Perencanaan Abutment Jembatan

BAB 3 BAB 3

DATA-DATA YANG DIKETAHUI DATA-DATA YANG DIKETAHUI Data yang diperlukan dalam

Data yang diperlukan dalam perencanaan Kepala Jembatan (Abutment) adalah sebagai perencanaan Kepala Jembatan (Abutment) adalah sebagai berikut:berikut:

aa11 == 00..77 mm hh11 == 00..!! mm aa"" == 00..## mm hh"" == 00..!! mm bb11 == 00..$$ mm hh## == 11..%% mm bb"" == 00..!! mm hh$$ == 11..$$ mm bb## == 00..!! mm hh!! == 11..!! mm bb$$ == "" mm hh%% == 11..!! mm &

& ''aannaanng g AAbbuuttmmeenntt (()) == 11** mm &

& ++eebbaal l DDiinnddiinng g ''eenn,,ppaanngg ((tt)) == 00..$$!! mm &

& JJaarraak k AAnnttaar r DDiinnddiinng g ''eenn,,ppaanngg ((11)) == $$ mm (("")) == $$..7777!! mm &

& ++iinnggggi i AAbbuuttmmeenntt ((hh)) == $$ mm &

& eebbaar r DDaassaarr ((bb)) == ##..$$ mm &

& --eebbaan n aatti i / / --eebbaan n iidduup p (()) == %%000 t0 t22mm &

& --eebbaan n eerraattaa ((33)) == ""1100 tt22mm44 &

& 55uudduut t KKeemmiirriinnggaan n ((66nnkklliinnaassii)) (()) == ##00 88 &

& --J J --eett,,nn ((99bb)) == ""..$$ tt22mm asil 5,ndir ;,. 666-< pada

asil 5,ndir ;,. 666-< pada kedalaman $ m dari kedalaman $ m dari 'eil +'eil +anahanah  == 00..00"" >> + +?? == 1100 kkgg22ccmm ??ss == 00..11 kkgg22ccmm"" 33cc == !! kkgg22ccmm"" asil ab,rat,rium ;,. " asil ab,rat,rium ;,. " &

& aaccaam m ++aannaahh == eemmppuunng g hhiittaam m / / kkuulliit t kkeerraanngg< < ssaannggaat t lluunnaak k ((@@eerry y ss,, &

& ,,ll,,s s ssaarriinnggaan n ;;,,mm,,r r ""0000 == **.. >> &

& --eerraat t 66ssii ((99)) == 11..##!! tt22mm &

& --eerraat t JJeenniiss ((BB)) == ""..##77 &

& KKaaddaar r AAiirr ((CC)) == 77**..%% >> & Angka Atterberg :

& Angka Atterberg : --aattaas s aaiirr (()) == **$$ >> --aattaas s ''llaassttiiss (('')) == ##77 >> 66nnddeekks s ''llaassttiissiittaass ((''66)) == $$77 >> &

& EEnncc,,nnFFiinneedd ((33uu)) == 11..""!! tt22mm44 & Direct 5hear :

& Direct 5hear :

55uudduut t BBeesseer r DDaallaamm ((GG)) == ""00 HH K

K,,hheessii (()) == ""..!! tt22mm44

& akt,r Daya Dukung menurut +erIaghi (dengan 5udut Beser G = "0H) & akt,r Daya Dukung menurut +erIaghi (dengan 5udut Beser G = "0H)

G G == ""00 HH ; ;cc == 1111..** ; ;33 == ##.. ; ;99 == 11..77 ; ;3322;;cc == 00..####00!!11 ttaannGG == 00..##%%$$ &

& --eerraat t 66ssii ((99)) == 11..##!! tt22mm## &

& eebbaar r DDaassaar r AAbbuuttmmeenntt ((bb)) == ##..$$ mm &

& KKeeddaallaammaan n '',,nnddaassii ((dd)) == 11 mm &

?t) ?t)

BAB 4 BAB 4 TINJAU

TINJAUAN TEORAN TEORITISITIS -erdasar

-erdasarkan kan data&data data&data yg yg telah telah diketahui diketahui dari dari bab bab sebelumnysebelumnya< a< maka maka untuk untuk merencanakmerencanakanan struktur kepala embatan (Abutment) dengan dinding

struktur kepala embatan (Abutment) dengan dinding pen,pang berupa bet,n digunakan suatupen,pang berupa bet,n digunakan suatu rumus&rumus perhitungan berdasark

rumus&rumus perhitungan berdasarkan catatan an catatan pekuliahan ekayasa ',ndasi 1< sebagai pekuliahan ekayasa ',ndasi 1< sebagai berikut :berikut : 1. Kapasitas Daya Dukun

1. Kapasitas Daya Dukun  A. Kapasitas Da

 A. Kapasitas Daya Dukya Dukun U!ti"at# $ %& 'un U!ti"at# $ %& '

Kapasitas Daya Dukung Eltimate dideFinisikan sebagai

Kapasitas Daya Dukung Eltimate dideFinisikan sebagai tekanan terkecil yg dapat tekanan terkecil yg dapat  menyebabk

menyebabkan keruntuhan geser pada an keruntuhan geser pada tanah pendukung tepat di tanah pendukung tepat di baCah danbaCah dan di sekeliling p,ndasi.

di sekeliling p,ndasi.

Kapasitas Daya Dukung Ultimate pada pondasi

Kapasitas Daya Dukung Ultimate pada pondasi jalur dangkal (menurut Terzaghi):jalur dangkal (menurut Terzaghi): 3?

