HAND OUT BETON PRATEGANG DOSEN: HENDRIK SULISTIO
HAND OUT STRUKTUR BETON PRATEGANG SKS =3
FAKULTAS TEKNIK UNTAG 1945 SAMARINDA DOSEN : HENDRIK SULISTIO
MATERI 1. 2. 3. 4. 5. 6. 7. 8. . 1!. 11.
PENGENALAN UM UMUM TE TENTANG BE BETON PRATEGANG/SEJARAH BETON PRATEGANG PER ERBE BEDA DAAN AN BE BET TON PRA PRAT TEG EGAN ANG G DEN DENGA GAN N BETON BIASA. KEUNTUNGAN DA DAN KE KERUGIAN MA MASING2 METHODE. PEN ENGE GEN NAL ALAN AN BA BAH HAN BET ETO ON PR PRATEG EGAN ANG. G. SISTIM PENARIKAN PERHITUNGAN STATIKA PERHITUNGAN TEGANGAN PERL PERLET ETA AKAN KAN DAE DAERA RAH H AMAN MAN KAB KABEL EL ( TEN TEND DON ). MENENTUKAN TENDON. MENDE MENDESIG SIGN N LENGKA LENGKAP P BANGU BANGUNAN NAN PRA PRAT TEGANG. EGANG. ( DITU DITUANG ANGKAN KAN DALAM DALAM TUGAS TUGAS BESA BESAR R " #AKTU #AKTU SATU SEMESTER )
BEBERAPA REFERENSI YG DAPAT DIGUNAKAN
$ RE%ERENSI
RE%ERENSI
KOMITMEN $ ABSEN MINIMAL " 8! & HADIR. $ MENGIKUTI KULIAH TIDAK BOLEH MENGGUNAKAN SANDAL $ SELAMA PERKULIAHAN TIDAK DIPERKENANKAN MEROKOK. $ MAHASIS#A BISA INTERUPSI JIKA ADA HAL'HAL G INGIN DITANAKAN. ( NILAI TIDAK AKAN DIKURANGI JIKA BERAGUMEN ). $ HAND OUT DIATUR DENGAN KETUA TINGKAT ( TAK PERLU MENATAT ). $ ARA PENILAIAN * 1. TUGAS KEIL " 5 & 1!! & CONTOH TUGAS 2. TUGAS BESAR = 40 % BESAR PERHITUN GAN 3. MID TEST " 2! & 4. %INAL TEST " 35 &
PENDAHULUAN ( PHILOSO%I BETON BIASA ) $ S+,- -0- 00+ B ---9 0- -9- :-; <<=:-+ -- :-; +;;+ 9--= -> -=+ 0-+:- -9 9--= -+> ;- <;-- <+-0+ ? -@- 0-;-+ -9- 0> <-- ;-;-2 - +--< > 0-;- ;-;-2 -+ +=+- =-- -@-.
TEGANGAN TARIK $ T;-;- -+ +--< :; +=+- =-- -@- <:-- +0+-:-'-. M<-; +- @- ,,+, 09:- +--< =-<=-; -;. H-:- -;+- :-; - 0-@:-; ,,+, @-> 0-;- ; :; - +-;+- -+ ,, @-> 9-:- ; :; <-+ :; +- <-,--. H- ++-9 :; <:-- +- -=-:- 0 2 -; =-@-;> 0-- <+0> -- -:- - <-+ :-; +- ,,.
RETAK'RETAK $ D+0-<=+; + -2 +0+- -@-;- <=-- <=- 0-=- -+ ? -- - --< -@- -;-> :; <=-- 0< =00 --- :; -9-:- -;+ 0. P0:- -@-;- -+- --- ---9 ,-- -;+ 0.
R+, B-<
R+, B-<
SEJARAH BETON PRATEGANG $ De!" "#"$" e&e'"(" )e*+e,-) '"" ).',-& !"!"+" ,"*- #"&"' 'e!!-"" /',."+. ,"(" ,e)/ +e"*" &". $".)- #e!" 'e',e*." )e!"!" 2"#" ,e)/ 'e&"&-. ",e& ,"" $"! #.)"*. 2"#" ")- .)- )e*$")" .. ).#" ,e*("+.& #.&"+""" Ke!"!"&" #e'. e!"!"&" )e*"#. +e'-" .. #.+e,"," &e$"2" 2*")e" +e)e&"( ,e,e*"2" ")- K"*e" 2# ")- .)- ).#" "#" $"! #"2") 'ee&"+" #e!" 'e'-"+" "2" $! 'e$e,"," &e$"2$" 2*")e!"! .. M"" (.&"!&"( e2e*"$"" '"+$"*"") )e*("#"2 !"!"+" ..
EUGENE FREYSSINET 6 PERAN7IS 198 $
B"*-&"( 2"#" )"(- 198 +e/*"! .+.$-* e,"!+"" ;*".+ ,e*("+.& 'e!")"+. e+-&.)" .. U)- 2e*)"'" "&.$" F*e$++.e) 'e!e'-"" ,"(" ,e*-*"!$" 2*")e!"! 2# -+"("8 +e,e&-'$" )e&"( #.+e,"," 3 ("& $".)- : 1. Creep ( Rangkak ) = Me'e#e$" -+-* +)*-)-* )e*-+ 'ee*-+ ".,") 2e*-,"(" #"&"' +)*-)-**.+)"& $"! 'e',e)- ,"(" ,e)/ 2. Reak!a!" = Me'""!$" "")<",e& ,"" $! 'e!"&"'. )"*." )e*-+ 'ee*-+ -!" ".,") #"&"' +)*-)-* *.+)"& $"! 'e',e)- ,"(" ,"" #. S"p = Me!!e&..*$" "!"* "") ")"- 2"#" ",e& e#-" --! -+-* +)*-)-*
SOLUSI $ U <;--0+ 9- + =-<- -+:-9 <;;-- $e%&n - $a'a % %"ngg" * 09+;;- -;- - -0-0+ -=- +--0+ - @+- --= =;-9:- 9--= =;-;- =-- -- + --- + 0<:- 0-9 +;;+ 0-+. D+0-<=+; + +- -9 <+=-- =- 0- 0+0+< pen'angkaran -- - 0+0+< =-+-:- :-; 0-;- -+> 09+;;- +- ;- !"!%" +re,!!"ne%.
