Data Konstruksi Struktur a. Ketentuan umum Data:
Panjang Jembatan (L) Lebar Jalan Lebar Trotoar Lebar Keseluruhan Jumlah Gelagar Tngg Gelagar Tngg "#g $am%ng Jembatan Jara' antar gelagar Jumlah aragma Tebal La%san +s%al Tebal $lab Jara' Permu'aan tanah #engan #asar sunga
b. Konstruks
= = = = = = = = = = = =
19.50 m 7.50 m 1.15 m 9.80 m 5.00 bu buah 1.! m &.8 m 1.5 m *.00 bu b uah 0.05 m 0.& m !.00 m
i
T%e Jembatan -utu "eton () -utu bes tulangan (/) Kelas Jalan Jens Perleta'an "erat jens beton berat jens as%al
= = = = = = =
Kon,ensonal &5 -%a *00 -% -%a (-uatan T #an 100) 2lastomer "earng &5 '34m && '34m
Baja (besi tulangan) fy
=
240 M Mp pa
berat jens baja berat jens ar
= =
78.50 '34m 9.80 '34m
i
T%e Jembatan -utu "eton () -utu bes tulangan (/) Kelas Jalan Jens Perleta'an "erat jens beton berat jens as%al
= = = = = = =
Kon,ensonal &5 -%a *00 -% -%a (-uatan T #an 100) 2lastomer "earng &5 '34m && '34m
Baja (besi tulangan) fy
=
240 M Mp pa
berat jens baja berat jens ar
= =
78.50 '34m 9.80 '34m
PERHITUNGAN SLAB LANTAI LANTAI JEMBATAN JEMBATAN DATA SLAB LANTAI JEMBATAN: Tebal Tebal slab lantai lantai jembatan Tebal Tebal lapisan perkerasan perkerasan aspal Tebal Tebal genangan air hujan Jarak antara balk balk gelagar "ebar jalur lalu lintas "ebar trtar "ebar ttal jembatan &anjang bentang jembatan BAHAN STRUKTUR Mutu Beton 'uat Tekan betn M*ulus elastik betn M*ulus -eser M*ulus -eser
ts ta th s b! b2 b "
= = = = = = = =
0.2 0.05 0.05 !.5 #.5 !.!5 $.%0 !$.50
f + - = +;(29(!<υ))
= = = =
25 2,500 0.2 $#$!.#
α
=
0.0000!
fy
=
400
fy +s
= =
240 2!0000
= = = =
25 22 $.%0 #%.50
= = = =
!., ! 0.2 5
= = = =
2 !.! 0.4$ !.5$
υ
'e/sien muai panjang untuk betn Mutu Baja untuk baja tulangan 1 !, mm 3,$ tegangan leleh baja untuk baja tulangan ≤ !, mm 324 tegangan leleh baja M*ulus elastis baja Berat Jenis Bahan Berat betn bertulang Berat aspal Berat jenis air Berat baja
a s
ANALISIS BEBAN SLAB LANTAI LANTAI JEMBA J EMBAT TAN Berat Sendiri Sa! antai je"!atan #MS$: 6aktr beban ultimit 'ms 7itinjau slab lantai jembatan selebar b Tebal Tebal slab lantai lantai jembatan h = ts Berat sen*iri 8ms = b9h9 Be!an Mati Ta"!ahan #MA$: 6aktr beban umltimit "apisan aspal :ir hujan
'ma 8maa = ta9b9a 8mas = th9b9 Beban mati tambahan
Be!an Mati Tru% &T& #TT$
6aktr beban ultimit 'tt = Beban hi*up pa*a plat injak berupa r*a gan*a leh Truk (beban T) yang besarnya T = 6aktr beban *inamis untuk pembebanan truk *iambil 7": = T TT = (!<7":)9T Beban truk T = Be!an An'in #E($
' + 6aktr Beban ultimit = Beban garis merata tambahan arah hri>ntal pa*a permukaan lantai jembatan akibat angin yang meniup ken*araan *i atas jembatan *ihitung *engan rumus 'e/sien seret ? = 'eepatan angin renana @ = T+ = 0.00!29?9@E2 = Bi*ang Aertikal yang *itiup angin merupakan bi*ang samping ken*araan *engan tinggi *i atas lantai jembatan h Jarak antar r*a ken*araan &+ = (!;29h;9T+) Transfer angin ke lantai jembatan
= = =
Pen'aruh Te")eratur 6aktr beban ultimit ntuk memperhitungkan tegangan maupun *efrmasi struktur yang timbul akibat pe temperaturC *iambil perbe*aan temperatur yang besarnya setengah *ari selisih antara temperatur maksimum *an temperatur minimum rata3rata pa*a lantai jembat
Temperatur maksimum rata3rata Temperatur minimum rata3rata &erbe*aan temperatur pa*a slab ke/sien panjang muai betn m*ulus elastis betn
Tma Tmin ∆ T = (Tma 3 Tmin);2
α +
= = = = =
Mo"en Pada Sa! Lantai Je"!atan 6rmasi pembebanan slab untuk men*apatkan mmen maksimum pa*a bentang me *ilakukan seperti p* gambar. Mmen maksimum p* slab *ihitung ber*asarkan met*e ne ay slab *engan beban sebagai berikut 8ms = 5 kD;m 8ma = !.5$ kD;m &tt = !,0 kD &e = 0.#405#! kD ∆ T = !2.5 0?
'e/sien mmen lapangan *an mmen tumpuan untuk bentang menerus *engan be merataC terpusatC *an perbe*aan temperatur a*alah sebagai berikut
s ke/sien mmen = k untuk beban merataC 8 ntuk beban terpusatC & ntuk beban temperaturC ∆ T
!.5 m
= M = k989sE2 M = k989s M = k9α9∆Τ9+9FE,
Mo"en a%i!at !erat sendiri #MS$ Mmen tumpuan Mms = 0.0%,, 98ms9sE2 Mmen lapangan Mms = 0.04!# 98ms9sE2 Mo"en a%i!at !e!an "ati ta"!ahan #MA$ Mmen tumpuan Mma = 0.!04! 98ma9sE2 Mmen lapangan Mma = 0.054 98ma9sE2 Mo"en a%i!at !e!an tru% #TT$ Mmen tumpuan Mtt = 0.!52 9&tt9s Mmen lapangan Mtt = 0.!40# 9&tt9s Mo"en a%i!at !e!an an'in #E($ Mmen tumpuan Me = 0.!52 9&e9s Mmen lapangan Me = 0.!40# 9&e9s Mo"en a%i!atte")eratur # T$ Mmen tumpuan Me = 5.,+30# 9α9∆ T9+9sE, Mmen lapangan Me = 2.%!+30 9α9∆ T9+9sE,
= =
0.$,#!25 0.4$!25
= =
0.,#24!##5 0.!$,!%5
= =
,0.45$ 2#.4,5
= =
0.!#,5!5%$ 0.!52$#
= =
5.5%+30, 0.02#%5%52
Mo"en Sa! :
Jenis Beban
'*e beban
Berat Fen*iri Beban mati tambahan Beban truk GTG Beban angin &ebgaruh temperatur
'ms 'ma 'tt 'e 'et
D ! 2 , 4 5
6aktr Beban ! ! ! ! !
Mmen tumpuan (kDm) 0.$,# 0.,#2 ,0.45$ 0.!#4 0.00
6aktr beban !., 2 2 !.2 !.2
Ko"!inasi*+
D
Jenis Beban ! 2 , 4 5
Berat Fen*iri Beban mati tambahan Beban truk GTG Beban angin &ebgaruh temperatur
Ko"!inasi*1
Mmen Mmen tumpuan lapangan (kDm) (kDm) !., 0.$,# 0.4$ 2 0.,#2 0.!$, 2 ,0.45$ 2#.4,# ! 0.!#4 0.!5 ! 0.00 0.02% Tota Mo"en uti"it Mu ,
6aktr Beban
Mu tumpuan (kDm) !.2!% 0.#45 0.$!% 0.!#4 0.00 -./0-0
D
Jenis Beban ! 2 , 4 5
Berat Fen*iri Beban mati tambahan Beban truk GTG Beban angin &ebgaruh temperatur
Mmen Mmen tumpuan lapangan (kDm) (kDm) !., 0.$,# 0.4$ 2 0.,#2 0.!$, ! ,0.45$ 2#.4,# !.2 0.!#4 0.!5 !.2 0.00 0.02% Tota Mo"en uti"it Mu ,
6aktr Beban
'uat tekan betn Tegangan leleh baja Tebal &lat "antai Tebal selimut betn 6aktr bentuk *istribusi tegangan betn Hasi Tulangan pa*a kn*isi seimbang ρb = β1* 0.85 * f c'/ f y * 600 / ( 600 + f y )
f fy h * β!
