Tug.xlsx
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Gambar
Penyelesaian
L a b P
= = = =
8.12 5.06 3.06 0.6
m m m ton
: ● Mencari Ra ∑MB = 0 RA1 L ( P b ) RA1 8.12 ( 0.6 3.06 ) RA1 8.12 ( 1.8 ) RA1 = 1.836 8.12 RA1 = 0.226 ton ● Mencari Ra ∑MA = 0 RB1 L ( P a ) RB1 8.12 ( 0.6 5.06 ) RB1 8.12 ( 3.0 ) RB1 = 3.036 8.12 RB1 = 0.374 ton ● Check ∑KV = 0 ( RA + RB ( 0.23 + 0.37
) ) 0.6
● MOMEN ME = ME = ME =
RA x a 0.226 x 5.06 1.144 ton m
-
P 0.6 0.6 0
= = =
0 0 0
= = =
0 0 0
= = = =
0 0 0 0
Gambar
Penyelesaian
L c d q
= = = =
12.06 6.03 6.03 0.6
: ● Mencari Ra RB2 L RB2 12.06 RB2 12.06 RB2 12.06 RB2 12.06 RB2 = 32.72 12.06 RB2 = 2.714 ● Mencari Ra RC1 L RC1 12.06 RC1 12.06 RC1 12.06 RC1 12.06 RC1 = 10.91 12.06 RC1 = 0.905
m m m ton m ∑MB = 0 q c ( 0.6 6.03 ( 3.62 ( 3.62 9.0 33
RB2 RB2 2.7135 x = x
=
● Momen max
c + d ) 6.03 + 6.03 ) 3.0 6.03 )
∑MA = 0 q c ( 0.5 c ) 0.6 6.03 ( 0.5 6.03 ) 3.62 ( 0.5 6.03 ) 3.62 3.015 11
0 0 0 0 0
= = = = =
0 0 0 0 0
ton
) ) 3.618
-
2
x
q x c 0.6 x 6.03 3.618 0
0
0.5 q 0.6 2.714 0.6 4.523
= = = = =
ton
● Check ∑KV = 0 ( RB2 + RC1 ( 2.7135 + 0.9
● Mencari titik x dmx = dx
0.5 0.5
q x x
m
= = =
0 0 0
= = = =
0 0 0 0 OK
Mx Mx Mx Mx
= = = =
RA x 2.714 4.52 12.27 6.1 Tm
-
P P P
= = =
q x c 0.6 x 6.03 3.618 ton m
0.5 0.5 6.1359
q x x 0.6 4.52 4.52
0.097 0.6 0.697 3.34
2.643 3.618 0.975 4.192
3.217 5.436 2.219 3.618
5.436
Gambar Penyelesaian
L q
= =
9.06 m 0.6 ton m
: ● Mencari Ra RC2 L RC2 9.06 RC2 9.06 RC2 9.06 RC2 = 24.63 9.06 RC2 = 2.718 ● Mencari Ra RD1 L RD1 9.06 RD1 9.06 RD1 9.06 RD1 = 24.63 9.06 RD1 = 2.718
∑MB = 0 q L 0.6 9.06 5.436 x 24.63
RC2 RC2 2.718 x
=
x
=
L ) 9.06 )
= = = =
0 0 0 0
( 0.5 ( 0.5 4.5
L ) 9.06 )
= = = =
0 0 0 0
ton ∑MA = 0 q L 0.6 9.06 5.436 x 24.63
ton
● Check ∑KV = 0 ( RC2 + RD1 ( 2.718 + 2.718
● Mencari titik x dmx = dx
( 0.5 ( 0.5 4.5
) ) 5.436
-
2
x
q x L 0.6 x 9.06 5.436 0
0
0.5 q 0.6 2.718 0.6 4.5
q x x
= = =
0 0 0
m
● Momen max Mx Mx Mx Mx
= = = =
RA x 2.718 4.53 12.31 6.2 Tm
-
0.5 0.5 6.15627
q x x 0.6 4.53 4.53
= = = =
0 0 0 0 OK
