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8/17/2019 Statis Momen
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step 1
step 2 MOMEN INERSIA. I Rumus Umum :
= 12274.3
step 3 MOMEN LAWAN, W Rumus Umum :
= 1523.71 cm³
= 724.385 cm³
step 4 TEGANGAN :
cm4
y1
y2
5
25
5
20
z1
z2
yb = 16,94
ya = 8,06
)Ukuran daamcm!
"#
∫ = dA I .2
ρ
2
2
3
22
2
1
3
11 ...12
1...
12
1 z AII hb z AI hb Ix
tot +++=
y
I W =
a ATAS y
Ix
W =
b
BAWAH y
IxW =
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y1
z$3
y2
ya = 8,06
yb = 16,94
z$2
z$1
20
5
25
5
"#
)Ukuran daamcm!
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1) TEGANGAN GESER, t Rumus Umum :
a!. %aya$ )&'ns!
1200 ) 25 ( 5 ( 5.56 ! = 2.7157 k*cm+
25 ( 12274.3056
b!. ,adan )-'b!
1200 ) 5 ( 20 ( 6.94 ! = 13.5785 k*cm+
5 ( 12274.3056
1200 ) 5 ( ( 8.47 ! = 14.0349 k*cm+
5 ( 12274.3056
2) TEGANGAN NORMAL, Rumus Umum :
= / = = 8.89k*cm+
225
3) TEGANGAN LENTUR, Rumus Umum :
a! . %'ra as == m'n n'a b'rar s'ra aas 'rark )!
= 720000 = 472.532 k*cm+ )!
1523.7
b! . %'ra ,aa == m'n n'a b'rar s'ra aas 'r'kan )!
= 720000 = 993.946 k*cm+ )!
724.39
Ä ;ada ,aas nara %aya$ < ,adan
τa =
τb =
Ä ;ada ars /'ra kba ,aan ,adan %'n yb
τc =
5
I b
S D
.
.
=τ
N σ
A
P =σ
N σ
M σ W
M =σ
ATAS
I I M
W M
−
=σ
BAWAH
I I
M W
M −
=σ
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ambar >aram
?kk @rdna >aram
>aram ?'. 's'r sca'
2.7157 100 0.02715700113.5785 100 0.135785007
14.0349 100 0.140348892
>aram ?'. /rma sca'
8.88889 100 0.088888889
8.88889 100 0.088888889
>aram ?'. #'nur sca'
472.532 10000 0.047253182
993.946 10000 0.099394625
ya =8,06
yb = 16,94
z$2
z$1
20
5
25
5
y1
z$3
y2
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Parameter
b1 = 25 cm
h1 = 5 cm
b2 = 5 cm
h2 = 20 cm
STATIS MOMEN KE TEPI ATAS, (ya)
C = 25 ( 5 = 125 cm+
CC = 5 ( 20 = 100 cm+
y1 = 5 * 2 = 2.5 cm
y2 = 20 5 = 15 cm
2
ya = C.y1 CC.y = 8.05556 cmC CC
yb = )205! ya = 16.9444 cm
z1 = ya y1 = 5.55556 cm
z2 = y2 ya = 6.94444 cm
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z$1 = ya y1 = 5.55556 cm
z$2 = y2 ya = 6.94444 cm
z$3 = yb*2 = 8.47222 cm
b3 = 5 cm
h3 = yb cm
= 16.9 cm
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>k'au : > = 1.2
= 1200 k
>k'au : / = 2
2000 k
=
= C CC
= 225 cm+
>k'au : = 7.2 .m
720000 k.cm
= 1523.71 cm³
= 724.385 cm³
a
b1.
1 b
2.
2
C C
-?%
-,-D
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8
14
13,5792,716
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C = 600 ( 200 = 120000 mm2
CC = 200 ( 500 = 100000 mm2
y1 = 200 * 2 = 100 cm
y2 = 500 200 = 450 cm
2
ya = C.y1 CC.y2 = 259.091 cm
C CC
yb = )205! ya = 440.909 cm
600
5010 0 1 00 1 00 1 00 1 00
50
50
100
50
200
50100
50
50
150
250
350
450
550
650
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12/160 ?A. #A/?UR ?A. /BR#
993,946
472,5328,889
14
3,579
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b = 250 fc' = 25 N/mm2
h = 500 fy = 400 N/mm2
d' = 50 D = 19 mm
As tul = 2!"52# mm2
d = h $ d'
d = 450 As = 50"5%2As' = 50"5%2
d $ h/2 = 200
d $ d' = 400
0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( %%#,!4!,#9!"#5 200"00
0"5 & fc' & h & b ) As ) As'( & fy !!!%#1"9%#%#55
b = 250 fc' = 25 N/mm2
h = %00 fy = 400 N/mm2
d' = 50 D = 19 mm
As tul = 2!"52# mm2
d = h $ d'
d = 550 As = 50"5%2As' = 50"5%2
d $ h/2 = 250
d $ d' = 500
0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( 9%%,992,242"19 250"00
0"5 & fc' & h & b ) As ) As'( & fy !%#9%"9%#%#55
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b = 250 fc' = 25 N/mm2
h = 500 fy = 400 N/mm2
d' = 40 D = 19 mm
As tul = 2!"52# mm2
d = h $ d'
d = 4%0 As = 50"5%2
As' = 50"5%2
d $ h/2 = 210
d $ d' = 420
0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( #00,#10,9!"44 210"00
0"5 & fc' & h & b ) As ) As'( & fy !!!%#1"9%#%#55
b = 250 fc' = 25 N/mm2
h = 500 fy = 400 N/mm2
d' = 50 D = 19 mm
As tul = 2!"52# mm2
d = h $ d'
d = 450 As = 11!4"115 ==>PERHATAN JIKA TULAAs' = 50"5%2
d $ h/2 = 200
d $ d' = 400
0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( %%#,!4!,#9!"#5 19!"4!
