BAB 3 DATA-DATA YANG DIKETAHUI
Data yang diperlukan dalam perencanaan Kepala Jembatan (Abutment) adalah sebagai berikut: a1 a" b1 b" b# b$ & 'anang Abutment & +ebal Dinding 'en,pang & Jarak Antar Dinding 'en,pang & +inggi Abutment & ebar Dasar & -eban ati / -eban idup & -eban erata & 5udut Kemiringan (6nklinasi) & -J -et,n
= = = = = = () (t) (1) (") (h) (b) () (3) () (9b)
0.7 m 0.# m 0.$ m 0.! m 0.! m " m = = = = = = = = = =
h1 h" h# h$ h! h%
= = = = = =
0.! m 0.! m 1.% m 1.$ m 1.! m 1.! m
1* m 0.$! m $ m $.77! m $ m #.$ m %00 t2 t2m "10 t2m4 #0 8 ".$ t2m
asil 5,ndir ;,. 666-< pada kedalaman $ m dari 'eil +anah +anah = 0 .0 " > +? = 10 kg2cm ?s = 0.1 kg2cm" 3c = ! kg2cm" asil ab,rat,rium ;,. " & acam +anah = empung hitam / kulit kerang< sangat lunak (@ery s, & ,l,s saringan ;,m,r "00 = *. > & -erat 6si (9) = 1.#! t2m & -erat Jenis (B) = ".#7 & Kadar Air (C) = 7*.% > & Angka Atterberg : -atas air () = *$ > -atas 'lastis (') = #7 > 6ndeks 'lastisitas ('6) = $7 > & Enc,nFined (3u) = 1."! t2m4 & Direct 5hear : 5udut Beser Dalam (G) = "0 H K,hesi () = ".! t2m4 & akt,r Daya Dukung menurut +erIaghi (dengan 5udut Beser G = "0H) G = "0 H ;c = 11.* ;3 = # . ;9 = 1 .7 ;32;c = 0.##0!1 tan G = 0.#%$ & -erat 6si (9) = 1.#! t2m# & ebar Dasar Abutment (b) = #.$ m & Kedalaman ',ndasi (d) = 1 m & K,hesi () = ".! t2m"
?t)
BAB 4 TINJAUAN TINJAUAN TEORITIS TEOR ITIS
-erdasarkan -erdasarkan data&data yg telah diketahui dari bab sebelumnya< sebelumnya< maka untuk merencanakan merencanakan struktur kepala embatan (Abutment) dengan dinding pen,pang berupa bet,n digunakan suatu rumus&rumus perhitungan berdasarkan berdasarkan catatan pekuliahan ekayasa ',ndasi 1< sebagai berikut : 1. Kapasitas Daya Dukun A. Kapasitas Daya Daya Dukun Dukun U!ti"at# $ %& '
Kapasitas Daya Dukung Eltimate dideFinisikan sebagai tekanan terkecil yg dapat menyebabkan menyebabkan keruntuhan geser pada tanah pendukung tepat di baCah dan di sekeliling p,ndasi. Kapasitas Daya Dukung Ultimate pada pondasi jalur dangkal (menurut Terzaghi):
3? = "2# . 1.# . ;c / 9 . D . ;3 / 0.$ 9 . - . ;9 B. Kapasitas Daya Dukun U!ti"at# N#tt( $ %n& '
3n? = "2# . 12# 12# . ;c / 9 . D (;3 & 1) 1) / 0.$ 9 . - . ;9 ). Kapasitas Daya Dukun A"an $ %s '
3s
=
3n?