Mencari momen primer gaambar diketahui : P = l1 = l2 = l3 = a = b = c = d = AB = BC = CD =
0.6 8.12 12.06 9.06 5.06 3.06 6.03 6.03 2.6 EI 1.6 EI 1.6 EI
qBC = Qcd =
PENYELESAIAN Mab = P = = =
a b^2 l1^2 0.6 5.06 9.36 65.9 28.43 65.93 0.431 tm +
Mba = P = = = Mbc = = = = Mcb = = = =
a^2 b l1^2 0.6 25.6 3.06 65.9 47 65.93 -1 tm 11 q
l2^2
192 11 0.6 145 192 960 192 5.0 tm + 5q
l2^2
192 5 0.6 145 192 436 192 -2 tm -
0.6 0.6
Mcd =
= =
1 8 0.125 6.156 tm
q
l3^2
0.6 82.0836 +
ANGKA STIFFNESS K1
=
EI l
=
2.6 8.12 0.320197
= K2
=
EI l
=
1.6 12.06 0.13267
= K3
= = =
ANGKA DISTRIBUSI B = ba ®
EI l 1.6 9.06 0.13245
bc
®
3 4 3 4 totsl
C
=
cb
®
cd
®
total
K1
=
K1 + K2 0.3201970443 0.320197 + 0.13267
K1 =
= = K2
=
K2 K1 + K2 = 0.1326699834 0.320197 + 0.13267 = = =
K2
0.13267 0.452867 0.292956 1
=
K2 K2 + K3 = 0.13267 0.13267 + 0.13245 =
K3
0.320197 0.452867 0.707044
=
0.13267 0.26512 0.500414
=
K3
K2 + K3 = 0.13245 0.13267 + 0.13245 = = =
0.13245 0.26512 0.499586 1
TABEL CROSS Buhul Batang Angka distr M primer
∑M
Mencari Reaksi A,B,C,D A ab -
B ba bc cb -0.7070 -0.2930 0.431 -1 5 -0.250 -1.427 -2.854 -1.183 0.148 -0.0523 -0.1046 -0.043 0.005 -0.0019 -0.0038 -0.002 0.000 -1.050 -3.675 3.676
C cd -0.500 -0.500 -2 6.156 -1.9435 -1.940 -0.591 0.296 0.295 -0.022 0.011 0.011 -0.001 0.000 0.000 -4.523 4.523
RA = RA1 = = =
+ 0.226 +
0.226 + -0.097 TON
RB = RB1
+
=
0.374 +
= =
0.374 + 3.340
RB = RC1
+
=
0.90 +
= =
0.90 + 4.19
RD = RD1
a
-
=
2.718 -
= =
2.718 2.219
= Mab
+
=
1.050 +
= = =
1.050 + 1.050 + 2.686 tm
Mma= ME = 1.144108 = -1.542 tm RB ki= P
-
= =
0.6 0.697 t
RB k = RB = 3.340 = 2.643 t
Reaksi A,B,C,D MA l1
Mencari x dmx = dx
- MB l1 1.050 3.676 8.12 8.12 0.129 0.453
0 RB kanan 2.643 -
TON RB2
- MA l1 2.714 2.714
+ MB l1 1.050 + 8.1 0.129 +
+ MB l2 3.675 + 8.1 0.453 +
-
3.676 12.1 0.305 -
TON RC2
- MB l2 2.72 2.72
+ MC l2 3.68 + 12.06 0.30 +
+ MC l3 4.52 + 12.06 0.38 +
TON MC l3 4.523 9.06 0.499 TON a ( Mba - Mab ) l1 5.06 ( 3.675 1.050 ) 8.12 0.623153 ( 2.625 ) 1.635964 tm a 2.686 tm RA
4.52 9.06 0.50
MC l2 4.523 12.1 0.375
Mmax2
= RB kanan = 2.643 = 11.6445 = 1.94075
b
= x
.
