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a = 1.2 m P1 = 1 t Semua Penampang batang : A
b = 1.2 m Modulus elastisitas baja : E
PERHITUGAN REAKSI PERLETAKAN
∑MA = 0
- RB x (a+a+a+a+a+a) + PF x (b+b) = 0
- RB x 7.2 + 2.4 = 0
RB x 7.2 = 2.4
RB = 0.333333 t (↑)
∑MB = 0
RA x (a+a+a+a+a+a) + PF x (b+b)
RA x 7.2 + 2.4
RA x 7.2 + 2.4 = 0
RA = 0.333333 t ()
KONTROL (∑V)
∑V = 0
RA - RB = 0
0.333333 - 0.3333333 = 0
0 = 0 TERKONTROL
AB
b
b
b
b
b
a a a a a a
P1
DC
FE
HG
JI
K L N P R T U
M O Q S
W
Y
AA
V
X
Z
AB
1 2
9
5 634
87 10
12
1311 1
4
15
17
1618 19
20
21
22
25
24
26
2729
28
30
3331
32
34
36
383735
3940 4243
44
48
5253
51
4746
45
4950
23
41
P
∑H = 0
HA + PF = 0
HA + 1 = 0
HA + 1 = 0
HA = -1 t
HA = 1 t (←)
Simpul A
∑H = 0
S2 COS 45.00 + HA
S2 0.71 + 1
S2 0.71 = -1
A S2 = -1.414
HA S2 = 1.414 tekan
∑V = 0
S1 + S2 SIN 45.00 + RA
S1 + -1.14 + -0.333
S1 + -1.473
TANα = b S1 = -1.47
a S1 = 1.47 (↓) tekan
= 1
α = 45.00
simpul C
= 0
S3 S4 = 0
C S4 = 0
S3 - S1 = 0
S3 = S1
S1 S3 = 1.47 tarik
simpul D
= 0
S2 X COSα + S5 X COSα - S4
S5 1.00 + S5 X 0.71 - 0
S6 S5 X 0.7071 = -1.00
S4 S5 = -1.41
S5 = 1.41 tarik
S2 COSα
= 0
S2 S2 X SINα - S5 X SINα + S6
1 - 1 + S6
S6 = 0
TINJAU GAYA HORISONTAL(∑H)
∑H
∑V
∑H
∑V
RA
S1 S2
simpul F
S10 = 0
S9 = -1
S9 P = 0
S10 - S6 = 0
S10 = S6
S10 = 0
S6
simpul E
S7 ∑H = 0
S8 SINα S9 + S8 X COSα - S5 X COSα
S8 -1 + S8 X 0.707 - 1
S8 COSα S8 X 0.7071 = 1
S9 S8 = 1.4142 tarik
S5 COSα = 0
S5 S7 + S8 X SINα - S3 - S5 X SINα
S7 + 1 - 1.47 - 1
S5 SINα S7 - 1.47
S3 S7 = 1.47 tarik
simpul G
S11 = 0
S12 = 0
S12 = 0
S12
∑V = 0
S11 + S7 = 0
S7 S11 = -1.47
S11 = 1.47 tekan
simpul H
S13 S14 ∑H = 0
S13 SINα S12 - S13 X COSα - S8 X COSα
0.00 - S13 X 0.707 - 1
S13 COSα - S13 X 0.7071 - 1.00
S12 - S13 = 1.4142
S8 COSα S13 = 1.4142 tekan
∑V = 0
S8 S8 SINα S14 + S6 + S8 X SINα - S13 X SINα
S6 S14 + 0 + 1 - 1
S14 + 0
S14 = 0
∑H
∑V
∑V
∑H
simpul K
∑H = 0
S17 = 0
∑V = 0
S15 = 0
S17 S15 = 0
S15
simpul I
S15
S16 SINα ∑V = 0
S16 S16 X SINα + S15 - S13 X SINα - S11 = 0
S16 X 0.7071 + 0 - 1 - 1.47 = 0
P1 S16 COSα S16 X 0.7071 - 2.47 = 0
S18 S16 X 0.707 = 2.47
S16 = 3.4978 tarik
S13 COSα
S13 = 0
S18 + S16 X COSα - P1 - S13 X COSα = 0
S11 S13 SINα S18 + 2.4733 - 1 - 1 = 0
S18 - -0.473
S18 = -0.473
S18 = 0.4733 tekan
simpul J
= 0
S19 S22 - S18 = 0
S22 = S18 = 0
S22 = 0.47 tarik
S18 S22
S14 = 0
S19 + S14 = 0
S19 = 0
simpul L
= 0
S21 X SINα + S19 + S16 X SINα
S21 X 0.7071 + 0 + 0.335
S21 X 0.7071 + 0.335
S21 X 0.7071 = -0.335
S21 = -0.473
S17 S20 S21 = 0.4733 tekan
S16 S21 = 0
S20 + S17 + S16 X COSα + S21 X COSα
S19 S20 + 0 + 0.335 + 0.33
S20 + 0.67
S20 = -0.67
S20 = 0.67 tekan
simpul N
= 0
S24 - S20 = 0
S24 = 0.67 tarik
∑V = 0
S20 S24 S23 = 0
S23
∑H
∑H
∑V
∑V
∑H
∑H
simpul M
S21 S23 S25 SINα S25 ∑V = 0
S21 SINα S25 X SINα + S23 - S21 X SINα = 0
S25 X 0.7071 + 0 - 0.335 = 0
S21COSα S25 COSα S25 X 0.7071 = 0
S22 S26 S25 = 0
∑H = 0
S26 + S25 X COSα - S21 X COSα - S22 = 0
S26 + 0 - 0.335 - 0.00 = 0
S26 - 0.335
S26 = 0.335 tarik
simpul O
S27
∑V = 0
S7 = 0
∑H = 0
S26 S30 S30 + S26 = 0
S30 = -0.335
S30 = 0.335 tekan
simpul P
∑V = 0