/9.D
D. B#*an +aksi"u" yan A"an $ %a!! '
3all = - . . 3s Keterangan : D 9 3 ;c< ;3< ;9 ;9
= = = = = = =
ebar Dasar ',ndasi (m) Kedalaman Dasar ',ndasi (m) K,hesi (t2m ) -erat 6si +anah (t2m ) 9 . D (t2m ) akt,r Keamanan akt,r Daya Du Dukung yang dipengaruhi 5udut Ba Baya Be Beser Dalam (G) ²
³
²
,. Daya Dukun Tana yan Diiinkan A. Aki*at Tana Tana Akti&
+ekanan +anah Akti? adalah tanah urugan bergerak l,ngs,r menekan dinding. 1. +ekanan +anah Akti? Ka
=
tan ( $!H & ²
G "
)
'a1 = 3. Ka 'a" = 9 . Ka. 'a = 3. . Ka / 12" . . " ". +ekanan +anah Akti? +,tal 'a = 3. . Ka / 12" . . " . Ka 'h = 'a . c,s '@ = 'a . sin Keterangan : 'a = +ekanan +anah Akti? Ka = K,eFisien +ekanan +anah Akti? #. 'a esultant 'ar = +inggi 'a1
'a1 / 'a"
'a1 = +inggi 'a" 'a" = +itiik K,,rdinat 'ar 'ar () =
12" . 12# . ('a1 . 12" ) / ('a" . 12# )
B. Aki*at Tana /asi&
+ekanan +anah 'asi? adalah gaya dinding mend,r,ng dinding penahan ke arah 1. K,eFisien +ekanan +anah 'asi? Kp
G c
(tan $!
=
²
)
". 6ntensitas +ekanan +anah 'asi? 12" . . . Kp 'p = #. encari 'p esultant 12" . . Kp . 'p1 = +inggi 'p1 = 12" . 12# . . Kp . 'p" = +inggi 'p" = 12# . ²
²
²
Keterangan : 'p Kp
= =
+ekanan +anah 'asi? K,eFisien +ekanan +anah 'asi?
). Ru"us K(n0(! T#0aap G#!in2i0
s
=
m. @ h
dimana< s L 1.! D. Ru"us K(nt0(! T#0aap Gu!in
,
=
M r N M , dimana< , berkisar antara 1.! & ".0
MC.Mp.A
E. Ru"us K(nt0(! T#0aap Kapasitas Daya Dukun
O luas 3ma
P =
3min
=
3ma
P
3al l @ @ 3all
Q1/ Q1&
%. e %. e -
R R
a1 a" b1 b" b# b$ bSt,talT 3
= = = = = = = = =
0.7 m 0.# m 0.$ m 0.! m 0.! m " m #.$ m "10 t2m4 %00 t2m
h1 h" h# h$ h! h% hSt,talT d h7
= = = = = = = = =
0.! 0.! 1 .% 1 .$ 1 .! 1.! $ 1 1.1!$701
BAB /EREN)ANAAN .1 A*ut"#nt .1.1 A*ut"#nt D#nan )(unt#0&(0t
1. encari uas 'enampang ',ndasi Dengan ,unter?,urt A1 = h1 b = 0
A1 / A" A" / A# A# / A$ A$ / A! A! / A% A% / A7 A7 / A* A* / A A = 1<7 / 1<0! / 1 /0<1# /1<1# /1<1# / 0<#* / 0<#* / 0<0! 0<0! / 0<$ = %. " " m 4
". 5tatis ,men +erhadap 5umbu U
5 1 " # $ ! % 7 *
A (m4) 1. 7 0 1. 0 ! 1. 0 0 0. 1 # 1. 1 # 0. # * 0. # * 0. 0 ! 0. $ "
y (m ) 0."! 1.!! 0.7! 0.*######### " 1. ! " ".!! #. # M
A.y (m) 0. $ " ! 1 .% " 7 ! 0.7! 0.10$1%%7 "."! 0.!%"! 0.7! 0 .1 " 7 ! 1. # * % %.!%%%%7
#. 5tatis ,men +erhadap 5umbu V 5 A (m4) (m) 1 1. 7 0 1. 7 " 1. 0 ! 0.%! # 1. 0 0 1. $ 0. 1 # #.0%%%%%%%%7 ! 1. 1 # 1. % 0. # * 1."######### 7 0. # * 1.0%%%%%%%%7 * 0. 0 ! 1.1! 0. $ " 1."! M
A. (m) ".* 0 .% * " ! 1. 0.#*##### ".1#7! 0.$%"! 0. $ 0 .0 ! 7 ! 0. ! " ! .$#*####
$. +itik -erat +erhadap 5umbu U U1 = 5tatis ,men +erhadap 5umbu V uas +,tal !. +itik -erat +erhadap 5umbu V V1 = 5tatis ,men +erhadap 5umbu U uas +,tal
=
.$#*### %.""
