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BAB III
PERHITUNGAN PORTAL LANTAI 2
A.Perhitungan Portal
I2 I2
I1I1
A
B
C
D
E
1.82
4.00
5.33
h=
f =
S=
10.00L=
Gambar 3.1 Gambar Rencana Portal
1.Data Perhitungan
Bentang kuda kuda = 10 m
Tinggi kolom = 4 m
Tinggi kuda-kuda = 1,8 m
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!i"i miring kuda-kuda = #,33 m
$arak gording = 1,# m
$arak antar kuda-kuda = 4 m
%emiringan ata& = 0'
Berat &enutu& ata& = 10 kg(m) *!eng Gelombang+
Berat &laon dan &enggantung = 10 = 1 kg(m)
2.Pembebanan u!a"#u!a $a%&tang'
Balok /ang direncanakan menggunakan 3#0.3#0.10.12 = 142 cm
= 11# kg(m
I5 = 33300 cm4I/ = 1100 cm4
5 = 1640 cm3
/ = 242 cm3
a. Beban gording Berat "endiri &enutu& ata&7 4 m 5 10 kg(m5 1,# m = 20 kg Berat "endiri gording7 10 kg(m 5 4 m = 40 kg Berat "endiri kuda-kuda 7 1 ,# m 5 11# kg(m = 1,# kg
= ,# kg
Berat alat &en/ambung 7 10 5 Berat total = ,# kg tot = 66,# kg Berat 9idu& *P+ = 00 kg
P tot = 466,# kg
b.Beban merata
q= P
1
2 L
q=9 .499,75
1
2.10
= 866,## kg(m
c. Beban angin
Beban angin untuk gedung tertutu& dengan ata& "egitiga dengan kemiringan
: 2#o* P;I 160, 9al 0+ maka, %oei"ien angin tekan7
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00,. < -0,4 = 0,0 5 0 0,4 = 0
%oei"ien angin 9i"a& = -0,4>ntuk dinding ?ertikal di&i9ak angin, koei"ienn/a 0,60 dan untuk
dibelakang angin adala9 0,4
Pembebanan &ada ata&- ngin tekan *@t+
t = koei"ien angin tekan 5 Aarak kuda-kuda 5 @= 0,1 5 4 m 5 # kg(m = 10 kg(m
- ngin 9i"a& *@9+9 = koei"ien angin 9i"a& 5 Aarak kuda-kuda 5 @
= -0,4 5 4 5 # kg(m = -40 kg(m
Pembebanan kolom te&i- ngin tekan *@t+
t = koei"ien angin tekan 5 Aarak kuda-kuda 5 @= 0,6 5 4 m 5 # kg(m = 60 kg(m
- ngin 9i"a& *@9+9 = koei"ien angin 9i"a& 5 Aarak kuda-kuda 5 @
= -0,4 5 4 5 # kg(m = -40 kg(m
d. %ombina"i Pembebanan &ada %uda-kuda
Pembebanan teta&Beban mati beban 9idu& = 866,## kg(m
Pembebanan "ementaraBeban mati Beban 9idu& Beban angin
>ntuk kombina"i &embebanan &ada &embebanan angin diuba9 menAadi beban
?ertikal7 = t . co" 0o= 10 co" 0o= 6,362 kg(m = 9 . co" 0o= -40 co" 0o= - 3,#84 kg(m
= beban angint = 866,## 6,362
= 608,642 kg(m9 = 866,## *-3,#84+
= 821,622 kg(m
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>ntuk &er9itungan momen, maka dari beban diata" diambil &embebanan /ang
terbe"ar 7 *t = 608,642 kg(m+
(. Perhitungan ga)a"ga)a !alam %a!a %ortal
>ntuk mencari be"arn/a momen /ang terAadi &ada "truktur &ortal diata",
digunakan rumu" menurut Ra9men ormeln %leinlogel adala9 "ebagai berikut 7
a. %oei"ien
k=I2
I1.