S29 X SINα + S27 + S25 X SINα
S29 X 0.7071 + 0 + 0
S29 X 0.7071 = 0
S24 S28 S29 = 0 tarik
S25COSα S29COSα
S25 S29 ∑H = 0
S25SINα S29SINα S28 + S24 + S25 X COSα + S29 X COSα = 0
S27 S28 + 0.67 + 0 + 0 = 0
S28 + 0.67 = 0
S28 = -0.67
S28 = 0.67 tekan
simpul R
∑V = 0
S31 = 0
S31 = 0
S28 S32 ∑H = 0
S32 - S28
S31 S32 = S28
S32 = 0.67 tarik
simpul Q
S33 SINα ∑V = 0
S29SINα S31 S33 X SINα + S29 X SINα + S31
S29 S33 S33 X 0.7071 + 0 + 0
S33 X 0.7071 + 0
S29 COSα S33 COSα S33 X 0.7071 = 0
S30 S34 S33 = 0
∑H = 0
S34 - S33 X COSα + S29 X COSα - S30
S34 - 0 + 0 - 0.33
S34 - 0.335
S34 = 0.335 tarik
simpul U
∑H = 0
S36 = 0
∑V = 0
S36 S38 = 0
S38 = 0
S38
simpul T
∑H = 0
S37 X COSα + S32 - S33 X COSα + S36 = 0
S37 X 0.7071 + 0.67 - 0.00 = 0
S37 X 0.7071 = 0
S32 S36 S37 = 0
S33 S37 ∑V = 0
S35 + S37 X SINα - S33 X SINα = 0
S35 S35 + 0 - 0 - 0 = 0
S35 - 0
S35 = 0
simpul S
S35 ∑V = 0
S40 + S35 = 0
S40 = S35
S40 = 0
S39 ∑H = 0
S34 S39 + S34 = 0
S39 = -0.335
S39 = 0.335 tekan
S40
simpul V
S38 ∑H = 0
S37 S41 X COSα + S37 X COSα - S39 = 0
S41 X 0.7071 + 0 - 0.33 = 0
S41 X 0.7071 = 0.335
S41 = 0.4733 tarik
S39
∑V = 0
S42 + S41 X SINα + S38 + S37 X SINα = 0
S41 S42 + 0.3347 + 0 + 0 = 0
S42 + 0.3347 = 0
S42 S42 = -0.335
S42 = 0.3347 tekan
simpul X
S42 ∑H = 0
S43 = 0
S43 ∑V = 0
S47 - S42
S47 = S42
S47 = 0.3347 tarik
S47
simpul W
S40 S41 ∑H = 0
S46 X COSα - S41 X COSα - S43
S46 X 0.7071 - 0.335 - 0
S46 X 0.7071 - 0.335
S43 S46 X 0.7071 = 0.335
S46 = 0.4733 tekan
S46 ∑V = 0
S44 + S41 X SINα - S40 - S46 X SINα
S44 S44 + 0.3347 - 0 - 0.335
S44 - 0
S44 = 0
simpul Y
= 0
S44 S45 = 0
S45 = 0
S48 + S44 = 0
S48 = 0
S48 S48 = 0
simpul Z
S46 S47 = 0
S49 X COSα + S45 - S46 X COSα
S49 X 0.7071 + 0 - 0.335
S45 S49 X 0.7071 = 0.335
S49 = 0.4733 tarik
∑V = 0
S49 S51 + S49 X SINα + S47 - S46 X SINα
S51 S51 + 0.3347 + 0.335 - 0.335
S51 + 0.3347
S51 = -0.335
S51 = 0.3347 tekan
simpul AB
S51 = 0
S50 = 0
S50 ∑V = 0
S53 - S51 = 0
S53 = S51
S53 = 0.3347 tarik
S53
simpul AA
S48 ∑H = 0
S49 S52 X COSα - S50 - S49 X COSα
S52 X 0.7071 - 0 - 0.335
S52 X 0.7071 = -0.335
S50 S52 = -0.473
S52 = 0.4733 tarik
S52
∑H
∑V
∑H
∑H
TABER GAYA-GAYA BATANG AKIBAT BEBAN SATUAN DITITK F
NO BATANG TARIK TEKAN
1 - 1473.30
2 1414.214 -
3 1473.30 -
4 0 0
5 1414.21 -
6 0 0
7 1473.30 -
8 1414.214 -
9 1000
10 0 0
11 - 1473.30
12 0 0
13 - 1414.21
14 0 0
15 0 0
16 3497.769 -
17 0 0
18 - 473.2962
19 0 0
20 - 669.34
21 - 473.2962
22 473.30 -
23 0 0
24 669.34 -
25 0 0
26 334.671 -
27 0 0
28 - 669.342
29 0 0
30 - 334.671
31 0 0
32 669.34 -
33 0 0
34 334.671 -
35 0 0
36 0 0
37 0 0
38 0 0
39 - 334.671
40 0 0
41 473.29623 -
42 - 334.671
43 0 0
44 0 0
45 0 0
46 473.2962
47 334.67097 -
48 0 0
49 473.29623 -
50 0 0
51 - 334.671
52 473.29623 -
53 334.67097 -
a = 1.2 m P1 = 1.7 t Semua Penampang batang : A
b = 1.2 m P2 = 1 t Modulus elastisitas baja : E
PERHITUGAN REAKSI PERLETAKAN
∑MA = 0
- RB x (a+a+a+a+a+a) + P1G x (b+b+b) + P1I x (b+b+b+b) + P2L x a + P2N X (a+a)
+ P2P x (a+a+a) + P2R x (a+a+a+a) + P2T x (a+a+a+a+a) + P2U x (a+a+a+a+a+a) = 0
- RB x 7.2 + 6.12 + 8.16 + 1.2 + 2.4 + 3.6 + 4.8 + 6 + 7.2
- RB x 7.2 + 39.48 = 0