=
% .! % % % 7 %.""
%. W,lume Abutment Dengan ,unter?,rt (! Dinding 'enahan) W1 = (uas +,tal +,tal +ebal +ebal Dinding Jumlah Dinding 'en,pang) = (%<"" 0<$! !) !) = 1#.! m m 7. -erat Abutment Dengan ,unter?,urt O1 = (uas +,tal +,tal +ebal +ebal Dinding -J -et,n Jumlah Dinding 'en,pang) / O" = (%<"" 0<$! 0<$! "<$ !) !) = ##.!** + Atau O1 = W,lume Abutment -J -et,n = 1$ "<$ = ##.!** + .1., A*ut"#nt Tanpa )(unt#0&(0t
1. encari uas 'enampang ',ndasi +anpa ,unter?,urt A1 = h1 b
= 0
A1 / A" / A# / A$ / A! A! = 1<7 / 1<0! / 0<#* / 0<0! 0<0! / 0<$ = #. % 0 m 4
". 5tatis ,men +erhadap 5umbu U 5 A (m4) y (m ) 1 1. 7 0 0."! " 1. 0 ! 1.!! # 0. # * " $ 0. 0 ! ".!! ! 0. $ " #. # M
A.y (m) 0. $ " ! 1 .% " 7 ! 0.7! 0 .1 " 7 ! 1. # * % $. # 1 %
#. 5tatis ,men +erhadap 5umbu V 5 A (m4) (m) 1 1. 7 0 1. 7 " 1. 0 ! 0.%! # 0. # * 1.0%%%%%%%%7 $ 0. 0 ! 1.1! ! 0. $ " 1."! M
A. (m) ".* 0 .% * " ! 0. $ 0 .0 ! 7 ! 0. ! " ! $. ! ! !
$. +itik -erat +erhadap 5umbu U U" = 5tatis ,men +erhadap 5umbu V uas +,tal
=
$. ! ! ! #.%0
!. +itik -erat +erhadap 5umbu V V" = 5tatis ,men +erhadap 5umbu U uas +,tal
=
$. # 1 % #.%0
%. W,lume Abutment +anpa ,unter?,rt (! Dinding 'enahan) W1 = uas +,tal +,tal (1 & t) Jumlah -entang Abutment = #<% ($ & 0<$!) 0<$!) " = " ! .! " $ ! m W" = uas +,tal +,tal (" & t) Jumlah -entang Abutment
= #<% ($<77! ($<77! & 0<$!) 0<$!) " = # 1 .0 % * m W" = W1 / W" = "! / #1 = ! % .% " 1 # m 7. -erat Abutment +anpa ,unter?,urt O" = uas +,tal +,tal 'anang Abutment tanpa ,unter?,rt -J -et,n = #<% (1* & (0<$! (0<$! !)) "<$ = 1 # ! .* 1 + Atau O" = W,lume Abutment +anpa +anpa ,unter?,urt -J -et,n = %"% "<$ "<$ = 1 # ! .* 1 + ., Tana /#nisi .,.1 Tana Akti&
h7 = tan b$ = tan #0 " = 1.1!$7 m m 1. encari uas +anah Akti? A1 = 0
A.y (m) 0.!%"! 0 . # 7 ! 1! !.0%#"$%% "1.!%#"$7
#. 5tatis ,men +erhadap 5umbu V 5 A (m4) (m) 1 0. # * 1."#########
A. (m) 0.$%"!
" # $
1. " ! %. 0 0 1. 1 !
