PERHITUNGAN KOLOM LENTUR DUA ARAH (BIAXIAL) BIAXIAL) KOLOM PADA PORTAL BANGUNAN BANGUN AN
A. DATA DATA BAHAN BAH AN
f 1 = f r = E= υ =
T)(a&(a& l)l)+ a'a yield stress5 T)(a&(a& T)(a&(a& -i-a -i -a residual stress5 Mo,l- )la-*i a'a modulus of elasticity 5 5 A&(a Poi--o& Poisson's ratio5
240 70 200000 0.3
MPa MPa MPa
B. DA D ATA PROFIL BAJA B AJA Profil : *f *6
+ +2
+*
r
+! .f
WF 400.200..!3 +* = 400 f = 200 *6 = *f = !3 r= !# A = 4!0 / = 237000000 1 = !7400000 r / = !# r 1 = 4$.4 8/ = !!%0000 81 = !74000
"" "" "" "" "" ""2 ""4 ""4 "" "" ""3 ""3
C. DATA KOLOM Pa&'a&( )l)")& *+,.-. / Pa&'a&( )l)")& *+,.-. 1 Ga1a a-ial aia* )a& *)rfa*or Mo")& aia* )a& *)rfa*or *+,.-. / Mo")& aia* )a& *)rfa*or *+,.-. 1 Ga1a ()-)r aia* )a& *)rfa*or Fa*or r),-i )a*a& &* a-ial *)a& Fa*or r),-i )a*a& &* l)&*r Fa*or r),-i )a*a& &* ()-)r
L/ = 4$00 "" L1 = 4$00 "" N = 30$000 N M/ = %4$00000 N"" M1 = !$!00000 N"" 9 = 207000 N φ& = 0.$ φ = 0.%0 φf = 0.7$
D. SECTION PROPERTIES
G = E > ?2@! υ5 = 7#%23.07#% MPa +! = *f r = 2%.00 "" +2 = +* 2 @ + ! = 342.00 "" + = +* *f = 37.00 "" < = Σ ? @ * 3>3 = 2 @ !>3 @ f @ *f 3 !>3 @ + * 2 @ *f 5 @ *63 = 3$#7#2.7 ""4 6 = 1 @ +2 > 4 = #.$!$E!! ""# ! = π > 8/ @ ? E @ G @ < @ A > 2 = !2#2.% MPa 2 = 4 @ ? 8/ > G @ <5 2 @ 6 > 1 = 0.0002!# ""2>N2 / = *6 @ +*2 > 4 f *6 5 @ +* *f 5 @ *f = !2$%$2.0 ""3 1 = *f @ f 2 > 2 +* 2 @ *f 5 @ *62 > 4 = 2#$%4.0 ""3 / = "o,l- ;)&a";a&( ;la-*i- *+,. -. / G = "o,l- ()-)r 1 = "o,l- ;)&a";a&( ;la-*i- *+,. -. 1 < = Ko&-*a&*a ;&*ir *or-i 6 = o&-*a&*a ;*ir l)&(&( ! = o)fi-i)& "o")& *) *or-i la*)ral 2 = o)fi-i)& "o")& *) *or-i la*)ral + = *i&((i )r-i+ a,a&
KOLOM BAAL BENDNG
FAKTOR PAN
3 = L3 =
3 = L3 =
4$00
3400000 7000
2 = L2 = ! = L! =
237000000
B 237000000
GB/ = Σ
4$00
3400000 7000
! = L! =
4 = L4 =
A 237000000
2 = L2 = G A/ = Σ
4$00
3400000
L5 = !0$333 Σ > L5 = %%43 > L 5 > Σ > L 5 = !0.# 7000
3400000
L5 = !0$333 Σ > L5 = %%43 > L 5 > Σ > L 5 = !0.# Fa*or ;a&'a&( *) )f)*if *+,.-. / 7000
/ = ? 3@G A/@GB/ !.4@G A/ GB/5 0.#4 > ? 3@G A/@GB/ 2.0@G A/ GB/5 !.2
→
*+,.-. :
3 = L3 =
3 = L3 =
! = L! =
4$00
$000
B !7400000
$000
A !7400000 4$00
4 = L4 = GB1 = Σ
4$00
!2$0000
! = L! =
0.%#4%
!7400000
!2$00000
2 = L2 =
/ =
2 = L2 = G A1 = Σ
!2$00000
L5 = 7733 Σ > L5 = $000 > L 5 > Σ > L 5 = !.$ $000
!2$00000
L5 = 7733 Σ > L5 = 27$0 > L 5 > Σ > L 5 = 2. Fa*or ;a&'a&( *) )f)*if *+,.-. 1 $000
1 = ? 3@G A1@GB1 !.4@G A1 GB15 0.#4 > ? 3@G A1@GB1 2.0@G A1 GB15 !.2
→
=
0.$7$
E. PERHITUNGAN KEKUATAN 1. TAHANAN AKSIAL TEKAN
Fa*or *) olo" ,i+i*&( ,)&(a& r"- -)a(ai )ri* : a. U&* &ilai λ ≤ 0.2$ "aa *)r"a- olo" pendek : →
ω = !