$ D;- <++-> +re!,!!"ne% -9 9-0+ en-"p%akan 0- @+0 0 - 0-;-+ =-+;- -+ 0 -;> -- =-<=-; +- =-9 -+> <-- 09 -9- -=- +<-,--- 09:-> - ;- 0+0< ++ +<;+--9 pen-"p%aan !%rk%r !%rk%r ,ang ang!"ng /an $en%ang $en%ang ,ang pan'ang > +-< +-<-
0+-= -0+ - 0.
B =-- %:00+ =-<133 $ B =-- =-<- -+:+-0--- 0-'0-- ;- 000 9 +re,!!"ne% /aa %a0n 1## di Gare ar"%"e /" pea$0an (Le Ha3re(Peran-"!). %:00+ 0-;-+
-=- =--> 0;- +++ @@-:- 9 =-- -9+ -+ --< <;<-;- +9 -@ @+0 0 ++ - <:-- 09 +-.
KENDALA PERKEMBANGAN $ Pe*e',"!" +e&"-)$" ).',-&&"( e+-&.)" ,"*- $".)- ke!"%an /aa !eg" per0"%ngan !%rk%rn,a. Te*$")" 2e',e*." 2*")e"" e #"&"' +)*-)-* 'e.',-&" !"$"!"$" )"',"(" #.#"&"'$" +-&.) #.2e*(.)-!"$" M". r"% +)*-)-*$"6 '". ,e+"* #e*"") e(.2e*+)").+" ak"n !"% eng0"%ng ".,") #"*. !"$"!"$" )"',"(" .. #.#"&"' &.)e*")-* ,e)/ 2*")e" +e*.! #.-&-.> ga,a para!"% 4. $ H"& .. )e&"( 'e!("',") 2e*e',"!" +)*-)-* ,e)/ 2*")e" $"! +-&.) +e2e*). 2/*)"&2/*)"& !e#-! !e#-! ,e*).!") ,"$" #&& #" 2e*e',"!" ""& $"! 2e+") ("$"&"( 'e//& 2"#" +)*-)-* +)*-)-* $"! +e#e*("" )e*-)"'" 2"#" e',")" e',")" #" ,"!-","!-" +e#e*(""
PEMIKIRAN BARU $ M"" '--&&"( 2e'..*2e'..* ,"*- $"! (-+-+ 'ee*-" #.*. e #"&"' 2e'e"(" '"+"&"( !"$"!"$" 2"*"+.) .. N"'" $"! ).#" #"2") #.&e2"+" #"*. '"+"&"( .. $".)- !"$" 2"*"+.) 2"#" +)-*)-*+)*-)-* 0"per!%a%"! "#"&"( 53e! G,&n &"!. +e/*"! .+.$-* Pe*".+ $"! +"!") *e").; $"! )e&"( 'ee*,.)" ,-- a!%erp"e-en,a4 Be%&n Pre!&n%ra"n%4(2'""/) /aa %a0n 161 $"! #.+-+-& #e!" ?E%a%! L""%er! en Be%&n Pre-&n%ra"n%4 (2'""/) /aa %a0n 177 A2",.&" F*e$++.e) #."!!"2 2ee)-+ ,e)/ 2*")e" '/#e* '"" G,&n #."!!"2 +e,"!". $"! 'e',e*." /a!ar #" a%ar $eakang ""a0
%IP BERDIRI $ U)- 'e'2e*e*") e*"+"'" #.")"*" 2"*" "(&. ,e)/
2*")e" #. +e&-*-( #-." +e*)" 'e!//*#..* 2ee&.)." #" penge$angan ,e)/ 2*")e" +e"*" .)e*"+./"& '"" ")"+ 2*""*+" G,&n (Peran-"!) /an agne (Beg"a 2"#" )"!!"& 89 A!-+)-+ 1958 #.,e)-&"( +e/era%"&n In%erna%"&nae /e a Pre-&n%ra"n%e ")"- &e,.( #.e"& #e!" +.!")"$">FIP> #. 7"',*.#!e I!!*.+ Se,"!". P*e+.#e FIP $"! 2e*)"'" "#"&"( E-!ee F*e$++.e) $"! 2"#" ")- .)- ,e*-'- @3 )"(- Se"*" ,e*"&" #" ,e*!.&.*" #.,e*,"!". e!"*" FIP 'e$e&e!!"*"" /!!*e+ +.'2/+.-' #" *"2") *"2") e*" !-" 'e',"("+ '"+"&"('"+"&"( ,e)/ 2*")e" #" 'e$-+- *e/'e#"+. *e/'e#"+. +e*)" 'e',-") '/#e& /#e ,e)/ 2*")e" -)- #."#." #"+"* /&e( 2".)." 2".)." "+./"& #"*. )."2 e!"*" #"&"' 'e$-+- 2e*")-*" "+./"&$"
BAPAK PRATEKAN MENINGGAL 6 198 $ K+- %:00+ <+;;- +- =-- -;;- 8 J+ 162 + <=- +-<-:- + P-+0 +- + =<-;-> 900:- +- =-- -9 9+-;- 0-; -=- - 0-; +0+: :-; 0-. U <;-; @-0-'@-0-:- :-; - +-+> %IP -9 <<- =-- =<+- -=;9-;-- =- C +RE5SSINET EDAL4 =-0+-= -; :-; -9 @-0- -;+ =;<-;- =--. T-- =;9-;-- ++ <=-- -=;9-;-- +;;+ - =-+; 9<- -;+ 0+=+<-:-> :-; ++- -- =-0<=--'0<=-- =<- %IP. %:00+ 0-;-+ =0+ %IP +;-+- 9 E/ar/& T&rr&'a ( Span,&). 53e! G,&n a/aa0 Pre!"/en +IP ,ang ke%"ga.