Hn
*=h3* b Mn = Mu;I Hn = Mn9!0E3;(b9*E2) Hma
Hasi Tulangan yang *iperlukan ρb = 0.%59f;fy9(!3√9(!329Hn;(0.%59f)) Hasi tulangan minimum Hasi tulangan yang *iperlukan "uas tulangan yang *iperlukan 7iameter tungan yang *ipakai Jarak Tulangam yang *iperlukan
= = = = = =
6aktr tahanan mmen maksimum Rmax = 0.75 * ρb * f y * [ 1 – ½* 0.75 * ρb * f y / ( 0.85 * f c') ] faktr re*uksi kekuatan lentur faktr re*uksi kekuatan geser mmen renana ultimit tebal efektif plat injak 7itinjau plat injak selebar ! m mmen nminal renana 6aktr tahanan mmen
Mu tumpuan (kDm) !.2!% 0.#45 ,0.45$ 0.20% 0.00# .1/-.2
ρmin= (!.4;fy) ρ :s = ρ9b9*
s = π;497E29b;:s D 7igunakan tulangan :s = π;497E29b;s Tulangan bagi ; susut arah memanjang *iambil 50K tulangan pkk. 7iameter tungan yang *ipakai :s = 50K9:s s = π;497E29b;:s D 7igunakan tulangan :s = π;497E29b;s
= = = = = = = =
= = = = 7= = +,
7= = = +1 ,
'uat tekan betn Tegangan leleh baja M*ulus elstis betn m*ulus elastis baja Tebal slab lantai jembatan Tebal selimut betn Tebal efektif slab "uas tulangan slab &anjang bentang slab 7itinjau slab selebar ! m Beban terpusat Beban merata "en*utan ttal yang terja*i ( δttal) harus Lnersia brtt penampang plat M*ulus keruntuhan lentur betn Dilai perban*ingan m*ulus elastis
f fy + +s h * * = h3* :s " b & = &tt 8 = &ms < &ma ";240 Lg = !;!29b9hE, fr = 0.#9√f n = +s;+ n 9 :s Jarak garis netral terha*ap sisi atas betn = n 9:F;b Lnersia penampang retak yang *i transfrmasikan ke betn Lr = !;,9b9E,
= = = = = = = = = = = = = = = = = = = = = = = = = = =
Hasitulangan slab lantai jembatan
ρ=:s;b9*
= 6aktr ketergantungan aktu untuk beban mati (jangka aktu 15 tahun)C nilai ς = λ = ς/(1+509ρ) = "en*utan jangka panjang akibat rankak *ansusut δg = λ95;,%4989"E4;(+9Le) "en*utan ttal pa*a plat lantai jembatan ";240 = δtt = δe<δg =
m m m m m m m m
Mpa Mpa Mpa ;0?
Mpa Mpa Mpa
kD;m, kD;m, kD;m, kD;m,
m m kD;m
kD;m kD;m kD;m
2 !00 kD 0., !,0 kD
!.2
!.2 ,0 m;*et !.2$ kD;m 2m !.#5 m 0.#405#!42% kD
ngaruh an. 40 0? !5 0? !2.5 0? 0.0000! ;0? 2,500000 k&a
nerus
ban
33333331 &&JT 3 !$$2C Tabel 5
kDm kDm kDm kDm kDm kDm kDm kDm kDm kDm
M lapangan (kDm) 0.4$ 0.!$, 2#.4,# 0.!5 0.02%
Mu lapangan (kDm) 0.!0 0.,% 54.%#, 0.!5 0.02% 3-/03.
Mu lapangan (kDm) 0.!0 0.,% 2#.4,# 0.!%% 0.0,, 14/-35
25 400 200 ,0 0.%5
M&a M&a mm mm
0.02#0$,#5 .5#,2!0$,% 0.% 0. ,.0 kDm !#0 mm !000 mm #%.%25244,#% kDm 2.#2#5!#!05 k.....N 0.00#,2,5$2$ 0.000%#5 0.00#,2,5$2$ !245.0!0#$0#0! mm2 ! !!.4$4!22! mm *+30 +.50/5+ ""1 !2 22.505,$5,504 mm2 !%!.%0%$204, *+30 23./64 ""1
25 M&a 400 M&a 2,500 Mpa 2!0000 M&a 200 mm ,0 mm !#0 mm !,40.4! mm2 !500 mm !000 mm !,0 kD;m .5$ kD;m .25 mm .#.+<0% mm4 ,.5 Mpa %.$,!# Mpa !!$#%.!5#52 mm2 !!.$#%! mm
#.$
4.0!+
0.00#%%4#%! 2 !.4,44#420$$ 0/02.- ""
.25 0.!20 ";240
k.....N
Perhitungan Slab Trotoar
"erat $en#r Trotoar b 3o (m) 1 0.890 & 0.115 1.150 * 0.&1 5 0.05 ! 0.1!0 7 0.19* 8 0.150 9 0.150 10 $an#aran > ?
h (m) 0.&00 0.&00 0.&00 0.*00 0.*00 0.*00 0.&50 0.&50 0.550
$ha%e 1.000 0.500 1.000 0.500 1.000 0.500 0.500 0.500 1.000 0.!
Panjang (m) &.000 &.000 &.000 &.000 &.000 &.000 0.150 0.150 0.150 * Total
Berat sendiri per m lebar
"eban 6#u% %a#a %e#estran beban h#u% %a#a %e#estran %er m lebar tega' lurus b#ang gambar Ga/a 3o Jens beban ('3) 1 "eban horontal %a#a rallng 1 & "eban horontal %a#a 'erb 5 "eban ,ert'al merata 5
"erat ('3) 8.900 0.575 11.500 &.10 0.700 1.!00 0.091 0.070 0.09 &.5&
lengan (m) 0.**& 0.9& 0.575 1.08 1.1 1.&0 1.&&8 1.&! 1.5 1.5
28.576 !.287825
lengan (m) 1.&5 0.50 1.00
-omen ('3m) 1.&5 &.50 *.98
"omen akibat beban hidup pada pedestrian "tp
8.7#
"omen $ltimit %en&ana Slab Trotoar
a'tor beban ultmt berat sen#r %e#estran Kms a'tor beban ultmt beban h#u% %e#estran Kt% -omen a'bat berat sen#r %e#estran -omen a'bat beban h#u% %e#estran
Kms = Kt% = -ms = -t% =
"omen ultimit ren&ana slab trotoar
"u ' Kms("ms)Ktp("tp ' #*.57
"u Pembesian Slab Trotoar
-utu "eton = K:00 -utu "aja = <:9 Kuat Te'an "eton Tegangan leleh "aja Tebal $lab beton slmut beton
1.0 &.00 10.09 8.7
::::::::::::::::::; $3:0:&8*7:&00&
/ h #
= = = = =
-o#ulus elasts baja 2s b1 a'tor bentu' #strbus tegangan beton @aso Tulangan %a#a 'on#s sembang rb = b1A 0.85 A 4 / A !00 4 ( !00 / ) a'tor tahanan momen ma'smum @maD = 0.75 A rb A / A H 1 I A 0.75 A r b A / 4 ( 0.85 A ) a'tor re#u's 'e'uatan lentur a'tor re#u's 'e'uatan geser momen renana ultmt tebal ee't slab beton #=h:# #tnjau slab beton selebar 1 m (b) momen nomnal renana -n = -u4 a'tor tahanan momen @n = -nA10B:!4(bA#B&) @n C @maD @aso Tulangan /ang #%erlu'an rb = 0.85A4/A(1:MA(1:&A@n4(0.85A)) @aso tulangan mnmum rmn= &5A(1.*4/) @aso tulangan /ang #%erlu'an r Luas tulangan /ang #%erlu'an +s = rAbA# ameter tungan /ang #%a'a Jara' Tulangam /ang #%erlu'an s = %4*AB&Ab4+s D guna'an tulangan +s = %4*AB&Ab4s untu' tulangan longtu#nal #ambl 50 tulangan #ar tulangan %o'o' +s = 50A +s ameter tulangan /ang #%erlu'an Jara' tulangan /ang #%erlu'an s = %4*AB&Ab4+s D guna'an tulangan +s = %4*AB&Ab4s
= = = = = = = = = = =
= = = = = = 2 '
=
*
Pembesian Tiang %ailing
Jara' antar tang ralng "eban horontal %a#a ralng Ga/a horontal %a#a tang ralng Lengan terha#a% ss baEah tang ralng momen %a#a tang ralng a'tor beban ultmt momen ultmt renana Ga/a geser ultmt renana Pembesian %ailing:
L 61 6t% = 61AL / -t% = 6t%A/ Kt% -u = Kt%A-t% Fu = Kt%A6t%