-0.097
RB kiri 0.697
q
x 0.6 x 2.643 0.6 4.405394 m,
X 4.405394 9.703748
MC
+
= = =
0 0 x
=
x 0.5 X^2 0.5 19.4075
0.7552 7.2617
Penyelesaian
L a b P
= = = =
8.12 5.06 3.06 0.6
m m m ton
: ● Mencari Ra ∑MB = 0 RA1 L ( P b ) RA1 8.12 ( 0.6 3.06 ) RA1 8.12 ( 1.8 ) RA1 = 1.836 8.12 RA1 = 0.226 ton ● Mencari Ra ∑MA = 0 RB1 L ( P a ) RB1 8.12 ( 0.6 5.06 ) RB1 8.12 ( 3.0 ) RB1 = 3.036 8.12 RB1 = 0.374 ton ● Check ∑KV = 0 ( RA + RB ( 0.23 + 0.37
) ) 0.6
● MOMEN ME = ME = ME =
RA x a 0.226 x 5.06 1.144 ton m
-
P 0.6 0.6 0
= = =
0 0 0
= = =
0 0 0
= = = =
0 0 0 0
Gambar
Penyelesaian
L c d q
= = = =
12.06 6.03 6.03 0.6
: ● Mencari Ra RB2 L RB2 12.06 RB2 12.06 RB2 12.06 RB2 12.06 RB2 = 32.72 12.06 RB2 = 2.714 ● Mencari Ra RC1 L RC1 12.06 RC1 12.06 RC1 12.06 RC1 12.06 RC1 = 10.91 12.06 RC1 = 0.905
m m m ton m ∑MB = 0 q c ( 0.6 6.03 ( 3.62 ( 3.62 9.0 33
RB2 RB2 2.7135 x = x
=
● Momen max
c + d ) 6.03 + 6.03 ) 3.0 6.03 )
∑MA = 0 q c ( 0.5 c ) 0.6 6.03 ( 0.5 6.03 ) 3.62 ( 0.5 6.03 ) 3.62 3.015 11
0 0 0 0 0
= = = = =
0 0 0 0 0
ton
) ) 3.618
-
2
x
q x c 0.6 x 6.03 3.618 0
0
0.5 q 0.6 2.714 0.6 4.523
= = = = =
ton
● Check ∑KV = 0 ( RB2 + RC1 ( 2.7135 + 0.9
● Mencari titik x dmx = dx
0.5 0.5
q x x
m
= = =
0 0 0
= = = =
0 0 0 0 OK
Mx Mx Mx Mx
= = = =
RA x 2.714 4.52 12.27 6.1 Tm
-
P P P
= = =
q x c 0.6 x 6.03 3.618 ton m
0.5 0.5 6.1359
q x x 0.6 4.52 4.52
0.097 0.6 0.697 3.34
2.643 3.618 0.975 4.192
3.217 5.436 2.219 3.618
5.436
Gambar Penyelesaian
L q
= =
9.06 m 0.6 ton m
: ● Mencari Ra RC2 L RC2 9.06 RC2 9.06 RC2 9.06 RC2 = 24.63 9.06 RC2 = 2.718 ● Mencari Ra RD1 L RD1 9.06 RD1 9.06 RD1 9.06 RD1 = 24.63 9.06 RD1 = 2.718
∑MB = 0 q L 0.6 9.06 5.436 x 24.63
RC2 RC2 2.718 x
=
x
=
L ) 9.06 )
= = = =
0 0 0 0
( 0.5 ( 0.5 4.5
L ) 9.06 )
= = = =
0 0 0 0
ton ∑MA = 0 q L 0.6 9.06 5.436 x 24.63
ton
● Check ∑KV = 0 ( RC2 + RD1 ( 2.718 + 2.718
● Mencari titik x dmx = dx
( 0.5 ( 0.5 4.5
) ) 5.436
-
2
x
q x L 0.6 x 9.06 5.436 0
0
0.5 q 0.6 2.718 0.6 4.5
q x x
= = =
0 0 0
m
● Momen max Mx Mx Mx Mx
= = = =
RA x 2.718 4.53 12.31 6.2 Tm
-
0.5 0.5 6.15627
q x x 0.6 4.53 4.53
= = = =
0 0 0 0 OK
Mencari momen primer gaambar diketahui : P = l1 = l2 = l3 = a = b = c = d = AB = BC = CD =