0"5 & fc' & h & b ) As ) As'( & fy !4501!0"4%!5%214
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b = 250 fc' = 25 N/mm2
h = %00 fy = 400 N/mm2
d' = 40 D = 19 mm
As tul = 2!"52# mm2
d = h $ d'
d = 5%0 As = 11!4"115
As' = 50"5%2
d $ h/2 = 2%0
d $ d' = 520
0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( 1,005,%#1,9!1" 252"59
0"5 & fc' & h & b ) As ) As'( & fy !91!0"4%!5%214
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NGAN TIDAK SERAGAM
ACER:,ARA%AR @A RD ?U#// E/ #A,CD ,/E@ UNTUKMENCAPAI KESEIMBANGAN(LEBIH DEKAT KE AS YANGBESAR)
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b = 250 mm fc' = 2# N/mm2
h = %00 mm fy = 400 N/mm2
d' = 50 mm D = 1% mmAs tul = 201"0%192929# mm2
d = h $ d'
d = 550 mm As = ! D 1% %0!"15#9492
As' = ! D 1% %0!"15#9492
Statis Momen terhadap t!an"an tari#$ As %
d $ h/2 = 250 mm
d $ d' = 500 mm
d * = 0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( = 91,2%2,15#"90 =
0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!
Statis Momen terhadap tepi atas &!o# te"' Te#an &eton %
d * = 0"5 & fc' & h & b & h/2( ) As' & fy & d'( ) As & fy & d( 11##51459"4##42 =
0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!
Statis Momen terhadap t!an"an te#an$ As( %
h/2 $ d' = 250 mm
d $ d' = 500 mm
d * = 0"5 & fc' & h & b & h/2 $ d'( ) As & fy & d $ d'( = 91,2%2,15#"90 =
0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!
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Statis Momen terhadap titi# ) %
& = 125 mm d+- .+-s t+l +m+. bt 3 3++
1 = & 1 = 125 mm
2 = h/2 $ d' $ & 2 = 125 mm
! = d $ d' $ 2 ! = !#5 mm
d * = 0"5 & fc' & h & b & 1( $ As' & fy & 2( ) As & fy & !( 490,%!1,0#"95 =
0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!
Statis Momen terhadap "aris netra! penampan" &eton %
1 = & 1 = 0 mm
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2 = h/2 $ d' 2 = 250 mm
! = d $ h/2 ! = 250 mm
d * = 0"5 & fc' & h & b & 1( $ As' & fy & 2( ) As & fy & !( $ =
0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!
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mm2
mm2
250"00 mm d+- tul+.+ t+-3
!00"00 mm d+- t- +t+s bl3 t." T3+ bt
250"00 mm d+- tul+.+ t3+
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125"00 mm d+- t-t-3 &
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$ mm d+- d+- .+-s t+l +m+.
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MENGHITUNG d( *+ENTR,ID PLASTIS-
D = 19 mm
fc' = 2# N/mm2 As = 2!"52# mm2
fy = 400 N/mm2
As1 = 141#"%44 mm2
b = 400 mm As2 = 5%#"05#5 mm2
h = 400 mm As! = 5%#"05#5 mm2+ = h, As4 = 5%#"05#5 mm2
+ = 400 mm As5 = 141#"%44 mm2
d' = 50 mm
d = h $ d'
d = !50 mm
. Statis Momen terhadap "aris netra! penampan" &eton %
50
50mm
125 mm
200 mm
2#5 mm
!50 mm
c = h/2 $ +/2 c = 0 mm
1 = h/2 $ d1 1 = 150 mm
2 = h/2 $ d2 2 = #5 mm
! = h/2 $ d! ! = 0 mm
4 = d4 $ h/2 4 = #5 mm
5 = d5 $ h/2 5 = 150 mm
d* = 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( $ As4& fy & 4( $ As5& fy & 5(
0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy
0 = - mm dari garis netral
5,4%,5!"92
d- = d
c ) - $ 1( h $ 2d
c( / N $ 1(
dc= d' d
c=
d1=
d2=
d! =
d4 =
d5 =
h = 400
b = 400
6s5 6s4 6s! 6s2 6s1
6c
d1
d2
d!
d4
d5
1
24
5
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/ Statis Momen terhadap tepi atas &!o# te"an"an te#an &eton %
50mm
125 mm
200 mm
2#5 mm
!50 mm
c = h/2 c = 200 mm
1 = d1 1 = 50 mm
2 = d2 2 = 125 mm
! = d! ! = 200 mm
4 = d4 4 = 2#5 mm
5 = d5 5 = !50 mm
d* = 0"5 & fc' & h & b & c( ) As1& fy & 1 ) As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( ) As5& fy & 5(0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy
109#!1%#!"! = 200.00 mm dari tepi atas blok tegangan tekan beton
5,4%,5!"92
d1=
d2=
d! =
d4 =
d5 =
h = 400
b = 400
6s5 6s4 6s! 6s2 6s1
6c
d1d2
d!
d4
d5
1
2
! = c
4
5
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0 Statis Momen terhadap As1 %
50mm
125 mm200 mm
2#5 mm
!50 mm
c = d $ h/2 c = 150 mm
1 = d $ d1 1 = !00 mm
2 = d $ d2 2 = 225 mm
! = d $ d! ! = 150 mm
4 = d $ d4 4 = #5 mm
5 = d $ d 5 = 0 mm
d* = 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( ) As5& fy & 5
0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy
229#5#"51 = 150.00 mm dari As5
5,4%,5!"92
d1=
d2 =d
! =
d4 =
d5 =
h = 400
b = 400
6s5 6s4 6s! 6s2 6s1
6c
4
d1
d2
d!
d4
d5
! = c
2
1
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2 Statis Momen terhadap As2 %
50mm
125 mm200 mm
2#5 mm
!50 mm
c = d4 $ h/2 c = #5 mm
1 = d4 $ d1 1 = 225 mm
2 = d4 $ d2 2 = 150 mm
! = d4 $ d! ! = #5 mm
4 = d4 $ d4 4 = 0 mm
5 = d5 $ d4 5 = #5 mm
d* = 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( $ As5& fy &
0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy
41149!#9!"#5 = 75.00 mm dari As4
5,4%,5!"92
d1=
d2 =d
! =
d4 =
d5 =
h = 400
b = 400
6s5 6s4 6s! 6s2 6s1
6c
d1
d2
d!
