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"ial 8'89 &a"a- : non-compact co#*act :
[C]2011 : M!
Balok "olo# $Bea# Colu#n%
N"" N"" N"" N""
3
Pehitungan Struktur Baja Dengan Microsoft Excel
2. MOMEN NOMINAL BALOK PLAT BERDINDING PENUH
K&la-6i-a &a"a- aa U'89 &a"a- 5a- "&"85ai 898ra : "a9a "o"& o"ial 9o"o& 6'r89'8r
λ = / ) '( = / ) '( harus
>
4!.37$
λr
i/i'8- &-a r8"86 :
M = K- S f r K- = 1 @ * a r ) 1200 > 300 ar , * / ) ' ( @ 2$$0 ) f r , &-a λG ≤ λ f r = f 5 a. U'89 9&la-6i-a : ≤ G r . U'89 9&la-6i-a : f r = + f 5 * 1 @ λG @ λ ) 2 λr @ λ , λG H λr f r = f λr ) λG 2 . U'89 9&la-6i-a : ≤ f f = + f 5 ) 2 U'89 '&989 'or6i la'&ral : 5 f = f 5 ) 2 U'89 '&989 lo9al : →
→
→
≤ ≤
f 5 f 5
→ →
Ko&fi6i& "o"& '&989 'or6i la'&ral
+ = 12.$ M8 ) 2.$ M8 > 3 M A > 4 MB > 3 M+ = + = → ia"il
1.07 1.07
< 2.3
P&rai-a l8a6 la' aa '&r/aa l8a6 la' 6a5a
ar = / '( ) f 'f = 1 = 5 ) 2 @ 1)12 ' (3 1)3 /2 = A1 = A ) 2 @ 1)3 ' ( /2 =
1.1%1 Mo"& i&r6ia !#%$13# ""4 L8a6 &a"a- 32%3 ""2 ?ari@ari -ira6i a&ra/ la' 6a5a i'a"a/ 6&&r'i-a a-ia la' aa 5a- "&-ala"i r 1 = 1 ) A1 = '&9a $1 "" 2.1. Mom! !om"!#$ %&'##&#! *+ *o&" $#*$
L = L5 = ?ara9 a'ara &-&9a- la'&ral λG = L ) r 1 = A-9a 9&la-6i-a Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act
4000 77.!43
λ = 1.7# E ) f 5 =
$0.!07
""
Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non+co#*act
λr = 4.40 E ) f 5 =
[C]2011 : M!
Balok "olo# $Bea# Colu#n%
127.017
4
Pehitungan Struktur Baja Dengan Microsoft Excel
T&-a-a a8a 8'89 "o"& 9ri'i6 '&989 'or6i la'&ral
f
λG
<
f = + f 5 ) 2 = f = "a9a ia"il
f 5
λG a T&-a-a 9ri'i6 &a"a- i/i'8- 6&a-ai &ri98' : >
λ
12!.7! 12!.7!
MPa MPa
λr
<
λG ≤ λ λ ≤ λG λG H λr
f r = f 5 = ≤ λ f r = + f 5 * 1 @ λG @ λ ) 2 λr @ λ , = r f r = f λr ) λG 2 = f r = f r < f 5 f r = "a9a ia"il S = S; = Mo8l86 &a"a- &la6'i6
@ 211.!! @ 211.!! 211.!! 11%0000
MPa MPa MPa MPa MPa ""3
Ko&fi6i& alo9 la' &rii- &8/
K- = 1 @ * a r ) 1200 > 300 ar , * / ) ' ( @ 2$$0 ) f r , = 1.0%7 M = K- S f r = 27#$!!%7% N"" Mo"& o"ial &a"a- 2.2. Mom! !om"!#$ %&'##&#! $o,#$ %+,$"!- #'# #/#
Fa9'or 9&la-6i-a la' aa
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
Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non+co#*act
λr = 1.3$ 9& E ) f 5 = f = f 5 ) 2 = T&-a-a a8a 8'89 "o"& 9ri'i6 '&989 lo9al λG λ λG < < a B&ra6ar9a ilai 9&la-6i-a 6a5a "a9a '&r"a689 &a"aT&-a-a 9ri'i6 &a"a- i/i'8- 6&a-ai &ri98' :
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 = T&-a-a 9ri'i6 &a"a- f r < f 5 f r = "a9a ia"il
[C]2011 : M!
