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P₁ 1.5
P₂ 2.5 q₁ 2
C
P₄ 1
q₂ 1.5 A
2
P₃ 3.000 q₃ 1.5
E 3.5
F 4
B 2.5
D 1.5
ΣMA = = = RB =
0 -P₁ x 2 -q₁ x 2 x 1 + P₂ x 3.5 + P₃ x 7.5 + q₂ x 10 x 5 -RB x 10 + q₃ x 1.5 x 10.75 + P₄ x 11.5 -1.5 x 2 -2 x 2 x 1 + 2.5 x 3.5 + 3 x 7.5 + 1.5 x 10 x 5 -RB x 10 + 1.5 x 1.5 x 10.75 + 1 x 11.5 13.494 Ton
ΣMB = = = RA =
0 P₄ x 1.5 + q₃ x 1.5 x 0.75 - P₃ x 2.5 - P₂ x 6.5 - q₂ x 10 x 5 + RA x 10 - P₁ x 12 - q₁ x 2 x 11 1 x 1.5 + 1.5 x 1.5 x 0.75 - 3 x 2.5 - 2.5 x 6.5 - 1.5 x 10 x 5 + RA x 10 - 1.5 x 12 - 2 x 2 x 11 15.75625 Ton
Kontrol : ΣV = = = =
0 ( RA + RB ) - ( P₁ + P₂ + P₃ + P₄ + q₁ x 2 + q₂ x 10 + q₃ x 1.5 ) 29.25 29.25 0 Kontrol
Bidang D dari Kiri
Bidang D dari Kanan
DC DC'
DD DD'
DA
DA'
DE
DE'
DF
DF'
DB
= = = = = = = = = = = = = = = = = = = = = = = = =
0 Ton DC - P₁ 0 - 1.5 -1.5 Ton DC' - q₁ x 2 -1.5 - 2 x 2 -5.5 Ton DA + RA -5.5 + 15.756 10.256 Ton DA' - q₂ x 3.5 10.256 - 1.5 x 3.5 5.006 Ton DE - P₂ 5.006 - 2.5 2.506 Ton DE' - q₂ x 4 2.506 - 1.5 x 4 -3.494 Ton DF - P₃ -3.494 - 3 -6.494 Ton DF' - q₂ x 2.5 -6.494 - 1.5 x 2.5 -10.244 Ton
DB
DB'
DF
DF'
DE
DE'
DA
= = = = = = = = = = = = = = = = = = = = = = = = =
0 Ton DD + P₄ 0+1 1 Ton DD' + q₃ x 1.5 1 + 1.5 x 1.5 3.25 Ton DB - RB 3.25 - 13.494 -10.244 Ton DB' + q₂ x 2.5 -10.244 + 1.5 x 2.5 -6.494 Ton DF + P₃ -6.494 + 3 -3.494 Ton DF' + q₂ x 4 -3.494 + 1.5 x 4 2.506 Ton DE + P₂ 2.506 + 2.5 5.006 Ton DE' + q₂ x 3.5 5.006 + 1.5 x 3.5 10.256 Ton
DB'
DD
DD'
= = = = = = = = =
DB + RA -10.244 + 15.756 3.250 Ton DB' - q₃ x 1.5 3.25 - 1.5 x 1.5 1 Ton DD - P₄ 1-1 0 Ton
DA'
DC
DC'
= = = = = = = = =
DA - RA 10.256 - 15.756 -5.500 Ton DA' + q₁ x 2 -5.5 + 2 x 2 -1.5 Ton DC + P₁ -1.5 + 1.5 0 Ton
Bidang Moment Dari Kiri MC = 0 Tm MA = -P₁ x 2 - q₁ x 2 x 1 = -1.5 x 2 - 2 x 2 x 1 = -7 Tm ME = -P₁ x 5.5 - q₁ x 2 x 4.5 + RA x 3.5 - q₂ x 3.5 x 1.75 = -1.5 x 5.5 - 2 x 2 x 4.5 + 15.756 x 3.5 - 1.5 x 3.5 x 1.75 = 19.709 Tm MF = -P₁ x 9.5 - q₁ x 2 x 8.5 + RA x 7.5 - q₂ x 7.5 x 3.75 - P₂ x 4 = -1.5 x 9.5 - 2 x 2 x 8.5 + 15.756 x 7.5 - 1.5 x 7.5 x 3.75 - 2.5 x 4 = 17.734 Tm MB = -P₁ x 12 - q₁ x 2 x 11 + RA x 10 - q₂ x 10 x 5 - P₂ x 6.5 - P₃ x 2.5 = -1.5 x 12 - 2 x 2 x 11 + 15.756 x 10 - 1.5 x 10 x 5 - 2.5 x 6.5 - 3 x 2.5 = -3.1875 Tm MD = -P₁ x 13.5 - q₁ x 2 x 12.5 + RA x 11.5 - q₂ x 10 x 6.5 - P₂ x 8 - P₃ x 4 + RB x 1.5 - q₃ x 1.5 x 0.75 = -1.5 x 13.5 - 2 x 2 x 12.5 + 15.756 x 11.5 - 1.5 x 10 x 6.5 - 2.5 x 8 - 3 x 4 + 13.494 x 1.5 - 1.5 x 1.5 x 0.75 = 0.000 Tm Bidang Moment Dari Kanan MD MB
MF
ME
MA
MC
= = = = = = = = = = = = = = = =
0 Tm - P₄ x 1.5 - q₃ x 1.5 x 0.75 - 1 x 1.5 - 1.5 x 1.5 x 0.75 -3.1875 Tm - P₄ x 4 - q₃ x 1.5 x 1.875 + RB x 2.5 - 0.5 x q₂ x 2.5² - 1 x 4 - 1.5 x 1.5 x 1.875 + 13.494 x 2.5 - 0.5 x 1.5 x 2.5² 17.734 Tm - P₄ x 8 - q₃ x 1.5 x 5.875 + RB x 6.5 - 0.5 x q₂ x 6.5² - P₃ x 4 - 1 x 8 - 1.5 x 1.5 x 5.875 + 13.494 x 6.5 - 0.5 x 1.5 x 6.5² - 3 x 4 19.709 Tm - P₄ x 11.5 - q₃ x 1.5 x 9.375 + RB x 10 - 0.5 x q₂ x 10² - P₃ x 7.5 - P₂ x 3.5 - 1 x 11.5 - 1.5 x 1.5 x 9.375 + 13.494 x 10 - 0.5 x 1.5 x 10² - 3 x 7.5 - 2.5 x 3.5 -7 - P₄ x 13.5 - q₃ x 1.5 x 11.375 + RB x 12 - q₂ x 10 x 7 - P₃ x 9.5 - P₂ x 5.5 + RA x 2 - q₁ x 2 x 1 - 1 x 13.5 - 1.5 x 1.5 x 11.375 + 13.494 x 12 - 1.5 x 10 x 7 - 3 x 9.5 - 2.5 x 5.5 + 15.756 x 2 - 2 x 2 x 1 0
40
f
a
Bid 3
7 b
9
Bid 2
67
e 11
Bid 1 75
d Bid I II III
Luas 825 603 280 1708
X 37.5 70.5 86
Y 5.5 44.5 81.5
-31.728 cm
Yb =
Bid I II III
c
Luas 825 603 280
Ya =
AX 30938 42512 24080 97529
AY 4537.5 26834 22820 54191
Ixo + AY^2 Ixy = 235,034.333 + 790619.015195402 = 1025653.349 Cm´ =
Iy
= = =
Iyo + AX^2 428,122.333 + 659065.477166276 1087187.81 Cm´
=
=
97529 1708
=
57.1012881
Y
=
54191 1708
=
31.7277518
