beton

(1)

dik: dik:

ffyy 223300 ++ 4499 == 227799 MpaMpa 27.927.9 ffcc'' 2288 ++ 99 == 3377 MpaMpa

tteebbaal l ppllaat t == 1010 ccmm == 110000 mmmm syarat-syarat tumpuan

syarat-syarat tumpuan

tumpuan terjepit elastis, dengan jarak c.t.c

tumpuan terjepit elastis, dengan jarak c.t.c di anggap sebagai bentangdi anggap sebagai bentang

-- plat RK plat RK LLyy//LL 44 :: 44 ==

-- plat Koridorplat Koridor LLyy//LL 44 :: 33 == -- plat Perpusplat Perpus LLyy//LL !! :: 44 ==

-- plat Labplat Lab LLyy//LL !! :: 44 ==

-- plat Gudangplat Gudang LLyy//LL !! :: 44 ==

hitungan beban-beban hitungan beban-beban -- beban mati (Wdbeban mati (Wd

a

a. . bbee""aat t ##ee$$ddii""ii == 0..10 122  2244 == 22..8888 b.

b. bebebaba$ $ mamati ti %%pepe$&$&t&t&p p lala$t$taiaidd&c&ctiti$( $( ))** p

piippaa--ppiippaa  == 220000 == 22..0000 ,

,dd == 44..8888 -- beban hidup (WLbeban hidup (WL

a

a.. ((eedd&&$$( ( &&$$tt&&k k ""&&aa$$( ( kk&&lliiaa == 2200 == 22..00 b

b.. ppee""aallaattaa$ $ kkaa$$tt"" == 1100 == 11..00 ,

,LL == 44..0000 -- kombinasi beban (beban ultimit,Wukombinasi beban (beban ultimit,Wu

 && == 11..22 dd ++ 11..!! LL = = 11..22  22..8888 ++ 11..!!  22..00 = = 77..44!!

pe"it&$(a$ mme$ %de$(a$ tabel  1971 pe"it&$(a$ mme$ %de$(a$ tabel  1971   pelat RK pelat RK = = 00..0022 == 00..0022  77..44!! M M55yy == 00..0022 == 00..0022  77..44!! M Mtt66 == --00..0011 == --00..0011  77..44!! M Mttyy == --00..0011 == --00..0011  77..44!! 

 pelat koridorpelat koridor = = 00..0033!!88 == 00..0033!!88  99..88!! k k k(/m k(/m kk k k k(/m k(/m k(/m k(/m k/m k/m M M5566 &&..LL66 &.L6 &.L6 &.L6 &.L6 &.L6 &.L6 M M5566 &&..LL66

(2)

M

Mtt66 == --00..00!!!!11 == --00..00!!!!11  99..88!! M

Mttyy == --00..004433 == --00..004433  99..88!! 

 pelat perpuspelat perpus = = 00..0044 == 00..0044  99..88!! M M55yy == 00..0011!! == 00..0011!!  99..88!! M Mtt66 == --00..0077 == --00..0077  99..88!! M Mttyy == --00..0044 == --00..0044  99..88!! 

 pelat Labpelat Lab = = 00..0044 == 00..0044  99..88!! M M55yy == 00..0011!! == 00..0011!!  99..88!! M Mtt66 == --00..0077 == --00..0077  99..88!! M Mttyy == --00..0044 == --00..0044  99..88!! 

 pelat Gudangpelat Gudang = = 00..0044 == 00..0044  99..88!! M M55yy == 00..0011!! == 00..0011!!  99..88!! M Mtt66 == --00..0077 == --00..0077  99..88!! M Mttyy == --00..0044 == --00..0044  99..88!! kebutuhan tulangan lentur

kebutuhan tulangan lentur a

a.. ppeellaat t RRK K !