. U&* &ilai 0.2$ H λ ≤ !.20 "aa *)r"a- olo" sedang : →
ω = !.43 > !.# 0.#7 @ λ 5
. U&* &ilai λ I !.20 "aa *)r"a- olo" langsing : →
ω = !.2$ @ λ2
Menentukan a!a"ete! ke#an$%&n$an '
Fa*or ;a&'a&( *) )f)*if *)r+a,a; -" / Fa*or ;a&'a&( *) )f)*if *)r+a,a; -" 1 Pa&'a&( olo" *)r+a,a; -" / : Pa&'a&( *) )f)*if *)r+a,a; -" / Pa&'a&( olo" *)r+a,a; -" 1 : Pa&'a&( *) )f)*if *)r+a,a; -" 1 Para")*)r )la&(-i&(a& *)r+a,a; -" /
/ = 1 = L/ = L/ = / @ L/ = L1 = L1 = 1 @ L1 =
λ/ = ! > π @ L/ > r / @ f 1 > E 5 =
0.%# 0.# 4$00 4342 4$00 3#4 0.2$0
Para")*)r )la&(-i&(a& *)r+a,a; -"
λ1 = ! > π @ L1 > r 1 @ f 1 > E 5 =
0.%3#
Menentukan n&#a& akt! tekuk te!*a+a %u",u - '
λ/ = U&* ;ara")*)r )la&(-i&(a& *)r+a,a; -" / ω = a. Kolo" pendek : ω = !.43 > !.# 0.#7 @ λ 5 = . Kolo" sedang : ω = !.2$ @ λ2 = . Kolo" langsing : ω/ = → Fa*or *) *)r+a,a; -" /
0.2$0 !.0!4% !.0!4%
Menentukan n&#a& akt! tekuk te!*a+a %u",u '
λ1 = U&* ;ara")*)r )la&(-i&(a& *)r+a,a; -" 1 ω = a. Kolo" pendek : ω = !.43 > !.# 0.#7 @ λ 5 = . Kolo" sedang : ω = !.2$ @ λ2 = . Kolo" langsing :
0.%3# !.472$
"" "" "" ""
→
Fa*or *) *)r+a,a; -" 1
ω1 =
!.472$
f r/ = f 1 > ω/ = f r1 = f 1 > ω1 =
23#.4# !#2.%%2
MPa MPa
N&/ = A @ f r/ = N&1 = A @ f r1 = N& = φ& @ N& =
!%43 !3707#7 !3707#7 !!#$!$2
N N N N
Te$an$an tekuk '
T)(a&(a& *) *)r+a,a; -" / T)(a&(a& *) *)r+a,a; -" 1 Ta*anan ak%&a# tekan '
Ta+a&a& a-ial *)a& &o"i&al *+,.-. / Ta+a&a& a-ial *)a& &o"i&al *+,.-. 1 Ta+a&a& a-ial *)a& &o"i&al *)r)il Ta+a&a& a-ial *)a&
. MOMEN NOMINAL PENGARUH LOCAL BUCKLING PADA SA2AP
Mo")& &o"i&al ;)&a";a&( aia* ;)&(ar+ loal li&( ;a,a -a1a; &* : λ ≤ λ; a. P)&a";a&( compact : →
. P)&a";a&( non-compact : →
. P)&a";a&( langsing : →
M& = M; λ; H λ ≤ λr M& = M; M; Mr 5 @ λ λ;5 > λr λ;5 λ I λr M& = Mr @ λr > λ 52