RB = 5.483333 t (↑)
∑MB = 0
RA x (a+a+a+a+a+a) + P1G x (b+b+b) + P1I x (b+b+b+b) - P2K x (a+a+a+a+a+a) - P2L x (a+a+a+a+a)
- P2N x (a+a+a+a) - P2P (a+a+a) - P2R (a+a) - P2T x a = 0
RA x 7.2 + 6.12 + 8.16 - 7.2 - 6 - 4.8 - 3.6 - 2.4 - 1.2
RA x 7.2 + -10.92 = 0
RA = 1.516667 t (↑)
KONTROL (∑V)
∑V = 0
RA + RB - P2K - P2L - P2N - P2P - P2R - P2T - P2U = 0
1.516667 + 5.4833333 - 1 - 1 - 1 - 1 - 1 - 1 - 1 = 0
7 + -7 = 0
0 = 0 Terkontrol
∑H = 0
HA + P1G + P1I = 0
HA + 1.7 + 1.7 = 0
HA + 3.4 = 0
HA = -3.4 t
HA = 3.4 t (←)
Simpul A
S2 SINα ∑H = 0
S2 COS 45.00 - HA
S2 0.71 - 3.4
S2 0.71 = 3.4
A S2 COSα S2 = 4.808 tarik
HA
∑V = 0
S1 + S2 SIN 45.00 - RA
S1 + -3.876 - 1.516666667
S1 + 2.3592
S1 = -2.36
TANα = b S1 = 2.36 (↓) tekan
a
= 1
α = 45.00
simpul C
= 0
S3 S4 = 0
C S4 = 0
S3 - S1
S3 = S1
S1 S3 = 2.36 tekan
simpul D
S5 SINα = 0
S2 X COSα + S5 X COSα - S4
S5 3.400 + S5 X 0.71 - 0
S5 COSα S6 S5 X 0.7071 = -3.40
S4 S5 = -4.81
S5 = 4.81 tekan
S2 COSα
= 0
S2 S2 X SINα - S5 X SINα + S6
S2 SINα 3.4 - 3.4 + S6
S6 = 0
TINJAU GAYA HORISONTAL(∑H)
∑H
∑V
∑H
∑V
RA
S1 S2
simpul F
S10 = 0
S9 = 0
S9 = 0
S10 - S6 = 0
S10 = S6
S10 = 0
S6
simpul E
S7 ∑H = 0
S8 SINα S9 + S8 X COSα - S5 X COSα
S8 0 + S8 X 0.7071 - 3.4
S8 COSα S8 X 0.7071 = 3.4
S9 S8 = 4.8083 tarik
S5 COSα = 0
S5 S7 + S8 X SINα - S3 - S5 X SINα
S7 + 3.4 - 2.36 - 3.4
S5 SINα S7 - 2.36
S3 S7 = 2.36 tarik
simpul G
S11 = 0
S12 - P1
S12 = P1
P1 S12 S12 = 1.7 tarik
∑V = 0
S11 + S7 = 0
S7 S11 = -2.36
S11 = 2.36 tekan
simpul H
S13 S14 ∑H = 0
S13 SINα S12 - S13 X COSα - S8 X COSα
1.70 - S13 X 0.7071 - 3.4
S13 COSα - S13 X 0.7071 - 1.70
S12 - S13 = 2.4042
S8 COSα S13 = 2.4042 tekan
∑V = 0
S8 S8 SINα S14 + S6 + S8 X SINα - S13 X SINα
S6 S14 + 0 + 3.4 - 1.7
S14 + 1.7
S14 = -1.7
S14 = 1.7 tekan
simpul K
∑H = 0
P2 S17 = 0
∑V = 0
S15 - P2
17 S15 = P2
S15 = 1 tarik
15
∑H
∑V
∑V
∑H
simpul I
S15
S16 SINα ∑V = 0
S16 S16 X SINα + S15 - S13 X SINα - S11 = 0
S16 X 0.7071 + 1 - 1.7 - 2.36 = 0
P1 S16 COSα S16 X 0.7071 - 3.06 = 0
S18 S16 X 0.707 = 3.06
S16 = 4.3264 tarik
S13 COSα
S13 = 0
S18 + S16 X COSα - P1 - S13 X COSα = 0
S11 S13 SINα S18 + 3.0592 - 1.7 - 1.7 = 0
S18 + 0.3408
S18 = -0.341
S18 = 0.3408 tekan
simpul J
= 0
S19 S22 + S18 = 0
S22 = - S18
S22 = -0.34
S22 = 0.341 tekan
S18 S22
S14 = 0
S19 + S14 = 0
S19 = -1.7
S19 = 1.7 tekan
simpul L
= 0
S21 X SINα + S19 + S16 X SINα
P2 S21 X 0.7071 + 1.7 + 0.241
S21 X 0.7071 + 1.941
S21 X 0.7071 = -1.941
S21 = -2.745
S17 S20 S21 = 2.745 tekan
S16 S21 = 0
S20 + S17 + S16 X COSα + S21 X COSα
S19 S20 + 0 + 0.241 + 1.94
S20 + 2.18
S20 = -2.18
S20 = 2.18 tekan
simpul N
= 0
P2 S24 - S20 = 0
S24 = 2.18 tarik
∑V = 0
S20 S24 S23 - P2 = 0
S23 = P2
S23 S23 = 1 tarik
∑H
∑H
∑V
∑V
∑H
∑H
simpul M
S21 S23 S25 SINα S25 ∑V = 0
S21 SINα S25 X SINα + S23 - S21 X SINα = 0
S25 X 0.7071 + 1 - 1.941 = 0
S21COSα S25 COSα S25 X 0.7071 = 0
S22 S26 S25 = 0
∑H = 0
S26 + S25 X COSα - S21 X COSα - S22 = 0
S26 + 0 - 1.941 - 0.34 = 0
S26 - 2.282
S26 = 2.282 tarik
simpul O
S27
∑V = 0
S27 = 0
∑H = 0
S26 S30 S30 + S26 = 0
S30 = -2.282
S30 = 2.282 tekan
simpul P
P2 ∑V = 0