d4
d5
1
2
! = c5
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1 Statis Momen terhadap As0 %
50mm
125 mm200 mm
2#5 mm
!50 mm
c = d! $ h/2 c = 0 mm
1 = d! $ d1 1 = 150 mm
2 = d! $ d2 2 = #5 mm
! = d! $ d! ! = 0 mm
4 = d4 $ d! 4 = #5 mm
5 = d5 $ d! 5 = 150 mm
d* = 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( $ As4& fy & 4( $ As5& fy & 5(
0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy
0 = - mm dari As3
5,4%,5!"92
d1=
d2 =d
! =
d4 =
d5 =
h = 400
b = 400
6s5 6s4 6s! 6s2 6s1
6c
d1
d2
d!
d4
d5
1
24
5
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3 Statis Momen terhadap As/ %
50mm
125 mm
200 mm
2#5 mm
!50 mm
c = h/2 $ d2 c = #5 mm
1 = d2 $ d1 1 = #5 mm
2 = d2 $ d2 2 = 0 mm
! = d! $ d2 ! = #5 mm
4 = d4 $ d2 4 = 150 mm
5 = d5 $ d2 5 = 225 mm
d* = $ 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( $ As!& fy & !( $ As4& fy & 4( $ As5& fy & 5(
0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy
$41149!#9!"#5 = (75.00) mm dari As2
5,4%,5!"92
ATA7
d* = 0"5 & fc' & h & b & c( $ As1& fy & 1( $As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( ) As5& fy & 5(
0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy
41149!#9!"#5 = 75.00 mm dari As2 5,4%,5!"92
d1=
d2=
d! =
d4 =
d5 =
h = 400
b = 400
6s5 6s4 6s! 6s2 6s1
6c
d1d2
d!
d4
d5
1!
4
5
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4 Statis Momen terhadap As. %
50mm
125 mm
200 mm
2#5 mm
!50 mm
c = h/2 $ d1 c = 150 mm
1 = d1 $ d1 1 = 0 mm
2 = d2 $ d1 2 = #5 mm
! = d! $ d1 ! = 150 mm
4 = d4 $ d1 4 = 225 mm
5 = d5 $ d1 5 = !00 mm
d* = $ 0"5 & fc' & h & b & c( ) As1& fy & 1( $ As2& fy & 2( $ As!& fy & !( $ As4& fy & 4( $ As5& fy & 5(
0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy
$229#5#"51 = (150.00) mm dari As2
5,4%,5!"92
ATA7
d* = 0"5 & fc' & h & b & c( $ As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( ) As5& fy & 5(
0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy
229#5#"51 = 150.00 mm dari As2
5,4%,5!"92
d1=
d2=
d! =
d4 =
d5 =
h = 400
b = 400
6s5 6s4 6s! 6s2 6s1
6c
d1
d2
d!
d4
d5
!
5
4
2
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D-3t+hu- 8
utu bt : utu b+;+ :
b< = 200 mm fc ' = 25 + fy = 400 +
bf = %00 mm = 25 N/mm2 = 400 N/mm2
h = #00 mm
hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y
h $ hf = 500 mm >c = >y = 200,000 +>c = 2!500 N/mm2
R.+.+ bt : R.+.+ b+;+ :
= 0"00! = fy / >s
= 0"0020
D = 22
As = !0"1! mm2
Tul+.+ = 22 D 22
Centroid plastis, d"St+t-s m 3 t- +t+s +m+.
Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm
Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm
As1 = % As = 2,20"0 mm2 d1 = 50 mm 1 = d1 1 = 50 mm
As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm
As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm
As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm
As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mmAs% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm
As# = 2 As = #%0"2# mm2 d# = %50 mm # = d# # = %50 mm
4#00 √ fc' (
@c
@y
@y
600
5010 0 1 00 1 00 1 00 1 00
50
50
100
50
200
50100
50
50
150
250
350
450
550
650
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Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy
d * = 2,0##,952,51"2# = 259"091 mm d+- t- +t+s +m+. 3lm T
,020,1%#"%
d * = Ac1 & c1 ) Ac2 & c2( ) As1 & fy & 1 ) As2 & fy & 2 ) As! & fy & ! ) As4 & fy & 4 ) As5 & fy & 5 ) As% & fy & % ) As# & fy &
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Centroid plastis, d"St+t-s m 3 t- b+
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hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y
h $ hf = 500 mm >c = >y = 200,000 +
>c = 2!500 N/mm2
R.+.+ bt : R.+.+ b+;+ :
= 0"00! = fy / >s
= 0"0020
4#00 √ fc' (
@c
@y
@y
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D = 22
As = !0"1! mm2
Tul+.+ = 22 D 22
Centroid plastis, d"
St+t-s m 3 t- 3-- +m+.
Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"bf c1 = !00 mm
Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = 1/2"bf c2 = !00 mm
As1 = 2 As = #%0"2# mm2 d1 = 50 mm 1 = d1 1 = 50 mm
As2 = 2 As = #%0"2# mm2 d2 = 150 mm 2 = d2 2 = 150 mm
As! = # As = 2,%%0"9! mm2 d! = 250 mm ! = d! ! = 250 mm
As4 = # As = 2,%%0"9! mm2 d4 = !50 mm 4 = d4 4 = !50 mm
As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mm
As% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm
As# = 0 As = $ mm2 d# = 0 mm # = d# # = 0 mm
22 b+t+. D-+"22
Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy
d * = 2,40%,050,!5#"2% = !00 mm d+- t- 3-- +m+. 3lm T
,020,1%#"%
d * = Ac1 & c1 ) Ac2 & c2( ) As1 & fy & 1 ) As2 & fy & 2 ) As! & fy & ! ) As4 & fy & 4 ) As5 & fy & 5 ) As% & fy & % ) As# & fy &
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D-3t+hu- 8
utu bt : utu b+;+ :
b< = 200 mm fc ' = 25 + fy = 400 +
bf = %00 mm = 25 N/mm2 = 400 N/mm2
h = #00 mm
hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y
h $ hf = 500 mm >c = >y = 200,000 +>c = 2!500 N/mm2
R.+.+ bt : R.+.+ b+;+ :
= 0"00! = fy / >s
= 0"0020
D = 22
As = !0"1! mm2
Tul+.+ = 22 D 22
Centroid plastis, d"St+t-s m 3 t- +t+s +m+.
Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm
Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm
As1 = % As = 2,20"0 mm2 d1 = 50 mm 1 = d1 1 = 50 mm
As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm
As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm
As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm
As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mmAs% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm
As# = 2 As = #%0"2# mm2 d# = %50 mm # = d# # = %50 mm
4#00 √ fc' (
@c
@y
@y
600
5010 0 1 00 1 00 1 00 1 00
50
50
100
50
200
50100
50
50
150
250
350
450
550
650
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Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy
d * = 2,0##,952,51"2# = 259"091 mm d+- t- +t+s +m+. 3lm T
,020,1%#"%
Centroid plastis, d"St+t-s m 3 t- b+
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& #(
& #(
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D-3t+hu- 8
utu bt : utu b+;+ :
b< = 200 mm fc ' = 25 + fy = 400 +
bf = %00 mm = 25 N/mm2 = 400 N/mm2
h = #00 mm
hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y
h $ hf = 500 mm >c = >y = 200,000 +>c = 2!500 N/mm2
R.+.+ bt : R.+.+ b+;+ :
= 0"00! = fy / >s
= 0"0020
D = 22
As = !0"1! mm2
Tul+.+ = 22 D 22
Centroid plastis, d"St+t-s m 3 t- +t+s +m+.
Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm
Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm
As1 = % As = 2,20"0 mm2 d1 = 50 mm 1 = d1 1 = 50 mm
As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm
As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm
As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm
As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mm
As% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm
A # 2 A #%0 2# 2 d# %50 # d# # %50
4#00 √ fc' (
@c
@y
@y
600
50100 100 100 100 100
50
50
100
50
200
50100
50
50
150
250
350
450
550
650
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Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy
d * = 2,0##,952,51"2# = 259"091 mm d+- t- +t+s +m+. 3lm T
d * = Ac1 & c1 ) Ac2 & c2( ) As1 & fy & 1 ) As2 & fy & 2 ) As! & fy & ! ) As4 & fy & 4 ) As5 & fy & 5 ) As% & fy & % ) As#
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,020,1%#"%
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Centroid plastis, d"St+t-s m 3 t- b+
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D-3t+hu- 8
utu bt : utu b+;+ :
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b< = 200 mm fc ' = 25 + fy = 400 +
bf = %00 mm = 25 N/mm2 = 400 N/mm2
h = #00 mm
hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y
h $ hf = 500 mm >c = >y = 200,000 +
>c = 2!500 N/mm2
R.+.+ bt : R.+.+ b+;+ :
= 0"00! = fy / >s
= 0"0020
D = 22
As = !0"1! mm2
Tul+.+ = 22 D 22
Centroid plastis, d"St+t-s m 3 t- +t+s +m+.
Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm
Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm
As1 = % As = 2,20"0 mm2 d1 = 50 mm 1 = d1 1 = 50 mm
As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm
As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm
As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm
As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mm
As% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm
As# = ! As = 1,140"40 mm2 d# = %50 mm # = d# # = %50 mm
Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy
d * = 2,1#%,##,0%"15 = 2%%"!%4 mm d+- t- +t+s +m+. 3lm T
,1#2,220"94
Centroid plastis, d"St+t-s m 3 t- b+
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,1#2,220"94
mbu3t-+
h $ d* = #00 $ 2%%"!%4 = 4!!"%!% mm d+- t- b+
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D-3t+hu- 8
utu bt : utu b+;+ :
b< = 200 mm fc ' = 25 + fy = 400 +
bf = %00 mm = 25 N/mm2 = 400 N/mm2
h = #00 mm
hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y
h $ hf = 500 mm >c = >y = 200,000 +>c = 2!500 N/mm2
R.+.+ bt : R.+.+ b+;+ :
= 0"00! = fy / >s
= 0"0020
D = 22
As = !0"1! mm2
Tul+.+ = 22 D 22
Centroid plastis, d"St+t-s m 3 t- +t+s +m+.
Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm
Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm
As1 = 11 As = 4,11"4% mm2 d1 = 50 mm 1 = d1 1 = 50 mm
As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm
As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm
As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm
As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mmAs% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm
As# = ! As = 1,140"40 mm2 d# = %50 mm # = d# # = %50 mm
4#00 √ fc' (
@c
@y
@y
600
50 5050
50
100
50
200
50100
50
50
150
250
350
450
550
650
50 50 50 50 50 50 50 50 50
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Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy
d * = 2,214,00,!5#"2% = /24'525 mm d+- t- +t+s +m+. 3lm T
,9!2,4%"!%
d * = Ac1 & c1 ) Ac2 & c2( ) As1 & fy & 1 ) As2 & fy & 2 ) As! & fy & ! ) As4 & fy & 4 ) As5 & fy & 5 ) As% & fy & % ) As#
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Centroid plastis, d"St+t-s m 3 t- b+
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& #(
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& #(
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& #(
& #(
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& #(
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& #(
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A" = 12 & 40
A" = 2 & 12
Bd-+t 8
&1 = 12/2
&2 =12 ) 2/2
Titi# &erat pe
&+ = &1"A
A
&+ = 14"2!52
&b = 12 ) 2
&b = 25"#%4#
utu bt : utu b+;+ : D = 1%
fc ' = 200 B./cm2 fy = 4000 B./cm2 As = 201"0% mm2
= 200 B./cm2 = 4000 B./cm2 2"010% cm2
dulus >l+st-s-t+s ?t dulus >l+st-s-t+s ?+;+, >s
>c = >y = 2,100,000 B./cm2
>c = 210190"!9 N/mm2
R.+.+ bt : R.+.+ b+;+ :
= 0"00! = fy / >s
= 0"0019
Centroid plastis, d"
St+t-s m 3 t- 3-- +m+.
Ac1 = 0"5 & fc & 12 & 40 = 1%00 3."cm c1 = 1/2 & 12 c1 = %
Ac2 = 0"5 & fc & 2 & 12 = 5#120 3."cm c2 = 12 ) 2/2 c2 = 2%
1!#20 3."cm
As1 = 5 As = 10"05!10 cm2 d1 = ! cm 1 = ! cm
As2 = 5 As = 10"05!10 cm2 d2 = 9 cm 2 = 9 cm
As! = 2 As = 4"02124 cm2 d! = 15 cm ! = 15 cm
As4 = 2 As = 4"02124 cm2 d4 = 2% cm 4 = 2% cm
As5 = 2 As = 4"02124 cm2 d5 = !# cm 5 = !# cm
4#00 √ fc' (
@c
@y
@y
90
150
260
370
400
120
120
280
30
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d* = !,#11,95"0# = 1!"14515! cm d-u3u d+- t- 3-- +m+.