".1! ". $ ".7######### M
" .% * 7 ! 1$.$ #.1!%1*1! "0.70%1*1
$. +itik -erat +erhadap 5umbu U U# = 5tatis ,men +erhadap 5umbu V uas +,tal
=
"0.70%1* *.7*
!. +itik -erat +erhadap 5umbu V V# = 5tatis ,men +erhadap 5umbu U uas +,tal
=
"1.!%#"! *.7*
%. W,lume +anah Akti? Wa = uas +,tal +,tal +anah +anah 'anang Abutment = *<7* 1* = 1 ! * .0 # ! m 7. uas ,unter?,rt Ac = uas 'enampang Dengan ,unter?,rt & uas 'enampang +anpa +anpa ,unter?,rt = %<"" & #<% = ". % # m 4 *. W,lume ,unter?,rt Wc = uas ,unter?,rt +ebal +ebal Dinding Jumlah Dinding 'en,pang = "<%# 0<$! 0<$! ! = !.0%"! m . W,lume +,tal +anah Akti? W# = W,lume +anah Akti? & W,lume W,lume ,unter?,rt = 1!* & !<1 = 1 ! " .1 " * m 10. -erat +,tal +anah Akti? O# = W,lume +,tal +anah +anah Akti? -J +anah = 1!" 1<#! = " 0 ! .# 7 # + .,., Tana /asi&
1. uas +anah 'asi? A = h" b1 = 0
O% = W,lume +anah 'asi? 'asi? -J +anah = #<% 1<#! = $. * % + $. +itik -erat terhadap 5umbu U U% = 0
1. -erat -eban erata O$ = 3 sin b$ = "10 sin #0 #0 " 1* = # 7*0 + ". +itik -erat +erhadap 5umbu U U$ = (0
1. -erat -eban idup dan -eban ati O! = (-eban idup dan -eban ati) 'anang 'anang Abutment = %00 1* = 10 *00 + ". +itik -erat +erhadap 5umbu U U! = (0
1. K,eFisien +anah Akti? Ka =
tan4
$!
&
G "
=
ta n 4
$!
&
"0 "
= 0.$0" ". 6ntensitas +ekanan +anah Akti? = h1 / h" / h# / h$ / (h7 tan ) = 0
1. K,eFisien +anah 'asi? Kp =
ta n 4
$!
/
G "
=
ta n 4
$!
/
#0 "
=
#
". 6ntensitas +ekanan +anah 'asi? =h" = 0.! m 'p 1 = 12" Kp 9 4 b = 12" # 1<#! 0
esultante Baya +,tal +,tal pada Abutment dengan ,unter?,rt -erat (O1) pada titik berat ( U1
= =( = = =
# #. ! * * 1.!17$17 % ." " %."" % ." "
esultante Baya +,tal +,tal pada Abutment tanpa ,unter?,rt -erat (O") pada titik berat ( U"
= =( = = =
1 # !. * 1 1."%70#* #.%0 #.%0 # .% 0
M -erat OA M uas M 5tatis ,men terhadap 5umbu U M 5tatis ,men terhadap 5umbu V
= = = =
##.!** % ." " %.!%%%7 .$ # * # # #
1. esultante +itik -erat +,tal (OA) (OA) terhadap 5umbu 5um bu U U = 1#.## : .*1!
=
1.$"!71 m
". esultante +itik -erat +,tal (OA) (OA) terhadap 5umbu 5um bu V V = 1 0 . 1 " 7 : .*1!
=
1.111*$ m
#. +itik -erat OA teradi pada K,,rdinat (U
<
1.111*#!%"!7 )
esultante Baya +,tal +,tal pada +anah 'engisi (sisi belakang Abutment) -erat +anah 'engisi (O#) = pada titik berat ( U#
" 0 !. # 7 # # ".#!*$1! * .7 * *.7* * .7 *
esultante Baya +,tal +,tal pada +anah 'engisi (sisi depan Abutment) -erat +anah 'engisi (O%) = pada titik berat ( U%
$.*% 0." 0."0 0."0 0 ." 0
M -erat O+ M uas M 5tatis ,men terhadap 5umbu U M 5tatis ,men terhadap 5umbu V
= = = =
" 0 ! .# 7 # # * .7 * "1.!%#"! " 0 .7 0 % 1 *
1. esultante +itik -erat +,tal (OA) (OA) terhadap 5umbu 5um bu U U = "0 "0.7$%" : *.7700!