M;/ = f 1 @ / = Mo")& ;la-*i- *+,.-. / Mr/ = 8/ @ f 1 f r 5 = Mo")& a*a- *) *+,.-. / M;1 = f 1 @ 1 = Mo")& ;la-*i- *+,.-. 1 Mr1 = 81 @ f 1 f r 5 = Mo")& a*a- *) *+,.-. 1 λ = f > *f = K)la&(-i&(a& ;)&a";a&( -a1a; Ba*a- )la&(-i&(a& "a-i"" &* ;)&a";a&( compact
λ; = !70 > f 1 =
30#240 202300000 #33#!#0 2%$0000 !$.3$
N"" N"" N"" N""
!0.%73
Ba*a- )la&(-i&(a& "a-i"" &* ;)&a";a&( non-compact
λ
/
λ;
λr = 370 > f 1 f r 5 = λ 0 ,a&
B)r,a-ara& &ilai )la&(-i&(a& -a1a; "aa *)r"a- ;)&a";a&(
2.37
λr non-compact
M"en n"&na# t*+.%,. - ' compact :
M&/ = M;/ =
N""
M&/ = M;/ M;/ Mr/5 @ λ λ;5 > λr λ;5 = 2!#7%!%! N"" M&/ = Mr/ @ λr > λ 52 = langsing : N"" M&/ = 2!#7%!%! N"" non-compact Mo")& &o"i&al &* ;)&a";a&( : non-compact :
M"en n"&na# t*+.%,. '
M&1 = M;1 = N"" M&1 = M;1 M;1 Mr15 @ λ λ;5 > λr λ;5 = $$!$32 N"" non-compact : M&1 = Mr1 @ λr > λ 52 = langsing : N"" M&1 = $$!$32 N"" non-compact Mo")& &o"i&al &* ;)&a";a&( : compact :
5. MOMEN NOMINAL PENGARUH LOCAL BUKLING PADA BADAN
K)la&(-i&(a& ;)&a";a&( a,a& Ga1a a-ial l)l)+
λ = + > * 6 = 4.37$ N1 = A @ f 1 = 20!400 N N > φ @ N1 5 = 0.!# N
a. Ba*a- )la&(-i&(a& "a-i"" &* ;)&a";a&( compact : N > φ @ N1 5 ≤ 0.!2$ U&* &ilai →
U&* &ilai →
λ; = !#0 > f 1 @ ? ! 2.7$ @ N > φ @ N1 5 N > φ @ N1 5 I 0.!2$ λ; = $00 > f 1 @ ? 2.33 N > φ @ N1 5 ≥ ##$ >
f 1
. Ba*a- )la&(-i&(a& "a-i"" &* ;)&a";a&( non-compact : →
λr = 2$$0 >
f 1 @ ? ! 0.74 @ N > φ @ N1 5
N > φ @ N1 5 / λ; = !#0 > f 1 @ ? ! 2.7$ @ N > φ @ N1 5 = λ; = $00 > f 1 @ ? 2.33 N > φ @ N1 5 = λ; = ##$ > f 1 = λ; = Ba*a- )la&(-i&(a& "a-i"" ;)&a";a&( compact U&* &ilai :
3.14
#%.7! 42.%2# #%.7!
Ba*a- )la&(-i&(a& "a-i"" ;)&a";a&( non-compact
λr = 2$$0 > λ
0
f 1 @ ? ! 0.74 @ N > φ @ N1 5 = λ; λ 0 ,a&
B)r,a-ara& &ilai )la&(-i&(a& a,a& "aa *)r"a- ;)&a";a&(
!44.!$!