X Y AX^2 AY^2 AXY Ixo Iyo -19.601 -26.228 316974 567513 424131 8318.75 386718.75 -13.399 0 108254 0 0 225572.25 4070.25 28.899 28.228 233838 223106 228409 1143.33333 37333.3333 659065 790619 652539 235034.333 428122.333
= = =
=
=
53.272 85 - 31.7277517564403 =
Ix
Imax
X
( Ix + Iy ) 2
Ixyo + AXY 0 + 652539.403439319 652539.403 Cm´
( 0.5 x (Iy - Ix ))² + Ixy²
+
( 1,025,653.349 + 1,087,187.810 ) + 2 1709684.918
Ixyo 0 0 0 0
Cm´
( 0.5 x (1,087,187.810 - 1,025,653.349 ))² + 652,539.403²
Imin
=
( Ix + Iy ) 2
( 0.5 x (Iy - Ix ))² + Ixy²
-
( 1,025,653.349 + 1,087,187.810 ) 2
=
403156.2413
=
tan 2θ
=
tan 2θ
=
( 0.5 x (1,087,187.810 - 1,025,653.349 ))² + 652,539.403²
Cm´
Ixy Iy - Ix 652539.4034 1,087,187.810 - 1,025,653.349
tan 2θ
=
10.6044545
θ
=
42.3064694
Menghitung Tegangan Pada Profil Analisa Profil Akibat Putaran Bidang Maka Ya dan Yb : Ya' = = =
Ya x Cos ( θ ) - X x Sin ( θ ) X' = Ya x Sin ( θ ) + X x Cos ( θ ) 53.2722482435597 x Cos ( 42.306 ) - 57.1012880562061 x Sin=( 42.306 53.2722482435597 ) x Sin ( 42.306 ) + 57.1012880562061 x Cos ( 42.30 0.963 78.087 cm = cm
Yb' = = =
Yb x Cos ( θ ) - X x Sin ( θ ) -31.7277517564403 x Cos ( 42.306 ) - 57.1012880562061 x Sin ( 42.306 ) 14.970 cm
Momen Tahanan Terhadap Sumbu X W atas = = = W bawah = = =
Ix / Ya' 1,709,684.918 / 0.963 1775165.52 cm³
Momen Tahanan Terhadap Sumbu Y Wy
= = =
Iy / X' 403,156.241 / 78.087 5162.919 cm³
Ix / Yb' 1,709,684.918 / 14.970 114205.66 cm³
Sa-a = = =
Luas Bid 3 x Y 280 x 28.2277517564403 7903.77049 cm³
Sgn = = =
Sa-a + Luas Bid 2a x Y 7903.77049180328 + 222.549765807963 x 12.3638758782201 10655.3482 cm³
Sb-b = = =
Sb-b + Luas Bis 2b x Y 10655.3481729799 + 222.549765807963 x ( -10.3638758782201 ) 8721.96956 cm³
Perhitungan Tegangan Pada Titik C Diketahui dari Perhitungan Sebelumnya : 0.000 MC = Tm = -1.500 DC = T = 0.000 NC = T 1709684.918 Cm´ Ix = 1775165.516 cm³ W atas = 114205.660 W bawah = cm³ 7903.770492 cm³ Sa-a = 10655.34817 cm³ Sgn = 8721.969555 cm³ Sb-b = Tegangan Geser σ atas
= = =
MC / W atas 0.000 x 10µ / 1,775,165.516 0.000 Kg/Cm²
0.000 x 10µ Kg Cm -1.500 x 10³ Kg
σ bawah
Tegangan Lentur Pada Potongan a-a Sedikit Keatas : 40 b = cm τ aa
=
DC x Sa-a b x Ix
=
-1.500 x 10³ x 7903.77049180328 40 x 1,709,684.918
MC / W bawah 0.000 x 10µ / 114,205.660 0.000 Kg/Cm²
Pada Potongan a-a Sedikit kebawah : 9 b = cm τ aa'
-17.336
=
= = =
Kg/Cm²
=
DC x Sa-a b x Ix
=
-1.500 x 10³ x 7903.77049180328 9 x 1,709,684.918 -77.049
=
Kg/Cm²
Potongan Tepat pada GN : 9 b = cm τ gn
=
DC x Sgn b x Ix
=
-1.500 x 10³ x 10655.3481729799 9 x 1,709,684.918 -103.872
=
Kg/Cm²
Potongan Sedikit Diatas b-b : 9 b = cm τ bb
=
=
DC x Sb-b b x Ix
=
-1.500 x 10³ x 8721.96955503513 9 x 1,709,684.918 -85.025
τ bb'
Kg/Cm²
Tegangan Normal σN = = =
NC / A 0 / 1708 0
Potongan Sedikit Diatas b-b : 75 b = cm
Kg/Cm²
=
=
DC x Sb-b b x Ix
=
-1.500 x 10³ x 8721.96955503513 75 x 1,709,684.918 -10.203
Kg/Cm²
Perhitungan Tegangan Pada Titik A Diketahui dari Perhitungan Sebelumnya : -7.000 -7.000 x 10µ Kg Cm MA = Tm = 10.256 10.256 x 10³ Kg DA = T = 0.000 NA = T 1709684.918 Cm´ Ix = 1775165.516 cm³ W atas = 114205.660 W bawah = cm³ 7903.770492 cm³ Sa-a = 10655.34817 cm³ Sgn = 8721.969555 cm³ Sb-b = Tegangan Geser σ atas
= = =
MA / W atas -7.000 x 10µ / 1,775,165.516 -0.394 Kg/Cm²
σ bawah
Tegangan Lentur Pada Potongan a-a Sedikit Keatas : 40 b = cm τ aa
=
DA x Sa-a b x Ix
=
10.256 x 10³ x 7903.77049180328 40 x 1,709,684.918 118.535
=
= = =
MA / W bawah -7.000 x 10µ / 114,205.660 -6.129 Kg/Cm²
Pada Potongan a-a Sedikit kebawah : 9 b = cm τ aa'
Kg/Cm²
=
DA x Sa-a b x Ix
=
10.256 x 10³ x 7903.77049180328 9 x 1,709,684.918 526.823
=
Kg/Cm²
Potongan Tepat pada GN : 9 b = cm τ gn
=
DA x Sgn b x Ix
=
DA x 10655.3481729799 9 x 1,709,684.918 710.228
=
Kg/Cm²
Potongan Sedikit Diatas b-b : 9 b = cm τ bb
=
=
DA x Sb-b b x Ix
=
10.256 x 10³ x 8721.96955503513 9 x 1,709,684.918 581.359
Potongan Sedikit Diatas b-b : 75 b = cm τ bb'