h
s=
20400
20400. 4
5,33=0,750 m
=f
h=
1,82
4=0,455 m
m=1+ = 1 0,4## = 1,4## m
B = *k 1+ m = *0,#0 1+ 1,4## = 4,6## m
C = 1 m = 1 5 1,4## = 3,61 m
D = B m 5 C = 4,6## 1,4## 5 3,61 = 10,24 m
A
B
C
D
E
10.00L=
1.82
4.00h=
f =
W
b.Ti&e I *akibat beban dari ata& dan angin ara9 ?ertikal+
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- Perhitungan momen beban mati
@ = t = 608,642 kg(m
;B = ;E =w L2(3+5 . m )
16N=
908,946 x 102(3+5 . 1,455)16 .10,64
= -#482,03 kgm
;C =w L
2
8+m MB =
908,946x102
8 1,4## 5 *-#482,03+
= 11321,8 *-68,31+
= 336,#1 kgm
- Reaksiakhir
F= F=
w , L
2 =
908,946 .10
2 = 4#44,3 kg
H = H=MB
h=
(5486,03)4
= 131,#1 kg
- Perhitungan momen beban hidup
P = 00 kg
m = . P. J = . 00 kg . 10 m = #00 kgm
= 8. mL
2 = 8.50010
2 = 40 kg(m
;B = ;E =w L2(3+5 . m)
16N=
40x102(3+5 .1,455)16 .10,64
= -41,4 kgm
;C =w L
2
8+m MB =
40x102
81,4## 5 *-41,4+
= #00 *-3#1,22+
Gambar 3. Pembebanan ra9 Fertikal
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= 148,34 kgm
- Reaksi akhir
F= F=w , L
2=
40 .10
2= 00 kg
H = H=MB
h=
(241,42)4
= 20,3## kg
- Perhitungan momen beban angin
t = 60 kgm
@ = t 5 0,#
= 60 kgm 5 0,# = 4#
;B = ;E =w L2(3+5 . m )
16N=
45x102(3+5 . 1,455)16 . 10,64
= -1,20 kgm
;C =w L
2
8+m MB =
45x102
81,4## 5 *-1,20+
= #2,# *-36#,1+
= 12,3 kgm
- Reaksiakhir
F= F=w , L
2=
45 .10
2= # kg
H = H=
MBh =
(271.60)4 = 2,6 kg
Eari &er9itungan diata" dida&atkan 9a"il 7
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HE
B
C
D
VA
HE
VE
ME
--
HA
-
+
-
+
S/2
wf16
MA
A E
;B = ;E = -#482,03 kgm
;C = 336,#1 kgm
F = F = 4#44,3 kg
H = H= 131,#1 kg
N=VA sin+HA cos=4544,73sin200+1371,51cos200=2843,18kg
= VA co" < = 4544,73cos20o = 40,24 kg
Gambar3.3 Eiagram ;omen, Ga/a Jintangdan Ga/a Dormal
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E = co"< D "in < = 40,24 co" 0o 843,18 "in 0o = 468#,#1 kg
c. Ti&e II *akibat beban angin ara9 9oriKontal+
= t . co" #o= 10 co" 0o= 6,362 kg(m = 9 . co" #o= -40 co" 0o= - 3,#86 kg(m
A
B
C
D
E
10.00L=
1.82
4.00h=
f =
Ei&akai nilai /ang terbe"ar = 6,362 kg(m
- Perhitungan momen primer
Gambar 3.4 Pembebanan ngin Pada ta& ra9 HoriKontal
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L=w f
2(C+m)8.N
=9,396 x 1,82
2(3,91+1,455)8 . 10,64
= 1,0 kgm
;B= L wfh2
= 1,0 9,396 .1,82 . 42
= 1,0 34,0
= 3#, kgm
;C= -w f
2
4 mL = - 9,396 .1,82
2
4 1,4## 5 3#,
= -,8 #1,3
= -43,#4 kgm
;E = L - wfh
2 = 1,0
9.396 .1,82 . 4
2
= 1,0 34,0
= -33,13 kgm
- Reaksi akhir
F=-F= -wfh(1+m)
2L= -
9,396 .1,82 .4(1+1,455)2.10
= -8,36 kgH=
Xh
w f2
4= 1,077
4
9,396 .1,822
4
= - 0,26 ,8
= -8,046 kg