Balok "olo# $Bea# Colu#n%
2%.$$ 120.00
MPa
λr compact
240.00 @ @ 240.00 240.00
MPa MPa MPa MPa MPa
$
Pehitungan Struktur Baja Dengan Microsoft Excel
S = S; =
Mo8l86 &a"a- &la6'i6 Ko&fi6i& alo9 la' &rii- &8/
11%0000
""3
K- = 1 @ * a r ) 1200 > 300 ar , * / ) ' ( @ 2$$0 ) f r , = 1.0!% M = K- S f r = 310%!2774 N"" Mo"& o"ial &a"a- 3. MOMEN NOMINAL PENGARUH LAE!AL BUCKLING
Mo"& o"ial 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
Paa- &'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 Paa- &'a- "ii"8" alo9 5a- 'a/aa5a 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 > 3M A > 4MB > 3M+ = 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 = Paa- &'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"ial 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"ial 8'89 9a'&-ori : bentang sedang M M < M = 2!!1$$#!1 N"" → Mo"& o"ial 5a- i-8a9a
[C]2011 : M!
Balok "olo# $Bea# Colu#n%
#
Pehitungan Struktur Baja Dengan Microsoft Excel
4. TAHANAN MOMEN LENTUR
a. Mo"& o"ial &ra6ar9a &-ar8/ local ,uckling . Mo"& o"ial alo9 la' &rii- &8/ : Mo"& o"ial &ra6ar9a '&989 'or6i la'&ral Mo"& o"ial &ra6ar9a local ,uckling . 6a5a . Mo"& o"ial &ra6ar9a &-ar8/ lateral ,uckling Mo"& o"ial '&r9&il 5a- "&&'89a Ta/aa "o"& l&'8r
M = 30!#2!4!0 N"" M = M = M = M = φ M =
27#$!!%7% 310%!2774 2!!1$$#!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" $#!-"!- : →
ω = 1.2$ λ2
Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 ; Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 5 Paa- '&989 &f&9'if i/i'8- 6&a-ai &ri98' : Paa- 9olo" '&r/aa 68"8 ; : Paa- '&989 &f&9'if '&r/aa 68"8 ; Paa- 9olo" '&r/aa 68"8 5 : Paa- '&989 &f&9'if '&r/aa 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!
Balok "olo# $Bea# Colu#n%
7
Pehitungan Struktur Baja Dengan Microsoft Excel
λ; = 1 )π L9; ) r ; f 5 ) E =
0.7!7#
P#m*& $#!-"!-#! *&6#'# +m%+ / 8
λ5 = 1 ) π L95 ) r 5 f 5 ) E =
0.%71$
M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ 7 8
λ; = U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 ; ω = a. Kolo" *en(ek : ω = 1.43 ) 1.# @ 0.#7 λ = . Kolo" se(ang : ω = 1.2$ λ2 = . Kolo" langsing : ω; = Fa9'or '&989 '/.6. ;
0.7!7# @ 1.333# @ 1.333#
M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ / 8
λ5 = U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 5 ω = a. Kolo" *en(ek : ω = 1.43 ) 1.# @ 0.#7 λ = . Kolo" se(ang : ω = 1.2$ λ2 = . 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/aa a96ial '&9a o"ial '/.6. ; Ta/aa a96ial '&9a o"ial '/.6. 5 Ta/aa a96ial '&9a o"ial '&r9&il Ta/aa a96ial '&9a
N; = A f r; = 1$13$17 N N5 = 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 a9ia' &a '&rfa9'or M8 = %$000000 Mo"& a9ia' &a '&rfa9'or φ N = 113!#71 Ta/aa a96ial '&9a φ M = 24!%300!1 Ta/aa "o"& l&'8r El&"& 5a- "&a/a -a5a a96ial '&9a a "o"& l&'8r /ar86 "&"&8/i
[C]2011 : M!
Balok "olo# $Bea# Colu#n%
N N"" N N""
!