TY LIN 6 193 BARKELEY $ Kee!an --< =<-;- 0'0 <+ =-- 9 0+:- <<=9+;- ;-:-' ;-:- =--0+> 0:;':; -9 <-+> ;- <:0-; +-; - + --- =--. Naan,a T.5. L"n* !e&rang kea0"ran Ta"8an* Gr Be!ar /" Ca"9&rn"a Un"3er!"%, Barkee, - 0-; 0+;
E;+ :-; 0-;- 9-0+. D--< -9 17#
PENEMUAN T. LIN $ +- <;<-- +:- <;-+ 4L&a/ Baan-"ng4. D;- -- ++ -- -- - =-;-;- ++ - ;-:- :-; 0<++- =-> 09+;;0-;+- -+ - -- :-; -9 +-=- -=- ++<-;+ 0=9:-. P-- - 0+<-; ++ + --< 0 +- @-+ - - --:- +- @- << -=-=> 0-;- ;-;- =-- 0<- =-<=-; 0 @- <--.
LOAD BALANING $ KABEL PRATEGANG DIBERI BENTUK DAN GAA G SEDEMIKIAN RUPA> SEHINGGA SEBAGIAN DARI BEBAN RENANA G TELAH DITETAPKAN DAPAT DIIMBANGI SEPENUHNA. PADA KEADAAN SEIMBANG STRUKTUR TIDAK TERJADI LENDUTAN DAN KARENA ITU TIDAK BEKERJA MOMEN LENTUR APAPUN> DAN TEGANGAN PADA SELURUH BETON BEKERJA MERATA.
P ABELES 6 UK194 PARTIAL PRESTRESSING PRESTRESSING
$ +ULL PRESTRESING * %RESSINET TIDAK MENGIJINKAN MENGIJINKAN ADA TA TARIKAN () MAHAL. $ PARTIAL PRESSTRESS PR ESSTRESSING ING * * PRINSIP PENULANGAN PENAMPANG $ SEIRING DENGAN LOAD BALANCING .
TUGAS RUMAH BUAT MAKALAH
MUSI PROGRESS
MODEL TEST TEROONGAN ANGIN
SURAMADU MUSIBAH JEMBATAN RUNTUH
MUSIBAH SURAMADU
CISUALISASI PRATEGANG
KESIMPULAN PERTEMUAN
END
PRAY
SARAT BETON UNTUK PRATEGANG $ U =-- +=- < :-; +;;+ ( <+ , 3!)> -<<=:-+ 0+,- =:0- - -;- :-; -9> <<=:-+ <0 -0+0+-0 - <0 <0 -0+0+-0 -0+0+ -0 ; :-; +;;+ 0- -=- <+<;-;-';-;- ;-;-';-; - +9 0-. S+,-'0+,- ++ 0-;- =+; <;9+-- 9+-;- ;-;- :-; = 0- -+- 0+,-'0+,- 0.
$ P-- -; +-0- - -'- --< SNI +<-<0 -0+0+-0 ( E ) +9;- ;- =<-- :-; =-. P-- =--> =<-- 9 ;-:- =000 -;0; -<-> <-- +=--+ <0 ; ( E ) +9;- ;- =<-- :-; =-. $ M AI * E " 1.8!!.!!! 5!!F ( =0+" =0- +9) 6
6!
6
SYARAT BAJA PRATEGANG P"#" 2*.+.2$" #.!-"" $a'a $er% %"ngg" +-2"$" e(.&"!" )e!"!" $"! #.".,")" /&e( +.;")+.;") ,"" #"2") #.2e*e.& Je.+ e.+ $"! #.2"". #"&"' ,e)/ 2*")e" : a. Ka8a% $a'a ( 8"re) Be,e*"2" "") ,"" +e""* #.!",-!" +e(.!!" 'e',e)- +-")- ",e& P"#" 2*e)e)./.! ",e& .. ).#" )e*,-!-+ P"#" 2/+) )e)./.! ",e& #.,-!-+ #e!" 2.2" ,e*!.!. 6 )e#/ , Ta" $a'a(!%ran/ : #."'e)e* 3 '' B."+"$" ,-"( "") #.&.&.)" 2"#" +-")- "") .).6+. .*e +)*"# D.!-"" 2# 2*e)e)./.! Ba%ang $a'a ( $ar) : #."'e)e* 80 ''
-- =<+- ;-;- " P*e)e)./.! : K",e& #.)"*. #-&- +e,e&-' ,e)/ #./* , P/+) )e)./.! : K",e& #.)"*. +e)e&"( ,e)/ --2 e*"+ Pe',e*." 2*" )e!"!" ,.+" 2e-( 6 ;-&& 2*e+)*e++.! <+e,"!." +""6 2"*)."& 2*e+)*e++.! F-&& 2*e+)*e++.! = T.#" ,/&e( "#" ,"!." )"*. P"*)."&&$ 2*e+)*e++.! = B/&e( "#" ,"!." )"*.