!ulangan ulangan LapanganLapangan

-- !!iinnggggi "i "##eekkttii# $# $eettoonn ika dipakai e$&t&p

ika dipakai e$&t&p bet$ bbet$ b == 22 cmcm == d

diiaammeettee" " tt&&llaa$$((aa$$ == 1100 mmmm

i$((i ;fektif et$ a"a d =

i$((i ;fektif et$ a"a d = 100100 -- 2020

-- i$((i ;fektif et$ a"a ydy =

i$((i ;fektif et$ a"a ydy = 100100 -- 2020

--%

% ttuullaannggaan n llaappaannggaan n aarraah h && 

 <<aa##ii  &&llaa$$((aa$ $ bbeett$$ M

M&& == 22..9988 kkmm % % &&$$tt&&k k aa""aa    ddi i ppaakkaai i MMLL   k k == MM&& = = 22..998822  0 0..88  11000000  77 0 0..99 pp ffyy ++ kk == 00 fc' fc' 0 0..99 pp 227799 pp 227799 ++ 00..!!!!33 == 00 37 37 &.L6 &.L6 &.L6 &.L6 M M5566 &&..LL66 &.L6 &.L6 &.L6 &.L6 &.L6 &.L6 M M5566 &&..LL66 &.L6 &.L6 &.L6 &.L6 &.L6 &.L6 M M5566 &&..LL66 &.L6 &.L6 &.L6 &.L6 &.L6 &.L6 10 10 > b d > b d p p ffyy

(3)

m maakka a ddi i ddaappaat t pp11 == !!22..770099 p p22 == 00..0000223388 d diippaakkaai i p p == 00..0000223388 c

ceecck k ttee""aaddaapp ppmmii$$ == 1.41.4

=

= 1.41.4 == 00..00000022 ffyy 227799

k

kaa""ee$$a a p p == 00..0000223388 ?? ppmmii$$ 00..00000022 mmaakka a ddiippaakkaai i p p ==



 ll&&aa# # tt&&llaa$$((aa$ $ ppee""ll&& )

)## == pp  bb  dd =

= 00..00000022  11000000  77 == 3377 dipakai t&la$(a$ diamete" 10 mm

dipakai t&la$(a$ diamete" 10 mm maka a"ak t&la$(a$$ya:

maka a"ak t&la$(a$$ya: #

# == == == 220088..88!! mmmm

)

)## 3377!!..3344 adi &$t&k t&la$(a$ a"a  pelat <@ dipakai

adi &$t&k t&la$(a$ a"a  pelat <@ dipakai

P%'-'

ceck a"ak a$ta" t&la$(a$ 220 mm ? 3 ? 300mm A ? 00 mm ceck a"ak a$ta" t&la$(a$ 220 mm ? 3 ? 300mm A ? 00 mm

k #iplaBB.CCC k #iplaBB.CCC 

 ttuullaannggaan n aarraah h yy 

 ""aa##ii  tt&&llaa$$((aa$ $ bbeett$$ M

M&& == 22..9988 %&%&$t$t&k &k a"a"a a y dy dipipakakai ai MlMly y dede$($( k k == MM&& = = 22..9988  0 0..88  11000000  !! 0 0..99 pp ffyy ++ kk == 00 fc' fc' 0 0..99 pp 227799 pp 227799 ++ 00..888822 == 00 37 37 4 4..444499 pp -- 227799 pp ++ 00..888822 == 00 m maakka a ddi i ddaappaat t pp11 == !!22..77008877 p p22 == 00..00003311!! d diippaakkaai i p p == 00..00003311!! c

=

= 1.41.4 == 00..00 ffyy 227799

k

kaa""ee$$a a p p == 00..00003311!! ?? ppmmii$$ 00..00000022 mmaakka a ddiippaakkaai i pp maka pe$&la$(a$ a"a y di pakai &(a

maka pe$&la$(a$ a"a y di pakai &(a

P%'-''

ceck a"ak a$ta" t&la$(a$ 200 mm ? 3 ? 300mm A ? 00 mm ceck a"ak a$ta" t&la$(a$ 200 mm ? 3 ? 300mm A ? 00 mm

k #iplaBB.CCC k #iplaBB.CCC Pelat RK Pelat RK tulangan tumpuan tulangan tumpuan )

) titinnggggi ei e##eekkttii# b# beettoonn

ika dipakai pe$&t&p bet$pb =

ika dipakai pe$&t&p bet$pb = 22 ccmm == 2200 mmmm diamete" t&la$(a$ = diamete" t&la$(a$ = 1100 mmmm 1 1//44DDEEbb 11//44..DD..1100..11000000 k/m k/m 10 10 > b d > b d p p ffyy

(4)

i$((i ;fektif et$ a"a tAtydt =

i$((i ;fektif et$ a"a tAtydt = 100100 -- 2020 -- 0.0. 