Pehitungan Struktur Baja Dengan Microsoft Excel
&r6a"aa i'&ra96i a96ial '&9a a "o"& l&'8r 6 : N8 ) φ N H 0.20 U'89 ilai
N8 ) φ N > ! ) % * M 8 ) φ M , N8 ) φ N ≤ 0.20 N8 ) 2 φ N > * M8 ) φ M ,
→
U'89 ilai →
N8 ) φ N =
0.3732
≤ 1.0 ≤ 1.0
>
0.2
N8 ) φ N > ! ) % * M 8 ) φ M , = N8 ) 2 φ N > * M8 ) φ M , =
0.712$ @ 0.712$
Nilai i'&ra96i a96ial '&9a a "o"& l&'8r = < 0.712$ 1.0 AMAN (OK) . TAHANAN GESER
Ko'rol 'a/aa -&6&r o"ial la' aa 'aa &-a98 : K&'&ala la' aa 'aa &-a98 /ar86 "&"&8/i 65ara'
/2 ) '( 42.7$
#.3# <
E ) f 5
1!3.#0
Ga5a -&6&r a9ia' &a '&rfa9'or L8a6 &a"a- aa Ta/aa -a5a -&6&r o"ial Ta/aa -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$#00
N ""2 N N
AMAN (OK)
< 1.0 (OK)
:. INTERAKSI GESER DAN LENTUR
El&"& 5a- "&"i98l 9o"ia6i -&6&r a l&'8r /ar86 ila989a 9o'rol 6. : S5ara' 5a- /ar86 i&8/i 8'89 i'&ra96i -&6&r a l&'8r : M8 ) φ M > 0.#2$ 8 ) φf 1.37$
[C]2011 : M!
Balok "olo# $Bea# Colu#n%
%
Pehitungan Struktur Baja Dengan Microsoft Excel
M8 ) φ
M8 ) φ M = 8 ) φf = M > 0.#2$ 8 ) φf = <
[C]2011 : M!
Balok "olo# $Bea# Colu#n%
0.3!1# 0.7407 0.!44# 1.35 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&/ aa 'iel( stress T&-a-a 6i6a resi(ual stress Mo8l86 &la6'i9 aa #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!
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
"" "" "" "" "" ""2 ""4 ""4 "" "" ""3 ""3
11
Perhitungan Struktur Baja Dengan Microsoft Excel
BEAM +
C. DATA BALOK KOLOM (RAFTER)
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 ) *21 > 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
Paa- &l&"& '/.6. ; Paa- &l&"& '/.6. 5 ara9 898-a la'&ral ?ara9 a'ara &-a98 I&r'i9al aa aa T&al la' &-a98 I&r'i9al aa aa Mo"& "a96i"8" a9ia' &a '&rfa9'or Mo"& aa 1)4 &'a- Mo"& i '&-a/ &'a- Mo"& aa 3)4 &'a- Ga5a a96ial a9ia' &a '&rfa9'or Ga5a -&6&r a9ia' &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 = "o8l86 -&6&r ? = Ko6'a'a 8'ir 'or6i ( = 9o6'a'a 8'ir l&-98- / = 'i--i &r6i/ aa ; = "o8l86 &a"a- la6'i6 '/. 6. ; 5 = "o8l86 &a"a- la6'i6 '/. 6. 5
[C-2011: M!
Balok "olo# $Bea# Colu#n%
'f '(
/ /2
/'
r
/1 0f
12
Perhitungan Struktur Baja Dengan Microsoft Excel
C1 = 9o&fi6i& "o"& '&989 'or6i la'&ral C2 = 9o&fi6i& "o"& '&989 'or6i la'&ral E. PERHITUNGAN KEKUATAN S5ara' 5- /ar86 i&8/i 8'89 alo9 &-a &-a98 "a9a ilai : < a ) / = 2.$!4 3.00
a ) / ≤ 3.0
berla&u rumus balo& dengan penga&u $OK%
K&'&ala la' aa &-a &-a98 I&r'i9al 'aa &-a98 "&"aa- /ar86 "&"&@ / ) '( 7.07 E ) f 5 8/i : 4!.37$ 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"ial &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&ra6ar9a ilai 9&la-6i-a 6a5a "a9a '&r"a689 &a"aMo"& o"ial &a"a- i/i'8- 6&a-ai &ri98' : <
compact
M = M = 30!#2!4!0 N""
co#*act :
[C-2011: M!