= = = = = = = =
Kuat Te'an "eton Tegangan leleh "aja Tebal tang ralng slmut beton -o#ulus elasts baja a'tor bentu' #strbus tegangan beton @aso Tulangan %a#a 'on#s sembang rb = b1A 0.85 A 4 / A !00 4 ( !00 / ) a'tor tahanan momen ma'smum @maD = 0.75 A rb A / A H 1 I A 0.75 A r b A / 4 ( 0.85 A ) a'tor re#u's 'e'uatan lentur a'tor re#u's 'e'uatan geser momen renana ultmt tebal ee't tang ralng Lebar tang ralng momen nomnal renana a'tor tahanan momen
/ h # 2s b1
= = =
#=h:# b -n = -u4 @n = -nA10B:!4(bA#B&)
%n
@aso Tulangan /ang #%erlu'an rb = 0.85A4/A(1:MA(1:&A@n4(0.85A)) @aso tulangan mnmum @aso tulangan /ang #%erlu'an Luas tulangan /ang #%erlu'an ameter tulangan /ang #%a'a Jumlah tulangan /ang #%erlu'an
= = =
+
%ma,
rmn= (1.*4/) r +s = rAbA# n = +s4(%4*AB&) Digunakan tulangan
= = = = = = = =
= = = = = =
#
D
Fu Fu F = (M)4!AbA# AF AF = Fu:AF Fs
= = = = = = =
+, = (%4*AB&)
=
$ = +,A/A#4Fs
=
Pembesian tulangan -eser
Ga/a geser ultmt Ga/a geser ultmt
guna'an seng'ang ber%enam%ang Luas Tulangan Geser (seng'ang) /ang #%erlu'an Jara' tulangan geser (seng'ang) /ang #%erlu'an Digunakan sengkang P/%01T$-3 P43T 13K
6
P43T 13K 3%30 "/41T3- /"B3T3 Beban Truk T TT
a'tor beban ultmt "eban h#u% %a#a %lat nja' beru%a ro#a gan#a oleh Tru' (beban T) /ang besarn/a a'tor beban #nams untu' %embebanan tru' #ambl "eban tru' T
Ktt
=
T L+ TTT = (1L+)AT
= = =
h ta b b = bta u 's 2=*700AM r = b4&
= = = = = = = = =
"omen pada plat 1n9ak
Tebal %lat nja' tebal la%san as%al lebar b#ang 'onta' ro#a tru'
Kuat te'an beton +ng'a %oson $tan#ar mo#ulus o sol reton mo#ulus elast' beton Lebar %en/ebaran beban ter%usat -omen maD. Pa#a %lat nja' a'bat ro#a #htung#engan rumus l = (2AhB4(1&A(1:uB&)A's))B0.&5 -maD = TTT4&A(1:(rAM&4l)B0.!) -omen ultmt %lat nja' arah melntang jembatan -u = Ktt A-maD
= = =
Pembesian Plat 1n9ak 3rah "elintang embatan
Kuat te'an beton Tegangan leleh baja Tebal Plat nja' Tebal selmut beton a'tor bentu' #strbus tegangan beton @aso Tulangan %a#a 'on#s sembang rb = b1A 0.85 A 4 / A !00 4 ( !00 / ) a'tor tahanan momen ma'smum @maD = 0.75 A rb A / A H 1 I A 0.75 A r b A / 4 ( 0.85 A ) a'tor re#u's 'e'uatan lentur a'tor re#u's 'e'uatan geser momen renana ultmt tebal ee't %lat nja' tnjau %lat nja' selebar 1 m momen nomnal renana a'tor tahanan momen
/ h # b1
= = = = = =
#=h:# b -n = -u4 @n = -nA10B:!4(bA#B&)
= = = = = = = =
@n @aso Tulangan /ang #%erlu'an rb = 0.85A4/A(1:MA(1:&A@n4(0.85A)) @aso tulangan mnmum @aso tulangan /ang #%erlu'an Luas tulangan /ang #%erlu'an ameter tungan /ang #%a'a Jara' Tulangam /ang #%erlu'an
C
@maD
rmn= (1.*4/) r +s = rAbA# s = %4*AB&Ab4+s guna'an tulangan +s = %4*AB&Ab4s
= = = = = =
D
2 '
P43T 13K 3%30 "/"33- /"B3T3 Beban Truk T TT
a'tor beban ultmt "eban h#u% %a#a %lat nja' beru%a ro#a gan#a oleh Tru' (beban T) /ang besarn/a a'tor beban #nams untu' %embebanan tru' #ambl "eban tru' T
Ktt
=
T L+ TTT = (1L+)AT
= = =
h ta b b = bta u 's 2=*700AM r = b4&
= = = = = = = = =
"omen pada plat 1n9ak
Tebal %lat nja' tebal la%san as%al lebar b#ang 'onta' ro#a tru'
Kuat te'an beton +ng'a %oson $tan#ar mo#ulus o sol reton mo#ulus elast' beton Lebar %en/ebaran beban ter%usat -omen maD. Pa#a %lat nja' a'bat ro#a #htung#engan rumus l = (2AhB4(1&A(1:uB&)A's))B0.&5 -maD = TTT4&A(1:(rAM&4l)B0.!) -omen ultmt %lat nja' arah melntang jembatan -u = Ktt A-maD
= = =
Pembesian Plat 1n9ak 3rah "elintang embatan
Kuat te'an beton Tegangan leleh baja Tebal Plat nja' Tebal selmut beton a'tor bentu' #strbus tegangan beton
/ h # b1
= = = = =
@aso Tulangan %a#a 'on#s sembang rb = b1A 0.85 A 4 / A !00 4 ( !00 / ) a'tor tahanan momen ma'smum @maD = 0.75 A rb A / A H 1 I A 0.75 A r b A / 4 ( 0.85 A ) a'tor re#u's 'e'uatan lentur a'tor re#u's 'e'uatan geser momen renana ultmt tebal ee't %lat nja' #=h:# tnjau %lat nja' selebar 1 m b momen nomnal renana -n = -u4 a'tor tahanan momen @n = -nA10B:!4(bA#B&) @n C @maD @aso Tulangan /ang #%erlu'an rb = 0.85A4/A(1:MA(1:&A@n4(0.85A)) @aso tulangan mnmum rmn= (1.*4/) @aso tulangan /ang #%erlu'an r +s = rAbA# Luas tulangan /ang #%erlu'an ameter tungan /ang #%a'a Jara' Tulangam /ang #%erlu'an s = %4*AB&Ab4+s D guna'an tulangan +s = %4*AB&Ab4s
= = = = = = = = =
= = = = = = 6 '
momen ('3m) .9* 0.51 !.!1 &.98 0.79 1.9&5 0.11& 0.09 0.*1 .!* 2*.75 *.*87
::::::::; ::::::::; ::::::::;
PPPJJ@ 1987 PPPJJ@ 1987 PPPJJ@ 1987
'3m '3m km
&5 -%a *00 -%a &00 mm 0 mm
&10000 -%a 0.85 0.0&70975
$3:0:&8*7:&00&
!.57!&109* 0.8 0.! 0.57 170 mm 1000 mm 8.&1&0*! '3m 1.&&&1!1! N'.....O 0.00*15& 0.000875 0.00*15& 580.!0*950 mm& 1& 19*.79&&* 5* 75#.;822#6;
&90.0&*751 mm& 10 &70.5**7!99 25* #!.5;265! mm&
1.7 1 1.7 0.7 1.19 & &.8 .*
m '34m '3 m '3m '3m '3
&5 -%a &*0 -%a &00 mm 0 mm &10000 -%a 0.85 0.05757** 7.*7&**18 0.8 0.! &.8 170 mm 150 mm &.975 '3m 0.!8!&7*51
0.00&907&05 0.0058 0.0058 1*8.75 mm& 8 &.959&87&& 8
:
.* '3 *00 3 &1&50 3 1&750 3 3 *00 3 !
&8.&7*88 mm& 9.&9&00!! mm #**
$3:0:&8*7:&00&
& 100 '3 0. 10 '3
0.& m 0.05 m 0.5 m 0.55 m &5 -Pa 0.15 81500 '34m &500000 '34m& 0.&75 0.!!59&5!5 m &.&801&& '3m *!.!!5!0&**
&5 -Pa *00 -Pa &00 mm 0 mm 0.85 0.0&70975 !.57!&109* 0.8 0.! *!.!7 '3m 170 mm 1000 mm 58.&0005 '3m &.018*08*1
N'.....O 0.00511551 0.000875 0.00511551 90&.9!!95& mm& 1& 1&5.&51&5** mm 25 ;*!.78 mm&
& 100 '3 0. 10 '3
0.& m 0.05 m 0. m 0.5 m &5 -Pa 0.15 81500 '34m &500000 '34m& 0.175 0.!!59&5!5 m .&&99778! '3m !!.*599557