 ""aa##ii  tt&&llaa$$((aa$ $ bbeett$$ M

M&& == !!..0088 kkmm (untuk penulangan tumpuan dipakai *t& +*ty,(untuk penulangan tumpuan dipakai *t& +*ty,

k k == M&M& = = !!..0088  0 0..88  11000000  77  0 0..99 pp ffyy ++ kk == 00 fc' fc' 0 0..99 pp 227799 pp 227799 ++ 11..3311 == 00 37 37 4 4..444499 pp -- 227799 pp ++ 11..3311 == 00 m maakka a ddi i ddaappaat t pp11 == !!22..77007700 p p22 == 00..0000448844 d diippaakkaai i p p == 00..0000448844 c

=

= 1.41.4 == 00..00000022 ffyy 227799

k

kaa""ee$$a a p p == 00..0000448844 ?? ppmmii$$ 00..00000022 mmaakka a ddiippaakkaai i p p ==

)luas tulangan perlu )luas tulangan perlu

) )## == pp  bb  dd = = 00..00000022  11000000  77 = = 3377!!..3344

dipakai t&la$(a$ diamete" 10 mm dipakai t&la$(a$ diamete" 10 mm maka a"ak t&la$(a$$ya :

maka a"ak t&la$(a$$ya : #

# == == == 220088..88!! mmmm

)

)## 3377!!..3344 adi &$t&k t&la$(a$ t&mp&a$ a"a  di pakai

adi &$t&k t&la$(a$ t&mp&a$ a"a  di pakai

P%'-'

ceck a"ak a$ta" t&la$(a$ 200 ? 3 = 300 mm A 00 mm

)

) lluuaas s ttuullaannggaan n ssuussuutt pelat RK pelat RK )# )# #&#&t #&#&t == 0 0..22 bb  = = 00..22  11000000  1 10000 110000 = = 2200 ata& ata& )

)## ##&&##&&tt == 2200FF  )# )# ppkkkk == 77..22!!8888

d

diippaakkaai i ddiiaammeettee" " tt&&llaa$$((aa$ $ ##&&##&&t t == 88 mmmm # # == == == 3377 mmmm ) )## 77..2277 10 10 > b d > b d p p ffyy mm mm 1 1//44DDEEbb 11//44..DD..1100..11000000 mm mm mm mm 1 1//44DDEEbb 11//44..DD..88..11000000

(5)

m

moommeenn kkooee##.. **uu iillaai i k k PpPpeerrlluu PP ((kkmm ((**ppaa M MLL 33!!..88 33..22!! 00..772244 00..000022!!00 00..00 M Mllyy 2200..!! 11..8833 00..4400!! 00..0000119944 00..00 M Mtt !!!!..11 ..8877 11..33003399 00..000044!!77 00..00 M Mttyy 44..33 44..8822 11..00771133 00..0000338844 00..00 t&la$(a$ #&#&t t&la$(a$ #&#&t t t ty ty b b.. PPeellaat t ppeerrppuuss m

moommeenn kkooee##.. **uu iillaai i k k PpPpeerrlluu PP ((kkmm ((**ppaa M MLL 44.. 77..1188 11..9944 00..00007722 00..00 M Mllyy 11!!.. 22..!!00 00..77!!9988 00..0000220077 00..00 M Mtt 77 1111..8833 22..!!228833 00..00112244 00..00 M Mttyy 44.. 88..99 11..99009999 00..0000!!88 00..00 t&la$(a$ #&#&t t&la$(a$ #&#&t t t ty ty b b.. PPeellaat t LLaabb m

moommeenn kkooee##.. **uu iillaai i k k PpPpeerrlluu PP ((kkmm ((**ppaa M MLL 44.. 77..1188 11..9944 00..00007722 00..00 M Mllyy 11!!.. 22..!!00 00..77!!9988 00..0000220077 00..00 M Mtt 77 1111..8833 22..!!228833 00..00112244 00..00 M Mttyy 44.. 88..99 11..99009999 00..0000!!88 00..00 t&la$(a$ #&#&t t&la$(a$ #&#&t t t ty ty b b.. PPeellaat t GGuuddaanngg m

moommeenn kkooee##.. **uu iillaai i k k PpPpeerrlluu PP ((kkmm ((**ppaa M MLL 44.. 77..1188 11..9944 00..00007722 00..00 M Mllyy 11!!.. 22..!!00 00..77!!9988 00..0000220077 00..00 M Mtt 77 1111..8833 22..!!228833 00..00112244 00..00 M Mttyy 44.. 88..99 11..99009999 00..0000!!88 00..00 t&la$(a$ #&#&t t&la$(a$ #&#&t t t ty ty