K9+-;- =-;-;- " S.;")+.;")
,"": A.,") 2e!!e&..*" 2"#" ")#/!*" #.&e2"+" A.,") !e+e" : D"&"' #/!*"$" +e#.*. 2"#" -.) 2e"!"*" 6 )e2. #/!*" Ge+e" ",e& #e!" #.#.! 2e',-!-+$"
B . S9;- ;- 0+,-'0+,- * ' A+- -0+0+-0 ' A+- -;- - 00 -+ . A+- =-9- 00+ ( -) K9+-;- =-;-;- -* S+0+< =0+; - 18& S+0< =0 0++;15&
P<+0-- ;-;-2 =-=-<=-; <+-; $
P"#" +-")- 2e"'2"! $"! )e&"( #.e)"(-. #.'e+.$" ,e+"*$" !"$" 2*")e!"! ""& #" )*"+;e* &e)" ",e& +e*)" ,e+"*$" '/'e &e)-* $"! ,ee*" '"" -)- 'e'e*.+" )e!"!" )e!"!" $"! )e*"#. #. +e*") ")"+ #" ,""( ("*-+ #.)."- ,e,e*"2" e"#"" : 1 Ke"#"" ""& : " Te!"!")e!"!" ".,") !"$" 2*e+)*e++ ""& ,Te!"!" )e!"!" ".,") ,e*") +e#.*. 8 Se)e&"( e(.&"!" )e!"!": Te!"!" ".,") !"$" 2*e+)*e++ +-2e* Te!"!" ".,") ,e*") +e#.*. 2/+.+. 3 Se)e&"( ,e," &-"* ,ee*": Te!"!" ".,") ,e," &-"* Te!"!" "(.*6 +-2e*2/+.+. #"*. ("+.& 8 #" 3 "
RUMUS UMUM $ R-'-+ -'-': = P
G KABEL : D.'"" P = G"$" P*e+)*e++ ""&< "(.* F = &-"+ 2e"'2"! ,e)/ 6 )"2" #.-*"! &-"+ ,"" e = e+)e)*.+.)"+ #"&"' ",e& 6"*" ",e& e ).). ,e*") ,e)/ Y = "*" )e2. ")"+< ,""( $"! #.)."- e !"*.+ ,e*") I = '/'e .e*+." 2e"'2"! N/)e: )e" )"*. B.&" ",e& #.&e)"" #. ).). ,e*") ,e)/ "#. e = 0
$ " ' P/% ( M. ) / I
K-;- ;-<- * $ " Te!"!" ".,") !"$" 2*")e" +e)*.+6+e&"&)e" , Te!"!" ".,") '/'e $"! ).',-& "*e" e+e)*.+.)"+ #"*. P '/'e Pe Te!"!" #.")"+ +e*"): )"*. Te!"!" #.,""( +e*") : )e" Te!"!" ".,") ,e," &-"* '"-2- ,e*") +e#.*. Te!"!" #.+e*") ")"+ : )e" Te!"!" #.+e*") ,""( : )"*. # S-2e*2/+.+. 18 #" 3 Te!"!" #.+e*") ")"+< ,""( ,.+" )e" ")"- )"*.
P<+0-- σ =-- =-<=-; <=0+ -0 + =- P -0
Te!"!")e!"!" ("*-+ #.)."- #"&"' ,e,e*"2" e"#"": 1 Ke"#"" ""& : Pe"'2"! P*e"+) " Te!"!" ".,") !"$" 2*e+)*e++ ""& , Te!"!" ".,") ,e*") +e#.*. 2*e"+) 8 Se)e&"( e(.&"!" )e!"!" 6 2e"'2"! 2*e"+): " Te!"!" ".,") !"$" 2*e+)*e++ "(.* , Te!"!" ".,") ,e*") +e#.*. 2*e"+) 3 Se)e&"( ,e)/ #./*6 2e"'2"! 2*e"+): " Te!"!" ".,") !"$" 2*e+)*e++ "(.* , Te!"!" ".,") ,e*") +e#.*. 2*e"+)
RUMUS UMUM BERLAKU PADA KEADAAN I $ D."!*"' )e!"!" -
KETERANGAN GAMBAR $ Ke)e*"!" : $ " Te!"!" ".,") !"$" 2*e++)*e+ ""&<"(.* $ Te!"!" +e*") ")"+ ,.+" )e" ")"- )"*. $ Te!"!" +e*") ,""( : )e" $ , Te!"!" ".,") ,e*") +e#.*. 2*e"+) < /'2/+.)e $ Te!"!" +e*") ")"+ : Te" $ Te!"!" +e*") ,""( : T"*. $ S-2e*2/+.+. : 1 A.,") !"$" 2*e+)*e++ ""& ".,") BS P*e"+)
78 S-2e*2/+.+. : A.,") !"$" 2*e+)*e++ "(.*
".,") BS P*e"+) 73 S-2e*2/+.+. : A.,") !"$" 2*e+)*e++ "(.* ".,") BS P*e"+) "+) . 2&"e 7"+) . 2&"e : Te!"!" #.+e*") ,""(<")"+ ,.+" )"*.<)e" #Te!"!" ".,") '-")" &-"* )e!"!" #.+e*") ")"+ : Te" Te!"!" #.+e*") ,""( : )"*. e Te!"!" "(.* S-2e*2/+.+. #"*. 3 #e!" #
DAERAH AMAN KABEL $ ANALISA PENAMPANG MEMANJANG*
$
$
BAJA MENGALAMI TARIKAN AKIBAT GAA PRATEGANG> AKIBATNA BETON MENGALAMI
TEKANAN ANG BESARNA SAMA DENGAN P TARIKAN. P"D SEBELUM BEBAN LUAR BEKERJA> RESULTANTE GAA TARIK PADA BAJA DAN RESULTANTE GAA TEKAN PADA BETON BERHIMPIT AITU PADA TITIK BERAT BAJA. SETELAH BEBAN LUAR BEKERJA( BEBAN ERTIKAL)> BERARTI ADA MOMEN POSITI% AKIBAT BEBAN LUAR TERSEBUT MAKA PADA SETIAP PENAMPANG TIMBUL MOMEN PERLA#ANAN ANG BERASAL DARI MOMEN KOPEL ANTARA P DAN D M KOPEL " P.- ( ;.) L- ;-+0 @- P -= 0-; - ;-+0 @- D -9'-9 00-+ ;- 0-:- = :-; +<. D
G-+0 K@- D $ -. G-+0 @- D =-- K @-+ ;-;- -+ =-- 0- --0 $ . G-+0 @- D =-- K ;-;- +0- --0 " ! $ . G-+0 @- D +--- K?K- +- -;-;- -+ $ . G-+0 @- D =-- K- ;-;- +0- --9 " ! $ . G-+0 @- D +--0 K- @-+ -+ + 0- --9
G-<- T;-;- -. G-+0 K@-
-
DAERAH AMAN $ D--9 =-- =-<=-; <<-@-; - =-- +<-- +- - +<=-- + --9 0> +- -- @-+ ;-;- -+ +0- --0 <-= --9 $ J-+ -+:- ;-+0 @- D 9-0 @- +--++ K- ? K $ J-+ 0--; +;;- ;-+0 @- P :-; +;0 0<++- =- 09+;;- +< << = :-; 0-<- 0-:- ;- << -+- - - <-= - 0++.
