catatan kuliah beton2
TRANSCRIPT
-
8/17/2019 CATATAN KULIAH BETON2
1/10
As = As1 + Asf As1 = As - Asf
As = .bw.d Asf = f.bw.d = w + f
' '
BALOK "T" DENGAN TULANGAN TUNGGAL
s
0.85.fc
0.003
0.85.fc
s'
bw
dh
be
y
d -y
Ts1 Tsf
CcCf
h
a
. . . f. e - w f. e - w
0.85.fc'.hf.b'
fy
0.85.fc'.hf.b' ===> 0.85.fc'.hf.b'
fy
Tinjau regangan
0.003d - 0.003y = y.y
0.003d = y.y + 0.003y
0.003d = y.(0.003 + y)
Asf =
f.bw.d =
0.003y
=
f =fy.bw.d
yd - y
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST
-
8/17/2019 CATATAN KULIAH BETON2
2/10
...selanjutnya dianggap sebagai y balance
Kesetimbangan gaya H = 0
0.85.fc'.a.bw = As1.fy , dimana a = 1.y
0.85.fc'.1.y.bw = As1.fy ...selanjutnya y = yb
...pers ini dikali 1 dengan variable d /d
… subt pers y = 0.003d/(0.003 + fy)
0.003d
(As - Asf) fy.d
yb = (As - Asf).fy
0.85.fc'.1.bw
y =0.003d
0.003 + yyb =
0.003 + y
bw.d 0.85fc'.1xyb =
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST
-
8/17/2019 CATATAN KULIAH BETON2
3/10
fy , dimana y = fy /Es , dan Es = 200000 MPa
fc'
fy
fc'
fc'
fy - f = 0.85.1
600
600 + fy
- f
- f0.85.1
d
1
0.85.1
fy.d
bw.d 0.85fc'.1
0.003d
600=
600 + fy
0.003d=
0.003 + y
0.003 + y=
(As - Asf)x
fc'
fy
Tinjauan Kopel Momen /Momen Nominal
Mn = 0.85 fc'.1.yb.bw.[ d - ½.1.yb ] + 0.85 fc'.hf.b' [ d - ½ hf ]
Mn = 0.85 fc'.1.yb.bw.d - ½ 0.85 fc'.².yb².bw + 0.85 fc'.hf.b'. [ d - ½ hf ]
+ 0.85 fc'.hf.b'. [ d - ½ hf ] … kedua ruas dibagi bw.d²
xMn = 0.85 fc'.1. bw.d - ½ 0.85 fc'.².bw. [ - f ]
f
[ - f ] fy.d
0.85. fc'.1
fy.d
0.85. fc'.1
= 0.85.1600
600 + fy+
2
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST
-
8/17/2019 CATATAN KULIAH BETON2
4/10
0.85 fc'.1. bw.d - ½ 0.85 fc'.².bw.
+ 0.85 fc'.hf.b'. [ d - ½ hf ]/bw.d² … Mn/bw.d² = Rn
0.85 fc'.1. ½ 0.85 fc'.².bw.d²
+ 0.85 fc'.hf.b'. [ d - ½ hf ]/bw.d²
fy
Rn = bw.d² -bw.d²
[ - f ]½ 0.85 fc'.².
[ - f ]
Rn = 0.85 fc'.1. [ - f ] fy
-
[ - f ] fy
x0.85. fc'.1
fy
0.85. fc'.1bw.d²
bw.d²= [ - f ]
fy.d
0.85. fc'.1bw.d²
Mnx
bw.d²[ - f ]
fy.d
0.85. fc'.1
2
2
22
222
22
+ 0.85 fc'.hf.b'. [ d - ½ hf ]/bw.d²
0.85. fc'.10.85. fc'.1
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST
-
8/17/2019 CATATAN KULIAH BETON2
5/10
0.85 fc'.hf.b' [ d - ½ hf ]
0.85 fc'.hf.b' fy [d - ½ hf]
d
f.fy … dimana w = - fd
f.fy
dRn =
d - ½ hf
w.fy w².fy²
+ d - ½ hf1.7 fc'
Rn = [ - f ].fy - [ - f ]fy²
+1.7 fc'
bw.d²
… suku ketiga dikalikan 1
dg variable fy/fy
Rn = [ - f ].fy - [ - f ]fy²
+1.7 fc' fy.bw.d
Rn = [ - f ][ - f ].fy -fy²
1.7 fc'+
2
2
2
f.fy ===> Pers. Kuadrat (PK) dalam variable w
d
d - ½ hfRn - = 0fy²
1.7 fc'
w² - fy.w. +
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST
-
8/17/2019 CATATAN KULIAH BETON2
6/10
f.fy
d
dari pers di atas diperoleh
f.fy
d
fy².² - 2..f.fy² + fy².f² f.fy
1.7 fc' 1.7 fc' dd - ½ hf+
Rn =fy²
1.7 fc'.fy - f.fy - (² - 2..f + f²)
fy²+
Rn =
+ d - ½ hf
.fy - f.fy -1.7 fc'
Rn = [ - f ].fy - [ - f ] d - ½ hf1.7 fc'
2
Pers. Kuadrat (PK) dalam variable (Untuk Tulangan Tunggal)
+++=2
dd
y
1.7fc'
y.fyfy.