(6)

1 1 1.333 1.333 1. 1. 1. 1. 1. 1.   44 == 22..9988 kkmm   44 == 22..9988 kkmm   44 == --!!..0088 kkmm   44 == --!!..0088 kkmm   33 == 33..22!! kkmm m m m m m m k/m k/m k/m k/m k/m k/m

(7)

  33 == --..8877 kkmm   33 == --44..8822 kkmm   44 == 77..1188 kkmm   44 == 22..!!00 kkmm   44 == --1111..8833 kkmm   44 == --88..99 kkmm   44 == 77..1177117 k7 kmm   44 == 22..!!0011998 k8 kmm   44 == --1111..882277 kkmm   44 == --88..994444 kkmm   44 == 77..1177117 k7 kmm   44 == 22..!!0011998 k8 kmm   44 == --1111..882277 kkmm   44 == --88..994444 kkmm 2 200 mmmm 0 0..  1100 == 77 mmmm 1 100 -- 00..  1010 == !! mmmm !2 !2 = = 00..!!!!33 MMppaa  4 4..444499 pp -- 227799 pp ++ -- 227799 GG 227799 HH22 2 2  44..44448899 -- 227799 GG 7777884411 8.898 8.898 %%−−GGII H((H22 JJ44  2//2 I I I I

(8)

8.8978 8.8978 d

dee$$((aa$ $ ""&&mm&&# # ))** == 279279 GG 279.0279.0 8.90 8.90 0.0002 0.0002 .34 .34 $ d = $ d = !! mmmm = = 00..888822 MMppaa  4 4..444499 pp -- 227799 pp -- 227799 GG 227799 2 2  -- 227799 GG 7777 8.8978 8.8978 -- 227799 GG 77778822 8.8978 8.8978 de$(a$ "&m&# )* de$(a$ "&m&# )* == 279279 GG 278.97278.97 8.90 8.90 02 02 = = 0.00020.0002 mm mm I I I I I I

(9)



 1100 == 77 mmmm karena

karena momen momen tumpuan tumpuan arah arah & & + + y y sama sama maka maka penulangannya penulangannya pun pun sasa

= = 11..3311 MMppaa 4 4..444499 pp -- 227799 pp ++ 11..3311 -- 227799 GG 227799 HH22 --2 2  44..444499 -- 227799 GG 7777884411 --8.8978378 8.8978378 -- 227799 GG 77778811!!..99!! 8.898 8.898 de$(a$ "&m&# )* de$(a$ "&m&# )* == 279279 GG 278.9!278.9! 8.90 8.90 0.00484 0.00484 100 100

adi &$t&k t&la$(a$ t&mp&a$ a"a  da$ y di pakai

P-

ceck a"ak a$ta" t&la$(a$ 400 ?  = 00 mm A ? 00 mm

ceck a"ak a$ta" t&la$(a$ 400 ?  = 00 mm A ? 00 mm I I I I I I

(10)

in in  0022 3377!!..334444 1100--222200  0022 3322!!..11!! 1100--2200  0022 3300..00 1100--223300  0022 224499..!!1122 1100--333300 7 700..111100 !!--443300 4 499..992222 !!--0000 in in  0022 3377!!..334444 1100--222200  0022 3322!!..11!! 1100--2200  0022 994400..8822!! 1100--8899  0022 1133..44!!33 1100--11!!00 1 18888..11!! 88--228800 1 10022..!!9933 88--0000 in in  0022 3377!!..334444 1100--222200  0022 3322!!..11!! 1100--2200  0022 994400..8822!! 1100--8899  0022 1133..44!!33 1100--11!!00 1 18888..11!! 88--228800 1 10022..!!9933 88--0000 in in  0022 3377!!..334444 1100--222200  0022 3322!!..11!! 1100--2200  0022 994400..8822!! 1100--8899  0022 1133..44!!33 1100--11!!00 1 18888..11!! 88--228800 1 10022..!!9933 88--0000 /s (mm0 /s (mm0 dipakaidipakai tulangan tulangan /s (mm0 /s (mm0 dipakaidipakai tulangan tulangan /s (mm0 /s (mm0 dipakaidipakai tulangan tulangan /s (mm0 /s (mm0 dipakaidipakai tulangan tulangan