Kg/Cm²
=
=
DA x Sb-b b x Ix
=
DA x 8721.96955503513 75 x 1,709,684.918 69.763
Kg/Cm²
Tegangan Normal σN = = =
NA / A 0 / 1708 0
Kg/Cm²
Perhitungan Tegangan Pada Titik E Diketahui dari Perhitungan Sebelumnya : 19.709 19.709 x 10µ Kg Cm ME = Tm = 5.006 5.006 x 10³ Kg DE = T = 0.000 NE = T 1709684.918 Cm´ Ix = 1775165.516 cm³ W atas = 114205.660 W bawah = cm³ 7903.770492 cm³ Sa-a = 10655.34817 cm³ Sgn = 8721.969555 cm³ Sb-b = Tegangan Geser σ atas
= = =
ME / W atas 19.709 x 10µ / 1,775,165.516 1.110 Kg/Cm²
Tegangan Lentur Pada Potongan a-a Sedikit Keatas : 40 b = cm τ aa
=
DE x Sa-a b x Ix
=
5.006 x 10³ x 7903.77049180328 40 x 1,709,684.918 57.859
=
σ bawah
= = =
ME / W bawah 19.709 x 10µ / 114,205.660 17.258 Kg/Cm²
Pada Potongan a-a Sedikit kebawah : 9 b = cm τ aa'
Kg/Cm²
=
DE x Sa-a b x Ix
=
5.006 x 10³ x 7903.77049180328 9 x 1,709,684.918 257.151
=
Kg/Cm²
Potongan Tepat pada GN : 9 b = cm τ gn
=
DE x Sgn b x Ix
=
DE x 10655.3481729799 9 x 1,709,684.918 346.674
=
Kg/Cm²
Potongan Sedikit Diatas b-b : 9 b = cm τ bb
=
=
DE x Sb-b b x Ix
=
5.006 x 10³ x 8721.96955503513 9 x 1,709,684.918 283.771
Potongan Sedikit Diatas b-b : 75 b = cm τ bb'
Kg/Cm²
=
=
DE x Sb-b b x Ix
=
DE x 8721.96955503513 75 x 1,709,684.918 34.053
Kg/Cm²
Tegangan Normal σN = = =
NE / A 0 / 1708 0
Kg/Cm²
Perhitungan Tegangan Pada Titik F Diketahui dari Perhitungan Sebelumnya : 17.734 17.734 x 10µ Kg Cm MF = Tm = -6.494 -6.494 x 10³ Kg DF = T = 0.000 NF = T 1709684.918 Cm´ Ix = 1775165.516 cm³ W atas = 114205.660 W bawah = cm³ 7903.770492 cm³ Sa-a = 10655.34817 cm³ Sgn = 8721.969555 cm³ Sb-b = Tegangan Geser σ atas
= = =
MF / W atas 17.734 x 10µ / 1,775,165.516 0.999 Kg/Cm²
σ bawah
Tegangan Lentur Pada Potongan a-a Sedikit Keatas : 40 b = cm τ aa
=
DF x Sa-a b x Ix
=
-6.494 x 10³ x 7903.77049180328 40 x 1,709,684.918 -75.051
=
=
Kg/Cm²
=
DF x Sgn b x Ix
=
DF x 10655.3481729799 9 x 1,709,684.918 -449.681
MF / W bawah 17.734 x 10µ / 114,205.660 15.528 Kg/Cm²
Pada Potongan a-a Sedikit kebawah : 9 b = cm τ aa'
Potongan Tepat pada GN : 9 b = cm τ gn
= = =
Kg/Cm²
=
=
DF x Sa-a b x Ix
=
-6.494 x 10³ x 7903.77049180328 9 x 1,709,684.918 -333.558
Kg/Cm²
Potongan Sedikit Diatas b-b : 9 b = cm τ bb
Potongan Sedikit Diatas b-b : 75 b = cm
=
DF x Sb-b b x Ix
=
-6.494 x 10³ x 8721.96955503513 9 x 1,709,684.918
τ bb'
-368.088
=
Kg/Cm²
=
DF x Sb-b b x Ix
=
DF x 8721.96955503513 75 x 1,709,684.918 -44.171
=
Kg/Cm²
Tegangan Normal σN = = =
NF / A 0 / 1708 0
Kg/Cm²
Perhitungan Tegangan Pada Titik B Diketahui dari Perhitungan Sebelumnya : -3.188 -3.188 x 10µ Kg Cm MB = Tm = -10.244 DB = T = -10.244 x 10³ Kg 0.000 NB = T 1709684.918 Cm´ Ix = 1775165.516 cm³ W atas = 114205.660 W bawah = cm³ 7903.770492 cm³ Sa-a = 10655.34817 cm³ Sgn = 8721.969555 cm³ Sb-b = Tegangan Geser σ atas
= = =
MB / W atas -3.188 x 10µ / 1,775,165.516 -0.180 Kg/Cm²
σ bawah
Tegangan Lentur Pada Potongan a-a Sedikit Keatas : 40 b = cm τ aa
=
DB x Sa-a b x Ix
=
-10.244 x 10³ x 7903.77049180328 40 x 1,709,684.918 -118.391
=
=
Kg/Cm²
=
DB x Sgn b x Ix
=
DB x 10655.3481729799 9 x 1,709,684.918 -709.362
MB / W bawah -3.188 x 10µ / 114,205.660 -2.791 Kg/Cm²
Pada Potongan a-a Sedikit kebawah : 9 b = cm τ aa'
Potongan Tepat pada GN : 9 b = cm τ gn
= = =
Kg/Cm²
=
=
DB x Sa-a b x Ix
=
-10.244 x 10³ x 7903.77049180328 9 x 1,709,684.918 -526.180
Kg/Cm²
Potongan Sedikit Diatas b-b : 9 b = cm τ bb
Potongan Sedikit Diatas b-b : 75 b = cm
=
DB x Sb-b b x Ix
=
-10.244 x 10³ x 8721.96955503513 9 x 1,709,684.918 -580.651
=
τ bb'
Kg/Cm²
=
DB x Sb-b b x Ix
=
DB x 8721.96955503513 75 x 1,709,684.918 -69.678
=
Kg/Cm²
Tegangan Normal σN = = =
NB / A 0 / 1708 0
Kg/Cm²
Perhitungan Tegangan Pada Titik D Diketahui dari Perhitungan Sebelumnya : 0.000 MD = Tm = 1.000 DD = T = 0.000 ND = T 1709684.918 Cm´ Ix = 1775165.516 cm³ W atas = 114205.660 W bawah = cm³ 7903.770492 cm³ Sa-a = 10655.34817 cm³ Sgn = 8721.969555 cm³ Sb-b =