λr
Balok "olo# $Bea# Colu#n%
13
Perhitungan Struktur Baja Dengan Microsoft Excel
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"ial 8'89 &a"a- : non+co#*act :
1.2. P!-#&+6 *+ $o#$ (local buc&ling% #'# %#'#!
λ = / ) '( = K&la-6i-a &a"a- aa Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act
4!.37$
λ = 1#!0 ) f 5 =
10!.444
Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non+co#*act
λ
λr = 2$$0 ) f 5 = λ <
λ
a B&ra6ar9a ilai 9&la-6i-a aa "a9a '&r"a689 &a"aMo"& o"ial &a"a- i/i'8- 6&a-ai &ri98' : <
1#4.#02
λr compact
M = M = 30!#2!4!0 N"" M = M @ M @ Mr λ @ λ ) λr @ λ = @ N"" non+co#*act : 2 M = Mr λr ) λ = @ N"" langsing : M = 30!#2!4!0 N"" Mo"& o"ial 8'89 &a"a- : compact co#*act :
2. MOMEN NOMINAL BALOK PLAT BERDINDING PENUH
λ = / ) '( = 4!.37$ λr / ) '( H
K&la-6i-a &a"a- aa U'89 &a"a- 5a- "&"85ai 898ra :
4!.37$ "a9a "o"& o"ial 9o"o& 6'r89'8r
harus
40.344 i/i'8- &-a r8"86 : >
M = K- S f r K- = 1 @ * a r ) 1200 > 300 ar , * / ) ' ( @ 2$$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 > 3M A > 4MB > 3M+ =
[C-2011: M!
Balok "olo# $Bea# Colu#n%
0.%!
< 2.3
14
Perhitungan Struktur Baja Dengan Microsoft Excel
ia"il P&rai-a l8a6 la' aa '&r/aa 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' aa 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
""
Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non+co#*act
λr = 4.40 E ) f 5 =
127.017
T&-a-a a8a 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' :
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 = T&-a-a 9ri'i6 &a"a- f r < f 5 f r = "a9a ia"il S = S; = Mo8l86 &a"a- &la6'i6
240.00 @ @ 240.00 240.00 11%0000
MPa MPa MPa MPa MPa ""3
Ko&fi6i& alo9 la' &rii- &8/
K- = 1 @ * a r ) 1200 > 300 ar , * / ) ' ( @ 2$$0 ) f r , = 1.0!% M = K- S f r = 310%!2774 N"" Mo"& o"ial &a"a- 2.2. Mom! !om"!#$ %&'##&#! local buc&ling #'# #/#
K&la-6i-a &a"a- 6a5a
[C-2011: M!
λG = f ) 2 'f =
Balok "olo# $Bea# Colu#n%
7.#%
1$
Perhitungan Struktur Baja Dengan Microsoft Excel
9& = 4 ) / ) '( = 9& = ia"il
Fa9'or 9&la-6i-a la' aa
0.$7$ 0.$7$
< 0.3
Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- co#*act
λ = 0.3!
E ) f 5 =
10.%7
Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non+co#*act
λr = 1.3$ 9& E ) f 5 = f = f 5 ) 2 = T&-a-a a8a 8'89 "o"& 9ri'i6 '&989 lo9al λG λ λG < < a
2%.$$ 120.00
MPa
λr
T&-a-a 9ri'i6 &a"a- i/i'8- 6&a-ai &ri98' :
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 = T&-a-a 9ri'i6 &a"a- f r < f 5 f r = "a9a ia"il S = S; = Mo8l86 &a"a- &la6'i6
240.00 @ @ 240.00 240.00 11%0000
MPa MPa MPa MPa MPa ""3
Ko&fi6i& alo9 la' &rii- &8/
K- = 1 @ * a r ) 1200 > 300 ar , * / ) ' ( @ 2$$0 ) f r , = 1.0!% M = K- S f r = 310%!2774 N"" Mo"& o"ial &a"a- 3. MOMEN NOMINAL PENGARUH LAE!AL BUCKLING
Mo"& o"ial 9o"o& 6'r89'8r &-a &-ar8/ '&989 la'&ral 8'89 : L ≤ L a. B&'a- !' :
M = M = f 5 ; L ≤ L ≤ Lr . B&'a- '#!- : M = + * Mr > M @ Mr L r @ L ) L r @ L , L H Lr . B&'a- #!#!- : M = + π ) L * E 5 G ? > π E ) L 2 5 ( , →
→
≤ M
→
≤ M
Paa- &'a- "a96i"8" alo9 5a- "a"8 "&a/a "o"& la6'i6
L = 1.7# r 5 E ) f 5 = f L = f 5 @ f r = T&-a-a l&l&/ i98ra-i '&-a-a 6i6a
2307 "" 170 MPa Paa- &'a- "ii"8" alo9 5a- 'a/aa5a i'&'89a ol&/ "o"& 9ri'i6 '&989 Lr = r 5 C1 ) f L * 1 > 1 > C2 f L2 , = 'or6i la'&ral #7%4 "" Ko&fi6i& "o"& '&989 'or6i la'&ral
[C-2011: M!
