Soal 2 P1=
q=
12 kN
4I
2I
E
P2=
9,6 kN/m
B
A 6
L2=
2m
C
m
8
L3=
32 kN
3I
F
m
D
3
3
Gambarkan Diagram M&D utk balok diatas !
Penyelesaian : Membuat Diagram M akibat beban luar 76,8 kNm
1/8*q*L2 =
P2*L/4=
A1
A2
A2=1/2*L*
A1=1/12*q*L3 A1 =
48 kNm
409,6 m2
A2=
48
144 m2
Data : P1 P2 q
= = =
Diperoleh : A1 A2 MA MD
= = =
12 kN 32 kN 9,6 kNm
409,6 144 -24 0
Jarak L1 Jarak L2 Jarak L3 Jarak L4
= = = =
2 6 8 6
m m m m
a3 a4
= =
4m 3m
m2 m2 kNm kNm
L1 L1 L 2 L 2 6A1a1 6A2a 2 6EhA 6EhC 2M M B c I 2 L1I1 L2 I 2 L1 L2 I1 I1 I 2
MA
akibat bbn luar
akibat penuru penurunan nan
Terapkan pers. Clapeyron pd bentang AB & BC: MA
-24
-24
[
6 ---2I
]
[
6 ---2I
]
+
[
6 ---2I
]
+
+
2MB
2MB
2MB
[
6 ---2I
+
[
12 ---4I
+
[
20 ---4I
]
8 ---4I
]
8 ---4I
]
+
+
+
MC MC
MC MC
MC
[
8 ---4I
]
=
[
8 ---4I
]
=
[
8 ---4I
]
=
6x 409,6 - ----------------4 Ix
9830,4 - ----------------32
307,2 - ----------------I
x 8
4 6x 144,0 x 3 - ----------------3 Ix 6
I
2592,0 - ----------------18
1 4 4 ,0 - ----------------I ---------------------------------------
dikali I
Se ngga Men a ( 3
-24
)
: +
-72
(
2MB
+
(
5 ) + MC
)
2
=
-307,2
-
10 MB 10 MB
+ +
2 MC 2 MC
= =
-307,2 -307,2 -
10 MB 5 MB
+ +
2 MC MC
= =
-235,2 -117,6
0,0 0,0
+
72
___________________
Pers. (1)
Bentang BC & CD
+
2 MC
[
8 ---4I
+
6 ---3I
]
+
MD
[
]
+
2 MC
[
24 ---12 I
+
24 ---12 I
]
+
MD
[
]
+
2 MC
[
48 ---12 I
+
MD
[
[
8 ---4I
]
MB
[
8 ---4I
MB
[
8 ---4I
MB
Men a
=
6x 409,6 x - ----------------------4 Ix 8
2
]
=
9830,4 - ----------------32 I
2
]
=
307,2 - ----------------I
4 -
6x 144,0 x --------------------------3 I x 6
-
2592 -----------------18 I
144,0 -----------I ---------------------------------------
3
-
dikali I
: ( 2
MB
]
]
6 ---3I
)
+
(
2 MC
4 ) +
2MD
=
-307,2
-
144,0
-
144,0 144,0
2 MB 2 MB
+ +
8 MC + 8 MC +
2 MD 2 MD
= =
-307,2 -307,2
2 MB
+
8 MC +
2 MD
=
-451,2
MB
+
4 MC
MD
=
-225,6 ___________________
+
Pers. (2)
Bentang CD & DD'
MC
[
6 ---3I
]
+
2 MD
[
6 ---3I
+
+
MC
[
6 ---3I
]
+
2 MD
[
6 ---3I
MC
[
6 ---3I
]
+
2 MD
[
6 ---3I
Men a
0 ---I
]
+
0
]
+
]
MD'
[
0 ----
]
=
-
]
=
-
~
MD'
=
[
0
6x 144,0 x --------------------------3 I x 6
3
2592 -----------18
144,0 -----------I
-
---------------------------------------
: MC
(
2
) +
2 MD
(
2 )
=
-144,0
2 MC
+
4 MD 4 MD
= =
-144,0 -144,0
2 MC
+
4 MD
=
-144,0
0,5 MC
+
2 MD
=
-36,0 ___________________
Pers. (3)
dikali I
Sederhanakan Pers. (1); (2) dan (3) 5 MB
+
MC
MB
+
4 MC
+
0,5 MC
+
=
-117,60
-------------- Pers. (1)
MD
=
-225,60