S29 X SINα + S27 + S25 X SINα - P2
S29 X 0.7071 + 0 + 0 - 1.00
S29 X 0.7071 = 1
S24 S28 S29 = 1.4142 tarik
S25COSα S29COSα
S25 S29 ∑H = 0
S25SINα S29SINα S28 + S24 + S25 X COSα + S29 X COSα = 0
S27 S28 + 2.18 + 0 + 1 = 0
S28 + 3.18 = 0
S28 = -3.18
S28 = 3.18 tekan
simpul R
∑V = 0
P2 S31 - P2 = 0
S31 = P2
S31 = 1 tarik
S28 S32 ∑H = 0
S32 - S28
S31 S32 = S28
S32 = 3.18 tarik
simpul Q
S33 SINα ∑V = 0
S29SINα S31 S33 X SINα + S29 X SINα + S31
S29 S33 S33 X 0.7071 + 1 + 1
S33 X 0.7071 + 2
S29 COSα S33 COSα S33 X 0.7071 = -2
S30 S34 S33 = -2.828
S33 = 2.8284 tekan
∑H = 0
S34 - S33 X COSα + S29 X COSα - S30
S34 - 2 + 1 - 2.28
S34 - 1.282
S34 = 1.282 tarik
simpul U
P2
∑H = 0
S36 = 0
∑V = 0
S36 S38 - P2
S38 = P2
S38 = 1 tarik
S38
simpul T
P2 ∑H = 0
S37 X COSα + S32 - S33 X COSα + S36 = 0
S37 X 0.7071 + 3.18 - 2.00 = 0
S37 X 0.7071 = 0
S32 S36 S37 = 0
S33 S37 ∑V = 0
S35 + S37 X SINα - S33 X SINα - P2 = 0
S35 S35 + 0 - 2 - 1 = 0
S35 - 3
S35 = 3 tarik
simpul S
S35 ∑V = 0
S40 + S35 = 0
S40 = -3
S40 = 3 tekan
S39 ∑H = 0
S34 S39 + S34 = 0
S39 = -1.282
S39 = 1.282 tekan
S40
simpul V
S38 ∑H = 0
S37 S41 X COSα + S37 X COSα - S39 = 0
S41 X 0.7071 + 0 - 1.28 = 0
S41 X 0.7071 = 1.282
S41 = 1.8127 tarik
S39
∑V = 0
S42 + S41 X SINα + S38 + S37 X SINα = 0
S41 S42 + 1.2818 + 1 + 0 = 0
S42 + 2.2818 = 0
S42 S42 = -2.282
S42 = 2.2818 tekan
simpul X
S42 ∑H = 0
S43 = 0
S43 ∑V = 0
S47 - S42
S47 = S42
S47 = 2.2818 tarik
S47
simpul W
S40 S41 ∑H = 0
S46 X COSα - S41 X COSα - S43
S46 X 0.7071 - 1.2818 - 0
S46 X 0.7071 - 1.2818
S43 S46 X 0.7071 = 1.2818
S46 = 1.8127 tarik
S46 ∑V = 0
S44 + S41 X SINα - S40 - S46 X SINα
S44 S44 + 1.2818 - 3 - 1.282
S44 - 3
S44 = 3 tarik
simpul Y
= 0
S44 S45 = 0
S45 = 0
S48 + S44 = 0
S48 = -3
S48 S48 = 3 tekan
simpul Z
S46 S47 = 0
S49 X COSα + S45 - S46 X COSα
S49 X 0.7071 + 0 - 1.282
S45 S49 X 0.7071 = 1.2818
S49 = 1.8127 tarik
∑V = 0
S49 S51 + S49 X SINα + S47 - S46 X SINα
S51 S51 + 1.2818 + 2.2818 - 1.282
S51 + 2.2818
S51 = -2.282
S51 = 2.2818 tekan
simpul AB
S51 = 0
S50 = 0
S50 ∑V = 0
S53 - S51 = 0
S53 = S51
S53 = 2.2818 tarik
S53
simpul AA
S48 ∑H = 0
S49 S52 X COSα - S50 - S49 X COSα
S52 X 0.7071 - 0 - 1.282
S52 X 0.7071 = -1.2818
S50 S52 = -1.813
S52 = 1.8127 tekan
S52
∑H
∑V
∑H
∑H
TABEL GAYA-GAYA BATANG AKIBAT BEBAN LUAR
NO BATANG TARIK TEKAN
1 - 2359.21
2 4808.326 -
3 - 2359.21
4 0 0
5 - 4808.33
6 0 0
7 2359.21 -
8 4808.326 -
9 0 0
10 0 0
11 - 2359.21
12 1700 -
13 - 2404.2
14 - 1700
15 1000 -
16 4326.37 -
17 0 0
18 - 340.7928
19 - 1700
20 - 2181.95
21 - 2744.956
22 - 340.79
23 1000 -
24 2181.95 -
25 0 0
26 2281.8
27 0 0
28 - 3182.0
29 1414.214 -
30 - 2281.77
31 1000 -
32 3181.95 -
33 - 2828.427
34 1281.8 -
35 3000 -
36 0 0
37 0 0
38 1000 -
39 - 1281.77
40 - 3000
41 1812.6962 -
42 - 2281.77
43 0 0
44 3000 -
45 0 0
46 1812.6962 -
47 2281.7698 -
48 - 3000
49 1812.6962 -
50 0 0
51 - 2281.77
52 - 1812.696
53 2281.7698 -
TABEL PERHITUNGAN DEFLEKSI VERTIKAL DAN HORISONTAL DENGAN MENGGUNAKAN RUMUS FORMULA
NO S uQ (kg) uF(kg) A (cm²) E (kg/cm²) L (cm) ΔL =SL/AE uQ*ΔL uF*ΔL
1 -2359.21 0.1666667 -1.473 100 2100000 120 -0.001 -0.000224686 0.00198617772