0.000 x 10µ Kg Cm 1.000 x 10³ Kg
Tegangan Geser σ atas
= = =
MD / W atas 0.000 x 10µ / 1,775,165.516 0.000 Kg/Cm²
Tegangan Lentur Pada Potongan a-a Sedikit Keatas : 40 b = cm τ aa
=
=
DD x Sa-a b x Ix
=
1.000 x 10³ x 7903.77049180328 40 x 1,709,684.918 11.557
σ bawah
= = =
MD / W bawah 0.000 x 10µ / 114,205.660 0.000 Kg/Cm²
Pada Potongan a-a Sedikit kebawah : 9 b = cm τ aa'
Kg/Cm²
=
=
DD x Sa-a b x Ix
=
1.000 x 10³ x 7903.77049180328 9 x 1,709,684.918 51.366
Kg/Cm²
Potongan Tepat pada GN : 9 b = cm τ gn
=
DD x Sgn b x Ix
=
DD x 10655.3481729799 9 x 1,709,684.918 69.248
=
Kg/Cm²
Potongan Sedikit Diatas b-b : 9 b = cm τ bb
=
DD x Sb-b b x Ix
=
1.000 x 10³ x 8721.96955503513 9 x 1,709,684.918 56.683
=
Potongan Sedikit Diatas b-b : 75 b = cm τ bb'
Kg/Cm²
=
DD x Sb-b b x Ix
=
DD x 8721.96955503513 75 x 1,709,684.918 6.802
=
Kg/Cm²
Tegangan Normal σN = = =
ND / A 0 / 1708 0
Kg/Cm²
Perhitungan Tegangan Pada Titik Max Diketahui dari Perhitungan Sebelumnya : 13.307 13.307 x 10µ Kg Cm MMax = Tm = 0.000 0.000 x 10³ Kg D Mmax = T = 0.000 0.000 x 10³ Kg NMax = T = 1709684.918 Cm´ Ix = 1775165.516 cm³ W atas = 114205.660 W bawah = cm³ 7903.770492 cm³ Sa-a = 10655.34817 cm³ Sgn = 8721.969555 cm³ Sb-b = Tegangan Geser σ atas
= = =
MMax / W atas 13.307 x 10µ / 1,775,165.516 0.750 Kg/Cm²
Tegangan Lentur Pada Potongan a-a Sedikit Keatas : 40 b = cm τ aa
=
=
D Mmax x Sa-a b x Ix
=
0.000 x 10³ x 7903.77049180328 40 x 1,709,684.918 0.000
Kg/Cm²
σ bawah
= = =
MMax / W bawah 13.307 x 10µ / 114,205.660 11.652 Kg/Cm²
Pada Potongan a-a Sedikit kebawah : 9 b = cm τ aa'
=
=
D Mmax x Sa-a b x Ix
=
0.000 x 10³ x 7903.77049180328 9 x 1,709,684.918 0.000
Kg/Cm²
Potongan Tepat pada GN : 9 b = cm τ gn
=
D Mmax x Sgn b x Ix
=
D Mmax x 10655.3481729799 9 x 1,709,684.918 0.000
=
Kg/Cm²
Potongan Sedikit Diatas b-b : 9 b = cm τ bb
=
D Mmax x Sb-b b x Ix
=
0.000 x 10³ x 8721.96955503513 9 x 1,709,684.918
=
0.000
Kg/Cm²
Tegangan Normal σN = = =
NMax / A 0 / 1708 0
Kg/Cm²
Potongan Sedikit Diatas b-b : 75 b = cm τ bb'
=
=
D Mmax x Sb-b b x Ix
=
D Mmax x 8721.96955503513 75 x 1,709,684.918 0.000
Kg/Cm²
Menentukan Koordinat Bidang Kern Sebelum Berputar Mencari nilai i²x dan i²y
=
i²x
Ix A
= =
1,025,653.349 1,708.000 600.500
= = =
=
Iy A
48.9 ~
i²x / 48.8987119437939 ey 600.500 / 48.8987119437939 12.3
= = =
i²y / ~ 636.527 / ~ 0
Jadi Koordinat K1 ( 12.280 ; 0.000 ) Menentukan K2 dari garis Bungkus BC Menentukan Potongan Garis BC Terhadap Sumbu X dan Y Perpotongan Pada Sumbu X : X
= = =
Y₁ x ( X₂ - X₁ ) / ( Y₂ - Y₁ ) + X₁ 46.272 x ( -31.728 - 48.899 ) / ( 17.899 - 46.272 ) + 48.899 180.386
Perpotongan Pada Sumbu Y : Y = X₁ x ( Y₂ - Y₁ ) / ( X₂ - X₁ ) + Y₁ = 48.899 x ( 17.899 - 46.272 ) / ( -31.728 - 48.899 ) + 46.272 63.480 = 180.386 63.480
Jadi Garis BC memotong sumbu X pada X = Jadi Garis BC memotong sumbu Y pada Y = ex
= = =
i²x / 180.386 600.500 / 180.386 3.32896474
ey
= = =
i²y / 63.480 636.527 / 63.480 10.0271454
Jadi Koordinat K2 ( 3.329 ; 10.027 ) Menentukan K3 dari garis Bungkus CD Koordinat Titik C ( -31.728 ; 17.899 ) Koordinat Titik D ( -31.728 ; -57.101 ) Garis CD memotong sumbu X pada X = Garis CD memotong sumbu Y pada Y =
= =
Cm´
Menentukan K1 dari garis Bungkus AB Koordinat Titik A ( 48.899 ; 53.272 ) Koordinat Titik B ( 48.899 ; 46.272 ) Garis AB memotong sumbu X pada X = Garis AB memotong sumbu Y pada Y = ex
i²y
-31.728 ~
1,087,187.810 1708 636.527
Cm´
ex
= = =
i²x / -31.728 600.500 / -31.728 -18.926488
ey
= = =
i²y / ~ 636.527 / ~ 0
Jadi Koordinat K3 ( -18.926 ; 0.000 ) Menentukan K4 dari garis Bungkus DE Koordinat Titik D ( -31.728 ; -57.101 ) Koordinat Titik E ( -20.728 ; -57.101 ) Garis DE memotong sumbu X pada X = Garis DE memotong sumbu Y pada Y = ex