-------------- Pers. (2)
MD
=
-36,00
-------------- Pers. (3)
=
-117,6 -36,00 (+)
Tambahkan Pers. (1) dan (3) 5 MB
5 MB
+
MC
+
0,5 MC
+
MD
=
1,5 MC
+
MD
=
-153,60
-------------- Pers. (4)
Kurangkan Pers. (2) dan (4) 1 MB
+
4 MC
+
MD
=
-225,6
5 MB
+
1,5 MC
+
MD
=
-153,6 (-)
-4 MB
+
2,5 MC
=
-72
-117,6 -72
-------------- Pers. (5)
Sederhanakan Pers. (5) dan (1) 5 MB -4 MB
+ +
1 MC 2,5 MC
= =
12,5 MB -4 MB
+ +
2,5 MC 2,5 MC 16,5 MB
= = =
-294 -72 (-) -222,00
MB
=
MB
=
-222,00 16,5 -13,45
MC MC MC MC
= = = =
-72 -72 -72 -72
MC
=
-125,82 2,5 -50,33
-4 MB -4 -13,45 53,8182
+ + +
2,5 2,5 2,5 2,5
=
0,5 MC 0,5 -50,33 -25,164
+ + +
1 MD 1 MD MD MD MD
= = = = =
x 2,5 x 1
-
-36,0 -36,0 -36,0 -36,0 + -10,84
53,82
25,16
sehingga diperoleh : MB MC MD
= = =
-13,45 kN.m -50,33 kN.m -10,84 kN.m
Ceck menggunakan Pers. (2) MB -13,45
+ +
4 MC 4
-50,33
+
MD = -10,84 =
-225,6 -225,60
-22 5,6 =
-225 ,6 0
______
OK !!!
Free Body P1= 12
kN
M A
M A
MBA
A A
E
B
q=
MBc B
12
9,6
9,6*8/2 13,45/8 50,33/8
38,4 1,68 6,29
33,79
43,01
momen ujung
12,00
MDC=
50,33
D
13,45 kN.m
MC= 50,33
kN.m
38,40
38,40
16,00
16,00
2,00
2,00
1,68
1,68
8,39
8,39
2,24
2,24
6,29
6,29
2,67
2,67
1,81
1,81
23,53
8,47
33,79
43,01
reaksi ujung Total RA= 13,76
RB=
32,03
RC=
66,54
RD=
CHECK !!! RA + RB + RC + RD 13,76 +
32,03 +
66,54 +
=
q.L + P1 + P2
8,47 =
76,8
120,80 =
120,80
Momen Maksimum
Bentang BC M x=RB(x)-½q (x)2 x=RB-q.(x)=0
→D
x=
x=
Rb q 32,03 ------ = 10
3,34 m
dari Titik B
Mmak=Ra.(x)-½(q)(x)2 Mmax = 32,03 x = 106,89 = 53,445
3,34 53,445 kNm
-
3 50,33
-
0,5 x
Bentang CD MC=RCD(2)-MCD = 23,53 x = 70,582 = 20,25 KnM
50,33
9,6
D'
D
MD=
2,00
1,76
MD'D
6
2,00
1,76
MDD'= 10,84
10,84
~
8
MB=
12,00
kN
C
24,00 kN.m
reaksi Ujung akibat beban yg bekerja reaksi ujung akibat
P2 = 32
MCB MCD=
6
MA=
kN/m
3,3 ^2
32
12,0
ok …!!!
8,47
10,84 kN.m
P1=
q=
12 kN
E
2Ic
A
L2=
2m
P2=
9,6 kN/m
4Ic
B
L3=
6
C
32 kN
3Ic
F
8 m
D
3
3
50,33
24
Diagram
13,45
10,84
(-)
Bidang Momen
(-)
(-) (+)
(+)
Mmax =
20,25
53,44
Diagram 32,03
Bidang Lintang
1,76
(+) (-) 12,0
23,53
(+)
(+) (-) (-)
8,47
43,01
CHECKING dengan Program STAAD-PRO P2 =32 kN
q = 9,6 kN/m P1 =12 kN
D
C
B
A
DIAGRAM BID. MOMEN
DIAGRAM BID. LINTANG
REAKSI PERLETAKAN B
A
D
C
HASIL PERBANDINGAN CARA MANUAL DAN PROGRAM STAAD-PRO
GAYA RA RB RC RD MA MB MC
MANUAL 13,758 32,033 66,536 8,473 -24 -13,455
STAAD-PRO 13,75 32,057 65,54 9,452 -24 -13,498
SELISIH 0,008 0,024 0,996 0,979 0,000 -0,043
-50,327
-50,237
0,090
MD
-10,836
-10,949
-0,113
............OK !!!