3? = = "2# . "2# . 1.#  1.#  . ;c / . ;c / 9 . D 9 . D . ;3 . ;3 / 0.$ / 0.$ 9 . - 9 . - . ;9. ;9 B. Kapasitas Daya Dukun U!ti"at# N#tt( $ %n& '

B. Kapasitas Daya Dukun U!ti"at# N#tt( $ %n& ' 3n?

3n? = = "2# . 1"2# . 12#  . 2#  . ;c / ;c / 9 . D 9 . D (;3 & 1(;3 & 1) / 0.$ ) / 0.$ 9 . - 9 . - . ;9. ;9 ). Kapasitas Daya Dukun A"an $ %s '

). Kapasitas Daya Dukun A"an $ %s ' 3s

3s == 3n? 3n?  / 9 . D/ 9 . D 

D. B#*an +aksi"u" yan A"an $ %a!! ' D. B#*an +aksi"u" yan A"an $ %a!! '

3all

3all = = - - . .   . . 3s3s Keterangan :

Keterangan :

-- == eebbaar r DDaassaar r '',,nnddaassi i ((mm)) D

D == KKeeddaallaammaan n DDaassaar r '',,nnddaassi i ((mm))

 ==

99 ==

33 ==

 == aakktt,,r r KKeeaammaannaann ;

;cc< < ;;33< ;< ;99 == aakktt,,r r DDaayya Da Duukkuunng g yyaanng g ddiippeennggaarruuhhi i 55uudduut Bt Baayya Ba Beesseerr Dalam (G)

Dalam (G) ,. Daya Dukun Tana yan Diiinkan ,. Daya Dukun Tana yan Diiinkan  A. Aki*at T

 A. Aki*at Tana Akti& ana Akti& 

+ekanan +anah Akti? adalah tanah urugan bergerak l,ngs,r menekan dinding. +ekanan +anah Akti? adalah tanah urugan bergerak l,ngs,r menekan dinding. 1. +ekanan +anah Akti? 

1. +ekanan +anah Akti?  Ka Ka == GG )) "" ''aa11 == 33. . KKaa ''aa"" == 9 9 . . KKaa. .  ''aa == 33. .   . . KKa a / / 1122" " . .   . . "" ". +ekanan +anah Akti? +,tal

". +ekanan +anah Akti? +,tal

''aa == 33. .   . . KKa a / / 1122" " . .   . . " " . . KKaa ''hh == ''a a . . cc,,s s 

''@@ == ''a a . . ssiin n  Keterangan :

Keterangan :

''aa == ++eekkaannaan n ++aannaah h AAkkttii?  ?   K

Kaa == KK,,eeFFiissiieen n ++eekkaannaan n ++aannaah h AAkkttii?  ?   #. 'a esultant 

#. 'a esultant 

''aarr == ''aa1 1 / / ''aa"" +inggi 'a1

+inggi 'a1

K,hesi (t2m K,hesi (t2m²²))

-erat 6si +anah (t2m -erat 6si +anah (t2m³³)) 9 . D (t2m

9 . D (t2m²²))

tan

''aa11 == 1122" " . .  +inggi 'a"

+inggi 'a"

''aa"" == 1122# # . .  +itiik K,,rdinat 'ar

+itiik K,,rdinat 'ar

''aar r (()) == ((''aa1 1 . . 1122" " ) ) / / ((''aa" " . . 1122# # )) B. Aki*at Tana /asi& 

B. Aki*at Tana /asi& 

+ekanan +anah 'asi? adalah gaya dinding mend,r,ng dinding penahan ke arah +ekanan +anah 'asi? adalah gaya dinding mend,r,ng dinding penahan ke arah 1. K,eFisien +ekanan +anah 'asi? 

1. K,eFisien +ekanan +anah 'asi?  Kp

Kp == GG ))

cc ". 6ntensitas +ekanan +anah 'asi? 

". 6ntensitas +ekanan +anah 'asi?  'p

'p ==

#. encari 'p

#. encari 'p esultant esultant 

''pp11 == + +iinnggggi i ''pp11 == 1122" " . .  ''pp"" == + +iinnggggi i ''pp"" == 1122# # . .  Keterangan : Keterangan :

''pp == ++eekkaannaan n ++aannaah h ''aassii?  ?   K

Kpp == KK,,eeFFiissiieen n ++eekkaannaan n ++aannaah h ''aassii?  ?   ). Ru"us K(n0(! T#0aap G#!in2i0

). Ru"us K(n0(! T#0aap G#!in2i0

ss == mm. . @@ h h dimana< s L 1.!

dimana< s L 1.!

D. Ru"us K(nt0(! T#0aap Gu!in D. Ru"us K(nt0(! T#0aap Gu!in

,, == MMrr NN MMCC..-

-M

M ,, M M p p . . AA dimana<

dimana< , , berkisar berkisar antara antara 1.! 1.! & & ".0".0 E. Ru"us K(nt0(! T#0aap Kapasitas Daya Dukun E. Ru"us K(nt0(! T#0aap Kapasitas Daya Dukun

O O PP 33aallll luas luas 33mmaa == @@ QQ11// %%..ee RR -- - -33mmiinn == @@ QQ11&& %%..ee RR -- - -33mmaa PP 33aallll (tan (tan²²  $!  $! 12" .  .  12" .  . ²² . Kp . Kp 12" .  . Kp .  12" .  . Kp . ²² 12# .  . Kp .  12# .  . Kp . ²²

aa11 == 00..77 mm hh11 == 00..!! aa"" == 00..## mm hh"" == 00..!! bb11 == 00..$$ mm hh## == 11..%% bb"" == 00..!! mm hh$$ == 11..$$ bb## == 00..!! mm hh!! == 11..!! bb$$ == "" mm hh%% == 11..!! bbSStt,,ttaallTT == ##..$$ mm hhSStt,,ttaallTT == $$ 33 == ""1100 tt22mm44 dd == 11   == %%0000 tt22mm hh77 == 11..11!!$$770011 BAB  BAB  /EREN)ANAAN /EREN)ANAAN .1 A*ut"#nt  .1 A*ut"#nt  .1.1 A*ut"#nt D#nan

.1.1 A*ut"#nt D#nan )(unt#0&(0t )(unt#0&(0t 

1. encari uas 'enampang ',ndasi Dengan ,unter?,urt  1. encari uas 'enampang ',ndasi Dengan ,unter?,urt 