H =X
h+
w f2
4= 1,077
4 +
9,369 .1,822
4
= -0,26 ,8
= 8,046 kg
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= -10,433 kg
= VA co" < = 8,39cos20o = -,88 kg
E = co"< D "in < = *-,88+ co" 0o *-10,433+ "in 0o
= -10,6 kg
d. Ti&e III *akibat beban angin ara9 kolom 9oriKontal+
t = koei"ien angin tekan 5 Aarak kuda-kuda 5 @= 0,6 5 4 m 5 # kg(m = 60 kg(m
A
B
C
D
E
10.00L=
1.82
4.00h=
f =
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HA
B D
VA
MA
VE
-+
wf8
2.00
C -
H= (whHE) = -* 5 4 8,3+ = -06, kg
Eari &er9itungan diata" dida&atkan 9a"il 7
;B = 402,8 kgm
;C = -6#,02 kgm
Gambar3.Eiagram ;omen, Ga/a Jintangdan Ga/a Dormal
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;E = -313, kgm
F = -F = - kg
H = -06, kg
H= 8,3 kg
N=VA sin+HAcos=72sin 200+(209,7)cos200
= -1,2 kg
= VA co" < = 72cos20o = -2,2# kg
E = co"< D "in < = *-2,2#+ co" 0o *-1,2+ "in 0o
= *-23,#+ *-#,81+ = 136,38 kg
e. Tabel kombina"i &embebanan
kibat beban
merata
kibat angin
&ada ata&
kibat angin
&ada kolom
Ha"il *Eiambil
;omen /ang
terbe"ar +;mak" -#482,03 -43,#4 -402,8 #482,03 kgm
D 843,18 10,43 221,67 843,18 kg 40,24 kg -,88 kg -2,2# 40,24 kgE 468#,#1 -10,6 136,38 468#,#1 kg
;mak" = #482,03 kgm
D = 843,18 kg = 40,24 kg
E = 468#,#1 kg
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B. Perhitungan Dimen&i Penam%ang
Eigunakan baAa ti&e 3#0.3#0.10.12 *tabel &roil baAa 9al +
3
0.10
3.50
0.16
= 11#,0 kg(m
= 142,0 cm
5 = 1640 cm4
/ = 242 cm4
I5 = 33300 cm3
I/ = 1100 cm3
i5 = 1#,1 cm
i/ = 8,8 cm
b = 3#0 mm = 3# cm
9 =3#0 mm = 3# cm
tb = 10mm = 1,0 cm
t" = 12mm = 1,2 cm
1. ontrol tegangan
Wx
M
A
N+=
Gambar 3.8 BaAa 3#0.3#0.10.12
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=3 1640
03,#482
0,142
843,18
cm
kgcm
cm
kg+
(1400(301, cmkgijincmkg ==
2. ontrol tegangan ge&er
(811400#8,0
#8,0
cmkgx
ijinx
==
=
M = *b t"+ . 4.
htbhtsh +
= 43#.
0,13#
2,13#.+2,13#*
+
= 02,#3 cm
= N .
! .Ix: *PPBBI 1684 7 #+
2843,18 kg .706,53 cm
2
1,0cm .33300 cm4
= 20,34 kg(cm : 02,#3 kg(cm *N%+
3.50
0.10
3.50
0.16
22,301 k/!"
60,324 k/!"
22,301 k/!"
(. ontrol %erubahan bentu# %enam%ang
Gambar3.6 Eiagram Tegangan
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PPBBI O84 7 41 *1+ 7
h
! #
35cm1,0cm
#
3# cm # *N%+
;encari &anAang tekuk "endi-"endi *PPBBI 1684 9al 1#+
Jk = 1,0 J
= 1,0 5 #,33 = #,33 m = #,33 cm
L
h. Q 1,#
!
s =
5,33
0,35>1,25 0,35
0,016
= 1#,3 cm Q ,34 cm *N% +
Eari &er9itungan diata" ba9@a &enam&ang tidak beruba9 bentuk.
*. ontrol len!utan
*PPBBI, 168471#+ bata" lendutan mak"imum ara9 ?ertical untuk balok
&endukung ata& adala9 J(#0.