&5 -Pa *00 -Pa &00 0 0.85
0.0&70975 !.57!&109* 0.8 0.! !!.*! '3m 170 mm 1000 mm 8.07*9**!! '3m &.87*5!5559 N'.....O 0.00775& 0.000875 0.00775& 117.899!* mm& 1! 15&.5!90!9 mm 5* #!*.! mm&
2
PERHITUNGAN GELAGAR JEMBATAN BAL A. DATA STRUKTUR ATAS
Panjang bn!ang jmba!an "ba# ja$an (ja$%# $a$%&$n!a) "ba# !#!a# "ba# !!a$ jmba!an ,a#a- an!a#a ## mn ## mn af#agma 2ba$ $ab $an!a jmba!an 2ba$ $a4an a4a$ + #$ay 2ngg gnangan a# 3%jan 2ngg bang am4ng
"ba# g## 2ngg g## "ba# af#agma 2ngg af#agma
"= 1 = = 1 + * = = b= 3= b = 3 = ! = !a = !3 = 3a =
,%m$a3 ba$- af#agma 4anjang " ,a#a- an!a#a ba$- af#agma
n = = "/n =
B. BAHAN STRUKTUR Mutu beton :
%a! !-an b!n 9%$% $a!- :ng-a 4n 9%$% g# fn m%a 4anjang %n!%- b!n
& fc' = 0.8 * / 10 = ?c = @700 * √ fc' =
υ = = ?c / [*(1 + υ)] = O =
Mutu baja :
;n!%- baja !%$angan ngan < 1 mm 2gangan $$3 baja ;n!%- baja !%$angan ngan < P 1 mm 2gangan $$3 baja
;& fy = ;*10 = ;& fy = ;*10 =
Spe!"! G#a$!t% :
#a! b!n b#!%$ang #a! b!n !a- b#!%$ang (b!n #aba!) #a! a4a$ 4aa! #a! jn a#
>c = >'c = >a = >> =
&. ANALISIS BEBAN
1. ?R:2 A?BCRC (9A) 9A = Da-!# bban %$!m! #a! n# ( $f >g3! ) aa$a3 b#a! ba3an an bagan jmba!an yang m#%4a-an $mn !#%-!%#a$ !amba3 ngan $mn nn&!#%-!%#a$ yang 4-%$nya an b#fa! !!a4. ban b#a! n# ba$- af#agma 4aa ## 3!%ng bb. Panjang bn!ang ## #a! a!% ba$- af#agma ,%m$a3 ba$- af#agma 4anjang bn!ang " ban af#agma 4aa ## ban b#a! n# 4aa ## B. ,n 1
P$a! $an!a ## af#agma
"= E = b * (3 & !) * * >c = n = F = n * E / " =
"ba# (m) 1.50 0.50
2ba$ (m) 0.0 1.@0
aya g# an mmn 4aa 2&## a-ba! b#a! n# (9A) H9A =
#a! (-B/m) 5.00 5.00 F = F9A =
1/ * F9A * " =
99A =
1/8 * F9A * " =
. ?:B 9:2C 2:9:G:B (9:) 9: = Da-!# bban %$!m! ban ma! !amba3an ( superimposed dead load ) aa$a3 b#a! $%#%3 ba3an yang mnmb%$-an %a!% bban 4aa jmba!an yang m#%4a-an $mn nn&!#%-!%#a$ an m%ng-n ba#nya b#%ba3 $ama %m%# jmba!an. ,mba!an ana$ 3a#% mam4% mm-%$ bban !amba3an 4#! 1) Pnamba3an $a4an a4a$ (#$ay ) -m%an 3a# ) nangan a# 3%jan j-a !m #ana !a- b-#ja ngan ba- Panjang bn!ang ## " ban ma! !amba3an 4aa ## B. ,n
"ba# (m)
2ba$ (m)
#a! (-B/m)
:# 3%jan
1.50
ban ma! !amba3an
aya g# an mmn 4aa 2&## a-ba! bban !amba3an (9:) H9: = 99: =
0.05
I.80 F9: =
1/ * F9: * " = 1/8 * F9: * " =
'. BEBAN LALU-LINTAS
@.1. ?:B ":,;R JJ (2) 2 = Da-!# bban %$!m! ban -na#aan yg b#%4a bban $aj%# JJ !## a# bban !#bag #a!a (;nf#m$y !#b%! "a ) ;" an bban ga# (nf ?g "a ) ?" 4#! 4 amba# 1. ;" mm4%nya n!n!a K (-Pa) yg ba#nya !#gan!%ng 4 4anjang bn!ang " yg bban $a$%&$n!a 4#! amba# a!a% nya!a-an ngan #%m% baga b#-%! %n!%- " P 0 K = 8.0 -Pa K = 8.0 *( 0.5 + 15 / " ) -Pa %n!%- " 0
;n!%- 4anjang bn!ang "= 1I.50 m K= ?" mm4%nya n!n!a 4= Da-!# bban nam (namc "a :$$>anc) %n!%- ?" amb$ baga b#-%! %n!%- " P 50 ": = 0.@0 ": = 0.@ & 0.005*(" & 50) %n!%$ 50 L " L ": = 0.0 %n!%- " Q I0
,a#a- an!a#a g## ;n!%- 4anjang bn!ang " = ban $aj%# 4aa ##
= 1I.50 m
ma-a ": = F2 = K * =
P2 = (1 + ":) * 4 * = aya g# an mmn 4aa 2&# a-ba! bban $aj%# JJ H2 = 1/ * ( F2 * " + P2 ) = 92 = 1/8 * F2 * " + 1/@ * P2 * " =
@.. ?:B 2R; J2J (22) 22 = Da-!# bban %$!m! ban 3%4 4aa $an!a jmba!an b#%4a bban #a gana $3 2#%- (bban 2) yang ba#nya 2= Da-!# bban nam %n!%- 4mbbanan !#%- amb$ ": = P22 = ( 1 + ": ) * 2 = ban !#%- J2J
a= b=
Panjang bn!ang ## "= aya g# an mmn 4aa 2&# a-ba! bban !#%- J2J H22 = [ I/8 * " & 1/@ * a + b ] / " * P22 = 922 = H22 * "/ & P 22 * b = aya g# an mmn yang !#ja a-ba! 4mbbanan $a$%&$n!a amb$ yg mmb#-a 4nga#%3 !#ba# !#3aa4 2&## an!a#a bban JJ an bban J2J. H22 = aya g# ma-m%m a-ba! bban 2 9mn ma-m%m a-ba! bban
92 =
'. GA(A REM )TB*
2 = Da-!# bban %$!m! Pnga#%3 4ng#man a# $a$%&$n!a 4#3!%ng-an baga gaya a$am a#a3 mmanjan an angga4 b-#ja 4aa ja#a- 1.80 m a!a $an!a jmba!an. a#nya gaya #m a#a3 mmanjang jmba!an !#gan!%ng 4anjang !!a$ jmba!an ("!) baga b#-%! %n!%- "! P 80 aya #m G2 = 50 aya #m G2 = 50 + .5*("! & 80) %n!%$ 80 L "! %n!%- "! Q 18 aya #m G2 = 500
Panjang bn!ang ##
"= ng## = ,%m$a3 ## aya #m G2 = ,a#a- an!a#a ## = 22 =G2 / ng## = aya #m %n!%- "! P 80 m aya #m j%ga a4a! 4#3!%ng-an ba# 5M bban $aj%# JJ !an4a fa-!# bban nam.
aya #m
amb$ gaya #m
22 = 5 M bban $aj%# JJ !an4a fa-!# bban nam F2 = K * = P2 = 4 * = 22 = 0.05 * ( F2 * " + P2 ) = L 22 =
"ngan !3. 2!- b#a! ba$- ban mmn a-ba! gaya #m aya g# an mmn ma-m%m 4aa ba$- a-ba! gaya #m
y = 1.80 + !a + 3/ = 9 = 22 * y = H2 = 9 / " = 92 = 1/ * 9 =
+. BEBAN ANGIN )E,*
?E = Da-!# bban %$!m! aya angn !amba3an a#a3 3#n!a$ 4aa 4#m%-aan $an!a jmba!an a-ba! bban angn yang mn%4 -na#aan a!a $an!a jmba!an 3!%ng ngan #%m% 2?E = 0.001*N>*(H>) -B/m ngan N> = c4a!an angn #ncana H> = ban angn !amba3an yang mn%4 bang am4ng -na#aan 2?E = 0.001*N>*(H>) = ang #!-a$ yang !%4 angn m#%4a-an bang am4ng -na#aan ngan !ngg .00 m a!a $an!a jmba!an. 3= ,a#a- an!a#a #a -na#aan x x= ban a-ba! !#anf# bban angn - $an!a jmba!an F?E = 1/*3 / x * 2 ?E =
Panjang bn!ang ## aya g# an mmn 4aa ## a-ba! bban angn (?E)
"= H?E = 1/ * F?E * " = 9?E = 1/8 * F?E * " =
. PENGARUH TEMPERATUR )ET*
aya g# an mmn 4aa ## a-ba! 4nga#%3 !m4#a!%# 4#3!%ng-an !#3aa4 gaya yang !mb%$ a-ba! 4#g#a-an !m4#a!%# (!m4#a!%# mmn!) 4aa !%m4%an ($a!m#c ba#ng) ngan 4#baan !m4#a!%# ba# ∆2 = O = fn m%a 4anjang %n!%- b!n Panjang bn!ang ## "= -= Shear stiffness of elastomeric bearing, δ = O * ∆2 * "= Temperatur movement, D?2 = - * δ = aya a-ba! !m4#a!%# mmn!