A1 = A1 = h1  bh1  b == 0<!  #<$0<!  #<$ == 1.71.700 m4m4 A" = A" = (h" / h#)  b"(h" / h#)  b" == (0<! / 1<%)  0<!(0<! / 1<%)  0<! == 1.01.0!! m4m4 A# = A# = h"  (b# / b$ & 0<!)h"  (b# / b$ & 0<!) == 0<!  (0<! / " & 0<!)0<!  (0<! / " & 0<!) == 1.01.000 m4m4 A$ = A$ = 0<!  0<!  h"0<!  0<!  h" == 0<!  0<!  0<!0<!  0<!  0<! == 0.10.1## m4m4 A! = A! = 0<!  1<!  h!0<!  1<!  h! == 0<!  10<!  1<!  1<<!  1<!! == 1.11.1## m4m4 A% = A% = 0<!  b#  h!0<!  b#  h! == 0<!  00<!  0<!  1<<!  1<!! == 0.#0.#** m4m4 A7 = A7 = 0<!  b#  h!0<!  b#  h! == 0<!  00<!  0<!  1<<!  1<!! == 0.#0.#** m4m4 A* = A* = (h# & h!)  b#(h# & h!)  b# == (1<% & (1<% & 1<! )  1<! )  0<!0<! == 0.00.0!! m4m4 A =

A = h$  h$  a"a" == 1<$ 1<$  0< 0<## == 00..$$"" mm44 A +

A +,t,tal al == A1 A1 / A/ A" / A" / A# / A# / A$ / A$ / A! / A! / A% / A% / A7 / A7 / A* / A* / A

== 1<7 / 1<0! / 1 /0<1# /11<7 / 1<0! / 1 /0<1# /1<1# / 0<#* / 0<#* / 0<0<1# / 0<#* / 0<#* / 0<0! / 0<$! / 0<$ == %%.."""" mm44

". 5tatis ,men +erhadap 5umbu U ". 5tatis ,men +erhadap 5umbu U

55 A A ((mm44)) y y ((mm)) AA..y y ((mm)) 11 11..7700 00..""!! 00..$$""!! "" 11..00!! 11..!!!! 11..%%""77!! ## 11..0000 00..77!! 00..77!! $$ 00..11## 00..**################## 00..1100$$11%%%%77 !! 11..11## "" ""..""!! %% 00..##** 11..!! 00..!!%%""!! 77 00..##** "" 00..77!! ** 00..00!! ""..!!!! 00..11""77!!  00..$$"" ##..## 11..##**%% M M %%..!!%%%%%%%%77 #. 5tatis ,men +erhadap 5umbu V

#. 5tatis ,men +erhadap 5umbu V

55 A A ((mm44))   ((mm)) AA..  ((mm)) 11 11..7700 11..77 ""..** "" 11..00!! 00..%%!! 00..%%**""!! ## 11..0000 11.. 11.. $$ 00..11## ##..00%%%%%%%%%%%%%%%%77 00..##**########## !! 11..11## 11.. ""..11##77!! %% 00..##** 11..""################## 00..$$%%""!! 77 00..##** 11..00%%%%%%%%%%%%%%%%77 00..$$ ** 00..00!! 11..11!! 00..00!!77!!  00..$$"" 11..""!! 00..!!""!! M M ..$$##**######## $. +itik -erat +erhadap 5umbu U

$. +itik -erat +erhadap 5umbu U

UU1 1 == 55ttaattiis s ,,mmeen n ++eerrhhaaddaap p 55uummbbu u VV == ..$$##**###### uuaass++,,ttaall %%.."""" !!. . ++iittiik k --eerraat t ++eerrhhaaddaap p 55uummbbu u VV == %%..!!%%%%%%77

VV1 1 == 55ttaattiis s ,,mmeen n ++eerrhhaaddaap p 55uummbbu u UU %%.."""" uas +,tal

uas +,tal

%. W,lume Abutment Dengan ,unter?,rt (! Dinding 'enahan) %. W,lume Abutment Dengan ,unter?,rt (! Dinding 'enahan)

W1 =

W1 = (uas +(uas +,tal  +,tal  +ebal Dinding  Jumlah Dinding 'en,pang)ebal Dinding  Jumlah Dinding 'en,pang) == (%<""  (%<""  0<$!  !0<$!  !))

== 11##..! m! m

7. -erat Abutment Dengan ,unter?,urt  7. -erat Abutment Dengan ,unter?,urt 

O1 =

O1 = (uas +(uas +,tal  +,tal  +ebal Dinding  -J -et,n  Jumlah Dinding 'en,pang) / O"ebal Dinding  -J -et,n  Jumlah Dinding 'en,pang) / O" == (%<""  0<(%<""  0<$!  "<$  !$!  "<$  !))

== ####..!!*** +* +

Atau Atau O1 =

O1 = WW,lume Abutment  -J -et,n,lume Abutment  -J -et,n == 1$  1$  "<$"<$

== ####..!!*** +* +

.1., A*ut"#nt Tanpa )(unt#0&(0t  .1., A*ut"#nt Tanpa )(unt#0&(0t  1. encari

1. encari uas 'enampang ',ndasi +anpa ,unter?,urt uas 'enampang ',ndasi +anpa ,unter?,urt  A1 =

== 0<!  #<$0<!  #<$ == 1.71.700 m4m4 A" = A" = (h" / h#)  b"(h" / h#)  b" == (0<! / 1<%)  0<!(0<! / 1<%)  0<! == 1.01.0!! m4m4 A# = A# = 0<!  b#  h!0<!  b#  h! == 0<!  00<!  0<!  1<<!  1<!! == 0.#0.#** m4m4 A$ = A$ = (h# & h!)  b#(h# & h!)  b# == (1<% & (1<% & 1<! )  1<! )  0<!0<! == 0.00.0!! m4m4 A! = A! = h$  h$  a"a" == 1<$ 1<$  0< 0<## == 00..$$"" mm44 A

A ++,t,tal al == A1 A1 / / A" A" / / A# A# / / A$ A$ / A/ A!! == 1<7 / 1<0! / 0<#* / 0<01<7 / 1<0! / 0<#* / 0<0! / 0<$! / 0<$ == ##..%%00 mm44

". 5tatis ,men +erhadap 5umbu U ". 5tatis ,men +erhadap 5umbu U

55 A A ((mm44)) y y ((mm)) AA..y y ((mm)) 11 11..7700 00..""!! 00..$$""!! "" 11..00!! 11..!!!! 11..%%""77!! ## 00..##** "" 00..77!! $$ 00..00!! ""..!!!! 00..11""77!! !! 00..$$"" ##..## 11..##**%% M M $$..##11%%

#. 5tatis ,men +erhadap 5umbu V #. 5tatis ,men +erhadap 5umbu V

55 A A ((mm44))   ((mm)) AA..  ((mm)) 11 11..7700 11..77 ""..** "" 11..00!! 00..%%!! 00..%%**""!! ## 00..##** 11..00%%%%%%%%%%%%%%%%77 00..$$ $$ 00..00!! 11..11!! 00..00!!77!! !! 00..$$"" 11..""!! 00..!!""!! M M $$..!!!!!!