Jk = 1,0 J
= 1,0 5 #,33
= #,33 m
ma5=1
250L =
1
250#,33 = ,13 cm
= 5q"L4
348E I"
= 5.37 .5334
348 .2100000 .33300=0,61 cm : ma5 = ,13 cm *N%+
+. ontrol li%at
Ji&at "a/a&
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*PPBBI, 168474+ &a"al . a/at 2, untuk mema"tikan ba9@a "tabilita" batang-
batang tekan atau elemen /ang dibebani lentu rtidak terganggu ole9 ba9a/a
li&at &erbanding anantara lebar dan tebal &elat 9aru" memenu9i 7
!s
#10
$%$&
Eimana 7 d = tegangan tekan terbe"ar /ang terAadi *9arga mutlak 1+ r = 32 kg(cm untuk &elat-&elat /ang tidak di&erkuat
350
16#10
3267
449,68'21,875 #26,95 *N%+
Ji&at badan
!e"uai PPBBIO84 9alaman 4 Bab 2 a/at 3, ba9@a dalam &emerik"aan ter9ada&
ba9a/a li&at, keem&at "i"i badan itu diangga& ber"iat "endi. $ika &erbandingan
antara tinggi dan tebal badan lebi9 kecil dari 20, &emerik"aan ter9ada& ba9a/a
li&at dari badan tidak di&erlukan.
Perbandingan tinggi dantebal badan7350
10=35
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B E
A E
C
SAMB#$%A$ C &SAMB#$%A$ 'ADA
'#$CA( (A'S)A$%*
C
0.2
1.0
1.0
1.0
1.0
1.0
0.8
0.2
= 3#0 L 3#0 L 10 L 12
,. Perhitungan
-ambungan Pa!a Puna# a%&tang
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Eata &er9itungan 7
;ma5 = #48203 kgcmEma5 = 468#,#1 kg
D = 843,18 kgEirencanakan "ambungan menggunakan baut dan la".>ntuk tebal &elat &en/ambung /ang di&akai adala9 10 mm dan diameter
bautn/a adala9 12 mm.
1. Per9itungan !ambungan Baut
Tenga9S ,# d u d
S ,# *+ u *+
S ## u 1#4 di&akai Aarak u = 80 mm
8 cm di&akai Aarak u = 100 mm10 cm
Te&iS 1,# d u1 3 dS 1,# *+ u1 3 *+S 33 u1 22 di&akai Aarak ! = #0 mm# cm
Gambar3.10 Perletakan !ambungan
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di&akai Aarak ! = 20 mm2 cm
Gambar 3.11 Rencana !ambungan Baut
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a. %ontrol tegangan tarik baut
Plat &en/ambung tebal 10 mm, di&akai baut U 12 mm
/1 = 2 cm /1
= 2
= 32 cm
/ = 14 cm / = 14 = 162 cm
/3 = 4 cm /3 = 4 = #2 cm
/4 = 34cm /4 = 34 = 11#2 cm
/# = 44 cm /# = 44 = 1632 cm
/2 = #4cm /2 = #4 = 612 cm
V/ = 2812 cm
D1=M " . (1
2 (2 =
548603 kgcm .6cm
2" 6816 cm2 = 41,42 kg
D=M " . (
2
2 (2
=548603 kgcm .14 cm
2" 6816 cm2 = #23,41 kg
D3=M " . ( 3
2 (2 =
548603 kgcm .24cm
2" 6816 cm2 = 62#,8#0 kg
D4=M " . (
4
2 (2
=548603 kgcm .34cm
2" 6816 cm2 = 1328,8 kg
D#=M " . ( 5
2 (2 =
548603 kgcm .44cm
2" 6816 cm2 = 10,# kg
D2=M " . ( 6
2 (2
= 548603 kgcm .54 cm2" 6816 cm
2 = 13,123kg
>ntuk &er9itungan kontrol tegangan tarik baut diambil nilai D /ang terAau9
/aitu D2.
tarikbaut=N
1
4. ) .