2 4808.326 -0.7071068 1.414 100 2100000 169.705627 0.004 -0.002747615 0.00549522984
3 -2359.21 -0.1666667 1.414 100 2100000 120 -0.001 0.0002246864 -0.0019065273
4 0 0 0 100 2100000 120 0.000 0 0
5 -4808.33 0.7071068 1.414 100 2100000 169.705627 -0.004 -0.002747615 -0.0054952298
6 0 0 0 100 2100000 120 0.000 0 0
7 2359.21 0.1666667 1.473 100 2100000 120 0.001 0.0002246864 0.00198617772
8 4808.326 -0.7071068 1.414 100 2100000 169.705627 0.004 -0.002747615 0.00549522984
9 0 0 1.000 100 2100000 120 0.000 0 0
10 0 0 0.000 100 2100000 120 0.000 0 0
11 -2359.21 -0.17 -1.473 100 2100000 120 -0.001 0.0002246864 0.00198617772
12 1700 0 0.000 100 2100000 120 0.001 0 0
13 -2404.163 0.7071068 -1.414 100 2100000 169.705627 -0.002 -0.001373807 0.00274761492
14 1700 0 0.000 100 2100000 120 0.001 0 0
15 1000 0 0.000 100 2100000 120 0.001 0 0
16 1000 0.4714045 3.498 100 2100000 169.705627 0.001 0.0003809524 0.00282662426
17 0 0 0.000 100 2100000 120 0.000 0 0
18 -340.7928 -0.8333333 -0.473 100 2100000 120 0.000 0.0001622823 9.2169121E-05
19 -1700 0 0.000 100 2100000 120 -0.001 0 0
20 -2181.95 0.00 -0.669 100 2100000 120 -0.001 0 0.00083455613
21 -2744.956 -0.4714045 -0.473 100 2100000 169.705627 -0.002 0.0010456975 0.00104989377
22 -340.7928 -0.8333333 0.473 100 2100000 120 0.000 0.0001622823 -9.216912E-05
23 1000 0 0.000 100 2100000 120 0.001 0 0
24 2181.95 0 0.669 100 2100000 120 0.001 0 0.00083455613
25 0 0.942809 0.000 100 2100000 169.705627 0.000 0 0
26 2281.77 1.1666667 0.335 100 2100000 120 0.001 0.0015211798 0.00043636691
27 0 0 0.000 100 2100000 120 0.000 0 0
28 -3181.954 -0.7071068 -0.669 100 2100000 120 -0.002 0.0012857035 0.00121703724
29 1414.214 0.057191 0.000 100 2100000 169.705627 0.001 6.53611E-05 0
30 -2281.77 1.1666667 -0.335 100 2100000 120 -0.001 -0.00152118 0.00043636691
31 1000 0 0.000 100 2100000 120 0.001 0 0
32 3181.95 0 0.669 100 2100000 120 0.002 0 0.00121703724
33 -2828.427 -0.4714045 0.000 100 2100000 169.705627 -0.002 0.001077496 0
34 1281.77 0 0.335 100 2100000 120 0.001 0 0.00024512636
35 3000 0 0.000 100 2100000 120 0.002 0 0
36 0 0 0.000 100 2100000 120 0.000 0 0
37 0 -1.7071068 0.000 100 2100000 169.705627 0.000 0 0
38 1000 0 0.000 100 2100000 120 0.001 0 0
39 -1281.77 0.8333333 -0.335 100 2100000 120 -0.001 -0.000610367 0.00024512636
40 -3000 0 0.000 100 2100000 120 -0.002 0 0
41 1812.696 0.7071068 0.473 100 2100000 169.705627 0.001 0.0010358264 0.00069332204
42 -2281.77 -0.1666667 -0.335 100 2100000 120 -0.001 0.0002173114 0.00043636691
43 0 0 0.000 100 2100000 120 0.000 0 0
44 3000 0 0.000 100 2100000 120 0.002 0 0
45 0 0 0.000 100 2100000 120 0.000 0 0
46 1812.696 -0.7071068 -0.473 100 2100000 169.705627 0.001 -0.001035826 -0.000693322
47 2281.77 -0.1666667 0.335 100 2100000 120 0.001 -0.000217311 0.00043636691
48 -3000 0 0.000 100 2100000 120 -0.002 0 0
49 1812.696 0.7071068 0.335 100 2100000 169.705627 0.001 0.0010358264 0.00049025272
50 0 0 0.000 100 2100000 120 0.000 0 0
51 -2281.77 -0.1666667 -0.335 100 2100000 120 -0.001 0.0002173114 0.00043636691