2ngg ## 3 = 1.60 m ?-n!#!a = 3 / = 0.80 9mn a-ba! 4nga#%3 !m4#a!%# aya g# an mmn 4aa ## a-ba! 4nga#%3 !m4#a!%# (?2)
3= = 3/ = 9 = D?2* = H?2 = 9/" = 9?2 = 9 =
. BEBAN GEMPA )E/*
aya gm4a #!-a$ 4aa g## 3!%ng ngan mngg%na-an 4#c4a!an #!-a$ - ba>a3 mnma$ ba# 0.10 * g ( g = 4#c4a!an g#a!a ) a!a% a4a! amb$ 50M -fn gm4a 3#n!a$ !a!- -a$n. fn bban gm4a 3#n!a$ 3 = N * A 3 = fn bban gm4a 3#n!a$ N = fn g# aa# %n!%- >$aya3 gm4a >a-!% g!a# an -n !ana3 !m4a! A = Da-!# !4 !#%-!%# yg b#3%b%ngan ngan -a4a!a 4ny#a4an n#g gm4a (a-!$!a) a# !#%-!%#. Ea-!% g!a# !#%-!%# 3!%ng ngan #%m% 2 = * π * √ [ E! / ( g * P ) ] E! = #a! !!a$ yang b#%4a b#a! n# an bban ma! !amba3an P = --a-%an !#%-!%# yang m#%4a-an gaya 3#n!a$ yang 4#$%-an %n!%- mnmb%$ a!% a!%an $n%!an. f b
#a! !!a$ yang b#%4a b#a! n# an bban ma! !amba3an E! = F9A + F9: #a! n# F9A = ban ma! !amba3an F9: = Panjang bn!ang "= #a! !!a$ E! = (F9A + F9:)*" = ;-%#an ## b= 0.50 m 3= 9mn n#a 4nam4ang ## C = 1/1 * b * 3 = 9%$% $a!- b!n ?c = ?c = -a-%an $n!%# ## 4 = @8 * ?c * C / " = 2 = *π* √ [ E! / (g * P)] = Ea-!% g!a# n !ana3 aa# !#ma%- ang (m%m). "-a >$aya3 gm4a E$aya3 = fn g# aa# N= ;n!%- !#%-!%# jmba!an ngan a#a3 n 4$a! b!n b!n b#!%$ang ma-a fa-!# !4 !#%-!%# 3!%ng ngan #%m% A = 1.0 * D ngan D = 1.5 & 0.05 * n an D 3a#% amb$ Q 1 D = fa-!# 4#ang-aan n = j%m$a3 n 4$a! yang mna3an f#ma !#%-!%#. ;n!%- n$a n = 1 ma-a n= D = 1.5 & 0.05 * n = Da-!# !4 !#%-!%# A = 1.0 * D = fn bban gm4a 3#n!a$ 3 = N*A = fn bban gm4a #!-a$ = 50M * 3 = amb$ -fn gm4a #!-a$ = aya gm4a #!-a$
2?F = * E! =
F?F = 2?F / " =
ban gm4a #!-a$ aya g# an mmn 4aa ## a-ba! gm4a #!-a$ (?F)
H?F = 1/ * F?F * " = 9?F = 1/8 * F?F * " = 0. KOMBINASI BEBAN ULTIMATE
B. 1 @ 5 6 7
,n ban #a! n# (9A) ban ma! !amba3an (9:) ban $aj%# JJ (2) aya #m (2) ban angn (?E) Pnga#%3 2m4#a!%# (?2) ban gm4a (?F)
O9CB:AC 9O9?B ;"2C9:2? B. ,n ban 1 @ 5 6 7
#a! n# (9A) ban ma! !amba3an (9:) ban $aj%# JJ (2/22) aya #m (2) ban angn (?E) Pnga#%3 2m4#a!%# (?2) ban gm4a (?F)
Da-!# ban 1.0 .00 .00 .00 1.0 1.0 1.00
Da-!# ban 1.0 .00 .00 .00 1.0 1.0 1.00
mb&1
mb&
√ √ √ √ √
√ √ √ √ √
9 (-Bm) 176.0 11.6 100.8 70.00 5.0 @6.80 15.18
mb&1 9% (-Bm) 1658.8@ 6.7
[email protected] [email protected] @.@
@10I.@6
O9CB:AC :: ?A?R ;"2C9:2? B. ,n ban 1 @ 5 6 7
#a! n# (9A) ban ma! !amba3an (9:) ban $aj%# JJ (2/22) aya #m (2) ban angn (?E) Pnga#%3 2m4#a!%# (?2) ban gm4a (?F)
Da-!# ban 1.0 .00 .00 .00 1.0 1.0 1.00
H (-B) 61.75 .5 18@.@ 7.18 7. .@0 1.@
mb&1 H% (-B) @0.8 @6.51 68.85 1@.6 8.66
9mn %$!ma! #ncana g## aya g# %$!ma! #ncana g##
9% = H% =
10. P?9?AC:B CR?R 10.1. 2;":B:B "?B2;R 9mn #ncana %$!m! ## 9%!% b!n 9%!% baja !%$angan 2ba$ $ab b!n "ba# baan ## 2ngg ## "ba# aya4 2&## amb$ n$a yang !#-c$ a#
9% = fc' = fy = ! = b= 3= "/@ = = 1 * ! = bff = ' = ? = β1 =
& 00 ; & @0
amb$ $ba# f-!f aya4 2&## bff = 000 mm ,a#a- 4%a! !%$angan !#3aa4 $%a# b!n ' = 150 mm 9%$% $a! baja ? = .00?+05 9Pa Da-!# bn!%- !#b% !gangan b!n
Da-!# #%- --%a!an $n!%# 2ngg f-!f 2&## 9mn nmna$ #ncana Da-!# !a3anan mmn
#b = b1* 0.85 * fcQ/ fy * 600/(600+fy) = Rmax = 0.75*#b*fy*[1&1/*0.75*#b*fy/(0.85*fc')] = φ = = 3 & ' = 9n = 9%/ φ = Rn = 9n * 10 6 / (bff * ) = Rn L Rmax
Ra !%$angan yang 4#$%-an # = 0.85 * fcQ / fy * [ 1 & (1 – * Rn / ( 0.85 * fcQ ))] = Ra !%$angan mnm%m #mn = 1.@ / fy = "%a !%$angan yang 4#$%-an : = # * bff * = am!# !%$angan yang g%na-an :1 = 4/@ * = ,%m$a3 !%$angan yang 4#$%-an n = : / :1 = 12 D g%na-an !%$angan : = :1 * n = 2ba$ $m%! b!n ! = am!# ng-ang yang g%na-an = ,%m$a3 !%$angan !a4 ba# n! =
,a#a- b#3 an!a#a !%$angan S = ( b & n! * & * ! & * ) / (n! & 1) = 5 mm
;n!%- mnjamn aga# ## b#fa! a-!a$ ma-a !%$angan !-an amb$ 0M !%$angan !a#- 3ngga
:' = 0M * : = g%na-an !%$angan
+
D
13.4. KONTROL KAPASITAS MOMEN ULTIMATE
2ba$ $ab b!n "ba# f-!f aya4 "ba# baan ## 2ngg ## ,a#a- 4%a! !%$angan !#3aa4 $%a# b!n 2ngg f-!f 2&## "%a !%$angan %a! !-an b!n %a! $$3 baja ;n!%- ga# n!#a$ b#aa a$am aya4 2&## ma-a aya n!#na$ !-an b!n 4aa aya4 aya n!#na$ !a#- baja !%$angan Nc
,a#a- ga# n!#a$ Rgangan 4aa baja !%$angan !a#- 9mn nmna$ a4a!a mmn %$!m! * 9n = 506.I0 -Bm
2
! = bff = b= 3= ' = = 3 & ' = : = fc' = fy =
Nc = 0.85 * fc' * bff * ! = 2 = : * fy = a# n!#a$ a$am aya a = : * fy / ( 0.85 * fc' * bff ) = c = a / β1 =
ε = 0.00 * ( & c) / c = L 0.0 9n = : * fy * ( & a / ) * 10 &6 = φ * 9n = 9%
13.5. TULANGAN GESER
aya g# %$!m! #ncana 9%!% b!n 9%!% baja !%$angan Da-!# #%- --%a!an g# "ba# baan ## 2ngg f-!f ## %a! g# nmna$ b!n
& 00 ; & I
%a! !-an b!n %a! $$3 baja
H% = fc' = fy =
φ = b= = Hc = (√ fc') / 6 * b * * 10& =
φ * Hc = P#$% !%$angan g#
φ * H = H% & φ * Hc = aya g# yang 4-%$ !%$angan g#
H =
n!#$ mn ## !#3aa4 -%a! g# ma-m%m Hmax = / * √ fc' * [ b * ] * 10& = mn ba$- mmn%3 4#ya#a!an -%a! g# g%na-an ng-ang b#4nam4ang
: = π/@ * * n =
"%a !%$angan g# ng-ang ,a#a- !%$angan g# (ng-ang) yang 4#$%-an
A = : * fy * / H = 4 D 15 g%na-an ng-ang Paa baan g## 4aang !%$angan %%! mnma$ ngan #a !%$angan
ρ3 = :3 = ρ3 * b * =
"%a !%$angan %%! am!# !%$angan yang g%na-an ,%m$a3 !%$angan %%! yang 4#$%-an g%na-an !%$angan
-
n = :3 / ( π /@ * ) = @
13.'. LENDUTAN BALOK
9%!% b!n & 00 9%!% baja !%$angan ; & @0 9%$% $a! b!n 9%$% $a! baja 2ngg ba$- "ba# ba$- ,a#a- !%$angan !#3aa4 $%a# b!n 2ngg f-!f ba$- "%a !%$angan ba$- Cn#a b#%!! 4nam4ang ba$-
%a! !-an b!n %a! $$3 baja
fc' = fy =
?c = @700 * √ fc' = ? = 3= b= ' = = 3 & ' = : = Cg = 1/1 * b * 3 = f# = 0.7 * √ fc' * 10 = 9%$% -#%n!%3an $n!%# b!n B$a 4#banngan m%$% $a! n = ? / ?c = n * : = ,a#a- ga# n!#a$ !#3aa4 a!a b!n c = n * : / b = Cn#a 4nam4ang #!a- yang !#anf#ma-an - b!n 3!%ng bb. Cc# = 1/ * b * c + n * : * ( & c ) = y! = 3/ = 9mn #!a- 9c# = f# * Cg / y! =
9mn a-ba! bban ma! an bban 3%4 (9 +") B. ,n ban 1 @
#a! n# (9A) ban ma! !amba3an (9:) ban $a$%$n!a (2/22) aya #m (2) 9+" =
Cn#a f-!f %n!%- 4#3!%ngan $n%!an C = ( 9c# / 9+" ) * Cg + [ 1 & ( 9c# / 9+" ) ] * Cc# = Panjang bn!ang ba$- "=
[email protected]. "?B;2:B :C:2 ?R:2 A?BCRC (9A) F9A =
ban a-ba! b#a! n# "n%!an a-ba! b#a! n# (9A)
δ9A = 5/8@*F9A*"@ / ( ?c*C) = 10.@.. "?B;2:B :C:2 ?:B 9:2C 2:9:G:B (9:) F9: =
ban a-ba! b#a! n# "n%!an a-ba! b#a! n# (9A)
δ9: = 5/8@*F9:*"@ / ( ?c*C) = 10.@.. "?B;2:B :C:2 ?:B ":,;R JJ (2) P2 =
ban $aj%# JJ ban !#4%a!