Balok "olo# $Bea# Colu#n%
1#
Perhitungan Struktur Baja Dengan Microsoft Excel
+ = 12.$ M8 ) 2.$M8 > 3M A > 4MB > 3M+ = 0.%! M = f 5 ; = 30!#2!4!0 N"" Mo"& la6'i6 Mr = S; f 5 @ f r = 202300000 N"" Mo"& a'a6 '&989 L = L5 = Paa- &'a- '/.6. 5 ara9 898-a la'&ral 1$00 "" L Lr < < L a L T&r"a689 9a'&-ori : bentang pende& Mo"& o"ial i/i'8- 6&a-ai &ri98' :
M = M = f 5 ; = 30!#2!4!0 N"" M = + * Mr > M @ Mr L r @ L ) L r @ L , = @ N"" 2 M = + π ) L * E 5 G ? > π E ) L 5 ( , = @ N"" M = 30!#2!4!0 N"" Mo"& o"ial alo9 8'89 9a'&-ori : bentang pende& M M H M = 30!#2!4!0 N"" Mo"& o"ial 5a- i-8a9a 4. MOMEN NOMINAL PENGARUH LOCAL BUKLING PADA BADAN
K&la-6i-a &a"a- aa Ga5a a96ial l&l&/
λ = / ) '( = N5 = A f 5 = N8 ) φ N5 =
4!.37$ 201!400 0.234
N N
a. Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- compact : N8 ) φ N5 ≤ 0.12$ U'89 ilai →
U'89 ilai →
λ = 1#!0 ) f 5 * 1 @ 2.7$ N 8 ) φ N5 , N8 ) φ N5 H 0.12$ λ = $00 ) f 5 * 2.33 @ N8 ) φ N5 , ≥ ##$ )
f 5
. Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non-compact : →
λr = 2$$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 , =
Balok "olo# $Bea# Colu#n%
13#.104
17
Perhitungan Struktur Baja Dengan Microsoft Excel
λ
λ
λ < a B&ra6ar9a ilai 9&la-6i-a aa "a9a '&r"a689 &a"aMo"& o"ial 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"ial 8'89 &a"a- : compact co#*act :
5. TAHANAN MOMEN LENTUR
a. Mo"& o"ial &-ar8/ local ,uckling : Mo"& o"ial &-ar8/ local ,uckling aa 6a5a Mo"& o"ial &-ar8/ local ,uckling aa aa . Mo"& o"ial alo9 la' &rii- &8/ : Mo"& o"ial &-ar8/ '&989 'or6i la'&ral Mo"& o"ial &-ar8/ local ,uckling . 6a5a . Mo"& o"ial &-ar8/ lateral ,uckling . Mo"& o"ial &-ar8/ local ,uckling aa aa Mo"& o"ial '&r9&il 5a- "&&'89a Ta/aa "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$ λ2
Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 ; Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 5 Paa- '&989 &f&9'if i/i'8- 6&a-ai &ri98' : Paa- 9olo" '&r/aa 68"8 ; :
[C-2011: M!
Balok "olo# $Bea# Colu#n%
9; = 95 =
1.00 1.00
L; =
12000
""
1!