= = =
i²x / ~ 600.500 / ~ 0.0
~ -57.101 ey
= = =
i²y / -57.101 636.527 / -57.101 -11.147
Jadi Koordinat K4 ( 0.000 ; -11.147 ) Menentukan K5 dari garis Bungkus EF Menentukan Potongan Garis EF Terhadap Sumbu X dan Y Perpotongan Pada Sumbu X : X
= = =
Y₁ x ( X₂ - X₁ ) / ( Y₂ - Y₁ ) + X₁ 46.272 x ( -31.728 - 48.899 ) / ( 17.899 - 46.272 ) + 48.899 -36.055
Perpotongan Pada Sumbu Y : Y = X₁ x ( Y₂ - Y₁ ) / ( X₂ - X₁ ) + Y₁ = 48.899 x ( 17.899 - 46.272 ) / ( -31.728 - 48.899 ) + 46.272 -134.323 = -36.055 -134.323
Jadi Garis EF memotong sumbu X pada X = Jadi Garis EF memotong sumbu Y pada Y = ex
= = =
i²x / -36.055 600.500 / -36.055 -16.655156
ey
= = =
i²y / -134.323 636.527 / -134.323 -4.7387907
Jadi Koordinat K5 ( -16.655 ; -4.739 ) Menentukan K6 dari garis Bungkus FA Koordinat Titik F ( 8.899 ; 53.272 ) Koordinat Titik A ( 48.899 ; 53.272 ) Garis FA memotong sumbu X pada X = Garis FA memotong sumbu Y pada Y = ex
= = =
i²x / ~ 600.500 / ~ 0.0
~ 53.272 ey
= = =
i²y / 53.272 636.527 / 53.272 11.949
Jadi Koordinat K6 ( 0.000 ; 11.949 )
Double Integral MX -Mx EI Y
= = =
-P₁ x X-q₁/2 x X² +RA x ( X - 2 )+q₁/2 x ( X - 2 )² -q₂/2 x ( X - 2 )² -P₂ x ( X - 5.5 )-P₃ x ( X - 9.5 )+RB x ( X - 12 )+q₂/2 x ( X - 12 )² -q₃/2 x ( X - 12 )² + P₁ x X+ q₁/2 x X² - RA x ( X - 2 )- q₁/2 x ( X - 2 )² + q₂/2 x ( X - 2 )² + P₂ x ( X - 5.5 )+ P₃ x ( X - 9.5 )- RB x ( X - 12 )- q₂/2 x ( X - 12 )² + q₃/2 x ( X - 12 )² + P₁/6 x X³ + q₁/24 x X´ - RA/6 x ( X - 2 )³ - q₁/24 x ( X - 2 )´ + q₂/24 x ( X - 2 )´ + P₂/6 x ( X - 5.5 )³ + P₃/6 x ( X - 9.5 )³ - RB/6 x ( X - 12 )³ - q₂/24 x ( X - 12 )´ + q₃/24 x ( X - 12 )´ + C₁ x X+ C₂
Mencari Nilai C1 Dan C2 EI Y di Titik A = 0, X = 2 EI YA = + P₁/6 x X³ + q₁/24 x X´ + C₁ x X+ C₂ = + 1.5/6 x 2³ + 2/24 x 2´ + C₁ x 2+ C₂ = 3.333 + C₁ x 2+ C₂ Ei Y Di Titik B = 0, X = 12 Ei YB = + P₁/6 x X³ + q₁/24 x X´ - RA/6 x ( X - 2 )³ - q₁/24 x ( X - 2 )´ + q₂/24 x ( X - 2 )´ + P₂/6 x ( X - 5.5 )³ + P₃/6 x ( X - 9.5 )³ + C₁ x X+ C₂ = + 1.500/6 x 12³ + 2.000/24 x 12´ - 15.756/6 x ( 12 - 2 )³ - 2.000/24 x ( 12 - 2 )´ + 1.500/24 x ( 12 - 2 )´ + 2.500/6 x ( 12 - 5.5 )³ + 3.000/6 x ( 12 - 9.5 )³ + C₁ x 12+ C₂ = -552.135)³ + C₁ x 12+ C₂ Eliminasi 0= 0= 0= C₁ =
-552.135)³ + C₁ x 12+ C₂ 3.333 + C₁ x 2+ C₂ -555.469 + C₁ x 10 55.547
0= = C₂ =
3.333 + C₁ x 2+ C₂ 3.333 + 55.547 x 2+ C₂ -114.427
Menentukan Lendutan Pada Setiap Titik Lendutan Pada Titik C X= 0m EI YC = C₂ = -114.427 -114.427 x 10⁹ YC = 2153872031910.34 YC =
-0.0531
Cm
Lendutan Pada Titik A X= 2m EI YA = + P₁/6 x X³ + q₁/24 x X´ + C₁ x X+ C₂ = + 1.500/6 x 2³ + 2.000/24 x 2´ + 55.547 x 2 -114.427 = 0.000 0.000 x 10⁹ YA = 2153872031910.34 YA =
0.0000
Cm
Lendutan Pada Titik E X= 5.5 m EI YE = + P₁/6 x X³ + q₁/24 x X´ - RA/6 x ( X - 2 )³ - q₁/24 x ( X - 2 )´ + q₂/24 x ( X - 2 )´ + C₁ x X+ C₂ = + 1.500/6 x 5.5³ + 2.000/24 x 5.5´ - 15.756/6 x ( 5.5 - 2 )³ - 2.000/24 x ( 5.5 - 2 )´ + 1.500/24 x ( 5.5 - 2 )´ + 55.547 x 5.5 -114.427 = 193.21185 193.212 x 10⁹ YE = 2153872031910.34 YE =
0.0897
Cm
Lendutan Pada Titik F X= 9.5 m EI YF = + P₁/6 x X³ + q₁/24 x X´ - RA/6 x ( X - 2 )³ - q₁/24 x ( X - 2 )´ + q₂/24 x ( X - 2 )´ + P₂/6 x ( X - 5.5 )³ + C₁ x X+ C₂ = + 1.500/6 x 9.5³ + 2.000/24 x 9.5´ - 15.756/6 x ( 9.5 - 2 )³ - 2.000/24 x ( 9.5 - 2 )´ + 1.500/24 x ( 9.5 - 2 )´ + 2.500/6 x ( 9.5 - 5.5 )³ + 55.547 x 9.5 -114.427 = 159.25456 159.255 x 10⁹ YF = 2153872031910.34 YF =
0.0739
Cm
Lendutan Pada Titik B X= 12 m EI YB = + P₁/6 x X³ + q₁/24 x X´ - RA/6 x ( X - 2 )³ - q₁/24 x ( X - 2 )´ + q₂/24 x ( X - 2 )´ + P₂/6 x ( X - 5.5 )³ + P₃/6 x ( X - 9.5 )³ + C₁ x X+ C₂ = + 1.500/6 x 12³ + 2.000/24 x 12´ - 15.756/6 x ( 12 - 2 )³ - 2.000/24 x ( 12 - 2 )´ + 1.500/24 x ( 12 - 2 )´ + 2.500/6 x ( 12 - 5.5 )³ + 3.000/6 x ( 12 - 9.5 )³ + 55.547 x 12 -114.427 = 0 0.000 x 10⁹ YB = 2153872031910.34 YB =
0.0000
Cm