2%#,!99"%4
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Centroid plastis, d"St+t-s m 3 Tul+.+ 1 As1(
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Ac1 = 0"5 & fc & 12 & 40 = 1%00 3."cm c1 = 1/2 & 12 $ ! c1 = ! cm
Ac2 = 0"5 & fc & 2 & 12 = 5#120 3."cm c2 = 12 ) 2/2 $! c2 = 2! cm
As1 = 5 As = 10"05!10 cm2 d1 = 0 cm 1 = 0 cm
As2 = 5 As = 10"05!10 cm2 d2 = % cm 2 = % cmAs! = 2 As = 4"02124 cm2 d! = 12 cm ! = 12 cm
As4 = 2 As = 4"02124 cm2 d4 = 2! cm 4 = 2! cm
As5 = 2 As = 4"02124 cm2 d5 = !4 cm 5 = !4 cm
*A7. 8 A7/- 8 *As. 8 As/ 8 As0 8 As2 8 As1-
d* = 2,909,%9%"1%4% = 10"14515! cm d-u3u d+- Tul+.+ 1 As1(
2%#,!99"%4
1!"14515!0!10"14515!0!
!
+ARA ANDRE N,AN$ ST$ MT'
A" = 12 & 40
A" = 2 & 12
Ab =
Bd-+t 8
&1 = 12/2
&2 =12 ) 2/2
Titi# &erat pe
&+ = &1"A
A
&+ = 14"2!52
&b = 12 ) 2
&b = 25"#%4#
d' = !
utu bt : utu b+;+ : D = 1%
fc ' = 200 B./cm2 fy = 4000 B./cm2 As = 201 0% mm2
d; = *A7. )
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dulus >l+st-s-t+s ?t dulus >l+st-s-t+s ?+;+, >s
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>c = >y = 2,100,000 B./cm2
>c = 210190"!9 N/mm2
4#00 √ fc' (
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R.+.+ bt : R.+.+ b+;+ :
= 0"00! = fy / >s
= 0"0019
itik Centroid plastis penampang, d"
St+t-s m 3 t- 3-- +m+.
Ac1 = 0"5 & fc & 12 & 40 = 1%00 3."cm c1 = 1/2 & 12 c1 = %
Ac2 = 0"5 & fc & 2 & 12 = 5#120 3."cm c2 = 12 ) 2/2 c2 = 2%
1!#20 3."cm
As1 = 5 As = 10"05!10 cm2 d1 = ! cm 1 = 0 cm
As2 = 5 As = 10"05!10 cm2 d2 = 9 cm 2 = % cm
As! = 2 As = 4"02124 cm2 d! = 15 cm ! = 12 cm
As4 = 2 As = 4"02124 cm2 d4 = 2% cm 4 = 2! cm
As5 = 2 As = 4"02124 cm2 d5 = !# cm 5 = !4 cm
Sb = 0"5"fc'"Ab" &+ $ d'(
Sb = 1555%0 3."cm
0"5"fc'"Ab( ) As1 ) As2 ) As! ) As4 ) As5( & fy
ds = 2909%9%"1%4559 = 10"14515!0! mm d+- Tul+.+ 2 As2(
2%#!99"%!50910!
@c
@y
@y
ds = 0"5"fc'"Ab"&+ $ d'( ) As1"1 ) As2"2 ) As!"! ) As4"4 ) As5"5(
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40 cm2
!!% cm2
1% cm2
% cm
&2 = 2% cm
pan" tota!
2" A
cm
cm
cm
cm
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40 cm2
!!% cm2
1% cm2
% cm
&2 = 2% cm
pan" tota!
2" A
cm
cm
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cm
cm
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TUGAS 2 BETON PRESTRESS
Suatu jembatan beton prategang dengan penampang sebagai berikut :
Dengan data sebagai berikut :
Panjang jembatan = 30 m
Initial prestress = 2000 kN
Beban hidup = 12 kN/m
ksentrisitas !gs " !g! #e$ diketahui setelah masing"masing ttik berat !g! dan !gs diketahui!atatan : !g! = !enter gra%it& o' !on!rete #titik berat penampang beton$
!gs = !enter gra%it& o' steel #titik berat penampang baja/besi$
(itung tegangan :
" )ehilangan jangka pendek = 10*
" )ehilangan jangka panjang = +*
,utu beton :
'!u = +0 N/mm2
'!i = 30 N/mm2
(itung tegangan"tegangan &ang terjadi
" )ondisi trans'er
" )ondisi ser%i!e
Jawaban
1. OND!S! TRANS"ER
#uas $ena%$ang ba&'k
'ndisi
trans(er
1000
400
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b1 = -00 mm (1 = 1000 mm
h1 = 200 mm
b2 = 1+0 mm
h2 = .00 mm
b3 = -00 mm
h3 = 200 mm
1 = b1h1 = 0000mm2
2 = b2h2 = 0000mm2
3 = b3h3 = 0000mm2
= 1 2 3 = 2+0000mm2
= 444 mm2
&1 = (1 " 1/2h1 = 00 mm
&2 = 1/2h2 h3 = +00 mm
&3 = 1/2h3 = 100 mm
0000 5 00 0000 5 +00 0000 5 10
2+00+
+00 mm dari tepi ba6ah #bottom$
7 dimana (1 = 1000mm
+00 mm dari tepi atas #top$
)eng*itung !nertia
dimana 8
= -00 mm
= 0mm karena berhimpitan dg garis netral pe
= -00 mm
= 1/12 5 -00 5 200 93 0000 5 -00 92
= 1/12 5 1+0 5 .00 93 0000 5 0 92
)eng*itung +arak titik berat ,-entr'id dari te$i bawa* ,b'tt'% / 0b
&b = Σ i&i/
&b =
&b =
&a = (1 " &
b
&a =
I = Σ#Ii
id
i2$
d1 = &
a " 1/2h
1
d2 = &
a " 1/2(1
d3 = &
b " 1/2h3
I1 = 1/12#b1h13$ 1d12
I2 = 1/12#b2h23$ 2d22
400
150900
500
100
y1 =
y2 =
y! =
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= 1/12 5 -00 5 200 93 0000 5 -00 92
= 444 mm-
= 444 mm-
= 444 mm-Inertia total = 444 mm-
)'%en &awan ,se-ti'n %'du&us %'du&us $ena%$ang
""" pada bagian atas
""" pada bagian ba6ah
= 444 = CCC mm3
+00
= 444 = CCC mm3
+00
Jarak kern ,kern distan-e