52 -1812.696 -0.7071068 0.473 100 2100000 169.705627 -0.001 0.0010358264 -0.000693322
53 2281.77 -0.1666667 0.335 100 2100000 120 0.001 -0.000217311 0.00043636691
TOTAL -0.003526218 0.02317994026
HASIL PERHITUNGAN GAYA - GAYA BATANG
NO BEBAN LUAR (kg) SATUAN DI Q (kg) SATUAN DI F (kg)
BATANG TARIK TEKAN TARIK TEKAN TARIK TEKAN
1 - 2359.21 166.666667 - - 1473.30
2 4808.326 - - 707.106781 1414.21 -
3 - 2359.21 - 166.666667 1414.21 -
4 0 0 0 - 0.00 0.00
5 - 4808.33 707.106781 - 1414.21 -
6 0 0 0 - 0.00 0.00
7 2359.21 - 166.666667 - 1473.30 -
8 4808.326 - - 707.106781 1414.21 -
9 0 0 0 0 1000.00 1000.00
10 0 0 0 0 0.00 0.00
11 2359.21 - 166.666667 - 1473.30
12 1700 0 0 0.00 0.00
13 - 2404.1631 707.106781 - - 1414.21
14 1700 - - 0.00 0.00
15 1000 0 0 - 0.00 0.00
16 1000 - 471.404521 - 3497.77 -
17 0 0 0 - 0.00 0.00
18 - 340.79283 - 833.333333 - 473.30
19 - 1700 - 0 0.00 0.00
20 - 2181.95 - 0 - 669.34
21 - 2744.9559 - 0.47140452 - 473.30
22 - 340.79283 - 0.83333333 473.30 -
23 1000 - - 0 0.00 0.00
24 2181.95 - - 0 669.34 -
25 0 0 942.809042 - 0.00 0.00
26 2281.77 - - 1166.66667 334.67 -
27 0 0 0 - 0.00 0.00
28 - 3181.9538 - 707.106781 - 669.34
29 1414.214 - 57.1909584 - 0.00 0.00
30 - 2281.7698 1166.66667 - - 334.67
31 1000 0 0 - 0.00 0.00
32 3181.95 0 0 - 669.34 -
33 - 2828.4271 - 471.404521 0.00 0.00
34 1281.77 - 0 - 334.67 -
35 3000 - 0 - 0.00 0.00
36 0 0 0 - 0.00 0.00
37 0 0 - 1707.10678 0.00 0.00
38 1000 - 0 0 0.00 0.00
39 - 1281.7698 833.333333 - - 334.67
40 - 3000 0 0 0.00 0.00
41 1812.696 - 707.106781 - 473.30 -
42 - 2281.7698 - 166.666667 - 334.67
43 0 0 0 0 0.00 0.00
44 3000 0 0 0 0.00 0.00
45 0 0 0 0 0.00 0.00
46 1812.696 - - 707.106781 - 473.30
47 2281.77 - 166.666667 - 334.67 -
48 - 3000 - - 0.00 0.00
49 1812.696 - 707.106781 - 334.67 -
50 0 0 0 0 0.00 0.00
51 - 2281.7698 - 166.666667 - 334.67
52 - 1812.6962 - 707.106781 473.30 -
53 2281.77 - 166.666667 - 334.67 -
411t
a = 1.2 m P = 1 t Semua Penampang batang : A
b = 1.2 m Modulus elastisitas baja : E
PERHITUGAN REAKSI PERLETAKAN
∑MA = 0
- RB x (a+a+a+a+a+a) - 1 x (a+a+a+a) = 0
- RB x 7.2 - 4.8
- RB x 7.2 - 4.8 = 0
RB = -0.66667 t
RB = 0.666667
∑MB = 0
RA x (a+a+a+a+a+a) + P1G 1 x (a+a) = 0
RA x 7.2 + 2.4
RA x 7.2 + 2.4 = 0
RA = -0.33333 t
RA = 0.333333
KONTROL (∑V)
∑V = 0
RA + RB - P
0.333333 + 0.666667 - 1 = 0
1 - 1 = 0
0 = 0 OK
AB
b
b
b
b
b
a a a a a a
DC
FE
HG
JI
K L N P R T U
M O Q S
W
Y
AA
V
X
Z
AB
1 2
9
5 634
87 10
12
1311 1
4
15
17
1618 19
20
21
22
25
24
26
2729
28
30
3331
32
34
36
383735
3940 4243
44
48
5253
51
4746
45
4950
23
Panjang sisi miring = 1.697056
TANα = b
a SINα = 0.707107
= 1 COSα = 0.707107
α = 45.00
PERHITUNGAN TITIK BUHUL
Simpul A
∑H = 0
S2 COS 45.00 = 0
S2 0.707107 = 0
S2 = -0.70710678
= 0.70711 T (←) TEKAN
∑V = 0
S1 - S2 SIN 45.00 + RA = 0
S1 - 0.5 - 0.333333 = 0
S1 - 0.16666667 = 0
S1 = -0.1667
S1 = 0.1667 T TARIK
Simpul C
∑H = 0
S4 = 0
∑V = 0
S3 = -S1
S3 = 0.16667
S3 = 0.16667 T TEKAN
Simpul D
∑H = 0
S5 x COS + S4 - S2 x COSα = 0
S5 x 0.707107 + 0 - 0.70711 x 0.707107 = 0
S5 x 0.707107 + 0 - 0.5 = 0
S5 x 0.707107 - 0.5 = 0
S5 x 0.707107 = 0.5
S5 = 0.707107