Lendutan Pada Titik D X= 13.5 m EI YD = + P₁/6 x X³ + q₁/24 x X´ - RA/6 x ( X - 2 )³ - q₁/24 x ( X - 2 )´ + q₂/24 x ( X - 2 )´ + P₂/6 x ( X - 5.5 )³ + P₃/6 x ( X - 9.5 )³ - RB/6 x ( X - 12 )³ - q₂/24 x ( X - 12 )´ + q₃/24 x ( X - 12 )´ + C₁ x X+ C₂ = + 1.500/6 x 13.5³ + 2.000/24 x 13.5´ - 15.756/6 x ( 13.5 - 2 )³ - 2.000/24 x ( 13.5 - 2 )´ + 1.500/24 x ( 13.5 - 2 )´ + 2.500/6 x ( 13.5 - 5.5 )³ + 3.000/6 x ( 13.5 - 9.5 )³ - 13.494/6 x ( 13.5 - 12 )³ - 1.500/24 x ( 13.5 - 12 )´ + 1.500/24 x ( 13.5 - 12 )´ + 55.547 x 13.5 -114.427 = -102.04297 -102.043 x 10⁹ YD = 2153872031910.34 YD =
-0.0474
Cm
Lendutan Pada Titik M Max X= 6.368 m EI YMax = + P₁/6 x X³ + q₁/24 x X´ - RA/6 x ( X - 2 )³ - q₁/24 x ( X - 2 )´ + q₂/24 x ( X - 2 )´ + C₁ x X+ C₂ = + 1.500/6 x 6.368³ + 2.000/24 x 6.368´ - 15.756/6 x ( 6.368 - 2 )³ - 2.000/24 x ( 6.368 - 2 )´ + 1.500/24 x ( 6.368 - 2 )´ + 55.547 x 6.368 -114.427 = 214.71972 214.720 x 10⁹ YMax = 2153872031910.34 YMax =
0.0997
Cm
Akibat Beban Di Batang C - A MA
= = =
-P₁ x 2 - q₁ x 2 x 1 -1.5 x 2 - 2 x 2 x 1 -7 Tm
ME
= =
6.5 / 10 x -7 -4.550 Tm
MF
= =
2.5 / 10 x -7 -1.750 Tm
Akibat Beban Di Batang A - B ΣMA = P₂ x 3.5 + P₃ x 7.5 + q₂ x 10 x 5 - RB' x 10 0= 2.500 x 3.5 + 3.000 x 7.5 + 1.500 x 10 x 5 - RB' x 10 RB' = 10.625 Ton ΣMB = 0= RA' =
- P₃ x 2.5 - P₂ x 6.5 - q₂ x 10 x 5 + RA' x 10 - 3.000 x 2.5 - 2.500 x 6.5 - 1.500 x 10 x 5 + RA' x 10 9.875 Ton
Kontrol : ΣV = = = =
( RA' + RB' ) - ( P₂ + P₃ + q₂ x 10 ) ( 9.875 + 10.625 ) - ( 2.500 + 3.000 + 1.500 x 10 ) 20.5 - 20.5 0
MA
=
0 Tm
ME
= = =
RA' x 3.5 - 0.5 x q₂ x 3.5² 9.875 x 3.5 - 0.5 x 1.500 x 3.5² 25.375 Tm
MF
= = =
RA' x 7.5 - 0.5 x q₂ x 7.5² - P₂ x 4 9.875 x 7.5 - 0.5 x 1.500 x 7.5² - 2.500 x 4 21.875 Tm
MB
= = =
RA' x 10 - 0.5 x q₂ x 10² - P₂ x 6.5 - P₃ x 2.5 9.875 x 10 - 0.5 x 1.500 x 10² - 2.500 x 6.5 - 3.000 x 2.5 0 Tm
M pada titik M Max Awal Jarak Titik M Max Awal Terhadap Titik A = 6.368 - 2 = 4.368 M Max = RA' x 4.368 - 0.5 x q₂ x 4.368² - P₂ x 0.868 = 9.875 x 4.368 - 0.5 x 1.500 x 4.368² - 2.500 x 0.868 = 26.654141
m
Mencari Titik Mmax akibat Beban Pada Bentang AB ( M Max' ) M Max' = d Mx / dx = X = = = M Max' = = =
RA' x X - 0.5 x q₂ x X² - P₂ x ( X - 3.5 ) RA' x q₂ x X - P₂ ( RA' - P₂ ) / q₂ ( 9.875 - 2.500 ) / 1.500 4.917 m ( M Max Terhadap Titik A ) RA' x X - 0.5 x q₂ x X² - P₂ x ( X - 3.5 ) 9.875 x 4.917 - 0.5 x 1.500 x 4.917² - 2.500 x ( 4.917 - 3.5 ) 26.880 Tm
Akibat Beban Di Batang B - D MB
= = =
- P₄ x 1.5- q₃ x 1.5 x 0.75 - 1 x 1.5- 1.500 x 1.5 x 0.75 -3.1875 Tm
MF
= =
7.5 / 10 x -3.1875 -2.391 Tm
ME
= =
3.5 / 10 x -3.1875 -1.116 Tm
Mencari Tinggi L2 dan L9 pada titik M Max' Tinggi M pada L2 di Titik M Max : = =
( 10 - 4.917 ) / 10 x -7 -3.558 Tm
Tinggi M pada L9 di Titik M Max : = =
4.917 / 10 x -3.1875 -1.567 Tm
Perhitungan Luas dan Perhitungan Jarak Titik Berat L1 A T L1
⅓ = = = = =
2 m 7 Tm ⅓xAxT ⅓x2x7 4.6666667 Tm²
L2 A T L2
⅟₂ = = = = =
10 7 ⅟₂ x A x T ⅟₂ x 10 x 7 35
L3 A T L3
L4 A T L4
L5 A T L5
L6 A T L6
m Tm
3.5 m 25.375 Tm ⅔xAxT ⅔ x 3.5 x 25.375 59.208 Tm²
= = = = =
4.917 - 3.5 25.375 AxT 1.417 x 25.375 35.948 Tm²
= = = = =
0.75
Titik Berat L2 Terhadap Titik A TB L2 = ⅓xA = ⅓ x 10 = 3.333 m
⅓
Titik Berat L3 Terhadap Titik A TB L3 = ⅝xA = ⅝ x 3.5 = 2.188 m
⅝
Titik Berat L4 Terhadap Titik A TB L4 = 3.5 + ⅟₂ x A = 3.5 + ⅟₂ x 1.417 = 4.208 m
⅟₂
Titik Berat L5 Terhadap Titik A TB L5 = 3.5 + ⅝ x A = 3.5 + ⅝ x 1.417 = 4.385 m
⅝
Titik Berat L6 Terhadap Titik A TB L6 = 7.5 - ⅟₂ x A = 7.5 - ⅟₂ x 2.583 = 6.208 m
⅟₂
Tm²
⅔ = = = = =
⅔ = = = = =
Titik Berat L1 Terhadap Titik C Tb L1 = 0.75 x A = 0.75 x 2 = 1.500 m
= Tm
4.917 - 3.5 = 26.880 - 25.375 = ⅔xAxT ⅔ x 1.417 x 1.505 Tm² 1.422
7.500 - 4.917 21.875 AxT 2.583 x 21.875 56.510 Tm²
= Tm
1.417
1.417 1.505
2.583
m
m Tm
m
L7 A T L7
⅔ = = = = =
L8 A T L8
⅔ = = = = =