Perhitungan Struktur Baja Dengan Microsoft Excel
L9; = 9; L; = L5 = L95 = 95 L5 =
12000 1$00 1$00
λ; = 1 )π L9; ) r ; f 5 ) E =
0.7!7#
Paa- '&989 &f&9'if '&r/aa 68"8 ; Paa- 9olo" '&r/aa 68"8 5 : Paa- '&989 &f&9'if '&r/aa 68"8 5
"" "" ""
P#m*& $#!-"!-#! *&6#'# +m%+ 7 8
P#m*& $#!-"!-#! *&6#'# +m%+ / 8
λ5 = 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/aa 68"8 ; ω = a. Kolo" *en(ek : ω = 1.43 ) 1.# @ 0.#7 λ = . Kolo" se(ang : ω = 1.2$ λ2 = . Kolo" langsing : ω; = Fa9'or '&989 '/.6. ;
0.7!7# @ 1.333# @ 1.333#
M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ / 8
λ5 = U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 5 ω = a. Kolo" *en(ek : ω = 1.43 ) 1.# @ 0.#7 λ = . Kolo" se(ang : ω = 1.2$ λ2 = . 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
Ta/aa a96ial '&9a o"ial '/.6. ; Ta/aa a96ial '&9a o"ial '/.6. 5 Ta/aa a96ial '&9a o"ial '&r9&il Ta/aa a96ial '&9a
N; = A f r; = N5 = A f r5 = N = φ N =
. INTERAKSI AKSIAL TEKAN DAN MOMEN LENTUR
Ga5a a96ial a9ia' &a '&rfa9'or Mo"& a9ia' &a '&rfa9'or Ta/aa a96ial '&9a Ta/aa "o"& l&'8r
[C-2011: M!
Balok "olo# $Bea# Colu#n%
N8 = 42$000 N M8 = 12#000000 N"" φ N = 12!#4!% N φ M = 2777#$#32 N""
1%
Perhitungan Struktur Baja Dengan Microsoft Excel
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/aa -&6&r o"ial la' aa &-a &-a98 i/i'8- 6&a-ai &ri98' : / ) '( ≤ 1.10 9 E ) f 5 U'89 ilai Ta/aa -&6&r $#*" : →
= 0.#0 f 5 A( 1.10 9 E ) f 5
U'89 ilai Ta/aa -&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/aa -&6&r $#*" : →
= 0.%0 A( 9 E ) / ) ' ( 2
A( = '( /' = 3200 ""2 9 = $ > $ ) a ) / 2 = $.74!! / ) '( = P&rai-a 'i--i '&r/aa '&al aa 4!.37$ 1.10 9 E ) f 5 = 7#.13# 1.37 9 E ) f 5 = %4.!24 / ) '( 1.10 9E ) f 5 / ) '( 1.37 9E ) f 5 < < a L8a6 &a"a- aa
Ta/aa -&6&r plastis
[C-2011: M!
Balok "olo# $Bea# Colu#n%
20
Perhitungan Struktur Baja Dengan Microsoft Excel
Ta/aa -&6&r o"ial 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/aa -&6&r o"ial 8'89 -&6&r : plastis φf = 34$#00 Ta/aa -a5a -&6&r 8 = 2$#000 Ga5a -&6&r a9ia' &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"ia6i -&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## < 1.35 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 aa aa 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
Balok "olo# $Bea# Colu#n%
1 > a ) /2 , (OK)
21
Perhitungan Struktur Baja Dengan Microsoft Excel
P&-a98 I&r'i9al aa la' aa /ar86 "&"85ai "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 "ii"8" = H 44$14 AMAN (OK)
Balok "olo# $Bea# Colu#n%
22
Perhitungan Struktur Baja Dengan Microsoft Excel
PERHITUNGAN KOLOM LENTUR DUA ARAH (BIA'IAL) K
A. DATA BAHAN
f 5 = f r = E= υ =
T&-a-a l&l&/ aa 'iel( stress T&-a-a 6i6a resi(ual stress Mo8l86 &la6'i9 aa #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 Paa- &l&"& '/.6. ; Paa- &l&"& '/.6. 5 Ga5a a96ial a9ia' &a '&rfa9'or Mo"& a9ia' &a '&rfa9'or '/.6. ; Mo"& a9ia' &a '&rfa9'or '/.6. 5 Ga5a -&6&r a9ia' &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
Perhitungan Struktur Baja Dengan Microsoft Excel
Fa9'or r&896i 9&98a'a 8'89 -&6&r
φf =
0.7$
D. SECTION PROPERTIES
G = E ) *21 > 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 ; = "o8l86 &a"a- la6'i6 '/. 6. ; G = "o8l86 -&6&r 5 = "o8l86 &a"a- la6'i6 '/. 6. 5 ? = Ko6'a'a 8'ir 'or6i ( = 9o6'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/ aa
[C]:2011 : M!