S5 = 0.707107 T TARIK
∑V = 0
S6 + S5 x SINα - S2 x SINα = 0
S6 + 0.707107 x 0.70710678 - 0.70711 x 0.707107 = 0
S6 + 0.5 - 0.5 = 0
S6 + 0 = 0
S6 = 0 T
RA
S1S2
S3
S1
S4
A
D
S6S5
S4
S2
Simpul F
∑H = 0
S9 = 0
∑V = 0
S10 + S6 = 0
S10 = -S6
S10 = 0
S10 = 0 T
Simpul E
∑H = 0
S8 x COSα + S9 + S5 x COSα = 0
S8 x 0.707107 + 0 + 0.707107 x 0.707107 = 0
S8 x 0.707107 + 0.5 = 0
S8 x 0.707107 = -0.5
S8 = 0.707107 T TEKAN
∑V = 0
S7 - S3 + S5 x SINα - S8 x SINα = 0
S7 - 0.16667 + 0.70710678 x 0.707107 - 0.707107 x 0.707107 = 0
S7 - 0.16667 + 0.5 - 0.5 = 0
S7 - 0.16667 = 0
S7 = 0.16667 T TARIK
Simpul G
∑H = 0
S12 = 0
∑V = 0
S11 + S7 = 0
S11 = -S7
S11 = -0.1667 T
S11 = 0.16667 T TEKAN
Simpul H
∑H = 0
S13 x COSα + S12 - S8 x COSα = 0
S13 x 0.707107 + 0 - 0.707107 x 0.707107 = 0
S13 x 0.707107 + -0.5 = 0
S13 x 0.707107 = 0.5
S13 = 0.707107
S13 = 0.707107 T TARIK
∑V = 0
S14 + S13 x SINα + S10 - S8 x SINα= 0
S14 + 0.707107 x 0.707107 + 0 - 0.707107 x 0.707107 = 0
S14 + 0.5 + 0 - 0.5 = 0
S14 + 0 = 0
S14 = 0 T
F
S10
S6
S9
S12G
S7
S3S5
S9
S8
E
S11
S7
S10S12
S8
S13
H
S14
Simpul K
∑H = 0
S17 = 0
∑V = 0
S15 = 0
Simpul I
∑V = 0
S16 x SINα+ S15 - S11 + S13 x SINα = 0
S16 x 0.70710678 + 0 - 0.17 + 0.707107 x 0.707107 = 0
S16 x 0.70710678 + 0 - 0.3 = 0
S16 x 0.70710678 = 0.3
S16 = 0.47140452
S16 = 0.47140452 T TARIK
∑H = 0
S18 + S16 x COSα + S13 x COSα = 0
S18 + 0.47140452 x 0.707107 + 0.707107 x 0.707107 = 0
S18 + 0.33333333 + 0.5 = 0
S18 + 0.83333333 = 0
S18 = -0.83333333
S18 = 0.83333333 T TEKAN
Simpul J
∑H = 0
S22 + S18 = 0
S22 = -S18
S22 = -0.83333
S22 = 0.833333 T TEKAN
∑V = 0
S19 + S14 = 0
S19 = -S14
S19 = 0
S19 = 0 T
Simpul L
∑V = 0
S21 x SINα + S19 + S16 x SINα = 0
S21 x 0.707107 + 0 + 0.471405 x 0.707107 = 0
S21 x 0.707107 + 0.33333333 = 0
S21 x 0.707107 = 0.33333333
S21 = 0.471405 T TEKAN
∑H = 0
S20 + S17 - S21 x COSα + S16 x COSα = 0
S20 + 0 - 0.47140452 x 0.707107 + 0.471405 x 0.707107 = 0
S20 + 0 - 0.33333 + 0.333333 = 0
S20 + 0 + 0 = 0
S20 = 0
S20 = 0 T
S17
I
S15
S11 S13
S18
S16
S15
S19
I
S18 S22
S14
J
L S20S17
S16 S21
S19
Simpul N
∑H = 0
S24 - S20 = 0
S24 = S20
S24 = 0 T
∑V = 0
S23 = 0
Simpul M
∑V = 0
S25 x SINα + S23 - S21 x SINα - P
S25 x 0.707107 + 0 - 0.471405 x 0.707107 - 1
S25 x 0.707107 + 0 - -0.4714 X 0.71 - 1
S25 x 0.707107 - 0.666667
S25 = 0.942809
S25 = 0.942809 T TARIK
∑H = 0
P S26 + S22 - S21 x COSα + S25 x COSα = 0
S26 + 0.833333 - 0.471405 x 0.707107 + 0.942809 x 0.707107 = 0
S26 + 1.166667 = 0
S26 = 1.166667 T TEKAN
Simpul O
∑H = 0
S30 - S26 = 0
S30 = S26
S30 = 1.166667
S30 = 1.166667 T TARIK
∑V = 0
S27 = 0
Simpul P
∑V = 0
S29 x SINα + S25 x SINα + S27 = 0
S29 x 0.707107 + -0.94280904 x 0.707107 + 0 = 0
S29 x 0.707107 + -0.66666667 + 0.71 = 0
S29 x 0.707107 - 0.04044011 = 0
S29 = 0.057191
S29 = 0.057191 T TARIK
∑H = 0
S28 + S24 + S25 x COSα + S29 x COSα = 0
S28 + 0 + 0.942809 x 0.707107 + 0.057191 x 0.707107 = 0
S28 + 0.707107 = 0
S28 = -0.70711
S28 = 0.707107 T TEKAN
S20 S24N
S23
S25
M
S23
S22
S21
S26
OS26 S30
S27
PS24
S29
S28
S25S27
Simpul R
∑H = 0
S32 - S28 = 0
S32 = S28
S32 = 0.707107 T TARIK
∑V = 0
S31 = 0