2.5 m 21.875 Tm ⅔xAxT ⅔ x 2.5 x 21.875 36.458 Tm²
L9 A T L9
⅟₂ = = = = =
10 m 3.1875 Tm ⅟₂ x A x T ⅟₂ x 10 x 3.1875 15.9375 Tm²
L10 A T L10
⅓ = = = = =
7.500 - 4.917 = 26.654 - 21.875 = ⅔xAxT ⅔ x 2.583 x 4.779 Tm² 8.231
1.5 m 3.1875 Tm ⅓xAxT ⅓ x 1.5 x 3.1875 Tm² 1.594
2.583 4.779
m Tm
Titik Berat L7 Terhadap Titik A TB L7 = 7.5 - ⅝ x A = 7.5 - ⅝ x 2.583 = 5.885 m
⅝
Titik Berat L8 Terhadap Titik A TB L8 = 10 - ⅝ x A = 10 - ⅝ x 2.500 = 8.438 m
⅝
Titik Berat L9 Terhadap Titik A TB L9 = ⅔xA = ⅔ x 10 = 6.667 m
⅔
Titik Berat L10 Terhadap Titik D TB L10 = 0.75 x A = 0.75 x 1.5 = 1.125 m
0.75
ΣMA
RB' ΣMB
= 0= =
0 - L2 x TB L2 + L3 x TB L3 + L4 x TB L4 + L5 x TB L5 + L6 x TB L6 + L7 x TB L7 + L8 x TB L8 - L9 x TB L9 - RB' x 10 - 35 x 3.333 - 59.208 x 2.188 - 35.948 x 4.208 - 1.422 x 4.385 - 56.51 x 6.208 - 8.231 x 5.885 - 36.458 x 8.438 - 15.938 x 6.667 - RB' x 10
= = 0= =
RA'
=
Kontrol
ΣV
77.10107 Tm³ 0 + L2 x ( 10 - TB L2 ) - L3 x ( 10 - TB L3 ) - L4 x ( 10 - TB L4 ) - L5 x ( 10 - TB L5 ) - L6 x ( 10 - TB L6 ) - L7 x ( 10 - TB L7 ) - L8 x ( 10 - TB L8 ) + L9 x ( 10 - TB L9 ) + RA' x 10 + 35 x ( 10 - 3.333 ) - 59.208 x ( 10 - 2.188 ) - 35.948 x ( 10 - 4.208 ) - 1.422 x ( 10 - 4.385 ) - 56.51 x ( 10 - 6.208 ) - 8.231 x ( 10 - 5.885 ) 36.458 x ( 10 - 8.438 ) + 15.938 x ( 10 - 6.667 ) + RA' x 10 69.73876 Tm³ = = = = =
0 ( RA' + RB' ) - ( -L2 + L3 + L4 + L5 + L6 + L7 + L8 - L9 ) ( 69.739 - 77.101 ) - ( -35 + 59.208 + 35.948 + 1.422 + 56.51 + 8.231 + 36.458 - 15.938 ) 146.840 - 146.840 0.000 Tm³
EI δ C = = = = = =
MC' - RA' x 2 + L1 x TB L1 - 69.739 x 2 + 4.667 x 1.5 -132.478 Tm´ -132.478 x 10⁹ / 2,153,872,031,910.340 -0.062 Cm
EI δ E = =
ME' + RA' x 3.5 - L3 x ( 3.5 - 2.188 ) + ( 0.5 x ( 7 - 4.55) x 3.5 ) x ( 2/3 x 3.5 ) + ( 4.55 x 3.5 ) x ( 0.5 x 3.5 ) + ( 0.5 x 3.5 x 1.116 ) x ( 1/3 x 3.5 )
=
+ 69.739 x 3.5 - 59.208 x ( 3.5 - 2.188 ) + ( 0.5 x ( 7 - 4.55) x 3.5 ) x ( 2/3 x 3.5 ) + ( 4.55 x 3.5 ) x ( 0.5 x 3.5 ) + ( 0.5 x 3.5 x 1.116 ) x ( 1/3 x 3.5 )
= = =
206.556 Tm´ 206.556 x 10⁹ / 2,153,872,031,910.340 0.096 Cm
EI δ F = =
MF' + RB' x 2.5 - L8 x ( TB L8 - 7.5 ) + ( 0.5 x 1.75 x 2.5 ) x ( 1/3 x 2.5 ) + ( 0.5 x ( 3.188 - 2.391 ) x ( 2.5 ) x ( 2/3 x 2.5 ) + ( 2.391 x 2.5 ) x ( 0.5 x 2.5 )
=
+ 77.101 x 2.5 - 36.458 x ( 8.438 - 7.5 ) + ( 0.5 x 1.75 x 2.5 ) x ( 1/3 x 2.5 ) + ( 0.5 x ( 3.188 - 2.391 ) x ( 2.5 ) x ( 2/3 x 2.5 ) + ( 2.391 x 2.5 ) x ( 0.5 x 2.5 )
= = =
169.528 Tm´ 169.528 x 10⁹ / 2,153,872,031,910.340 0.079 Cm
EI δ D = = = = = =
MD' - RB' x 1.5 + L10 x TB L10 - 77.101 x 1.5 + 1.594 x 1.125 -113.859 Tm´ -113.859 x 10⁹ / 2,153,872,031,910.340 -0.053 Cm
EI δ Max = = = = = =
MMax' + RA' x 4.917 - L3 x ( 4.917 - TB L3 ) + ( 0.5 x ( 7 - 3.558 ) x 4.917 ) x ( 2/3 x 4.917 ) + ( 3.558 x 4.917 ) x ( 0.5 x 4.917 ) + ( 0.5 x 1.567 x 4.917 ) x ( + 69.739 x 4.917 - 59.208 x ( 4.917 - 2.188 ) + ( 0.5 x ( 7 - 3.558 ) x 4.917 ) x ( 2/3 x 4.917 ) + ( 3.558 x 4.917 ) x ( 0.5 x 4.917 ) + ( 0.5 x 1.567 x 232.130 Tm´ 232.130 x 10⁹ / 2,153,872,031,910.340 0.108 Cm
Mencari Titik Potong Bidang Momen Pada Bentang A - E Mx
= = =
- P₁ x X - q₁ x 2 x ( X - 1 ) + RA x ( X - 2 ) - 0.5 x q₂ x ( X - 2 )² - 1.500 x X - 2.000 x 2 x ( X - 1 ) + 15.756 x ( X - 2 ) - 0.5 x 1.500 x ( X - 2 )² -0.750 X² + 13.256 X -30.513
Akar - Akar Persamaan X₁
=
=
-b +
-13.256 +
=
X₂
=
= =
b² - 4 x a x c 2xa
2.720
-b -
( 13.256 )² - 4 x ( -0.750) x ( -30.513) 2 x -0.750 m
( Digunakan Karena Memenuhi Syarat)
b² - 4 x a x c 2xa
-13.256 -
14.955
( 13.256 )² - 4 x ( -0.750) x ( -30.513) 2 x -0.750 m
( Tidak Digunakan Karena Tidak Memenuhi Syarat)
Mencari Titik Potong Bidang Momen Pada Bentang F - B Mx
= = =
- P₄ x X - q₃ x 1.5 x ( X - 0.75 ) + RB x ( X - 1.5 ) - 0.5 x q₂ x ( X - 1.5 )² - 1 x X - 1.500 x 1.5 x ( X - 0.75 ) + 13.494 x ( X - 1.5 ) - 0.5 x 1.500 x ( X - 1.5 )² -0.750 X² + 12.494 X -20.241