$. +itik -erat +erhadap 5umbu U $. +itik -erat +erhadap 5umbu U

UU" " == 55ttaattiis s ,,mmeen n ++eerrhhaaddaap p 55uummbbu u VV == $$..!!!!!!

uuaass++,,ttaall ##..%%00

!. +itik -erat +erhadap 5umbu V !. +itik -erat +erhadap 5umbu V

VV" " == 55ttaattiis s ,,mmeen n ++eerrhhaaddaap p 55uummbbu u UU == $$..##11%%

uuaass++,,ttaall ##..%%00

%. W,lume Abutment +anpa ,unter?,rt (! Dinding 'enahan) %. W,lume Abutment +anpa ,unter?,rt (! Dinding 'enahan)

W1 =

W1 = uas +uas +,tal  (1 & t)  Jumlah -entang Abutment ,tal  (1 & t)  Jumlah -entang Abutment  == #<%  ($ & 0#<%  ($ & 0<$!)  "<$!)  "

== ""!!..!!""$$!! mm W" =

== #<%  ($<7#<%  ($<77! & 0<$!7! & 0<$!)  ")  " == ##11..00%%** mm W" W" == W1 W1 / / W"W" == "! / "! / #1#1 == !!%%..%%""11## mm 7. -erat Abutment

7. -erat Abutment ++anpa ,unter?,urt anpa ,unter?,urt  O" =

O" = uas +uas +,tal  'anang Abutment tanpa ,unter?,rt  -J -et,n,tal  'anang Abutment tanpa ,unter?,rt  -J -et,n == #<%  (1* & (0<$#<%  (1* & (0<$!  !))  "<$!  !))  "<$

== 11##!!..**11 ++

Atau Atau O" =

O" = WW,lume Abutment +,lume Abutment +anpa ,unter?,urt  -J -et,nanpa ,unter?,urt  -J -et,n == %"% %"%  "< "<$$ == 11##!!..**11 ++ ., Tana /#nisi ., Tana /#nisi .,.1 Tana Akti&  .,.1 Tana Akti&  h7 = h7 = tan  tan   b$ b$ == tan tan #0  "#0  " == 11..11!!$$7 m7 m 1. encari uas +anah Akti?  1. encari uas +anah Akti? 

A1 = A1 = 0<!  h0<!  h!  b#!  b# == 0<!  10<!  1<!  0<<!  0<!! == 00..##77!! mm44 A" = A" = h"  h"  (b# (b# / b/ b$)$) == 0<!  (0<!  (0<! / "0<! / ")) == 11..""!! mm44 A# = A# = (h# / h(h# / h$)  b$)  b$$ == (1<(1<% / 1<$)  "% / 1<$)  " == %% mm44 A$ = A$ = 0<!  h0<!  h7  b$7  b$ == 0<!  10<!  1<1!  "<1!  " == 11..11!!$$7 m7 m44 A +

A +,tal =,tal = A1 / A" / A# / A$A1 / A" / A# / A$ == 0<#* / 1<"0<#* / 1<"!/ % / 1<1!!/ % / 1<1! == **..77777 m7 m44

". 5tatis ,men +erhadap 5umbu U ". 5tatis ,men +erhadap 5umbu U

55 A A ((mm44)) y y ((mm)) AA..y y ((mm)) 11 00..##** 11..!! 00..!!%%""!! "" 11..""!! 00..77!! 00..##77!! ## %%..0000 ""..!! 11!! $$ 11..11!! $$..##**$$00001177!! !!..00%%##""$$%%%% M M ""11..!!%%##""$$77 #. 5tatis ,men +erhadap 5umbu V

#. 5tatis ,men +erhadap 5umbu V

55 A A ((mm44))   ((mm)) AA..  ((mm)) 11 00..##** 11..""################## 00..$$%%""!!

"" 11..""!! ""..11!! ""..%%**77!!

## %%..0000 ""..$$ 11$$..$$

$$ 11..11!! ""..77################## ##..11!!%%11**11!! M

M ""00..7700%%11**11 $. +itik -erat +erhadap 5umbu U

$. +itik -erat +erhadap 5umbu U

UU# # == 55ttaattiis s ,,mmeen n ++eerrhhaaddaap p 55uummbbu u VV == ""00..7700%%11**

uuaass++,,ttaall **..77**

!. +itik -erat +erhadap 5umbu V !. +itik -erat +erhadap 5umbu V

VV# # == 55ttaattiis s ,,mmeen n ++eerrhhaaddaap p 55uummbbu u UU == ""11..!!%%##""!!

uuaass++,,ttaall **..77**

%. W,lume +anah Akti?  %. W,lume +anah Akti? 

Wa =

Wa = uas +uas +,tal +,tal +anah  'anang Abutment anah  'anang Abutment  == *<7* *<7*  1* 1*

== 11!!**..00##!! mm 7. uas ,unter?,rt  7. uas ,unter?,rt 

Ac =

Ac = uas 'enampang Dengan ,unter?,rt & uas 'enampang +uas 'enampang Dengan ,unter?,rt & uas 'enampang +anpa ,unter?,rt anpa ,unter?,rt  == %<"" %<"" & #<%& #<%

== ""..%%## mm44 *. W,lume ,unter?,rt  *. W,lume ,unter?,rt 

W

Wc =c = uas ,unter?,rt  +uas ,unter?,rt  +ebal Dinding  Jumlah Dinding 'en,pangebal Dinding  Jumlah Dinding 'en,pang == "<%# "<%#  0<$ 0<$!  !!  !