G-+0 @- P $ M = "M DL -- MTL $ P.- " M.DL -- MTL $ B--0 --9 * - " MDL/P( + -+ KB --9) $ B--0 --0* -" MTL/P( + -+ K--9)
1, Me!(.)-! +e)./ 2*/2e*).e+ ,"&/ /'2/+.)e
$ B"&/ 2*"e)" : ; 45 E, = 14 105 K!<'8 $ Be)/ ,e*)-&"! : ; 810 E, = 105 103 K!<'8 $ = 6 E, ; 81 < E, ; 45 = 6 105 105 < 14 105 = $ $ $ $ $ $
0@5 J"#. &e,"* 2e!!"). ,e)/ = 0@5 800 = 150 ' F = 150 80 = 3000 '8 $ = 150 ' )(#2 "&"+ F )/)"& = 490 3000 = @90 '8 J-' +)").+ '/'e = 38018 3000 150 = @@018 '3 Y, = -' F Y < J-' F = @@018 < @90 ' Y" = 10 9@ = 3 '
KERN I /'2 = I 2*" F 2*" 6 $"$,8 I F 8 = 1090853 490 6 9@58 1<18 150 803 3000 538 = 84 530 99 '4 .8 = I < F = 84 530 99 < @90 = 3103 '8 " = .8 < $, = 3130 < 9@ = 3155 '8 , = .8 < $" = 3030 < 3 = 49@ '8
U <;;-<- --9 -<- 9-0 ++@- -=- --- * 1. K--- * ;-;- -+- ;-:- =0000 -- ;-;- -+- .0( -+- M) 0==0+0+ +- 9 -- ;-;- -+ +0- --0. A1 " MDL/P 2. S-9 9+-;- ;-;- * ' T;-;- -+- ;-:- =000 -9+ ' T; -+- .0 ( -+- MDL) 0==0+0+ +- 9 -- ;. T-+ +0- --0 -2 " MDL/P-
3. S- - - @- * ' ;. A+- ( --- -9+) ' ;. A+- ;-:- =000 -9+ ' ;. A+- - -( -+- MTL) ' 0==0+0+ +- 9 -- ;. T-+ +0- --9 -3 " MTL/P-3
3 1 2
-1
-2
;
P-<=-; K<=0+ $ K--- -- =-<=-; * ' T;-;- -+- ;-:- =000 -- S==0+0+> ;-;- -+- 0 =-0 ( MDL ). +- 9 -- :-; ;-;- -+ +0- --0. -1 " MDL / P $ S-9 9+-;- ;-;- ( P-<=-; =-0 ) '".,") *Te!"!" !"$" 2*e+)*e++ "(.* 'Te! A.,") ,+ 2*e"+) 6 MDL
0==0+0+
$ L"-)" T.#"
,/&e( "#" )"*. #.+e*") ")"+ "8= MDL < P/ 'Te! A.,") !"$" 3 Se)e&"( ,e)/ #./* 2*e+)*e++ "(.* 6 2e"'2"! 2*e"+) : 'Te! A.,") ,+
+-2e*2/+.+.
7/'2/+.)e 6 MTL
T.#" ,/&e( "#" )e!"!" )"*. #.+e*") ,""( "3 = MTL < P" 'Te! A.,") "#3 4 Se)e&"( ,e," &-"* ,ee*" : 'Te! A.,") ,e," &-"* 6 MLL +-2e*2/+.+.
T.#" ,/&e( "#" )e! T"*. #.+e*) ,""( "4 = 6 MTL MLL < 6 P"
K0+ -+- K-F -
; <=
; =-0
KF
B+- +++- --:- ;-;- -+ --< . H-0 +0+ ;- * - " ( . % . - ) / P " ( - . % . ) / P
KESIMPULAN PERTEMUAN 2 $ END
PRAY
E-<= =< $ B- @<-- =-;-; 3! < 2!! !>5! !>2 !>2! !>15
!>62
!>18
!>21 !>2
1>4!
M-- $
L+ - ( -;+ -- ) " 1!!! ;/<> L+ - P " 1! T $ B@ =-;-; " 2>5 /<3 $ B@ -; " 2>5 /<3 $ T;-;- -- " !>38 ,F $ T;-;- -9+ " !>33 ,F D+-9+ * J<-- -+ - <=0+ :-; ++ -+ --0 - =-- I :-; +=000 - =- --+ -; :-; + 00-9 - =-- +=-0-;. B-; @<-- " 3! <> - +--0 - <=- 0-+0 ( =+ = ;-<- ).
P-:-- * 1. H+; 0+ ==+0 - =--. H+; C S+ ==+0 -+ - <=0+. B+- - =-- +- -+ , 45 ;- E" 1>4 1!5 ;/<2> - =- +- -+ =- , 21 ;- E " 1>!5 1!5 K;/<2 2. B-=- 0- ;-:- =000 <- :-; -=- +=+ - =-- =-- +0+ -- ( S< +<-+ 9 =- ).