F2 = ban m#a!a "n%!an a-ba! bban $aj%# JJ (2) δ2 = 1/@8* P2*" / (?c*C) + 5/8@*F2*"@ / ( ?c*C) = 10.@.. "?B;2:B :C:2 :: R?9 (2) 92 =
9mn a-ba! gaya #m "n%!an a-ba! gaya #m (2)
δ2 = 0.06@ * 92 * " / ( ?c*C) = 10.@.@. "?B;2:B :C:2 ?:B :BCB (?E) F?E =
ban a-ba! !#anf# bban angn 4aa -na#aan "n%!an a-ba! bban angn (?E)
δ?E = 5/8@*F?E*"@ / ( ?c*C) =
[email protected]. "?B;2:B :C:2 P?B:R;G 2?9P?R:2;R (?2) 9mn a-ba! !m4#a!%# mmn! "n%!an a-ba! 4nga#%3 !m4#a!%# (?2)
9?2 =
δ?2 = 0.06@ * 9?2 * " / ( ?c*C) =
[email protected]. "?B;2:B :C:2 ?:B ?9P ? 9P: : (?F) F?F =
ban gm4a #!-a$ "n%!an a-ba! bban gm4a (?F)
δ?F = 5/8@*F?F*"@ / ( ?c*C) =
"n%!an ma-m%m B. 1 @ 5 6 7
δma- = "/@0 = ,n ban
#a! n# (9A) ban ma! !amba3an (9:) ban $aj%# JJ (2/22) aya #m (2) ban angn (?E) Pnga#%3 2m4#a!%# ((? ?2) ban gm4a (?F)
0.0815 mb&1 (-Bm) 0.01@6 0.001 0.0107 0.0005 0.000@
0.075 L "/@0 O
Pmban 2&##
11. BALOK DIA6RAGMA 11.1. BEBAN PADA BALOK DIA6RAGMA
!#b% bban $an!a 4aa ba$- af#agma aa$a3 baga b#-%! ;-%#an ba$- af#agma "ba# b = 0.0 2ngg 3 = 1.00 Panjang bn!ang ba$- af#agma = 1.50 2ba$ $an!a $an! a ! = 0.0
#a! n# (9A) B. ,n 1
m m m m
"ba#
P$a! $an!a a$- af#agma
2ba$
1.50 0.0
0.0 0.80
#a! (-B/m) 5.00 5.00 F9A =
ban (-B/m) 7.50 6.00 1.50
aya g# an mmn a-ba! b#a! n# H9A = 1/ * F9A * = 99A = 1/1 * F 9A * = ban ma! !amba3an (9:) B. ,n 1
"ba#
"a4.:4a$+#$ay :# 3%jan
2ba$
1.50 1.50
0.10 0.05
#a! (-B/m) .00 I.80 F9A =
ban (-B/m) .0 0.7@ @.0@
aya g# an mmn a-ba! bban ma! !amba3an H9: = 1/ * F9: * = 99: = 1/1 * F 9: * = ban !#%- J2J (22) ban 3%4 4aa $an!a jmba!an b#%4a bban #a gana $3 2#%- (bban 2) yang ba#nya 2= ": = Da-!# bban nam %n!%- 4mbbanan !#%- amb$ ban !#%- J2J aya g# an mmn a-ba! bban J2J
P22 = (1 + ":) * 2 = H22 = 1/ * P22 = 922 = 1/8 * P22 * =
mbna bban %$!m! B. ,n bban 1
#a! n# (9A) b.ma! !amb (9:) ban !#%- J2J (22)
Da-!# ban 1.0 .00 .00
H (-B) 10.1 .0 70.00
9 (-Bm) .5 0.76 6.5
11.. 9O9?B :B :: :: ?A?R R?BN:B: :"O C:DR:9: 9mn %$!m! #ncana ba$- af#agma aya g# %$!m! #ncana ba$- af#agma
H% (-B) 1.16 6.05
[email protected] 15I.15
9% = H% =
14. PEMBESIAN BALOK DIA6RAGMA 14.1. TULANGAN LENTUR
9mn #ncana %$!m! ba$- af#agma 9% = 78.8I5 -Bm 9%!% b!n & 00 %a! !-an b!n 9%!% baja !%$angan ; & @0 %a! $$3 baja 9%$% $a! b!n 9%$% $a! baja "ba# ba$- 2ngg ba$- ,a#a- 4%a! !%$angan !#3aa4 $%a# b!n Da-!# bn!%- !#b% !gangan b!n
9% = fc' = fy = ?c = @700 * √ fc' = ? = b = b = 3 = 3 = ' =
β1 =
ρb = β1* 0.85 * fcQ/ fy * 600/(600+fy) = Rmax = 0.75* ρb*fy*[1&1/*0.75*ρb*fy/(0.85*fc')] = φ =
Da-!# #%- --%a!an $n!%# 2ngg f-!f ba$- 9mn nmna$ #ncana Da-!# !a3anan mmn
= 3 & ' = 9n = 9%/ φ = 6 Rn = 9n * 10 / (bff * ) = Rn L Rmax
Ra !%$angan yang 4#$%-an Ra !%$angan mnm%m "%a !%$angan yang 4#$%-an am!# !%$angan yang g%na-an
ρ = 0.85 * fcQ / fy * [ 1 & √ (1 – * Rn / ( 0.85 * fcQ ))] = ρmn = 1.@ / fy = : = ρ * b * = :1 = 4/@ * = n = : / :1 =
,%m$a3 !%$angan yang 4#$%-an g%na-an !%$angan
4
D
: = :1 :1 * n =
14.4. TULANGAN GESER
aya g# %$!m! #ncana 9%!% b!n 9%!% baja !%$angan Da-!# #%- --%a!an g# "ba# baan ## 2ngg f-!f ## %a! g# nmna$ b!n
& 00 ; & @
H% = fc' = fy =
%a! !-an b!n %a! $$3 baja
φ = b= = Hc = (√ fc') / 6 * b * * 10& = φ * Hc = P#$% !%$angan g#
φ * H = H% & φ * Hc = aya g# yang 4-%$ !%$angan g#
H =
n!#$ mn ## !#3aa4 -%a! g# ma-m%m Hmax = / * √ fc' * [ b * ] * 10& = mn ba$- mmn%3 4#ya#a!an -%a! g# g%na-an ng-ang b#4nam4ang
: = π/@ * * n =
"%a !%$angan g# ng-ang ,a#a- !%$angan g# (ng-ang) yang 4#$%-an
A = : * fy * / H = g%na-an ng-ang
4
D
Pmban ba$- af#agma
14
-
K-T
1I.50 7.50 1.15 I.80 1.50 0.50 1.60 0.0 1.00 0.0 0.0 0.05 .80
m m m m m m m m m m m m m
@ b3 @.875 m
00 5.00 9Pa 500 9Pa 0.0 I7I 9Pa 1.0.?&05 °N
@0 @00 94a @ @0 94a
5.00 @.00 .00 I.80
-B/m -B/m -B/m -B/m
1.
1I.50 m I -B @ b3 1.8@6158@6 -B/m
ban (-B/m) 7.50 17.50 1.85 6.85
61.750 -B 176.01 -Bm
1.
1I.50 m
ban (-B/m)
0.7@ .I
.5@ -B 11.6 -Bm
.0
!a
8.00 -Pa @@.00 -B/m
m I0 m
m
1.50 m 0.@0 1.00 -B/m I.@0 -B
16.0 -B 100.8 -Bm
.0 100 -B 0.@0
[email protected] -B
5.00 m 5.00 m
1I.50 m 18@.@ -B 10I8.15 -Bm
18@.@ -B 100.8 -Bm
.0
m 180 m
0m
1I.50 m @ b3 50 -B 1.50 m 6.5 -B
1.00 66.00 15.00 50.00 50.00
-B/m -B -B -B -B
.80 m
[email protected] -Bm 7.18 -B 70.00 -Bm
1.
1. 0 m/! 1.I6 -B/m .00 m 1.75 m 0.7@0571@86 -B/m
1I.50 m 7.1 -B 5.00 -Bm
0 °N 1.0.?&05 °N 1I.50 m 15000 -B/m 0.00I m 58.50 -B
1.60 m 0.80 m @6.800 -Bm .@00 -B @6.800 -Bm
an I.81 m/!
6.85 -B/m .I -B/m 1I.50 m 570.0075 -B 1.60 m 0.1706666667 m@ @5 94a @5I5 -Pa 5I11 -B/m 0.I75 !-
0.18
1 1.5 1.5 0.1 0.110 0.10 0.110 6.8@ -B
. -B/m 1.@ -B 15.181 -Bm
mb&
√ √ √
√ mb& 9% (-Bm) 1658.8@ 6.7
[email protected] [email protected]
mb& 9% (-Bm) 1658.8@ 6.7
[email protected]
56.16 @1.7
mb& H% (-B) @0.8 @6.51 68.85 1@.6
15.18 @080.@0
mb& H% (-B) @0.8 @6.51 68.85
.88 1.@
@10I.@6 -Bm 778.65 -B
@10I.@6 @.I @00 00 500 1600 @875 1500 @00 1500 150 .0.?+05
-Bm 94a 94a mm mm mm mm mm mm mm mm 9Pa
0.85
0.06I8575 6.5@7660I@ 0.80
1@50 mm 516.818787I -Bm 1.687I707I O
0.00@@06@ 0.005 I6.@ mm 0 mm 706.86 mm 1.05 4
1060.87506 mm 0 mm 1 mm 6 mm @I.6 mm
O 180.865618 mm 14
00 mm 1500 mm 500 mm 1600 mm 150 mm 1@50 mm 1060.88 mm @.I 94a @00 9Pa Nc 2 6@I500 B @@1150.08 B
1.5I mm 157.16 mm 0.0@7 O 5866.80 -Bm @6I.10I165 -Bm @10I.@6 -Bm O
778.65 -B @.I 9Pa @00 9Pa 0.75 500 mm 1@50 mm 60.I57 -B
@5.18 -B
6.@@ -B @5.@6 -B
@11.88 -B H L Hmax O 1 65.@65 mm 5.75 mm 433
1
0.001 75 mm mm 5.@6
1
@.I 9Pa @00 9Pa @5 9Pa .0.?+05 9Pa 1.60 m 0.50 m 0.15 m 1.@5 m 0.01060 m 0.1706666667 m@ @I.III86 -Pa 8.5 0.0I0 m 0.181 m 0.1@66 m@ 0.80 m
[email protected] Bmm
9mn (-Bm) 176.0 11.6 100.8 70.00 @80.