= 444 mm
= 444 mm
2. OND!S! SER!3E
#uas $ena%$ang ba&'k
b1 = -00 mm b3 = -00 mm (2 = 1200 mm
h1 = 200 mm h3 = 200 mm
b2 = 1+0 mm b- = 1000 mm
h2 = .00 mm h- = 200 mm
1 = b1h1 = -00 5 200 = 0000mm2 2 = b2h2 = 1+0 5 .00 = 0000mm2
3 = b3h3 = -00 5 200 = 0000mm2
- = b-h- = 1000 5 200 = 200000mm2
= 1 2 3 - = -+0000mm2
= 444 mm2
I3 = 1/12#b3h33$ 3d32
I1
I2
I3
;1 = I / &
a
;2 = I / &
b
;1
;2
kt = ;
2 /
kb = ;
1 /
)eng*itung +arak titik berat ,-entr'id dari te$i bawa* ,b'tt'% / 0b
400
150900
500
100
y1 =
y2 =
y! =
1
1900y1 =
1100y4 =
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&1 = (1 " 1/2h1 = 00 mm
&2 = 1/2h2 h3 = +00 mm
&3 = 1/2h3 = 100 mm
&- = (2 " 1/2h- = 1100 mm
0000 5 00 0000 5 +00 0000 5 100 200000 5 110
-+00+
444 mm dari tepi ba6ah #bottom$
7 dimana (2 = 1200mm
444 mm dari tepi atas #top$
)eng*itung !nertia
dimana 8
00 "
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)'%en &awan ,se-ti'n %'du&us %'du&us $ena%$ang
""" pada bagian atas
""" pada bagian ba6ah
= 444 = CCC mm3
444
= 444 = CCC mm3
444
)eng*itung Beban
. kN/m1
2- kN/m3
12 kN/m
-kN/m "" luas penampang plat 5 1 m 5 B Beto1000 5
>otal ser%i!e load = Berat sendiri balok beban hidup Berat plat di atas balok
= 22 kN/m
,omen maksimum &ang terjadi di tengah bentang #moment at midspan$ :
, =
,omen pada kondisi trans'er #moment at trans'er$ :
,i = . 5 30 92
,i = .
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00
0+
dimana7 Pi = 2000 kN
0 5 2000 = 100 kN
0+ 5 2000 = 1
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444 mm3 e = %%%"%# mm
#1
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#lass 27 post"tensioned$
= "03. 5 +0 9 1/2
= "2++ N/mm2
= 033 5 +0
= 1.+0N/mm2
esi%$u&an
1 Pada kondisi trans'er #at trans'er$
>egangan &ang terjadi
.-2 N/mm2 "1< N/mm2egangan &ang terjadi
12
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nampang
400
200
200
1000
150
500
500
400
400
d1 =
d! =
yb =
y+ =
'ndisi trans(er
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400
200
200
1000
150
500
500
400
400
d1 =
d! =
yb =
y+ =
'ndisitrans(er
200
1000
200
1000
4!!"!!
1!!"!!
2%%"%#
!!!"!!
y+ =
d1 =
d2 =
d4 =
'ndisiser6i-e
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92
92
92
33 92
400
200
1000
150
0
#%%"%#
2%%"%#
%%%"%#
yb =
d2 =
d! =
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1000 mm
109"
00 5 1000 mm 5109" 5 2- kN/m3
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skala tegangan = 30
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1+ 0+3
skala tegangan = 30
3
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nan'rHad $ada
b'umnya
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02-
0-1.2
0302
02-
0-1.2
0302
021-
02..
012+
023++
A 1 : 30NTUKANERAH ATAUSUAIKAN AGARBARNYAS DILIHAT
A 1 : 30NTUKANERAH ATAUSUAIKAN AGARBARNYA
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0+331
012+
0-1.<
0-32
0-23+
0-00+
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TUGAS 1 BETON PRESTRESS
Suatu jembatan beton prategang dengan penampang sebagai berikut :
(itung besaran penampang untuk kondisi trans'er dan ser%i!e berupa :
1 @uas penampang
2 >itik berat penampang
3 Inertia penampang
- ,odulus penampang #se!tion modulus$ atau momen la6an
Ba&'k $restress diatas dua tu%$uan :
Panjang balok = 1+ m
Initial ga&a prestress = 1100 kN
Beban hidup = 12 kN/m
ksentrisitas !gs " !g! = 32+ mm
(itung tegangan di tengah bentang
)ehilangan jangka pendek = 10*
)ehilangan jangka panjang = 10*
Aimana7
'!u = +0 N/mm2
'!i = 30 N/mm2
Jawaban
'ndisi
trans(er 1000 mm
'ndisi ser6i-e
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1. OND!S! TRANS"ER
#uas $ena%$ang ba&'k
b1 = -00 mm (1 =
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= 1/12 5 -00 5 200 93 0000 5 2
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= 444 mm2
&1 = (1 " 1/2h1 = .+0 mm&2 = 1/2h2 h3 = 3
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= 1/12 5 -00 5 200 93 0000 5 --......
= 1/12 5 1+0 5 3+0 93 +2+00 5 23030303030303
= 1/12 5 -00 5 200 93 0000 5 +0+30303030303
= 1/12 5 1000 5 200 93 200000 5 2--.....