P-:-- * 3. B+- +=--+ ;-:- =000 -- 00- P " 475 - +=9+;- 9+-;- ;-;- 00- 2!&> 9+;-9 ;-;-2 +< =-- - <=0+ ( ;-<-- +-;-< ;-;- )> =-- 0-- 0 * ( +;-9 -; ). -. K+0+ -- . S-9 9+-;- ;-;- . 0-9 =- -;- + . S-9 +<-+ - 9+=.
A0 D"*. 2e*(.)-!" #.#"2") :
1.6! 1.4!
2>!! !>5! I I
II -"75
!>2 !>2! !>15
II
:-F"!>63
!>2! III
"65 I !>62
I
!>18
:F"!.7 !>21 !>2
1. -. M;9+; 0+ ==+0 =-<=-; - =-- L-0 ( <2 )
J-- 9= --0 ( < )
S-+0 << ( <3)
%1 " 2! . 5! "1!!! %2 " 2 . . 15 . 15 " 225 %3 " 2! . 1!! " 2!!! %4 " 2 . . 21 . 21 " 441 %5 " 2! . 62 " 124!
13! 115 7! 27 1!
13!.!!! 25.875 14!.!!! 11.!7 12.4!!
% TOTAL " 4!6 " ( % T . : ) / % T- " 32!182 /4!6 " 65 < - " 14! Q : " 14! Q 65 " 75 <
32!.182
M< I0+- =-0 I1
1/12 . 5! . 2!3
1!!! . 652
" 4 258 333
I2
2 . 1/36 . 154
225 . 5!2
"
I3
1/12.2!.1!!3
2!!! . 52
" 1 716 667
I4
2 . 1/36 . 214
441 . 382
"
I5
1/12 . 62 . 2!3
124! . 552
" 3 72 334
565 312 647 6!8
+2 " I / % " ( 1! 8! 254 / 4!6 ) " 2238 <2 - " +2 / : " 2238 / 65 " 34>43 < " +2 / :- " 2238 / 75 " 2>84 <
" 1! 8! 254 <4
1. Me!(.)-! Se)./ P*/2e*).e+ ,"&/ /'2/+.)e B"&/ 2*"e)" : ;45 E, = 14 105 !<'8
Ke* K/'2/+.)e
B"&/ 2*"e)" : ;81 E, = 105 105 !<'8
. = I
J"#. = E, ; 45< E, ;81 = 105 105 < 14 105 = 0@5 Le,"* 2e!!"). 2&") ,e)/ ,e*)-&"! = 0@5 800 = 150 ' F = 150 80 = 3000 '8 $ = 150 ' 6 +' ,""( +)").+ '/'e = 38018 3000 150 = @@018 '3 $, = F $ < F = @@018 < @90 = 9@ ' $" = 10 9@ = 3 ' I /'2 = I 2*"e)" F 2*"e)" 6 $,$,8 I F 8
K" = . < $, = 3103 <9@ = 3199 ' K, = . < $" = 3103 < 3 = 4985 '
K+0+ -- $ P- --+ < + T; -- " !>38 , " !>38 45! ;/<2 " !>38 . 45! "171 ;/<2
B0 =-- * 3! <
" % . B@ " !>4!6 . 2>5 " 1>2265 /
M< <-+<< @-+ +;-9 -;. M <- " 1/8 ² = 1/8 . 1,2265 . 30² = 137,98 tm = 13 798 000 kg/cm’ Kondisi awal ideal ila diag!am tegangan s " s-
" ! +-;;-= +- <+<- -+. s " s ++ -- " ' 171 ;/<2 s- " ' P/% ( P. . - )/I ( M . - / I ) 0 " ' P / 4!6 ( P ( 65 '18 ) . 75 / 1!8!254 ) ( 1378!!! . 75 ) / 1!87254 P " 8!416 ; 8!4 T
s
" ' P/% ( P. . ) / I ( M . / I ) '171 " ' P / 4!6 Q ( P . (65 Q 18 ) 65 / 1!8!254 ) ( 1378!!! . 65) / 1!8!254 P " 254 172 KG DIBULATKAN 524 TON J-+ :-; <- +--9 P <- " 524 . 3-. K&n/"!" a8a : G-:- =000 -- P " 475 B- =--> --+ < +. s- " ' P/% ( P. . - ) / I ( M . - / I ) " 475!!! / 4!6 ( 475!!! (65'18) 75 ) / 1!8!254 ((1378!!! . 75 ) / ( 1!8!254 )) " ' 38>58 K;/<2 T; -- " '171 ;/<2 s " ' P/% ( P. . ) / I ( M . / I ) " ' ( 475!!! / 4!6) ( 475!!! ( 65'18) . 65) / ( 1!8!254 )) Q ((1378!!! . 65 ) / ( 1!8!254 )) " ' 147>3 ;/<2 ; --" '171 ;/<2. . S-9 9+-;- ;-;- 2! & * P " !>8 P " 38! B- P-- --+ < + T;-;- -9+ " !>33 45! " 15! ;/<2 s- " ' P/% ( P. . - ) / I ( M . - / I ) " ' ( 38!!!! / 4!6) ( 38!!!! ( 65'18) . 75) / ( 1!8!254 )) Q ((1378!!! . 75 ) / ( 1!8!254 )) " 4>72 ;/<2 ; -9+ " '15! ;/<2. s " ' P/% ( P. . ) / I ( M . / I ) " ' ( 38!!!! / 4!6) ( 38!!!! ( 65'18) . 65) / ( 1!8!254 )) Q ((1378!!! . 65 ) / ( 1!8!254 )) " ' 1!1>51 ;/<2 ; -9+ '15! ;/<2. . S-9 P- -; 00-+ + ( <- ) B- =-- ;- - 0-;-+ + * 0 " 0 - =-- 0 -; " 1>2265 % -; B@ -; " 1>2265 !>2 . 2 . 2>5 " 2>2265 /
M< <-+<< @-+ +;-9 -; * " 2>2265 /.2265 . 3!2 " 25!>48 < " 25!48!!! ;.< s- " ' P/% ( P. . - ) / I ' ( M . - / I ) " ' ( 38!!!! / 4!6) ( 38!!!! ( 65'18) . 75) / ( 1!8!254 )) Q ((25!48!!! . 75 ) / ( 1!8!254 )) " '126>56 ;/<2 ; -9+ " '15! ;/<2. s " ' P/% ( P. . ) / I ( M . / I ) " ' ( 38!!!! / 4!6) ( 38!!!! ( 65'18) . 65) / ( 1!8!254 )) Q ((25!48!!! . 65 ) / ( 1!8!254 )) " ' 34>1 ;/<2 ; -9+ " '15! ;/<2. . S-9 +<-+ - 9+= * B- K<=0+. B- -;+ -- =9 " 1 / <<+- << <-0+<< +- @- +;-9 -;. M <- " 1/8 V # W . $% M <- " 1/8 . 1 . 3!V # W . 10 . 30 = 187,5 tm = 1870000 kgcm.