=
".#10#$ m
". esultante +itik -erat +,tal (OA) (OA) terhadap 5umbu 5um bu V V = "1 "1.71#" : *.7700!
=
".$1*0$ m
#. +itik -erat OA teradi pada K,,rdinat (U
<
".$1*0#%*"71 )
..3 R#su!tant# Gaya 6#0tika! R7
@ = / OA / O+ / 3 sin / 'a@ = 10*00 / 1% / "10 / #7*0 #7*0 / *" = 1 ! 7 * *. * + -esar masing&masing masing&masin g Baya Wertikal dan K,,rdinatnya = 10 *00 OA = 1%.$7 O+ = "10."## 3= # 7 *0 'a@ = *".07%
( U
= = = = =
@. @. U = . U / OA . U / O+ . U / 3 . U / 'a@ . U U = ((10*00 0<7!) / (1% 1<$) / ("10 "<#1) / (#7*0 "<$) / (*" "<#!))21!7* = 1."!7!" m ..4 R#su!tant# Gaya H(0i(nta! R
h = 'ah 'ah / 3h = 1$#% / (3 c,s b$ b$ ) = 1$#% / "10 c,s #0 #0 b$ = 7 * #. 1 ! +
-esar masing&masing Baya ,riI,ntal dan K,,rdinatnya 'ah = 1 $#% 3h = %!$7.1!
( U
= =
h . V = 3h . V / 'ah . V V = ((%!$7 $
... R#su!tant# $R' Da0i Gaya 6#0tika! $R7' an Gaya H(0i(nta! $R'
= X (@4) (@4) / (h4) =X( 1!7*4 / 7*#4 = 1 7 % ". # +
)
.8. K(nt0(! T#0aap G#s#0
Yb = S 12" Z "2# T G = "2# "2# G = "2# "2# "0 "0 = 1 # .# # # #
Diambil nilai maksimum sebagai ni
O = O1 / O" / O# / O$ / O! / O% = #$ / 1#! / "0! / #7*0 / 10*00 10*00 / $.*% = 1 $ ! . 7 + ['h = 'ah & 'pr = 1$#% & 1<7 = 1 $ # $. " * + O tan Yb / cd ['h 1$! tan 1#<## / (#<$ "
gs =
1.! (
OK
.9 K(nt0(! T#0aap Gu!in
O1 O" O# O$ O! O% [O
+abel perhitungan Baya Wertikal dan ,men Baya Wertikal Jarak ,men (+) (m) ( +m ) ##.!** 1.!17$1%#$% ! 0 . % 7 1 # !. * 1 1."%70#7!!"" 1 7 ". 1 7 "0!.#7#"*!!*"% ".#!*$1!$!*% $*$.#!!!#1!01 #7* 0 ". $ 0 7" 10*00 0.7! *1 00 $ .* % 0. " 0. 7 " 1$!.71""*!!*"% 17**0.$7#!#1!01
gl =
[ C [ gl
= = = $.%$$#"
[ C ' ar V 17**0 1%!* "<# \
1.!
(
OK
.: Kapasitas Daya Daya Dukun A. Kapasitas Daya Daya Dukun U!ti"at# U!ti"at# $T#0ai' $T#0ai'
3? = "2# 1<# .;c / 9 D.;3 / 0<$ 9 -.;9 = ("2# 1<# "
3n? = "2# 1<# .;c / 9 D.( ;3 & 1) / 0<$ 9 -.;9 = ("2# 1<# "
3s =
3n? ?