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K1 K1 = = 00..88 = = 00..77994400 0 0..!!!!2288 == 00 -- 44 44..444499 00..!!!!33 -- 1111..779944  _b_b

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+ + 00..888822 == 00 H H22 -- 44 44..444499 00..88882244 4.4 4.4 4 411 -- 11..770022 .298 .298  _mi$_mi$

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a a = = 00 4 4 44..444499 11..3311 24.044 24.044

''

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-- 00..000088 %% 3377 -- 3300  K1 K1 = =  !00!00 fy fy !00 + fy!00 + fy = = 00..88  3377  00..77994400  !00!00 2 27799 !!0000 ++ 227799 = = 24.971324.9713  !00!00 2 27799 887799 = = 00..008899  00..!!88 = = 00..00!!1111 08  fc'  K 08  fc'  K₁₁

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= = 00..004488 0 0..00000022 ?? 00..00448822    _mak#_mak#

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@N<EN<pe"p&#(&da$( @N<EN<pe"p&#(&da$( hitungan beban-beban hitungan beban-beban -- beban mati (Wdbeban mati (Wd

a

a. . bbee""aat t ##ee$$ddii""ii == 0..10 122  2244 == 22..8888 b.

b. bebebaba$ $ mamati ti %p%pe$e$&t&t&p &p lala$t$taiaidd&c&ctiti$( $( ))** p

piippaa--ppiippaa  == 220000 == 22..0000 ,

,dd == 44..8888 -- beban hidup (WLbeban hidup (WL

a

a.. ((eedd&&$$( ( &&$$tt&&k k kk""iidd""ppee""pp&&##llaabb((&&ddaa$$(( == 440000 b

b.. ppee""aallaattaa$$ kkaa$$tt"" == 1100 ,L ,L -- kombinasi beban (beban ultimit,Wukombinasi beban (beban ultimit,Wu

 && == 11..22 dd ++ 11..!! LL = = 11..22  22..8888 ++ 11..!!  44..0000 = = 99..88!! k"id" k"id"  k k == M&M& = = 33..22!!  == 0.0. 0 0..88  11000000  77  4 4..44 pp -- 227799 pp ++ 00..7722 == 00 -- 227799 GG 227799 HH22 -- 44 44..44 00..7722440022 2 2  44..44 -- 227799 GG 7777884411 -- 1122..990099 8.9 8.9 -- 227799 GG 7777882288..009911 8.9 8.9 = = 279279 GG 278.98278.98 8.90 8.90 k k == M&M& = = ..8877  == 1.1. 0 0..88  11000000  77  4 4..44 pp -- 227799 pp ++ 11..330044 == 00 -- 227799 GG 227799 HH22 -- 44 44..44 11..330033994499 2 2  44..44 -- 227799 GG 7777884411 -- 2233..2200 8.9 8.9 -- 227799 GG 7777881177..7799 8.9 8.9 = = 279279 GG 227788..99!! !!22..770077 8.90 8.90 # = # = == == 220088..8877 mmmm ## ) )## 3377!!..3344 k/m k/m k(/m k(/m k/mk/m k/m k/m k(/m k(/m k(/m k(/m k/m k/m 10 10 > b d > b d 10 10 > b d > b d 1 1//44DDEEbb 11//44..DD..1100..11000000 I I I I I I I I I I I I

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# = # = == == 224400..!!7788 mmmm ## ) )## 3322!!..11!! # # == == == 222233..99333388 mmmm ) )## 3300.. # # == == == 313144..44887777 mmmm ) )## 224499..!!11