&egangan Q tegangan akiat ean 'id() " σ-- " ' M . -F / I " ' (1875!!!! . 63 ) / 2455!8 " ' 48>15 ;/<2 σ " M . F / I " ' ( 1875!!!! . 7 ) / 2455!8 " 74>14 ;/<2 σ- " 43/63 . σ -- " 43/63 . ( '48>15 ) " '32>86 ;/<2
S==0+0+ ;- -. * σ- - " ' 126>56 Q 32>86 " '15>42 ;/<2 σ - " ' 34>1 74>14 " 3>23 ;/<2
; ++ -9+ " !>33 . 21! " ' 7! ;/<2
D+-;-< ;-;- -
'48>45
'48>45 '38>8
'4>72
'126>56
'32>86
'15>42
σ--
-
'147>3 (-)
'1!1>51
'34>1
74>14
()
()
( <-- 9+= )
,++09
3>23 ()
E-<= =< ( DAERAH AMAN KABEL ) $ B- @<-- =-;-;
1!!!! KG BERGERAK
3! < !>5! !>2 !>15 !>18
!>2!
!>6!
!>21 !>2
1>4!
0- D-+ 0- - =-- ;- < K'45! - E " 2.1! 5 - - @+0 " 2>5 /< 3. S-; :-; + 0<=- ;- < , 21 - E " 1>51! 5 - - @+0 " 2>5.1! 5. K00+ <+<- =<-- 0-;-+ +* ' M-- 9+= -;+ --" 1!!! ;/8! P> ;-<---9 --9 -<- ( 0;-9 -;). P@ * H+; +- --9 -<- =-- ++ 1>2> - 3> <+- - 00- --9 -<-.
P;- - $ K<=0+
-F" 62
F"8
-" 75
" 65
2!! !>5!
II
I III
!>2 !>15 !>18
II !>2!
I I !>6!
!>66
!>21 !>2
1>4!
1. M;9+; 0+ ==+0 =-<=-; - =--* L-0 --9 ( <2)
J-- 9--= --0(M)*
S-+0 <<
%1 " 15 5!" 75! %2 " 2. !.5. 15 . 18"27! %3 " 2!.1!5 " 21!! %4 " 2!.!>5.2!.21 " 42!! %5 " 2!.6! "12!!
132>5 11 72>5 27 1!
375 3213! 15225! 1134! 12!!!
474!
3!7!6
G0 - ? M< I0+$ " %.:/ % " 3!7!5/474! " 64>8 65 < $ - " 14! Q 65 " 75 < $ M< I0+-* I " 1/12.5!.15 75!.67>5 " 3.431.25! I " 2. 1/36.15.18 27!.54 72.18! I " 1/12.2!.1!5 21!!. 7>5 " 2.!47.5!! I " 1/12. 6!. 2! 42!. 38 " 616.77! I " 1/12. 6!. 2! 12!!. 55 " 3.67!.!!! 1!.557.7!! 1
3
2
3
2 3 4 5
2"
3
3 3
2
2
2
K ? <=0+ $ $ $
I " I/% " 1!5577!!/474! " 2227>36 <2 K- " + /: " 2227>36 / 65 " 34>37 < K " + / :- " 2227>36/ 75 " 21>7! < M;9+; 0+ ==+0 -+ - <=0+* B- P-- " , 45 ;- E" 2 . 1!5 B B-; " , 21 ;- E" 1>5 . 1!5 " 1>5 . 1!5 / 2 . 1!5 " !>75 @-+ - =;;-+ " !>75 . 2!! " 15! <. % " 15! . 2! " 3!!! <2 : " 15! < 9--= --0. J-+ J< % " 475! 3!!! " 774! <2 :F " %.: / % " ( 3!7!7 ( 3!!! . 15! )) / 774! " 7>8 " 8 < -+ --0. I <= " I P-- % =-- ( :F Q :)² # I % . V J-+ @-+ <-< " +V " I / % " 233156! / 774! " 3!1> <2 K-F " 3!1> / 8 " 31>55 < KF " 3!1> / 62 " 4>87 < 2
2 2
2. M- --9 -<- - $ U <- --9 -<- -> <-- 9-0 ++@- -=- ---- 0-;-+ + * -. K--- -- ( - =-- ) . K--- 0-9 9+-;- =-;-; . K-- 0-9 =- -; + ( - =-- ). . K--- 0-9 - - @- ( - <=0+ ) - " M / P +<-- - " J-- ++ - - K. M " M< :; @- =-- 0+-= D =-<=-;. D P " G-:- P000. P
T-9-=- <;9+; U <;9+; 0-:- <<'<< +-<=-; 1>2 - 3 +=;-- ;-+0 =;-9 < ++ 1>2> - 3 G-+0 =;-9 M1 * O+- <-0+<< " 25/6 < 3!>!! ((3!'5)/3!).5 " 125/3! " 25/6. +9- ;-<- 56/6 MI " ( L')/L . G= M1 L-0 +-; =;-9 " . 3! . 25/6 " 62>5! <2 G-+0 =;-9 M2 * 2!/3 G-+0 =;-9 M2 " 2!/3 < L-0 +-; =;-9 * . 3! . 2!/3 " 1!! <2 G= M2 G-+0 =;-9 M3* G-+0 =;-9 M3 " 7>5 M 7>5 L-0 B+-; =;-9 M3 " 7>5 . 3! . " 112>5 <2 G= M3 Kea/aan a * K--- -- - =-- * P " P " 45! T 5 5 5 B- " - 0++ - =-- 0 " % =-- . B@ =-- " !>474! . 2>5 " 1>185 <