== !!..00%%""!! mm . W,lume +,tal +anah Akti?  . W,lume +,tal +anah Akti? 

W# =

W# = WW,lume +anah Akti? & W,lume +anah Akti? & W,lume ,unter?,rt ,lume ,unter?,rt  == 1!* & 1!* & !<1!<1

== 11!!""..11""** mm 10. -erat +,tal +anah Akti?  10. -erat +,tal +anah Akti? 

O# =

O# = WW,lume +,tal +,lume +,tal +anah Akti?  anah Akti?  -J +anah-J +anah == 1!"  1!"  1<#!1<#!

== ""00!!..##77## ++ .,., Tana /asi&  .,., Tana /asi&  1. uas +anah 'asi?  1. uas +anah 'asi? 

A =

A = h"  h"  b1b1 == 0<! 0<!  0< 0<$$ == 00.."" mm44 ". W,lume +anah 'asi?  ". W,lume +anah 'asi? 

W% =

W% = uas +uas +anah 'asi?  'anah 'asi?  'anang Abutment anang Abutment  == 0<" 0<"  1* 1*

== ##..%% mm #. -erat +anah 'asi?  #. -erat +anah 'asi? 

O% =

O% = WW,lume +anah ',lume +anah 'asi?  -J +anahasi?  -J +anah == #<%  #<%  1<#!1<#!

== $$..**%% ++

$. +itik -erat terhadap 5umbu U $. +itik -erat terhadap 5umbu U

U% =

U% = 0<!  0<!  b1b1 == 0<! 0<!  0< 0<$$ == 00.."" mm

!. +itik -erat terhadap 5umbu V !. +itik -erat terhadap 5umbu V

V% = V% = (0<!  h") (0<!  h") / h1/ h1 == (0<!  (0<!  0<!) / 0<!) / 0<!0<! == 00..77!! .3 B#*an +#0ata .3 B#*an +#0ata 1. -erat -eban erata 1. -erat -eban erata

O$ =

O$ = 3  sin   3  sin   b$  b$   == "10  sin #"10  sin #0  "  1*0  "  1* == ##77**00 ++

". +itik -erat +erhadap 5umbu U ". +itik -erat +erhadap 5umbu U

U$ =

U$ = (0<! b$) / b(0<! b$) / b# / b" / b1# / b" / b1 == (0<!  ") (0<!  ") / 0<! / 0<! / / 0<! / 0<! / 0<$0<$ == ""..$$ mm

#. +itik -erat +erhadap 5umbu V #. +itik -erat +erhadap 5umbu V

V$ =

V$ = (0<!  (0<!  h7) / hh7) / h == (0<!  (0<!  1<1!) / 1<1!) / $$ == $$..!!7777##!! mm

.4 B#*an Hiup an B#*an +ati .4 B#*an Hiup an B#*an +ati 1. -erat -eban idup dan -eban ati 1. -erat -eban idup dan -eban ati

O! =

O! = (-eban idup dan -eban ati)  '(-eban idup dan -eban ati)  'anang Abutment anang Abutment  == %00 %00  1* 1*

== 1100**0000 ++

". +itik -erat +erhadap 5umbu U ". +itik -erat +erhadap 5umbu U

U! =

U! = (0<! a1(0<! a1) / b1) / b1 == (0<!  (0<!  0<7) / 0<7) / 0<$0<$ == 00..77!! mm

#. +itik -erat +erhadap 5umbu V #. +itik -erat +erhadap 5umbu V

V! =

V! = h & hh & h$$ == $ & 1$ & 1<$<$ == ""..%% mm

. T#kanan Tana Akti& Dan Tana /asi&  . T#kanan Tana Akti& Dan Tana /asi&  ..1 T#kanan Tana Akti& 

1. K,eFisien +anah Akti?  1. K,eFisien +anah Akti? 

K Kaa== ttaann44 $$!! && GG "" == ttaann44 $$!! && "0"0 "" == 00..$$00"" ". 6ntensitas

". 6ntensitas ++ekanan +anah Akti? ekanan +anah Akti?   =  = h1 / h" / h# / h$ / (h7  tan )h1 / h" / h# / h$ / (h7  tan ) == 0<! / 0<! / 1<% / 1<$ / (1<10<! / 0<! / 1<% / 1<$ / (1<1!  tan #08)!  tan #08) == $$..%%%%%%%%77 mm 'a 1 = 'a 1 = 3  Ka    b3  Ka    b == "10  0<$ "10  0<$  $<7  #<$ $<7  #<$ == 11%%####..%%!! ++ 'a " = 'a " = 0<!  9  Ka 0<!  9  Ka  4  b 4  b == 0<!  1<#!  0<$  $<70<!  1<#!  0<$  $<74  #<$4  #<$ == ""$$..!!00$$77 ++

#. enentukan 'a esultan (' ar) #. enentukan 'a esultan (' ar)

' ar = ' ar = 'a 1 / ''a 1 / 'a "a " == 1%## 1%## / "$/ "$ == 11%%!!**..11!! ++ 'ah = 'ah = ' ar  c,s ' ar  c,s  == 1%!*  c1%!*  c,s #0,s #0 == 11$$##%% ++ 'a

'a@ =@ = ' ar  sin ' ar  sin  == 1%!* 1%!*  sin # sin #00 == **""..0077%% ++

$. enentukan +itik K,,rdinat ' ar $. enentukan +itik K,,rdinat ' ar

'

' ar ar . . V1 V1 = = S S 'a 'a 1 1   12" 12"   T T / / S S 'a 'a " "   12# 12#   TT V1 =

V1 = S(1%##  0<!  $<7) / ("!  12#  $<7)T 2 1%!*S(1%##  0<!  $<7) / ("!  12#  $<7)T 2 1%!* == ""..##""11**$$ mm

..,T#kanan Tana /asi&  ..,T#kanan Tana /asi&  1. K,eFisien +anah 'asi?  1. K,eFisien +anah 'asi? 