0.1@7 m@ 1I.50 m
6.85 -B/m 0.01@6 m
.I -B/m 0.0010 m
I.@0 -B 1.00 -B/m 0.01067 m
70.00 -Bm 0.000@I
0.7@0571@86 -B/m 0.000@ m
@6.80 -Bm 0.000 m
. -B/m 0.0018 m
m mb& (-Bm) 0.01@6 0.001 0.0107 0.0005
mb& (-Bm) 0.01@6 0.001 0.0107
0.000 0.07@ L "/@0 O
0.0018 0.08@ L "/@0 O
10.15 -B .51 -Bm
.06 -B 0.757 -Bm
100 -B 0.@0
[email protected] -B 70.00 -B 6.5 -Bm
9% (-Bm) .I1 1.51 5.500 57.0@
57.0@ -Bm 15I.15 -B
57.0@ -Bm 5 9Pa @00 9Pa 500 9Pa .0.?+05 9Pa 00 mm 1000 mm 50 mm 0.85 0.070I75 6.57610I8 0.80
I50 mm 71.6I6875 -Bm 0.6@560@I O 0.00066556II 0.005 18I.6I mm 16 mm 01.06 mm 0.I@ 1+
@0.1@ mm
15I. -B @.I 9Pa @0 9Pa 0.75 00 mm I50 mm 7.05 -B 177.768 -B
&18.55 -B &@.78 -B
[email protected] -B H L Hmax O 1 6.1I5 mm &
[email protected] mm 433
PERENCANAAN ELASTOMERIC BEARING Data Perencanaan Bentang Jembatan (L) Beban a,2bat DL (R DL) Beban a,2bat LL (R LL) Per-utaran !udut muta, (R!) Peruba5an !u5u ma,!2mum (ST) Pen*u!utan g2rder ,arena te,anan (SPT) penyusutan gir*er karena sifat susut betn (S S;)
Moduu! ge!er ea!tomer (G) a,tor -embebanan () ST; * Ba+a
"#$%&#'
Pergera,an Tem-eratur 3oe<2!2en O STem- 4 (O) ( ST) (L) Pen*u!utan g2rder =PT =S;
0& mm 0 mm
3etebaan Ea!tomer2c Bear2ng teba tota ea!tomer (5rt) Q 0 S! d2mana 4 > (=Tem- ? =PT ? =S;) 5rt 4 d2guna,an ea!tomer dengan teba tota dengan teba -era-2! (5r2) dan +uma5 a-2!an (n)
4 16.'1 mm &0" 7" '
8,uran Ea!tomer2c Bear2ng a,tor ,eamanan ,etebaan bantaan S2 4 L 4 Pan+ang bantaan 9 4 Lebar bantaan dengan !*arat U! P
L9 05r2(L?9)
d2mana
U" P
&.11 GS : ".11 GS
U! Tegangan rata rata ter5ada- tota beban U" Tegangan rata rata ter5ada- beban 52du-
&&
U!
4
U"
4
GL9 05r2(L?9) R LL L9
D2guna,an cara -er52tungan @tr2a and error@ dengan a!um!2 L4 6"" mm 94 6"" mm !e52ngga
L9 05r2(L?9) 7.'6/
S2 4 4
GL9 05r2(L?9) 6.$6/
U! 4
4
R LL L9 ".7"&1'01/'
U" 4
4 N2a2 De<e,!2endutan -ada bantaan d2mana ! 4 S2 4 d2da-at V2 4 W 4
!e52ngga
#.$%%#5
P
'.&610/
MPa
MPa
6.$6/ MPa 7.'6/ ".&7 X ԑ2 5r2
4
(AAST;O E &7.6./.'.'%&) &1. mm
Rota!2 ma,!2mum -ada bantaan 0W Rca-ac2t* 4 L 4 "."7 rad2an F R! 4 "#"0
O,
3omb2na!2 beban dan rota!2 -ada bantaan a 8-2
4 &6.$7&7"&
F
7.'6/
o,
b S5ear de
P
/GS2(&%"#0(R!n)(L5r2)Y) F U!
4 /.''16&$
F
7.'6/ o,
3ontro Stab22ta! Ea!tomer2c Bear2ng Menurut AAST;O E. &7.6./.'.1%&# bear2ng 5aru! d2 de!a2n untu, da-at memenu52 bata! a*an ter5ada- ,omb2na!2 beban un2t. D2mana -er!amaann*a *a2tu G F U! 4 6.$6/ U! 4 0A%B &#$0(5r2L) d2mana A4 S2Z(&?(0L9)) "."7'7'//$ A4 0.16 B4 S2(S2?0)Z(&?(L79) "."1'0"6' B4 !e52ngga
U! 4
76.60&'$60
F
6.$6/ o,
Perencanaan -at ba+a -ea-2! ea!tomer & Pada ,ond2!2 bata! a*an '5r2U! 5! Q * 4 0.'$110/ mm 0 Pada ,ond2!2 bata! ea5 05r2UL 5! Q A(*) 4 "."""/ mm d2guna,an -at ba+a !eteba ' mm Deta2 La-2!an Ea!tomer2c Bear2ng ' a-2! daam dengan ,etebaan '/ mm 0 a-2! uar dengan ,etebaan & mm 7 a-2! ba+a -enguat dengan teba ' mm !e52ngga tota teba ea!tomer2c bear2ng adaa5 54 &/' mm b> 4 6"" mm b* 4 6"" mm Perencanaan Ang,ur a Juma5 dan d2ameter ang,ur DL!er 4 066 ,N 4 066""" N Ga*a gem-a ma,!2mum ,eara5 5or2Honta ;EK 4 &0.& ,N 4 &0&"" N a-ab2a d2guna,an baut dengan u 4 7"" MPa Rr 4 [! > Rn Q ;EK D2mana ! 4
Ab 4 \ dYN! ma,a# Ab 4 !e52ngga# Rn 4 dan Rr 4 ! > Rn 4
Rn 4 "#7 > Ab > u > N! a-ab2a# d2ameter baut (d) dan +uma5 baut (N!) 10./6&70$ mmY 07&'6&.7 &/1$&.70$
0" 0
N Q
&0&""
b Pan+ang Ang,ur b. Pn 4 b. "#/.
b 4
d2mana m 4 ,oe<. Ge!er 4 ".6/ ".6 untu, ea!tomer *ang d2eta,an d2ata! beton 0/ MPa
&&.&/10/ MPa
Beban tota ara5 5or2Honta !ebe!ar ;EK 4 &0&"" N untu, beban *ang d2der2ta -er!atu ang,ur# *a2tu &0&"" P&bot 4 0 4 17"/" N P&bot n2a2 A& 4 Stre!! brg0 4 &&70.'/0$ mm (Lua! -er!atuan baut) !e52ngga# -an+ang baut *ang d2-eru,an adaa5 A& Lembed 4 d baut 4 /67.&&6176 mm d2guna,an -an+ang ang,ur dengan bag2an tertanam !edaam !e52ngga tota -an+ang ang,ur adaa5 &/" mm ? teba tota bantaan ea!tomer 4 '"' mm#
&$./ m 066."" ,N 0""."" ,N "."0 rad 0/ C 0& mm 0 mm &.& M-a &.0 &1/ M-a 7"" M-a ".""""&" ; ]? ".""/01/ m /.01/ mm
''.$& mm mm mm a-2!
SNI '$160""
M&a
c5ec, M&a
o,
P
&&
".1/
mm bua5
o,
&/" mm
Data Konstruksi Struktur a. Ketentuan umum Data:
b. Konstruks
Panjang Jembatan (L) Lebar Jalan Lebar Trotoar Lebar Keseluruhan Jumlah Gelagar Tngg Gelagar Tngg "#g $am%ng Jembatan Jara' antar gelagar Jumlah aragma Tebal La%san +s%al Tebal $lab Jara' Permu'aan tanah #engan #asar sunga
= = = = = = = = = = = =
19.50 m 7.50 m 1.15 m 9.80 m 5.00 buah 1.! m &.8 m 1.5 m *.00 buah 0.05 m 0.& m !.00 m
B3B 111 ST%$KT$% B3-$3 3T3S . Peren&anaan Tiang Sandaran
A -utu "eton () A -utu "es Tulangan (/) A Tngg $an#aran A Jara' $an#aran A mens $an#aran A $elmut beton A > Tulangan Tulangan $eng'ang
= = = = = = = =
momen lentur
= = = = = = = =
Ga/a Geser
momen ultmt Ga/a Geser
=
&5 -%a *00 -%a 1.&0 m &.00 m bagan atas 100 D 1!0 mm 0 mm 1 mm 8 mm & &
bagan baEah
D D
100
D D
100
&00 'gm & & &00 'g m. Lentur G. Geser 1!0
D D
1.* 1.*
:
0
D D =
= = =
+s
=
@n
=
1 * b
= = =
mn
=
+s
= = = =
-a'a Jumlah Tulangan (n)
=
Tulangan GeserQ guna'an > 8 mm = 0.80 m Fu = F = =
=
0.85 / 0.85 0.051 1.* /
D
.1*
-u D
= #&
D D *0000 D
&500
1 : R 1 : &@n 0.85 D D
0.090*8*&918
=
1.* *00
=
0.1
D
=
DbD# 0.00500 D 0.0000*550 m& *5.50 mm & *5.50 1&.!7
=
&800 1 1
3 R D b D #
1 & 8!!7
0.* buah
R
D
&5
> D F
;
($eara teorts t#a' %erlu mengguna'an seng'ang)Q ma'a #%asang tulangan mnmum $maD = 1 D & +,mn
= =
14 R D b D s / 1
D
D
D
=
&800
N'.....O
#
=
&5
D
= ma'a guna'an tulangan > 8 mm
Jara' $eng'ang (s)
5*.1!7
mm &
+, 1 *
= D
=
50.&* mm& .1* D
+, D / 14 R D b
Ja# untu' %enggunaan tulangann/a a#alah sebaga ber'ut A Tulangan Lentur = & > 1 A Tulangan Geser = > 8 : !0
=
mm mm
2. Perhitungan Plat Kantile>er Trotoar
Lebar Trotoar Tebal Trotoar A Perhtungan -omen Lentur A Pembebanan
( Beban "ati
= =
1.15 m 0.&0 m
=
61
=
100 'g
=
6&
=
500 'g
=
6
=
500 'g
P1 P& P P* P5 P!