"1.7 # = 1"."17% 17% +2m4 =
/
(9.D)
/
(1<#! 1)
D. B#*an +aksi"u" A"an
3 all = - 3s = #<$ 1* 1* $
+abel perhitungan +ekanan +anah ateral (+anah (+anah Akti? ) dan ,men Baya Wertikal Jarak ,men (+) () ( + ) 'a 1 1 % # #. % $ * " % 7 7 ! % ".#"1*#1 #7#.0%*#1* 'a " " $. ! 0 $ 7 " $ 0 1 % $ ".#"1*#1 !!%%.*%0"!*77 ['a 1 % ! *. 1 ! " 1 7 7 # # #*$.%$$177 [ = [O & [V = 17**0 17**0 & #*$ = 1$0#0.! +
)
[ [O 1$0#0.! = 1$!.7 = 0.# 0.#7* 7* m
U=
b " #.$ = " = 0.7%"11 m
e1 =
&
U
&
0.#7**%#
b % #.$ = % = 0.!%%%7 m
e" =
e1
\
0.7%"11#7
\
0.7%"11#7
\
b % #.$ % 0 .! % % % % % % % % 7
......................
Tiak OK
.11 K(nt0(! Daya Dukun A"an
Jika e = -2%< maka 3 min = 0< dan ika e \ -2% maka akan negati?< sehingga teradi tegangan tarik Diambil e \ -2% @ (1 / 2 & (% e) ) 3= - 1!7**.* (1 / 2 & (% 0<7%)) = #<$ 1* #. $ 1!7**.* #<$ 1* = %0$.!! +2m4
3 maks =
1!7**.* #<$ 1* = &**.*1# +2m4
3 min =
(1 / \
3s (
(% 0<7%)) #. $ 1"."17% +2m4 )
3s (
(% 0<7%)) #. $ 1"."17% +2m4 )
(1 & P
m m m m m m m m m
G (t) 1 " (9b) (9)
= = = = = = = =
"0 H #0 H 0.$! m $ m $.77! m 1* m ".$ t2m 1.#! t2m n Sdinding pen,pangT
n 1 n " ;c ;3 ;9 ;32;c
= = = = = = =
=
!
"0 m "#.*7! m 11.* #. 1.7 0.##0!0* ".! +24
BUT+ENT
1 = " = # = $ = ! = % = 7 = * = =
1. 7 m 0.%! m 1. m #.07 m 1. m 1."# m 1.07 m 1.1! m 1."! m
y1 = y" = y# = y$ = y! = y% = y7 = y* = y =
0."! m 1.!! m 0 .7 ! m 0.*## m " m 1. 1.! m " m ".!!m #. #.# m
m m4
=
1.!" m
m m4
=
1.0% m
1 = 1.7 m
y1 = 0."! m
" = # = $ = ! =
0.%! 1.07 1.1! 1."!
m m m m
m m4
=
1."7 m
m m4
=
1 ." m
y" = 1.!! m y# = " m y$ = ".!! m y! = #. #.# m
1 = " = # = $ =
1."# m ".1! m ".$ m ".7# m
y1 = y" = y# = y$ =
1. ! m 0. 7 ! m ". ! m $.#*! m
m m4
=
".#% m
m m4
=
".$% m
+ <
1.0%0!!7 )
1.0%0!!7 1.!17$17
m4
+ < m4
= =
%. ! % % % 7 m . $ # * # # # m
1."00!!% )
1."00!!% 1."%70#*
= =
$.#1% m $.!!! m
/ / / /
1#!.*1 #. % 0 $ .# 1 % $ .! ! !
= = = =
1 % .$ 7 + .*1! m4 1 0. 1 " % 7 m 1 #. # # # m
+ <
".$!%0#$ )
".$!%0#$ ".#!*$1!
m4
+ < m4
0.7! / / / /
( ( ( ( (
= =
" 1. ! % # " ! m " 0. 7 0 % 1 * m
= =
0.1! m 0.0$ m
= = = =
"10."### + *. 7 7 0 1 m 4 " 1. 7 1 # " ! m " 0. 7 $ % 1 * m
)
0.7! 0." $. * % 0. " 0 0. 1 ! 0. 0 $
0 .7 ! < 1.$"!70 < ".#10#$" < ". $ < ".#!*$1! <
". % ) 1. 1 1 1 * # % ) ". $ 1 * 0 # 7 ) $. ! 7 7 # ! ) ". # " 1 * # )
( (
".#!*$1! < ". $ <
ai aman yaitu "2#
)
". # " 1 * # ) $. ! 7 7 # ! )
.
.................
Tiak OK
.................
OK