K Kpp== ttaann44 $$!! // GG "" == ttaann44 $$!! // #0#0 "" == ##

". 6ntensitas +ekanan +anah 'asi?  ". 6ntensitas +ekanan +anah 'asi? 

 =h"  =h" == 00..!! mm 'p 1 = 'p 1 = 12"  Kp  9 12"  Kp  9  4  b 4  b = = 12"  12"  # #  1<#!  1<#!  0<!4  0<!4  #<$ #<$ == 11..77""11""!! ++ #. enentukan 'p esultan (' pr) #. enentukan 'p esultan (' pr) ' pr ' pr == ''''11 == 11..77""11""!! ++

$. enentukan +itik K,,rdinat ' pr $. enentukan +itik K,,rdinat ' pr

' pr ' pr . V" . V" = = S 'p S 'p 1 1   12" 12"  T T V" = V" = (S1<7"  0<!  0<!(S1<7"  0<!  0<!T) 2 1<7" +T) 2 1<7" + == 00..$$##00##11 mm . R#su!tan Gaya . R#su!tan Gaya

..1 R#su!tant# Titik B#0at T(ta! 5A ..1 R#su!tant# Titik B#0at T(ta! 5A

esultante Baya +

esultante Baya +,tal pada ,tal pada Abutment dengan Abutment dengan ,unter?,rt ,unter?,rt 

--eerraatt((OO11)) == ####..!!****

ppaadda a ttiittiik k bbeerraat t ( ( UU11<<VV11)) = = (( 11..!!1177$$1177 uuaass((AA++,,ttaall)) == %%.."""" 55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u UU == %%.."""" 55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u VV == %%.."""" esultante Baya +

esultante Baya +,tal pada ,tal pada Abutment tanpa Abutment tanpa ,unter?,rt ,unter?,rt 

--eerraatt((OO"")) == 11##!!..**11

ppaadda a ttiittiik k bbeerraat t ( ( UU""<<VV"")) = = (( 11..""%%7700##**

uuaass((AA++,,ttaall)) == ##..%%00

55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u UU == ##..%%00 55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u VV == ##..%%00 M

M--eerraattOOAA == ####..!!****

M

Muuaass == %%..""""

M

M 55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u UU == %%..!!%%%%%%77 M

M 55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u VV == ..$$##**###### 1. esultante +itik -erat

1. esultante +itik -erat ++,tal (O,tal (OA) terhadap 5umA) terhadap 5umbu Ubu U U

U == 11##..#### :: ..**11!! == 11..$$""!!7711 mm ". esultante +itik -erat

". esultante +itik -erat ++,tal (O,tal (OA) terhadap 5umA) terhadap 5umbu Vbu V V

V == 1100..11""77 :: ..**11!! == 11..111111**$$ mm #. +itik -erat OA teradi pada K,,rdinat (U<V)

#. +itik -erat OA teradi pada K,,rdinat (U<V)

== (( 11..$$""!!7700**$$** << 11..111111**##!!%%""!!77 )) .., R#su!tant# Titik B#0at Tana /#nisi 5T

esultante Baya +

esultante Baya +,tal pada ,tal pada ++anah 'engisi (sisi anah 'engisi (sisi belakang Abutment)belakang Abutment)

--eerraat t ++aannaah h ''eennggiissi i ((OO##)) == ""00!!..##77#### ppaadda a ttiittiik k bbeerraat t ( ( UU##<<VV##)) = = (( ""..##!!**$$11!!

uuaass((AA++,,ttaall)) == **..77**

55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u UU == **..77** 55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u VV == **..77** esultante Baya +

esultante Baya +,tal pada ,tal pada ++anah 'engisi (sisi anah 'engisi (sisi depan Abutment)depan Abutment)

--eerraat t ++aannaah h ''eennggiissi i ((OO%%)) == $$..**%% ppaadda a ttiittiik k bbeerraat t ( ( UU%%<<VV%%)) = = (( 00..""

uuaass((AA++,,ttaall)) == 00..""00

55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u UU == 00..""00 55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u VV == 00..""00 M

M--eerraattOO++ == ""00!!..##77####

M

Muuaass == **..77**

M

M 55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u UU == ""11..!!%%##""!! M

M 55ttaattiis s ,,mmeen n tteerrhhaaddaap p 55uummbbu u VV == ""00..7700%%11** 1. esultante +itik -erat

1. esultante +itik -erat ++,tal (O,tal (OA) terhadap 5umA) terhadap 5umbu Ubu U U

U = "= "00..77$$%%"" :: **..77770000!! == ""..##1100##$$ mm ". esultante +itik -erat

". esultante +itik -erat ++,tal (O,tal (OA) terhadap 5umA) terhadap 5umbu Vbu V V

V = "= "11..7711##"" :: **..77770000!! == ""..$$11**00$$ mm #. +itik -erat OA teradi pada K,,rdinat (U<V)

#. +itik -erat OA teradi pada K,,rdinat (U<V)

== (( ""..##1100##$$""""$$1177 << ""..$$11**00##%%**""7711 )) ..3 R#su!tant# Gaya 6#0tika! R7

..3 R#su!tant# Gaya 6#0tika! R7 @

@ ==   / / OOA A / / O+ O+ / / 3 3 sin sin   / / 'a@'a@ == 10*00 / 1% / "10 / #710*00 / 1% / "10 / #7*0 / *"*0 / *" == 11!!77****..** ++