"olo# .entur Dua /rah $Biaxial%
24
Perhitungan Struktur Baja Dengan Microsoft Excel
K
3 = L3 =
3 = L3 =
4$00
34!00000 7000
2 = L2 = 1 = L1 =
237000000
B 237000000
GB; = Σ
4$00
34!00000 7000
1 = L1 =
4 = L4 =
A 237000000
2 = L2 = 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 aa- '&989 &f&9'if '/.6. ; 7000
9; = * 3G A;GB; > 1.4G A;> GB; > 0.#4 , ) * 3G A;GB; > 2.0G A;> GB; > 1.2! ,
→
'/.6. J :
3 = L3 =
3 = L3 =
1 = L1 =
4$00
$000
B 17400000
$000
[C]:2011 : M!
A 17400000 4$00
4 = L4 = GB5 = Σ
4$00
12$0000
1 = L1 =
0.%#4!%
17400000
12$00000
2 = L2 =
9; =
2 = L2 = 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
"olo# .entur Dua /rah $Biaxial%
2$
Perhitungan Struktur Baja Dengan Microsoft Excel
Fa9'or aa- '&989 &f&9'if '/.6. 5
95 = * 3G A5GB5 > 1.4G A5> GB5 > 0.#4 , ) * 3G A5GB5 > 2.0G 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$ λ2
M!!*+#! #m*& $#!-"!-#! 8
Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 ; Fa9'or aa- '&989 &f&9'if '&r/aa 68"8 5 Paa- 9olo" '&r/aa 68"8 ; : Paa- '&989 &f&9'if '&r/aa 68"8 ; Paa- 9olo" '&r/aa 68"8 5 : Paa- '&989 &f&9'if '&r/aa 68"8 5 Para"&'&r 9&la-6i-a '&r/aa 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/aa 68"8 J
λ5 = 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/aa 68"8 ; ω = a. Kolo" *en(ek : ω = 1.43 ) 1.# @ 0.#7 λ = . Kolo" se(ang : ω = 1.2$ λ2 = . Kolo" langsing : ω; = → Fa9'or '&989 '&r/aa 68"8 ;
0.2!$0 @ 1.014% @ 1.014%
M!!*+#! !"$#" 9#*o& *+ *&6#'# +m%+ / 8
U'89 ara"&'&r 9&la-6i-a '&r/aa 68"8 5 a. Kolo" *en(ek :
[C]:2011 : M!
"olo# .entur Dua /rah $Biaxial%
λ5 = ω =
0.%3!# @
2#
Perhitungan Struktur Baja Dengan Microsoft Excel
. Kolo" se(ang : . Kolo" langsing : Fa9'or '&989 '&r/aa 68"8 5
ω = 1.43 ) 1.# @ 0.#7 λ = ω = 1.2$ λ2 = 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; = N5 = 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/aa 68"8 ; T&-a-a '&989 '&r/aa 68"8 5 T#6#!#! #"#$ *#! 8
Ta/aa a96ial '&9a o"ial '/.6. ; Ta/aa a96ial '&9a o"ial '/.6. 5 Ta/aa a96ial '&9a o"ial '&r9&il Ta/aa a96ial '&9a
2. MOMEN NOMINAL PENGARUH LOCAL BUCKLING PADA SA=AP
Mo"& o"ial &a"a- a9ia' &-ar8/ loal 89li- aa 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. ; M5 = 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
Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non+co#*act
λ
>
λ
λr = 370 ) f 5 @ f r = λ < a
B&ra6ar9a ilai 9&la-6i-a 6a5a "a9a '&r"a689 &a"a-
[C]:2011 : M!
"olo# .entur Dua /rah $Biaxial%
2!.37!
λr non-compact
27
Perhitungan Struktur Baja Dengan Microsoft Excel
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"ial 8'89 &a"a- : non-compact co#*act :
Mom! !om"!#$ *6'.%. / 8
M5 = M5 = @ N"" M5 = M5 @ M5 @ Mr5 λ @ λ ) λr @ λ = $$1$3!2! N"" non+co#*act : M5 = Mr5 λr ) λ 2 = langsing : @ N"" M5 = $$1$3!2! N"" Mo"& o"ial 8'89 &a"a- : non-compact co#*act :
3. MOMEN NOMINAL PENGARUH LOCAL BUKLING PADA BADAN
K&la-6i-a &a"a- aa Ga5a a96ial l&l&/
λ = / ) '( = 4!.37$ N5 = A f 5 = 201!400 N N8 ) φ N5 = 0.1#! N
a. Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- compact : N8 ) φ N5 ≤ 0.12$ U'89 ilai →
U'89 ilai →
λ = 1#!0 ) f 5 * 1 @ 2.7$ N 8 ) φ N5 , N8 ) φ N5 H 0.12$ λ = $00 ) f 5 * 2.33 @ N8 ) φ N5 , ≥ ##$ )
f 5
. Ba'a6 9&la-6i-a "a96i"8" 8'89 &a"a- non-compact : →
λr = 2$$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$$0 ) λ
<
f 5 * 1 @ 0.74 N8 ) φ N5 , = λ λ < a
B&ra6ar9a ilai 9&la-6i-a aa "a9a '&r"a689 &a"a-
144.1$1
λr compact
Mom! !om"!#$ *6'.%. 7 8
[C]:2011 : M!