1.7fc'
.y2
1.7fc'
yRn f f
2f f
f 2
+
++=
2
hd
d
fy
1.7fc'
fy.fy
1.7fc'
.fy2
1.7fc'
fyRn f f
2f
2
f f
22
2
fy
0Rn2
hd.
d
fy
1.7fc'
fy.fy
1.7fc'
.2.fy
1.7fc'
fy f f
2f
2
f f
22
2
=
+
+
+
fy
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST
-
8/17/2019 CATATAN KULIAH BETON2
7/10
As = As1 + As2 + Asf
BALOK "T" DENGAN TULANGAN GANDA
d'
s
0.85.f
0.003
0.85.f
s'
bw
dh
be
y
d -y
Ts1
Tsf
Ts2
CcCf Csh a
As
As'=
'=
Dengan kesetimbangan gaya-gaya diperoleh pers sbb :
H = 0As.fyAs'.fy.b'0.85fc'.h.b.y0.85fc'. f w b1 =++
.b'0.85fc'.h).fyAs'(As.b.y0.85fc'. f w b1 =
w1
f
w1 .b0.85.fc'.
.b'0.85.fc'.h
.b0.85fc'.
).fyAs'(Asy
=
w1
f
w1 .b
.b'h
.b0.85.fc.
).fyAs(1y
=
w1
f
1 .b
.b'h
0.85.fc.
).fy.d(1y
=
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST
-
8/17/2019 CATATAN KULIAH BETON2
8/10
Atau y dihitung dg cara sbb :
selanjutnya y = yb ingat '/ =
.fyAs).fyAs'(As.b.y0.85.fc'. f w b1
=
w1
f
.b0.85.fc'.
).fyAsAs'(Asy
=
1w
f
0.85.fc'.
fy.d.
.d b
)AsAs'(Asy
=
1
f
0.85.fc'.
fy.d).'(y =
f .d
1
f b0.85.fc'.
..y =
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST
-
8/17/2019 CATATAN KULIAH BETON2
9/10
Tinjauan dg Mn untuk mendapatkan pers
( - . - f). fy.d ( - . - f). fy.d
0.85.fc'.1 0.85.fc'.1
Mn = ( - . - ).fy.d².bw - ½.0.85.fc'.1².bw.( - . - f)² fy² kedua ruas dibagi dg bw.d²
Mn = 0.85.fc'.1.d.bw + Asf.fy.(d - ½.hf) + .As.(d - d').fy- ½.0.85.fc'.1².bw.
+ Asf.fy.(d - ½.hf) + .As.(d - d').fy0.85².fc'².1²
2
).fyd'.As.(d2
hd.fy.As
2
.yd.b.y0.85.fc'.Mn f
f
b1
w b1 +
+
=
).fyd'.As.(d2
hd.fy.As.y.b.fc'.
2
0.85.y.d.b0.85fc'.Mn
f
f
2
bw
2
1 bw1 +
+=
- . - f y. . w - - . - f . y .
Asf.fy.(d - ½.hf) + .As.(d - d').fy
f fy (d - hf/2) + . fy (d - d')
d d
f fy (d - hf/2) + . fy (d - d')
d d
Rn = +bw.d² 1.7.fc'.d².bw
[Asf.fy.(d - ½.hf) + .As.(d - d').fy]/bw.d²
+bw.d²bw.d²
Rn =fy²
1.7.fc'( - . - f) fy - ( - . - f)².
Rn = ( - . - f) fy - ( - . - f)².fy²
+1.7.fc'
Rn = +.fy - ..fy - f.fy - (² - 2.² - 2..f + 2...f + ².² + f² ) ²fy
1.7.fc'
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST
-
8/17/2019 CATATAN KULIAH BETON2
10/10
f fy (d - hf/2) + . fy (d - d')
d d
Rn = .fy (1 - ) - f.fy - (fy²/1.7fc'). (1 - 2 + ²).² + (2.fy² / 1.7.fc') (f - .f). - (fy² f²/1.7.fc') + f.fy/d.(d - hf/2) + [ .(d - d').(fy/d) ].
fy f fy
d d
Pers. Kuadrat (PK) dalam variable ( Untuk Tulangan Ganda )
= 0+ Rn+ (d - ½.hf)+fy².f²
1.7.fc'- +² fy.(1 - ) + .(d - d')
2.fy².(f - .f)
1.7.fc'f.fy
+
fy².(1 - 2. + ²)
1.7.fc'-
Rn = .fy - ..fy - f.fy - (².(1 - 2 + ²) - 2..(f + .f) + f² ) ²fy
1.7.fc'
THE "T" FORMULA FROM ANDREZ_KO Created by : SONDRA RAHARJA, ST from ANDRE NOVAN, ST