-esar masing&masin

-esar masing&masing Baya Wertikal dan K,,rdinatnyag Baya Wertikal dan K,,rdinatnya  == 1100**0000 ((UU<<VV)) == O OAA== 11%%..$$77 ((UU<<VV)) == O O++== ""1100..""#### ((UU<<VV)) == 3 3== ##77**00 ((UU<<VV)) == ''aa@@ == **""..0077%% ((UU<<VV)) == @ @. . U U ==   . . U U / / OOA A . . U U / / O+ O+ . . U U / / 3 3 . . U U / / 'a@ 'a@ . . UU U = U = ((10*00  0<7!) / (1%  1<$) / ("10  "<#1) / ((10*00  0<7!) / (1%  1<$) / ("10  "<#1) / (#7*0  "<$) / (*"  "<#!))21!7*(#7*0  "<$) / (*"  "<#!))21!7* == 11..""!!77!!"" mm

..4 R#su!tant# Gaya H(0i(nta! R ..4 R#su!tant# Gaya H(0i(nta! R

h =

h = 'a'ah / 3hh / 3h

== 1$#% / (3  c,s   b1$#% / (3  c,s   b$  )$  ) == 1$#% / "10  c,s #1$#% / "10  c,s #0  b$  0  b$   == 77**##..11!! ++

-esar masing&masing

-esar masing&masing Baya ,riI,ntal dan K,,rdinatnyaBaya ,riI,ntal dan K,,rdinatnya

''aahh == 11$$##%% ((UU<<VV)) == 33hh== %%!!$$77..11!! ((UU<<VV)) == h h . V . V == 3h 3h . V . V / / 'ah 'ah . V. V V = V = ((%!$7  $<!) / (1$#((%!$7  $<!) / (1$#%  "<$!))27*%  "<$!))27*## == $$..117711%%## mm

... R#su!tant# $R' Da0i Gaya 6#0tika! $R7' an Gaya H(0i(nta! $R' ... R#su!tant# $R' Da0i Gaya 6#0tika! $R7' an Gaya H(0i(nta! $R'

  == X X (@(@4) 4) / / (h4)(h4) == X X (( 11!!77**4 4 / / 77**##44 )) == 1177%%""..## ++ .8. K(nt0(! T#0aap G#s#0 .8. K(nt0(! T#0aap G#s#0

YYb b == S S 1122" " Z Z ""22# # T T GG DDiiaammbbiil l nniillaai i mmaakkssiimmuum m sseebbaaggaai i nnii = = "2"2#  G#  G = = "2"2#  "#  "00 == 11##..######## O = O = O1 / O" / O# / O$ / O! / O%O1 / O" / O# / O$ / O! / O% == #$ / 1#! / "0! / #7*0 / 10*#$ / 1#! / "0! / #7*0 / 10*00 / $.*%00 / $.*% == 11$$!!..77 ++ ['h

['h == 'ah & 'pr'ah & 'pr == 1$#% 1$#% & 1<7& 1<7 == 11$$##$$..""** ++ gs = gs = O tan Yb / cd -O tan Yb / cd -['h ['h == 1$!  tan 1#<## / (#<$  "<!)1$!  tan 1#<## / (#<$  "<!) 1$#$."*1#%$"#%* 1$#$."*1#%$"#%* == ""..$$777711 \\ 11..!! (( OK OK  .9 K(nt0(! T#0aap Gu!in .9 K(nt0(! T#0aap Gu!in

+abel perhitungan Baya Wertikal dan ,men +abel perhitungan Baya Wertikal dan ,men B

Baayya a WWeerrttiikkaall JJaarraakk ,,mmeenn ( (++)) ((mm)) ((++mm)) O O11 ####..!!**** 11..!!1177$$11%%##$$%% !!00..%%77 O O"" 11##!!..**11 11..""%%7700##77!!!!"""" 1177""..1177 O O## ""00!!..##77##""**!!!!**""%% ""..##!!**$$11!!$$!!**%% $$**$$..##!!!!!!##11!!0011 O O$$ ##77**00 ""..$$ 0077"" O O!! 1100**0000 00..77!! **110000 O O%% $$..**%% 00.."" 00..77"" [[OO 11$$!!..7711""""**!!!!**""%% 1177****00..$$77##!!##11!!0011

gl = gl =[ C[ C [ gl [ gl == [ C[ C ' ar  V ' ar  V == 17**017**0 1%!*  "<# 1%!*  "<# == $$..%%$$$$##"" \\ 11..!! (( OK OK  )) .: Kapasitas

.: Kapasitas DayDaya Dukuna Dukun  A. Kapasitas Day

 A. Kapasitas Daya Dukun U!ti"ata Dukun U!ti"at# $T# $T#0ai'#0ai' 3?

3? == "2# "2#   1<# 1<# .;c .;c / / 9 9 D.;3 D.;3 / / 0<$ 0<$ 9 9 -.;9-.;9

== ("2#  1<#  "<!  11<*) / (1<#!  1  ("2#  1<#  "<!  11<*) / (1<#!  1  #<) / (0<$  1<#!  #<$  1<7)#<) / (0<$  1<#!  #<$  1<7) == ####..!"!" ++22mm44

B. Kapasitas Daya Dukun U!ti"at# N#tt( B. Kapasitas Daya Dukun U!ti"at# N#tt(

3n?

3n? == "2# "2#   1<# 1<# .;c .;c / / 9 9 D.( D.( ;3 ;3 & & 1) 1) / / 0<$ 0<$ 9 9 -.;9-.;9

== ("2#  1<#  "<!  11<*) / (1<#!  1  ("2#  1<#  "<!  11<*) / (1<#!  1  (#< & 1)) / (0<$  1<#!  #<$  1<7)(#< & 1)) / (0<$  1<#!  #<$  1<7) == ##""..%%0"0" ++22mm44

). Kapasitas Daya Dukun A"an ). Kapasitas Daya Dukun A"an

3s = 3s = 3n? 3n?  // ( ( 9 9 . . D D )) ? ?  == "1.7"1.7 // ((11<<##! !   11)) ## == 11""..""1717%% ++22mm44 D. B#*an +aksi"u" A"an D. B#*an +aksi"u" A"an

3 3 all all == -  -      3s3s == #<$  1#<$  1*  $<!*  $<! == 77$$77..7711** ++ .1; Sta*i!itas Eks#nt0isitas .1; Sta*i!itas Eks#nt0isitas +

+abel perhitungan +ekanan +anah ateral (+abel perhitungan +ekanan +anah ateral (+anah Akti?anah Akti? ) dan ) dan ,men,men B