= 444 mm-
= 444 mm-
= 444 mm-
= 444 mm-
Inertia total = 444 mm-
)'%en &awan ,se-ti'n %'du&us %'du&us $ena%$ang
""" pada bagian atas
""" pada bagian ba6ah
= 444 = CCC mm3
444
= 444 = CCC mm3
444
)eng*itung Beban
+1kN/m1
2- kN/m3
Beban hidup = 12 kN/m
>otal ser%i!e load = Berat sendiri balok Beban hidup
= 1
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,i = 1-3-- kNm
,omen pada kondisi ser%is #moment at ser%i!e$ :
1
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2. Pada k'ndisi ser6is ,at ser6i-e
Aari perhitungan besaran penampang dapat diketahui :
= 444 mm2 e =
444 mm3 e = .0+30303030303" 1/2 5 200
444 mm3 e = 505"!0 mm
= 213 4 -13 5 --<
= 2-< N/mm2
= 213 5
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Tegangan 0ang dii7inkan ,stress &i%its
1. Pada k'ndisi trans(er ,at trans(er
#lass 27 post"tensioned$
= "03. 5 30 9 1/2
= "1< N/mm2
= 0+ 5 30
= 1+00N/mm2
2. Pada k'ndisi ser6is ,at ser6i-e
#lass 27 post"tensioned$
= "03. 5 +0 9 1/2
= "2++ N/mm2
= 033 5 +0
= 1.+0N/mm2
esi%$u&an
1 Pada kondisi trans'er #at trans'er$
>egangan &ang terjadi
0 N/mm2 "1< N/mm2
33 N/mm2 1+00 N/mm2
2 Pada kondisi ser%is #at ser%i!e$
>egangan &ang terjadi
2-< N/mm2 "2++ N/mm2
1+- N/mm2 1.+0 N/mm2
' tt = "03.#'
!i$1/2 N/mm2
' !t = 0+'
!i N/mm2 #'le5ural members$
' ts = "03.#'
!u$1/2 N/mm2
' !s
= 033' !u
N/mm2 #'le5ural members$
' 1t =
' 2t =
' 1s
=
' 2s
=
,andnkan d'
'anan yan$'runan s'
c.s = ct, .,+D-ty f stl
)2"1! N/mm2 ) #"2% N/mm2
400
200
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'ndisi trans(er
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nampang
0
200
200
#50
!#5
2#5
2#5
0
yb =
!#5y+ =
d1 =
d! =
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200
200
1000
!44"#0
44"#0
2!0"!0
244"#0
y+ =
d1 =
d2 =
d4 =
'ndisi ser6i-e
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200
200
#50
200
%05"!0
!44"#0
44"#0
2!0"!0
244"#0
505"!0
yb =
y+ =
d1 =
d2 =
d! =
d4 =
400
200
200
#50150
%05"!0
!44"#0
44"#0
2!0"!0
244"#0
505"!0
yb =
y+ =
d1 =
d2 =
d! =
d4 =
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92
2
2
< 92
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skala tegangan = 30
-.. 01. 01++3
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skala tegangan = 30
213 00< 00
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nan
'rHad $adab'umnya
$ #"5 N/mm2
β-
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UTS BETON PRESTRESS
Suatu jembatan beton prategang dengan penampang sebagai berikut :
Dengan data sebagai berikut :
Panjang jembatan = 2+ m
Initial prestress = 1+00 kN
Beban hidup = 1+ kN/m
ksentrisitas !gs " !g! #e$ diketahui setelah masing"masing ttik berat !g! dan !gs diketahui!atatan : !g! = !enter gra%it& o' !on!rete #titik berat penampang beton$
!gs = !enter gra%it& o' steel #titik berat penampang baja/besi$
(itung tegangan :
" )ehilangan jangka pendek = 1+*
" )ehilangan jangka panjang = 10*
,utu beton :
'!u = +0 N/mm2
'!i = 30 N/mm2
(itung tegangan"tegangan &ang terjadi
" )ondisi trans'er
" )ondisi ser%i!e
Jawaban
1. OND!S! TRANS"ER
#uas $ena%$ang ba&'k
'ndisi
trans(er
1000
400
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b1 = -00 mm (1 = 1000 mm
h1 = 200 mm
b2 = 1+0 mm
h2 = .00 mm
b3 = -00 mm
h3 = 200 mm
1 = b1h1 = 0000mm2
2 = b2h2 = 0000mm2
3 = b3h3 = 0000mm2
= 1 2 3 = 2+0000mm2
= 444 mm2
&1 = (1 " 1/2h1 = 00 mm
&2 = 1/2h2 h3 = +00 mm
&3 = 1/2h3 = 100 mm
0000 5 00 0000 5 +00 0000 5 100
2+00+
+00 mm dari tepi ba6ah #bottom$
7 dimana (1 = 1000mm
+00 mm dari tepi atas #top$
)eng*itung !nertia
dimana 8
= -00 mm
= 0 mm karena berhimpitan dg garis netral p
= -00 mm
= 1/12 5 -00 5 200 93 0000 5 -00 92
= 1/12 5 1+0 5 .00 93 0000 5 0 92
)eng*itung +arak titik berat ,-entr'id dari te$i bawa* ,b'tt'% / 0b
&b = Σ i&i/
&b =
&b =
&a = (1 " &
b
&a =
I = Σ#Ii
id
i2$
d1 = &
a " 1/2h
1
d2 = &
a " 1/2(1
d3 = &
b " 1/2h3
I1 = 1/12#b1h13$ 1d12
I2 = 1/12#b2h23$ 2d22
400
150900
500
100
y1 =
y2 =
y! =
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= 1/12 5 -00 5 200 93 0000 5 -00 92
= 13010 mm-
= 2)0# mm3
+00
Jarak kern ,kern distan-e
= 444 mm
= 444 mm
2. OND!S! SER!3E
#uas $ena%$ang ba&'k
b1 = -00 mm b3 = -00 mm (2 = 1200 mm
h1 = 200 mm h3 = 200 mm
b2 = 1+0 mm b- = 1000 mm
h2 = .00 mm h- = 200 mm
1 = b1h1 = -00 5 200 = 0000mm2 2 = b2h2 = 1+0 5 .00 = 0000mm2
3 = b3h3 = -00 5 200 = 0000mm2
- = b-h- = 1000 5 200 = 200000mm2
= 1 2 3 - = -+0000mm2
= 444 mm2
I3 = 1/12#b3h33$ 3d32
I1
I2
I3
;1 = I / &
a
;2 = I / &
b
;1
;2
kt = ;
2 /
kb = ;
1 /
)eng*itung +arak titik berat ,-entr'id dari te$i bawa* ,b'tt'% / 0b
400
150900
500
100
y1 =
y2 =
y! =
900y1 =
1100y4 =
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&1 = (1 " 1/2h1 = 00 mm
&2 = 1/2h2 h3 = +00 mm
&3 = 1/2h3 = 100 mm
&- = (2 " 1/2h- = 1100 mm
0000 5 00 0000 5 +00 0000 5 100 200000 5 1100
-+00+
444 mm dari tepi ba6ah #bottom$
7 dimana (2 = 1200mm
444 mm dari tepi atas #top$
)eng*itung !nertia
dimana 8
00 "
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)'%en &awan ,se-ti'n %'du&us %'du&us $ena%$ang
""" pada bagian atas
""" pada bagian ba6ah
= 444 = 1"%04>)0 mm3
444
= 444 = 9"0%5>)0# mm3
444
)eng*itung Beban
. kN/m1
2- kN/m3
1+ kN/m
-kN/m "" luas penampang plat 5 1 m 5 B Beton 1000 5
>otal ser%i!e load = Berat sendiri balok beban hidup Berat plat di atas balok
= 2+ kN/m
,omen maksimum &ang terjadi di tengah bentang #moment at midspan$ :
, =
,omen pada kondisi trans'er #moment at trans'er$ :
,i = . 5 2+ 92
,i = -.