λr compact
M"en n"&na# t*+.%,. - ' compact : non-compact :
M&/ = M;/ = 30#240 N"" M&/ = M;/ M;/ Mr/5 @ λ λ;5 > λr λ;5 = N""
M&/ = Mr/ @ λr > λ 52 = N"" M&/ = 30#240 N"" Mo")& &o"i&al *+,.-. / : ;)&a";a&( compact langsing :
M"en n"&na# t*+.%,. '
M&1 = M;1 = #33#!#0 N"" M&1 = M;1 M;1 Mr15 @ λ λ;5 > λr λ;5 = non-compact : N"" 2 M&1 = Mr1 @ λr > λ 5 = langsing : N"" M&1 = #33#!#0 N"" Mo")& &o"i&al *+,.-. 1 : ;)&a";a&( compact compact :
6. TAHANAN MOMEN LENTUR
Mo")& &o"i&al )r,a-ara& ;)&(ar+ local buckling ;a,a -a1a; M&/ = Mo")& &o"i&al *+,.-. / M&1 = Mo")& &o"i&al *+,.-. 1 Mo")& &o"i&al )r,a-ara& ;)&(ar+ local buckling ;a,a a,a& M&/ = Mo")& &o"i&al *+,.-. / M&1 = Mo")& &o"i&al *+,.-. 1 Mo")& &o"i&al *)r)il5 1a&( ")&)&*a& → M&/ = Mo")& &o"i&al *+,.-. / → M&1 = Mo")& &o"i&al *+,.-. 1 Ta+a&a& "o")& l)&*r *+,.-. / Ta+a&a& "o")& l)&*r *+,.-. 1
2!#7%!%! N"" $$!$32 N"" 30#240 N"" #33#!#0 N""
2!#7%!%! $$!$32 φ @ M&/ = 2$3$!!272 φ @ M&1 = 4%#344$
N"" N"" N"" N""
4. INTERAKSI AKSIAL TEKAN DAN MOMEN LENTUR
N = 30$000 Ga1a a-ial aia* )a& *)rfa*or M/ = %4$00000 Mo")& aia* )a& *)rfa*or *+,.-. / M1 = !$!00000 Mo")& aia* )a& *)rfa*or *+,.-. 1 φ& @ N& = !!#$!$2 Ta+a&a& a-ial *)a& φ @ M&/ = 2$3$!!272 Ta+a&a& "o")& l)&*r *+,.-. / φ @ M&1 = 4%#344$ Ta+a&a& "o")& l)&*r *+,.-. 1 Kolo" 1a&( ")&a+a& (a1a a-ial *)a& ,a& "o")& l)&*r +ar- ")")&+i ;)r-a"aa& i&*)ra-i a-ial *)a& ,a& "o")& l)&*r - :
N N"" N"" N N"" N""
N > φ& N& 5 I 0.20 N > φ& N& 5 > % @ ? M/ > φ @ M&/ 5 M1 > φ @ M&1 5 → N > φ N& 5 ≤ 0.20 U&* &ilai N > 2 @ φ& N& 5 ? M/ > φ @ M&/ 5 M1 > φ @ M&1 5 → U&* &ilai
N > φ& N& 5 = 0.2#! / N > φ& N& 5 >%@? M/ > φ @ M&/ 5 M1 > φ @ M&1 5 = N > 2 @ φ& N& 5 ? M/ > φ @ M&/ 5 M1 > φ @ M&1 5 =
U&* &ilai :
≤ !.0 ≤ !.0
3.3
0.#3$ 0.#3$
Nilai i&*)ra-i a-ial *)a& ,a& "o")& l)&*r = 0 AMAN (OK) 0.#3$ !.0 7. TAHANAN GESER
K)*)ala& ;la* a,a& *a&;a ;)&(a +ar- ")")&+i -1ara*
+2 > *6 42.7$
#.3# @ 0
E > f 1 5
!3.#0
Plat badan memenuhi sa!at "OK#
Ko&*rol *a+a&a& ()-)r &o"i&al ;la* a,a& *a&;a ;)&(a : 9 = 207000 Ga1a ()-)r aia* )a& *)rfa*or A6 = *6 @ +* = La- ;)&a";a&( a,a& 3200 9& = 0.#0 @ f 1 @ A6 = 4#000 Ta+a&a& (a1a ()-)r &o"i&al φf @ 9& = 34$#00 → Ta+a&a& (a1a ()-)r 9 φf @ 9& 81ara* 1( +ar- ,i;)&+i : 0 AMAN (OK) 207000 34$#00
9 > φf @ 9& 5 =
0.$%%0
N ""2 N N
0 1.3 (OK)
8. INTERAKSI GESER DAN LENTUR
El)")& 1a&( ")"il o"i&a-i ()-)r ,a& l)&*r +ar- ,ilaa& o&*rol -. : 8a1ara* 1a&( +ar- ,i;)&+i &* i&*)raa-i ()-)r ,a& l)&*r :
M/ > φ M&/ 5 M1 > φ @ M&1 5 0.#2$ @ 9 > φf @ 9& 5 M/ > φ @ M&/ 5 =
!.37$ 0.372
M/ > φ
M1 > φ @ M&1 5 = 9 > φf @ 9& 5 = M&/ 5 M1 > φ @ M&1 5 0.#2$@ 9 > φf @ 9& 5 = !.0$!3
0
1.584
AMAN (OK)
0.3042 0.$%%0 !.0$!3