0.6 8.12 12.06 9.06 5.06 3.06 6.03 6.03 2.6 EI 1.6 EI 1.6 EI
qBC = Qcd =
PENYELESAIAN Mab = P = = =
a b^2 l1^2 0.6 5.06 9.36 65.9 28.43 65.93 0.431 tm +
Mba = P = = = Mbc = = = = Mcb = = = =
a^2 b l1^2 0.6 25.6 3.06 65.9 47 65.93 -1 tm 11 q
l2^2
192 11 0.6 145 192 960 192 5.0 tm + 5q
l2^2
192 5 0.6 145 192 436 192 -2 tm -
0.6 0.6
Mcd =
= =
1 8 0.125 6.156 tm
q
l3^2
0.6 82.0836 +
ANGKA STIFFNESS K1
=
EI l
=
2.6 8.12 0.320197
= K2
=
EI l
=
1.6 12.06 0.13267
= K3
= = =
ANGKA DISTRIBUSI B = ba ®
EI l 1.6 9.06 0.13245
bc
®
3 4 3 4 totsl
C
=
cb
®
cd
®
total
K1
=
K1 + K2 0.3201970443 0.320197 + 0.13267
K1 =
= = K2
=
K2 K1 + K2 = 0.1326699834 0.320197 + 0.13267 = = =
K2
0.13267 0.452867 0.292956 1
=
K2 K2 + K3 = 0.13267 0.13267 + 0.13245 =
K3
0.320197 0.452867 0.707044
=
0.13267 0.26512 0.500414
=
K3
K2 + K3 = 0.13245 0.13267 + 0.13245 = = =
0.13245 0.26512 0.499586 1
TABEL CROSS Buhul Batang Angka distr M primer
∑M
Mencari Reaksi A,B,C,D A ab -
B ba bc cb -0.7070 -0.2930 0.431 -1 5 -0.250 -1.427 -2.854 -1.183 0.148 -0.0523 -0.1046 -0.043 0.005 -0.0019 -0.0038 -0.002 0.000 -1.050 -3.675 3.676
C cd -0.500 -0.500 -2 6.156 -1.9435 -1.940 -0.591 0.296 0.295 -0.022 0.011 0.011 -0.001 0.000 0.000 -4.523 4.523
RA = RA1 = = =
+ 0.226 +
0.226 + -0.097 TON
RB = RB1
+
=
0.374 +
= =
0.374 + 3.340
RB = RC1
+
=
0.90 +
= =
0.90 + 4.19
RD = RD1
a
-
=
2.718 -
= =
2.718 2.219
= Mab
+
=
1.050 +
= = =
1.050 + 1.050 + 2.686 tm
Mma= ME = 1.144108 = -1.542 tm RB ki= P
-
= =
0.6 0.697 t
RB k = RB = 3.340 = 2.643 t
Reaksi A,B,C,D MA l1
Mencari x dmx = dx
- MB l1 1.050 3.676 8.12 8.12 0.129 0.453
0 RB kanan 2.643 -
TON RB2
- MA l1 2.714 2.714
+ MB l1 1.050 + 8.1 0.129 +
+ MB l2 3.675 + 8.1 0.453 +
-
3.676 12.1 0.305 -
TON RC2
- MB l2 2.72 2.72
+ MC l2 3.68 + 12.06 0.30 +
+ MC l3 4.52 + 12.06 0.38 +
TON MC l3 4.523 9.06 0.499 TON a ( Mba - Mab ) l1 5.06 ( 3.675 1.050 ) 8.12 0.623153 ( 2.625 ) 1.635964 tm a 2.686 tm RA
4.52 9.06 0.50
MC l2 4.523 12.1 0.375
Mmax2
= RB kanan = 2.643 = 11.6445 = 1.94075
b
= x
.
-0.097
RB kiri 0.697
q
x 0.6 x 2.643 0.6 4.405394 m,
X 4.405394 9.703748
MC
+
= = =
0 0 x
=
x 0.5 X^2 0.5 19.4075
0.7552 7.2617
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