Baayya a WWeerrttiikkaall JJaarraakk ,,mmeenn ( (++)) (()) ((++)) ''a a 11 11%%####..%%$$**""%%7777!!%% ""..##""11**##11 ##77##..00%%**##11** ''a a "" ""$$..!!00$$77""$$0011%%$$ ""..##""11**##1 !1 !%%..**%%00""!!**7777 [[''aa 11%%!!**..11!!""117777#### ##**$$..%%$$$$117777 [

[ == [O [O & & [V[V == 17**17**0 & #*$0 & #*$ == 11$$00##00..!! ++

U = U = [[ [O [O == 1$0#0.!1$0#0.! 1$!.7 1$!.7 == 0.0.##7*7* mm e1 = e1 = bb && UU "" == ##..$$ && 00..##77****%%## "" == 00..77%%""1111 mm e" = e" = bb %% == #.$#.$ %% == 00..!!%%%%%%77 mm e1 e1 \\ bb %% 00..77%%""1111##77 \\ #.$#.$ %%

00..77%%""1111##77 \\ 00..!!%%%%%%%%%%%%%%%%77 . . . .. Tiak OK Tiak OK 

.11 K(nt0(! Daya Dukun A"an .11 K(nt0(! Daya Dukun A"an

Jika e = -2%< maka 3 min = 0< dan ika e \ -2% maka akan negati?< sehingga teradi tegangan tarik Jika e = -2%< maka 3 min = 0< dan ika e \ -2% maka akan negati?< sehingga teradi tegangan tarik Diambil e \ -2%

Diambil e \ -2% 3 =

3 = @@  ((1 1 / / 2 2 & & ((% %   ee)) )) -- - -== 1!7**.*1!7**.*  (1 (1 / / 2 2 & & (%  (%  0<7%))0<7%)) ##<<$$ 11** ##..$$ 3 maks = 3 maks = 1!7**.*1!7**.*  ((1 1 // ((% %   00<<77%%)))) ##<<$$ 11** ##..$$ == %%00$$..!!!! ++22mm44 \\ 33s s (( 11""..""1177%% ++22mm4 4 )) 3 min = 3 min = 1!7**.*1!7**.*  ((1 1 && ((% %   00<<77%%)))) ##<<$$ 11** ##..$$ == &&****..**11## ++22mm44 PP 33s s (( 11""..""1177%% ++22mm4 4 ))

m m GG == ""00 HH nn11 == ""00 mm m m  == ##00 HH nn"" == ""##..**77!! mm m m ((tt)) == 00..$$!! mm ;;cc == 1111..** m m 11 == $$ mm ;;33 == ##.. m m "" == $$..7777!! mm ;;99 == 11..77 m m  == 11** mm ;;3322;;cc == 00..####00!!00** m m ((99bb)) == ""..$$ tt22mm  == ""..!! ++2244 m m ((99)) == 11..##!! tt22mm m m n n SSddiinnddiinng g ppeenn,,ppaannggTT == !! BUT+ENT BUT+ENT 1 1 == 11..77 mm y1 =y1 = 00..""!! mm " " == 00..%%!! mm y" =y" = 11..!!!! mm # # == 11.. mm yy# # == 00..77!! mm $ $ == ##..0077 mm y$ =y$ = 00..**#### mm ! ! == 11.. mm y! =y! = "" mm % % == 11..""## mm yy% % = 1= 1..! m! m 7 7 == 11..0077 mm y7 =y7 = "" mm * * == 11..11!! mm y* =y* = ".!!m".!!m   == 11..""!! mm yy  = #= #..# m# m

m m == 11..!!"" mm m4 m4 m m == 11..00%% mm m4 m4 1 1 == 11..77 mm yy1 1 == 00..""!! mm

" " == 00..%%!! mm yy" " == 11..!!!! mm ##== 11..0077 mm yy##== "" mm $ $ == 11..11!! mm yy$ $ == ""..!!!! mm ! ! == 11..""!! mm yy! ! = #= #..# m# m m m == 11..""77 mm m4 m4 m m == 11.."" mm m4 m4

11== 11..""## mm yy11== 11..!! mm " " == ""..11!! mm yy" " == 00..77!! mm ##== ""..$$ mm yy##== ""..!! mm $ $ == ""..77## mm yy$ $ == $$..##**!! mm

m m == ""..##%% mm m4 m4 m m == ""..$$%% mm m4 m4

+ + << 11..00%%00!!!!77 )) m4 m4  11..00%%00!!!!77 == %%..!!%%%%%%77 mm  11..!!1177$$1177 == ..$$##**###### mm + + << 11..""0000!!!!% )% ) m4 m4  11..""0000!!!!%% == $$..##11%% mm  11..""%%7700##** == $$..!!!!!! mm // 11##!!..**11 == 11%%..$$77 ++ // ##..%%00 == ..**11!! mm44 // $$..##11%% == 1100..11""%%77 mm // $$..!!!!!! == 11##..###### mm

+ + << ""..$$!!%%00##$$ )) m4 m4  ""..$$!!%%00##$$ == ""11..!!%%##""!! mm  ""..##!!**$$11!! == ""00..7700%%11** mm + + << 00..77!! )) m4 m4  00..77!! == 00..11!! mm  00.."" == 00..00$$ mm // $$..**%% == ""1100..""###### ++ // 00..""00 == **..77770011 mm44 // 00..11!! == ""11..7711##""!! mm // 00..00$$ == ""00..77$$%%11** mm (( 00..77!! << ""..%% )) (( 11..$$""!!7700 << 11..111111**##%% )) (( ""..##1100##$$"" << ""..$$11**00##77 )) (( ""..$$ << $$..!!7777##!! )) (( ""..##!!**$$11!! << ""..##""11**## ))

(( ""..##!!**$$11!! << ""..##""11**## )) (( ""..$$ << $$..!!7777##!! ))

ai

ai aman aman yaitu yaitu "2#"2#

..

. . . .

. . . Tiak OK Tiak OK 

. . . .