(P%a $an#aran) (Tang $an#aran) (Tang $an#aran) ("alo' Te%) (Plat Lanta) (Trotoar)
= = = = = =
A -omen Terha#a% Potongan tt' + ( 3kibat Beban 0idup
-61 -6& -6
= = =
100 500 500
D D D
( 3kibat Beban "ati
-P1
=
1*.&
D
-P& -P -P* -P5 -P!
= = = = =
&1.1& &&.1* 1&.9! *8*.80 *80.00
D D D D D umlah aki uml
-u
= =
-. Total 1Q15&.5
D D
& &
= =
A Ga/a Geser ($hear ores) "erat Total
= = =
P1 P& P P* P5 P! 1*.& 1Q05.* 'g
&1.1&
= = = = =
&5 -%a *00 mm h : % : 14& > Tulangan bD#&
*0
=
A Tulangan $lab Kantle,er h # K
mn
= =
0Q85 / 0.85
=
0.051&5
=
1.* / #'arena'an nla mn ; ma'a /ang #guna'an a#alah mn +s = DbD# = 0.005 ma'a guna'an tulangan > 1! mm +, 1 * Jara' $eng'ang (s) =
D D *00 D =
0.8 1 : R 1 : &K 0.85 D &5
: &!Q05 D
D
0.01&*!0
=
1.* *00
= =
D = D &00.9! 1&7.&5
1000 D &00.9! mm& .1* D D
-a'a tulangan /ang #guna'an untu' slab 'antle,er trotoar a#alah > 1! : 150 mm A Kontrol Terha#a% geser beton = F = 748 D b D h
748
D
1
#. Perhitungan Pelat bagian dalam ( Diren&anakan
Tebal Plat lanta 'en#araan (h) Tebal La%san +s%al (t) tebal la%san ar hujan (t h) -utu beton () -utu bes Tulangan (/) "erat Jens ("J) beton "erat Jens ("J) as%al "erat Jens ("J) ar hujan
= = = = = = = =
&0.00 m 5.00 m 5.00 m &5 -%a *00 -%a &500 'g4m &&00 'g4m 1000 'g4m
A "eban Kejut K
=
1 &0 50 L
T
= = =
10 Ton 10Q000 'g 8* D 5* m =
=
A "eban @o#a
A "#ang Konta' A Pen/ebaran beban ro#a (T) T
=
TDK tD D t/
Dm -Dm
= = = = =
0.15 Dm D T D tD D t/ 0.15 /m D T D tD D t/ 0.09
-omen lentur a'bat beban mat berat slab berat as%al berat ar hujan
= = =
0.&0 0.05 0.05
A "entang antar balo' (s)
=
tD D t/ =
10Q000 0.8*
D D
/m
=
D
&8Q89.99
D
D
&8Q89.99
D
D D D
&*00 &&00 1000
D D D
D
S#l D s&
D
!*0
menurut tabel P" 1970 #%eroleh
-/m
-Dm
= =
1.5*5 m 1 10 1 10
D
-/m
= =
ma'a moment total -D -/
= =
1 1 19Q1!.55 1&Q01*.89
D
-Dm
D
15&.7!9!
=
15&7.!9! 509.&&
= =
A Perhtungan baja tulangan untu' arah melntang -D = h = # = K =
&0Q8**.&* 3m &00 mm &00 : *0 = -D = >bD#& = 0Q85 D / = 0.85 D *00 = 0.051&5 D mn = 1.* = / #'arena'an nla mn ; ma'a /ang #guna'an a#alah mn +s = DbD# = 0.005 D ma'a guna'an tulangan > 1 mm +, = 1 D * Jara' $eng'ang (s) = 1&.!7 D 5!0 ma'a #%a'a tulangan > 1 : &00 mm A Perhtungan baja tulangan untu' arah memanjang -/ = h = # = +s = = ma'a guna'an tulangan > 1 mm
Jara' $eng'ang (s)
=
1&Q5&*.1& 3m &00 mm &00 : *0 = DbD# 0.005 D +s = 1 D * 1&.!7 D
1!0
mm &0Q8** D
0.8 1 : R 1 : &K
0.85 D D
&5 0.0*9101 1.* *00
= = =
1000 D 1&.!7 mm& .1* D 1000
1!0
=
mm
1000 D 1&.!7 mm& .1* D 1000
=
5!0 ma'a #%a'a tulangan > 1 : &00 mm
i
T%e Jembatan -utu "eton () -utu bes tulangan (/) Kelas Jalan Jens Perleta'an "erat jens beton berat jens as%al
= = = = = = =
berat jens baja berat jens ar
= =
Kon,ensonal &5 -%a *00 -%a (-uatan T #an 100) 2lastomer "earng &5 '34m && '34m 78.50 '34m 9.80 '34m
100 D &50 mm
h 1 &000 3m Gambar Po
&000 3 &000 &000
D D = =
1.* 1.*
= =
10.00 mm 1 m
&800 3m &800 3
= =
=
0.10 m
1 &
=
0.1
0.&8 D
1&.!7 mm&
=
=
1.&7 m&
1!5.!8 Ton4m&
0.1&* &
(1: R 1 : (& D18.58 ) 0.85 D &500 0.00*807 0.005
0.00*807
; ;
mn 0.00500
N'.....O
0.10
('arena 'urang #ar 1 buah ma'a #guna'an mnmum tulangan utama /atu & > 1)
100
D
1 &
D
1 &
100 &00
10
=
&1Q!!7
3
0.8
D
&1Q!!7
=
D
10
=
D
!5
!5 mm
8!!!.!!!!!7
3
8&
=
50.&*
D 14 R&5 D 100
50.&* mm& &00
=
!0.&9 mm
=
(ga/a horontal /ang harus #tahan tang:tang san#aran %a#a seta% torotar) (muatan horontal 'e arah melntang /ang harus #tahan oleh te% torotar) (muatan /ang #tahan oleh 'onstru's torotar)
&.00 0.1! 14& 14& 14& 1.00
D D D D D D
&.00 0.10 (0Q1! (0Q&5 (1Q0& 0.&0
D D D
1.00 1.00 1.00
D D D
1.0 0.*0 0.0
= = =
umlah akibat beban hidup '
1.0
=
1*.75 'gm
.58 0.55 0Q&5) 0Q&9) 1Q00) 1.00
= D D D D D
10 'gm &00 'gm 150 'gm !8* kgm
1*.& 'g &*00 0.10 0.10 0.&0 &*00 =
= D D D
1.0 0.97 0.90 0.50 0.0
= = = = =
&1.75 'gm &1.*8 'gm 11.!! 'gm &*&.*0 'gm 1**.00 'gm
at beban mati
'
!56.*! kgm
h momen total
'
1.& D 1.& D 115.&51! 'gm
- *5!.0*
=
1.! 1.!
1&.9!
*8*.8
*80.00
= = &!Q05 &.!
3m Tm
&&.1* 10Q5.*0 3
/
14& D 1000
=
*00 -%a
D
1
= =
10 D
5Q50 &
1 : R 1 : & D 0Q&! 0.000!!19*85 0.005
0.85 D &5 = !.!1 D 10 :* =
D D 1Q15&.5
.5 D 10 :
0.005 5.50
=
1&7.&5 mm &
1! &
=
&00.9! mm&
1000
=
1!&.* mm
5.50 mm 0.&! -%a
=
10Q5.*0 1000
D
=
0.05
=
1.&88
C
0Q*5
5.50
&0 50
19.50
1.&88 0.5*
=
&8Q89.99 'g4m&
0.8*
D
0.5*
=
1Q91.!5 'gm
=
0.8*
D
0.5*
=
1Q&01.*9 'gm
=
1 1 1
= = =
*80 'g4m& 110 'g4m& 50 'g4m&
berat total ?dl
'
6!* kg@m2
1Q875 &
=
0.09
15&.7!9! 'gm
=
15&7.!9!
3m
50.9&& 'gm
&0Q8**.&* 1&Q5&*.1&
D 1000
=
509 3m
3m 3m
10 D
= 1!0 &
1 : R 1 : & D 1Q0! 0.85 D &5 0.00&!1 0.0050 0.005 1!0.00
=
5!0 mm &
1 &
=
1&.!7 mm&
1!0.00
=
5!0 mm &
1 &
=
1&.!7 mm&
&!.90 mm
&!.90 mm
1.0& -%a
tongan -elntang Tang $an#aran
0.&8 Tm 0.&8 T
!.0&9 m
&1.1& 'g 0.*5 0.&0 1.00 *80.00 'g
D D D
&*00 &*00 &*00
= = =
&&.1* 'g 1&.9! 'g *8*.8 'g
-L *80.00 3
0.5* m
N'.....O
19Q1!.55 3m 1&Q01*.89 3m