MOMEN'MOMEN M-1 " L-0 ;= M1 0 " 62>5 . 1>185 " 74>!625 < M-2 " L-0 ;= M2 0 " 1!! . 1>185 ." 118>5 < M-3 " L-0 ;= M3 0 " 112>5 . 1>185 " 133>3125 < -
; --
P
J-- " M</B --1 " M-1 / P " 74>!635 < / 45! " !>165 < " 16>5 < --2 " M-2 / P " 118>5 263 < " 26>3! < A-3 " M-3 / P " 133>3125 < /45! " !>26 < " 2>6 <
K--- * ' S-9 9+-;- ;-;- * P " !>8! P " 36! B- P-- B- - 0++ - =-- * " 1>185 /
K--- * A1 " M1/P " 74>!625/36! " !>2!6 < " 2!>6! < A2 " M2/P " 118>5/36! " !>32 < " 32>! < A3 " M3/P " 133>3125/36! " !>37"37 < --- * P-- --- > =<-- 0-<- ;- --- -> @-+ 0-:M1 " M-1 " 74>!625 < M2 " M-2 " 118>5 < M3 " M-3 " 133>3125 <
14!
; ",
D P"!>8P
K--- $ ' ' '
S-9 =- -; 00-+ + P " 36! B- =-- B- * - 0++ - =-- - 0++ Q -;. ' " 1>185 % -; γ -; ' " 1>185 2. !>2. 2>5 = 2>185 /<
KEADAAN $ M1 " 62>5 . 2>185 " 136>5625 < $ M2 " 1!!. 2>185 " 218>5 < $ M3 " 112>5 . 2>185 " 245>8125 < $ A1 " M1/P " 136>5625/36! " !>37 < " 37> < $ A2 " M2/P " 218>5/36! " 6!>7 < $ A3 " M3/P " 245>8125/ 36! " !>683<" 68>3 < D 14!
G
- P"!>8 P
K--- $ $ $ $
' S-9 - - @' P " 36! ' B- <=0+ ' B- * - 0++ - <=0+ - - $ - <-- " 2>185 1" 3>185 /
KEADAAN D $ M1 " 62>5 . 3>185 25/6.1! " 24!>72 < $ M2 " 1!!.3>1852!/3. 1! " 385>167 < $ M3 " 112>5 . 3>185 7>5.1! " 433>3125 < $ A1 " M1/P " 24!>72/36!" !>668 <" 66>8 < $ A2 " M2/P " 385>167/36! " 1>!7< " 1!7 < $ A3 " M3/P " 433>3125/36! " 1>2!4 " 12!>4 <
K-F
D
KF
; -
14!
P"!>8P
$ G-<- -: - 1 -F -
-1"37>
2
-1"66>8 -2"6!>7
F
--1"165
3
-1"2!>6
--2"26>3
15.!! D---9 -<- -
-2"1!7 -3"68>3
--3"26 -2"32>
-3"12!>4
-3"37
- - --
--- * $ -- -+ << 0=+ +-01 +-- + ++ 1 1
$ $ $ $
1 + ++ 1 R- " X Y
LOAD BALANING $
B- 09-S- - 09--> ;- =-<=-; =0;+ 5!/75 < - -; L " 7>32 <> @- - - <-- 00- >836 /<. ++ ;-:- =-- P " 36! > - --2 -+:- +9- ;-<-. D+<+- <;9+; 0-:- ;-;-2 :; @-+ =-- =-<=-; < * ;- <;;-- -- L- B--+;
75/2
75 <
15>24 <
75/2
22>86 <
L/2
L/2 L
22>86 <
5!<
P:0-+- " 8>11 /<
$ G-- +<-; * $ # " 8 P9 /L² " ( 8 . 36! . !>1524 ) / 7>32V ">836 /< $ " 8>11 /< P
P
L " 7>32
$ $ $ $
B- U-- * " Q " >836 Q 8>11 " 1>645 /< M I'I " ( . LV * / L " ( 1>645 . 7>32V ) / 8 " 11>!18 < " 11!1>8 <
M " 1/8 ²
$ $ $ $ $
K T;-;- T;-;- ++ * M B * , 35! ;/<2 ,F " !>83 , " !>83 . 35! " 2!>5 ;/<2 D+<-- 1 MPA " 1!>1 1!>2 " 28>4 MPA Tegangan %ar"k " !>25 Z ,F " !>25 Z 28>4 " 1>334 MPA 9-0 -- <=-- =-- ;- <=- - 9-0+ @+- + 0-- <+. S-9 + - -=- +<+- " 13>5 ;/<2 Tegangan Tekan " !>45 2!>5 " ' 13!>72 ;/<2 ;/<2 $ T;-;- Q ;-;- :; @-+ * $ A+- M " T; - " M / " 6 < / 9V ( 6 . 11!1>8 . 1