"olo# .entur Dua /rah $Biaxial%
2!
Perhitungan Struktur Baja Dengan Microsoft Excel
M; = M; = 30!#2!4!0 N"" M; = M; @ M; @ Mr; λ @ λ ) λr @ λ = @ N"" non+co#*act : M; = Mr; λr ) λ 2 = langsing : @ N"" M; = 30!#2!4!0 N"" Mo"& o"ial '/.6. ; : &a"a- compact co#*act :
Mom! !om"!#$ *6'.%. / 8
M5 = M5 = #3!3#1#0 N"" M5 = M5 @ M5 @ Mr5 λ @ λ ) λr @ λ = non+co#*act : @ N"" 2 M5 = Mr5 λr ) λ = @ N"" langsing : M5 = #3!3#1#0 N"" Mo"& o"ial '/.6. 5 : &a"a- compact co#*act :
4. TAHANAN MOMEN LENTUR
Mo"& o"ial &ra6ar9a &-ar8/ local ,uckling aa 6a5a M; = Mo"& o"ial '/.6. ; M5 = Mo"& o"ial '/.6. 5 Mo"& o"ial &ra6ar9a &-ar8/ local ,uckling aa aa M; = Mo"& o"ial '/.6. ; M5 = Mo"& o"ial '/.6. 5 Mo"& o"ial '&r9&il 5a- "&&'89a → M; = Mo"& o"ial '/.6. ; → M5 = Mo"& o"ial '/.6. 5 Ta/aa "o"& l&'8r '/.6. ; Ta/aa "o"& l&'8r '/.6. 5
2!1#7%1%1 N"" $$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$11272 φ M5 = 4%#3!44$
N"" N"" N"" N""
5. INTERAKSI AKSIAL TEKAN DAN MOMEN LENTUR
Ga5a a96ial a9ia' &a '&rfa9'or Mo"& a9ia' &a '&rfa9'or '/.6. ; Mo"& a9ia' &a '&rfa9'or '/.6. 5 Ta/aa a96ial '&9a Ta/aa "o"& l&'8r '/.6. ; Ta/aa "o"& l&'8r '/.6. 5
[C]:2011 : M!
"olo# .entur Dua /rah $Biaxial%
N8 = M8; = M85 = φ N = φ M; = φ M5 =
30$000 %4$00000 1$100000 11#$1$2 2$3$11272 4%#3!44$
N N"" N"" N N"" N""
2%
Perhitungan Struktur Baja Dengan Microsoft Excel
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 M5 , N8 ) φ N ≤ 0.20 U'89 ilai N8 ) 2 φ N > * M8; ) φ M; > M85 ) φ M5 , →
≤ 1.0
→
≤ 1.0
N8 ) φ N = 0.2#1! > N8 ) φ N > !)%* M8; ) φ M; > M85 ) φ M5 , = N8 ) 2 φ N > * M8; ) φ M; > M85 ) φ M5 , =
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' aa 'aa &-a98 /ar86 "&"&8/i 65ara'
/2 ) '( 42.7$
#.3# <
E ) f 5
1!3.#0
"lat badan memenuhi s#arat $OK%
Ko'rol 'a/aa -&6&r o"ial la' aa 'aa &-a98 : 8 = 207000 Ga5a -&6&r a9ia' &a '&rfa9'or A( = '( /' = L8a6 &a"a- aa 3200 = 0.#0 f 5 A( = 4#0!00 Ta/aa -a5a -&6&r o"ial φf = 34$#00 → Ta/aa -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"ia6i -&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 M5 > 0.#2$ 8 ) φf
[C]:2011 : M!
"olo# .entur Dua /rah $Biaxial%
1.37$
30