ceck a"ak a$ta" t&la$(a$ 10 ? 3 = 300 mm A

ceck a"ak a$ta" t&la$(a$ 10 ? 3 = 300 mm A 00 mm00 mm

k k == M&M& = = 77..1188  == 1.1. 0 0..88  11000000  77  4 4..44 pp -- 227799 pp ++ 11..9944 == 00 -- 227799 GG 227799 HH22 -- 44 44..44 11..9944448822 2 2  44..44 -- 227799 GG 7777884411 -- 2288..3377 8.9 8.9 -- 227799 GG 7777881122..!!22 8.9 8.9 = = 279279 GG 278.9278.9 8.90 8.90 k k == M&M& = = 22..!!00  == 0.0. 0 0..88  11000000  77  4 4..44 pp -- 227799 pp ++ 00..7788 == 00 -- 227799 GG 227799 HH22 -- 44 44..44 00..7788221199 2 2  44..44 -- 227799 GG 7777884411 -- 1100..229900 8.9 8.9 -- 227799 GG 7777883300..771100 8.9 8.9 = = 279279 GG 278.98278.98 8.90 8.90 # # == == == 202088..8877 mmmm ) )## 3377!!..3344 1 1//44DDEEbb 11//44..DD..1100..11000000 1 1//44DDEEbb 11//44..DD..1100..11000000 1 1//44DDEEbb 11//44..DD..1100..11000000 10 10 > b d > b d 10 10 > b d > b d 1 1//44DDEEbb 11//44..DD..1100..11000000 I I I I I I I I I I I I

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# # == == == 242400..!!7788 mmmm ) )## 3322!!..11!! # # == == == 8383..4433773344 mmmm ) )## 994400..8833 # # == == == 1122..888833 mmmm ) )## 1133..44!! 1 1//44DDEEbb 11//44..DD..1100..11000000 1 1//44DDEEbb 11//44..DD..1100..11000000 1 1//44DDEEbb 11//44..DD..1100..11000000

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= = 44..0000 = = 11..00 = = ..00 y y 2 2 MMppaa kk == M&M& == 11..8833  0 0..88  11000000  !! 4 4..44 pp -- 227799 pp ++ 00..4411 == 00 -- 227799 GG 227799 H2H2 -- 44 44..44 00..44 2 2  44..444488991199 -- 227799 GG 7777884411 -- 99..!!2211 8.9 8.9 -- 227799 GG 7777883311..337799 8.9 8.9 = = 279279 GG 278.98278.98 8.90 8.90 0 044 MMppaa kk == M&M& == 44..8822  0 0..88  11000000  77 4 4..44 pp -- 227799 pp ++ 11..007711 == 00 -- 227799 GG 227799 H2H2 -- 44 44..44 11..0077 2 2  44..444488991199 -- 227799 GG 7777884411 -- 1199..00!! 8.9 8.9 -- 227799 GG 7777882211..9933 8.9 8.9 = = 279279 GG 278.97278.97 8.90 8.90 = = == == 440033..00880099 mmmm ) )## 7700..1111 k/m k/m k/m k/m k/m k/m 10 10 > b d > b d 10 10 > b d > b d 1 1//44DDEEbb 11//44..DD..1100..11000000 I I I I I I I I I I I I

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= = == == !!!!..00777799 mmmm ) )## 4499..9922 9 944 MMppaa kk == M&M& == 1111..8833  0 0..88  11000000  !! 4 4..44 pp -- 227799 pp ++ 33..449999 == 00 -- 227799 GG 227799 H2H2 -- 44 44..44 33.. 2 2  44..444488991199 -- 227799 GG 7777884411 -- !!22..227700 8.9 8.9 -- 227799 GG 7777777788..773300 8.9 8.9 = = 279279 GG 278.89278.89 8.90 8.90 7 788 MMppaa kk == M&M& == 88..99  0 0..88  11000000  77 4 4..44 pp -- 227799 pp ++ 11..991100 == 00 -- 227799 GG 227799 H2H2 -- 44 44..44 11..9911 2 2  44..444488991199 -- 227799 GG 7777884411 -- 3333..998877 8.9 8.9 -- 227799 GG 7777880077..001133 8.9 8.9 = = 279279 GG 278.94278.94 8.90 8.90 # # == == == 22!!77 mmmm ) )## 118888..1177 1 1//44DDEEbb 11//44..DD..1100..11000000 10 10 > b d > b d 10 10 > b d > b d 1 1//44DDEEbb 11//44..DD..1100..11000000 I I I I I I I I I I I I I I I I I I

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# # == == == 448899..22227711 mmmm ) )## 110022..!!99 1 1//44DDEEbb 11//44..DD..1100..11000000

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= = 00..4411 MMppaa  = = 11..007711 MMppaa 

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= = 33..449999 MMppaa  = = 11..991100 MMppaa 

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