Akar - Akar Persamaan X
=
=
-b +
-12.494 +
=
X
=
= =
b² - 4 x a x c 2xa
1.819
-b -
( 12.494 )² - 4 x ( -0.750) x ( -20.241) 2 x -0.750 m
( Digunakan Karena Memenuhi Syarat)
b² - 4 x a x c 2xa
-12.494 +
14.840
( 12.494 )² - 4 x ( -0.750) x ( -20.241) 2 x -0.750 m
( Tidak Digunakan Karena Tidak Memenuhi Syarat)
Perhitungan Luas Bidang Momen Perhitungan Luas L1 L1 = ⅓xAxT = ⅓ x 2.000 x 7.000 = 4.667 Tm²
Titik Berat L1 Terhadap Titik C = ³⁄₄ x A = ³⁄₄ x 2.000 = 1.500 m
Perhitungan Luas L2 L2 = ⅓xAxT = ⅓ x 0.720 x 7.000 = 1.681 Tm²
Titik Berat L2 Terhadap Titik A = ¹⁄₄ x A = ¹⁄₄ x 0.720 = 0.180 m
Perhitungan Luas L3 L3 = ⅔xAxT = ⅔ x 2.780 x 19.709 = 36.522 Tm²
Titik Berat L3 Terhadap Titik A = 3.5 - ⅜ x A = 3.5 - ⅜ x 2.780 = 2.458 m
Perhitungan Luas L4 L4 = AxT = 1 x 0.868 x 19.709 = 17.101 Tm²
Titik Berat L4 Terhadap Titik A = 3.5 + 0.5 x A = 3.5 + 0.5 x 0.868 = 3.934 m
Perhitungan Luas L5 L5 = ⅔xAxT = ⅔ x 0.868 x -6.402 = -3.703 Tm²
Titik Berat L5 Terhadap Titik A = 3.5 + ⅝ x A = 3.5 + ⅝ x 0.868 = 4.042 m
Perhitungan Luas L6 L6 = AxT = 1 x 3.132 x -4.427 = -13.867 Tm²
Titik Berat L6 Terhadap Titik A = 7.5 - 0.5 x A = 7.5 - 0.5 x 3.132 = 5.934 m
Perhitungan Luas L7 L7 = ⅔xAxT = ⅔ x 3.132 x 17.734 = 37.034 Tm²
Titik Berat L7 Terhadap Titik A = 7.5 - ⅝ x A = 7.5 - ⅝ x 3.132 = 5.542 m
Perhitungan Luas L8 L8 = ⅔xAxT = ⅔ x 2.181 x 17.734 = 25.791 Tm²
Titik Berat L8 Terhadap Titik A = 7.5 + ⅜ x A = 7.5 + ⅜ x 2.181 = 8.318 m
Perhitungan Luas L9 L9 = ⅓xAxT = ⅓ x 0.319 x 3.188 = 0.339 Tm²
Titik Berat L9 Terhadap Titik A = 10 - ¹⁄₄ x A = 10 - ¹⁄₄ x 0.319 = 9.920 m
Perhitungan Luas L10 L10 = ⅓xAxT = ⅓ x 1.500 x 3.188 = 1.594 Tm²
Titik Berat L10 Terhadap Titik D = ³⁄₄ x A = ³⁄₄ x 1.500 = 1.125 m
∑MA 0 0 RB'
= = = =
0 - L2 x 0.180 + L3 x 2.458 + L4 x 3.934 + L5 x 4.042 + L6 x 5.934 + L7 x 5.542 + L8 x 8.318 - L9 x 9.920 - RB' x 10 - 1.681 x 0.180 + 36.522 x 2.458 + 17.101 x 3.934 + -3.703 x 4.042 + -13.867 x 5.934 + 37.034 x 5.542 + 25.791 x 8.318 - 0.339 x 9.920 - RB' x 10 47.589 Tm²
∑MB 0 0 RA'
= = = =
0 + L2 x ( 10 - 0.180 ) - L3 x ( 10 - 2.458 ) - L4 x ( 10 - 3.934 ) - L5 x ( 10 - 4.042 ) - L6 x ( 10 - 5.934 ) - L7 x ( 10 - 5.542 ) - L8 x ( 10 - 8.318 ) + L9 x ( 10 - 9.920 ) + RA' x 10 + 1.681 x ( 10 - 0.180 ) - 36.522 x ( 10 - 2.458 ) - 17.101 x ( 10 - 3.934 ) - -3.703 x ( 10 - 4.042 ) - -13.867 x ( 10 - 5.934 ) - 37.034 x ( 10 - 5.542 ) - 25.791 x ( 10 - 8.318 ) + 0.339 x ( 10 - 9.920 ) + RA' x 10 49.268 Tm²
Kontrol :
∑V
= = = = =
0 ( RA' + RB' ) - ( - L2 + L3 + L4 + L5 + L6 + L7 + L8 - L9 ) ( 49.268 + 47.589 ) - ( - 1.681 + 36.522 + 17.101 + -3.703 + -13.867 + 37.034 + 25.791 - 0.339 ) 96.857 - 96.857 0 Tm²
Menghitung Lendutan Pada Titik C EI δ C = - RA' x 2 + L1 x 1.500 = - 49.268 x 2 + 4.667 x 1.500 = -91.535 Tm³ = -91.535 x 10⁹ / 2,153,872,031,910.340 = -0.042 Cm Menghitung Lendutan Pada Titik E EI δ E = RA' x 3.5 + L2 x ( 3.5 - 0.180 ) - L3 x ( 3.5 - 2.458 ) = 49.268 x 3.5 + 1.681 x ( 3.5 - 0.180 ) - 36.522 x ( 3.5 - 2.458 ) = 139.950 Tm³ = 139.950 x 10⁹ / 2,153,872,031,910.340 = 0.065 Cm Menghitung Lendutan Pada Titik Max EI δ Max = RA' x 6.368 + L2 x ( 6.368 - 0.180 ) - L3 x ( 6.368 - 2.458 ) - L3 x ( 6.368 - 2.458 ) - L4 x ( 6.368 - 3.934 ) = 49.268 x 6.368 + 1.681 x ( 6.368 - 0.180 ) - 36.522 x ( 6.368 - 2.458 ) - 36.522 x ( 6.368 - 2.458 ) - 17.101 x ( 6.368 - 3.934 ) = 148.312 Tm³ = 148.312 x 10⁹ / 2,153,872,031,910.340 = 0.069 Cm Menghitung Lendutan Pada Titik F EI δ F = RB' x 2.5 + L9 x ( 2.5 - 0.080 ) - L8 x ( 2.5 - 1.682 ) = 47.589 x 2.5 + 0.339 x ( 2.5 - 0.080 ) - 25.791 x ( 2.5 - 1.682 ) = 98.695 Tm³ = 98.695 x 10⁹ / 2,153,872,031,910.340 = 0.046 Cm Menghitung Lendutan Pada Titik D EI δ D = - RB' x 1.5 + L10 x 1.125 = - 47.589 x 1.5 + 1.594 x 1.125 = -69.590 Tm³ = -69.590 x 10⁹ / 2,153,872,031,910.340 = -0.032 Cm