2 =2173,163 kg
1
4. 3,14 .(2,2)2 = #1,68 kg(cm
#1,68 kg(cm
: 0, *1400 kg(cm
+#1,68 kg(cm : 680 kg(cm *N%+
b.%ontrol ge"er akibat ga/a lintang
W=D
1
43,14" &
2 =4 985,51
1
4. 3,14 . 2,2
2
= 810,0 kg(cm : 0,#8 = 81 kg(cm* N% +
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%ombina"i tegangan ge"er X tegangan tarik /ang diAinkan
*PPBBI O84 9al. 28+
i =
#2,1 +
= +0,810*#2,168,#1 +
= 112,2 kg(cm) : 1400 kg( cm) *N%+
. Per9itungan !ambungan Ja"
a. Tebal la"
Tebal la" badan = Y 5 Z 5 4 = ,8 mm [ 3 mm
Tebal la" "a/a& = Y 5 Z 5 6 = 2,4 mm [ 2 mm
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b. !tati" momen la" ter9ada& la" bagian ba@a9
Bidang $umla9 b 9 $arak Jua" ;omen !tati" bua9 cm cm cm cm cm3
!1 1 0,00 0,20 0,30 1 3,20! 6,0 0,20 ,0 11,04 4,88!3 0,30 1,2# 10,4# 10,#6 110,4!4 6,0 0,20 16,# 11,04 1,#!# 6,0 0,20 0,8# 11,04 30,18!2 0,30 3,4# 36,## ,4 886,#
! 6,0 0,20 #8,30 11,04 243,23!8 1 0,00 0,20 #6,60 1 18,8
Total 101, 83,2
$arak titik berat &roil *"umbu 5+ akibat la" *ditinAau dari la" bagian ba@a9+7
Lb= V!( V
= 83,2cm3 (101, cm
= ,68 cm *dari la" bagian ba@a9+
$arak titik berat &roil *"umbu 5+ akibat la" *ditinAau dari la" bagian ata"+7La= 9 total &roil "etela9 dila" Lb
= #6,60 cm ,68cm
= 31,6 cm *dari bagian ata" la"+
Gambar 3.1 Perencanaan !ambungan Ja"
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I5 = 1
12b93 J
Bidang $umla9 b 9 $arak Jua" ;omen Iner"ia bua9 cm cm cm cm cm3
!1 1 0,00 0,20 ,68 1 406,88! 6,0 0,20 #,8 11,04 314,11!3 0,30 1,2# 12,## 10,#6 18#2,0#!4 6,0 0,20 ,3 11,04 64,14!# 6,0 0,20 #,#3 11,04 24,01!2 0,30 3,4# 13,16# ,4 222,1! 6,0 0,20 6, 11,04 32,3!8 1 0,00 0,20 31,6 1 4#6#,1
Total 101, ##4,36
b =25524,39
27,98=912,06 cm3
a =25524,39
31,92=799,77 cm3
c. %ontrol tegangan la"
kibat ;omen
$m=M*+=548603799,77 = 28#,6# kg(cm: 1400 kg(cm *N%+
d.kibat ga/a ge"er
= E(= 468#,#1 (101,= 46,# kg(cm
;enurut PPBBI 16847#
$i&=$2+3 ()
2# $i,in
$i&=685,952
+3 ( 49,25 )2
# $iin
Gambar 3.13 Titik Berat !ambungan Ja"
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$i& = 261,33 kg(cm : $iin = 0, 5 1400 kg(cm
$i& = 261,33 kg(cm : $iin = 680 kg(cm * N%+
3.50
0.10
3.50
0.16
4+,25 k/!"
6+1,233 k/!"
6+1,233 k/!"
D. Perhitungan antile/er $O/er&te#'
1. Per9itungan Pembebanan
a. Pembebanan kantile?er
Gambar 3.14 Eiagram Tegangan
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Berat "endiri &enutu& ata&7 4 m 5 10 kg(m5 1,# m = 20 kg( m
Berat "endiri gording7 11kg/m .4m.1!-+h
1,50m= 6,33
kg( mBerat "endiri kuda-kuda 7 1 ,# m 5 11# kg(m = 1 ,# kg ( m
= 21,83 kg( mBerat alat &en/ambung 7 10 5 Berat total = 2,183 kg ( m tot = 88,013 kg( m
Berat 9idu& *P+ = 00 kg ( mP tot = 488,013 kg( m
b. Reak"i /ang bekerAa;mak"= Y . . J
= Y 5 488,013 kg(m 5 *1,#+m
= #46,014 kgm = #4601,4 kgcmF = = 5 J= 488,013 kgm 5 1,#0 m= 3,016 kg
D = F5 "in