Simpul Q
∑V = 0
S33 x SINα + S31 + S30 + S29 x SINα = 0
S33 x 0.707107 + 0 + 1.166667 + 0.057191 x 0.707107 = 0
S33 x 0.71 + 1.2071 = 0
S33 x 0.71 = -1.207
S33 = 1.71 T TEKAN
∑H = 0
S34 - S33 x COSα + S29 x COSα + S30 = 0
S34 - 1.71 x 0.7071 + 0.06 x 0.71 + 1.17 = 0
S34 - 1.21 + 0.0404 + 1.17 = 0
S34 = 0 T
Simpul B
∑H = 0
S52 x COS 45.00 = 0
S52 x 0.707107 = 0
S52 = -0.70711
= 0.70711 T (←) TEKAN
∑V = 0
S53 - S52 x SIN 45.00 - RB = 0
S53 - 0.5 - -0.667 = 0
S53 - 0.166667 = 0
S53 = 0.1667 T TARIK
Simpul AB
∑H = 0
S50 = 0
∑V = 0
S51 + S53 = 0
S51 = -S53
S51 = -0.1667
S51 = 0.16667 T TEKAN
R S32S28
S31
Q
S31S33
S29
S30 S34
B
S52 S53
RB
AB
S51
S53
S50
Simpul AA
∑H = 0
S49 x COSα + S50 - S52 x COSα = 0
S49 x 0.707107 + 0 - 0.70711 x 0.707107 = 0
S49 x 0.707107 - 0.5 = 0
S49 = 0.707107 T TARIK
∑V = 0
S48 + S49 x SINα - S52 x SINα = 0
S48 + 0.707107 x 0.707107 - 0.70711 x 0.707107 = 0
S48 + 0.5 - 0.5 = 0
S48 + 0 = 0
S48 = 0 T
Simpul Y
∑H = 0
S45 = 0
∑V = 0
S44 + S48 = 0
S44 = -S48
S44 = 0
S44 = 0 T
Simpul Z
∑H = 0
S46 x COSα + S45 + S49 x COSα = 0
S46 x 0.707107 + 0 + 0.707107 x 0.707107 = 0
S46 x 0.707107 + 0.5 = 0
S46 x 0.707107 = -0.5
S46 = 0.707107 T TEKAN
∑V = 0
S47 - S51 - S46 x SINα + S49 x SINα = 0
S47 - 0.16667 - 0.70710678 x 0.707107 + 0.707107 x 0.707107 = 0
S47 - 0.166667 = 0
S47 = 0.166667 T TARIK
Simpul X
∑H = 0
S43 = 0
∑V = 0
S42 + S47 = 0
S42 = -S47
S42 = -0.16667 T
S42 = 0.166667 T TEKAN
S49S48
S50
S52
AA
S45
Y
S48
S44
Z
S47
S51
S46
S45
S49
X
S42
S43
S47
Simpul W
∑H = 0
S41 x COSα + S43 - S46 x COSα = 0
S41 x 0.707107 + 0 - 0.707107 x 0.707107 = 0
S41 x 0.707107 - 0.5 = 0
S41 = 0.707107 T TARIK
∑V = 0
S40 + S41 x SINα + S44 - S46 x SINα = 0
S40 + 0.707107 x 0.70710678 + 0 - 0.707107 x 0.707107 = 0
S40 + 0 = 0
S40 = 0 T
Simpul U
∑H = 0
S36 = 0
∑V = 0
S38 = 0
Simpul V
∑V = 0
S37 x SINα + S38 - S42 + S41 x SINα = 0
S37 x 0.707107 + 0 - 0.166667 + 0.707107 x 0.707107 = 0
S37 x 0.707107 + 0 + 0.333333 = 0
S37 x 0.707107 + 0.33333333 = 0
S37 = -0.4714
S37 = 0.471405 T TEKAN
∑H = 0
S39 - S37 x COSα + S41 x COSα = 0
S39 - 0.471405 x 0.70710678 + 0.707107 x 0.707107 = 0
S39 - 0.333333 + 0.5 = 0
S39 + 0.833333 = 0
S39 = 0.833333
S39 = 0.833333 T TARIK
Simpul S
∑H = 0
S34 + S39 = 0
S34 = -S39
S34 = -0.83333 T TEKAN
∑V = 0
S35 + S40 = 0
S35 = -S40
S35 = 0
WS41
S46S44
S40
S43
US36
S38
V
S41
S37 S38
S42
S39
S35
S39S34
S40
S
TABEL GAYA-GAYA BATANG AKIBAT BEBAN SATUAN DITITK P
NO BATANG TARIK TEKAN
1 166.66667 -
2 - 707.10678
3 - 166.66667
4 0 0
5 707.10678119 -
6 0 0
7 166.66667 -
8 - 707.10678119
9 0 0
10 0 0
11 - 166.66667
12 0 0
13 707.10678119 -
14 0 0
15 0 0
16 471.40452079 -
17 0 0
18 - 833.33333333
19 0 0
20 0 0
21 - 0.4714045208
22 - 0.8333333333
23 0 0
24 0 0
25 942.80904158 -
26 - 1166.6666667
27 0 0
28 707.10678119
29 57.190958418 -
30 1166.6666667 -
31 0 0
32 0 0
33 - 1707.1067812
34 0 -
35 0 0
36 0 0
37 471.40452079
38 0 0
39 833.33333333 -
40 0 0
41 707.10678119
42 - 166.66666667
43 0 0
44 0 0
45 0 0
46 - 707.10678119
47 166.66666667
48 0 0
49 707.10678119 -
50 0 0
51 - 166.66667
52 - 707.10678
53 166.66667 -