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0+
0
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444 mm3 e = %%%"%# mm
#112+ 5 1093 / -+0000$ "#112+ 5 1093 5 ..............< /1.03-.1+3-.
= 2+0 4 -. 5 12+<
= 103N/mm2
#112+ 5 1093 / -+0000$ #112+ 5 1093 5 ..............< /0.+21
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#lass 27 post"tensioned$
= "03. 5 +0 9 1/2
= "2++ N/mm2
= 033 5 +0
= 1.+0N/mm2
esi%$u&an
1 Pada kondisi trans'er #at trans'er$
>egangan &ang terjadi
-3 N/mm2 "1< N/mm2+2 N/mm2 1+00 N/mm2
2 Pada kondisi ser%is #at ser%i!e$
>egangan &ang terjadi
103 N/mm2 "2++ N/mm2
"11-. N/mm2 1.+0 N/mm2
' ts = "03.#'
!u$1/2 N/mm2
' !s = 033' !u N/mm2 #'le5ural members$
' 1t =' 2t =
' 1s
=
' 2s
=
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nampang
400
200
200
1000
150
500
500
400
400
d1 =
d! =
yb =
y+ =
'ndisi trans(er
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400
200
200
1000
150
500
500
400
400
d1 =
d! =
yb =
y+ =
'ndisitrans(er
200
1000
200
1000
4!!"!!
1!!"!!
2%%"%#
!!!"!!
y+ =
d1 =
d2 =
d4 =
'ndisiser6i-e
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92
400
200
1000
150
0
#%%"%#
2%%"%#
%%%"%#
yb =
d2 =
d! =
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1000 mm
109"
00 5 1000 mm 5109" 5 2- kN/m3
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skala tegangan = 30
+10 01<
# - 02
$ 13 02<
skala tegangan = 30
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12+< 0-2
skala tegangan = 30
2+0 00
1+$ 201+.2+ / 1.03-.1+3-.1+$ 2< 02
2223 0
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143/160
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02-
0-1.2
0302
02-
0-1.2
0302
021-
02..
012+
023++
1 : 30UKANAH ATAUAIKAN AGARRNYADILIHAT
1 : 30UKANAH ATAUAIKAN AGARRNYA
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0+331
012+
0-1.<
0-32
0-23+
0-00+
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3ONTO8 SOA# BETON PRESTRESS
Balok prestress diatas dua tumpuan :
Panjang balok = 1+
Initial ga&a prestress = 1100
Beban hidup = 12ksentrisitas !gs " !g! = 32+
(itung tegangan di tengah bentang
)ehilangan jangka pendek = 10*
)ehilangan jangka panjang = 10*
Aimana7
'!u = +0
'!i = 30
Jawaban
#uas $ena%$ang ba&'k
b1 = -00 mm
h1 = 200 mm
b2 = 1+0 mm
h2 = 3+0 mm
b3 = -00 mm
h3 = 200 mm
1 = b1h1 = 0000mm2
2 = b2h2 = +2+00mm2
3 = b3h3 = 0000mm2
= 1 2 3 = 212+00mm2
= 444 mm2
&1 =
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0000 5 .+0 +2+00 5 3
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= 444 mm
= 444 mm
)eng*itung Beban
+1kN/m1
2- kN/m3
Beban hidup = 12 kN/m
>otal ser%i!e load = Berat sendiri balok Beban hidup
= 1
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= -.. 4 1. 5 -0
= "0-2 N/mm2
= -.. 5 1. 4 -0
=
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Tegangan 0ang dii7inkan ,stress &i%its
1. Pada k'ndisi trans(er ,at trans(er
#lass 27 post"tensioned$
= "03. 5 30 9 1/2
= "1< N/mm2
= 0+ 5 30
= 1+00N/mm2
2. Pada k'ndisi ser6is ,at ser6i-e
#lass 27 post"tensioned$
= "03. 5 +0 9 1/2
= "2++ N/mm2
= 033 5 +0
= 1.+0N/mm2
esi%$u&an
1 Pada kondisi trans'er #at trans'er$
>egangan &ang terjadi
"0-2 N/mm2 "1< N/mm2
egangan &ang terjadi
. N/mm2 "2++ N/mm2
"1-1 N/mm2 1.+0 N/mm2
' tt = "03.#'
!i$1/2 N/mm2
' !t = 0+'
!i N/mm2 #'le5ural members$
' ts = "03.#'
!u$1/2 N/mm2
' !s
= 033' !u
N/mm2 #'le5ural members$
' 1t =
' 2t =
' 1s
=
' 2s
=
,andnkan d'
'anan yan$'runan s'
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m
kN
kN/mmm
N/mm2
N/mm2
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yb
a
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159/160
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