Page 1
cos 19 = 0.946 a = 1.5 m H = 8 m Jarak Portal (λ) = 6 m Mutu Baut = 360 Mpasin 19 = 0.326 L = 31 m h = 6.000 m Mutu Profil = 240 Mpa Mutu Las = 360 Mpa
Gaya angin = 70
= 1.5 / cos α = 1.586 m= 15.5 / cos α = 16.393 m
Asumsikan jarak gording = 1.800 m
==> n = ( 1.586 + 16.393 ) / 1.800 = 10.0 ≈ 10 buah
Asumsikan berat sendiri atap = 3.60
Dimensi GordingA. Dimensi Gording Variasi Tanpa Ada Track Stang
1. Muatan Tetap• Berat sendiri atap = 1.8 × 3.60 = 6.480 kg/m
• Berat sendiri gording = q = q kg/m +
q total = ( 6.480 + q ) kg/m
== ( 6.480 + q ) × cos 19 × 6.0 2 / 8= ( 27.5713 + 4.2548 q ) kg m
== ( 6.480 + q ) × sin 19 × 6.0 2 / 8= ( 9.4936 + 1.4651 q ) kg m
BAB IDIMENSIONING GORDING
kg/cm2
z1
z2
Maka banyak gording untuk bentang z1 + z2
kg/m2
MX1 q total × cos α × L2 / 8
MY1 q total × sin α × L2 / 8q cos
q sin
q
Sb.Y
Sb.X
h
H
a L a
z1
z2
z1
z2
Page 2
2. Muatan Angin2a. Angin Datang
= 70Koefisien = -0.02 × α × 0.4 = -0.02 × 19 × 0.4 = -0.152
= Koefisien × Jarak Gording ×= -0.152 × 1.8 × 70= -19.152 kg/m
== -19.152 × 6.0 2 / 8= -86.1840 kg m
= 0
2b. Angin Pergi= 70
Koefisien = -0.4= Koefisien × Jarak Gording ×= -0.400 × 1.8 × 70= -50.400 kg/m
== -50.400 × 6.0 2 / 8= -226.8000 kg m
= 0
3. Muatan Tak Terduga
= P × cos α × λ / 4= 100 × cos 19 × 6.0 / 4= 141.828 kg m
= P × sin α × λ / 4= 100 × sin 19 × 6.0 / 4= 48.8352 kg m
Kombinasi Momen• Akibat Muatan 1 + Muatan 2a (Angin Datang)
= ( 27.5713 + 4.2548 q ) + ( -86.1840 ) = ( -58.6127 + 4.2548 q ) kg m= ( 9.4936 + 1.4651 q ) + ( 0 ) = ( 9.4936 + 1.4651 q ) kg m
• Akibat Muatan 1 + Muatan 2b (Angin Pergi)= ( 27.5713 + 4.2548 q ) + ( -226.800 ) = ( -199.229 + 4.2548 q ) kg m= ( 9.4936 + 1.4651 q ) + ( 0 ) = ( 9.4936 + 1.4651 q ) kg m
• Akibat Muatan 1 + Muatan 3 (Muatan Tak Terduga)= ( 27.5713 + 4.2548 q ) + ( 141.828 ) = ( 169.399 + 4.2548 q ) kg m= ( 9.4936 + 1.4651 q ) + ( 48.8352 ) = ( 58.3288 + 1.4651 q ) kg m
Maka momen maksimum yang menentukan : = ( 169.399 + 4.2548 q ) kg m= ( 58.3288 + 1.4651 q ) kg m
Dicoba profil Channel Lips C 150×75×20×4.5Data: q = 11 kg/m Ix = 489 ix = 5.92 cm
Wx = 65.2 Iy = 99.2 iy = 2.664757 cm
Wy = 19.84 F = 13.97 E = 2100000q total = ( 6.480 + ### ) = 17.480 kg/m
qa kg/cm2
qa datang qa
MX2a qa datang × L2 / 8
MY2a
qa kg/cm2
qa datang qa
MX2b qa datang × L2 / 8
MY2b
MX3
MY3
MX Total
MY Total
MX Total
MY Total
MX Total
MY Total
MX Total
MY Total
cm4
cm3 cm4
cm3 cm2 kg/cm2
q datang
Sb.Y
Sb.X
P = 100 kgSb.Y
Sb.X
P cos
P sin
P
q pergi
Sb.Y
Sb.X
Page 3
Kontrol Tegangan
= + ≤
=( 16939.9 + 425.48 × 11.0 )
+( 5832.88 + 146.51 × 11.0 )
≤ 160065.2 19.84
706.8224 ≤ 1600 ….. OK
Kontrol Lendutan
=5
+1
384 E × Ix 48 E × Ix
=5 0.175 × cos 19 × 600 4
+1 100 × cos 19 × 600 3
384 2100000 × 489 48 2100000 × 489= 0.686 cm
=5
+1
384 E × Iy 48 E × Iy
=5 0.175 × cos 19 × 600 4
+1 100 × cos 19 × 600 3
384 2100000 × 99.2 48 2100000 × 99.2= 1.164 cm
F = + = 0.686 2 + 1.164 2 = 1.351 cm
=L
=600
= 3.333 cm180 180
F < ….. OK
B. Dimensi Gording Variasi Dengan Track StangDirencanakan gading-gading kap memiliki 3 medan ekonomis
2.00 m
2.00 m
2.00 m
1. Muatan Tetapq total = ( 6.480 + q ) kg/m
== ( 6.480 + q ) × cos 19 × 6.0 2 / 8= ( 27.5713 + 4.2548 q ) kg m
=
= ( 6.480 + q ) × sin 19 × ( 6.0 / 3 / 8= ( 1.0548 + 0.1628 q ) kg m
2. Muatan Angin2a. Angin Datang
= -86.1840 kg m= 0 kg m
2b. Angin Pergi= -226.8000 kg m= 0 kg m
3. Muatan Tak Terduga== 100 × cos 19 × 6.0 / 4= 141.828 kg m
== 100 × sin 19 × ( 6.0 / 3 ) / 4= 16.2784 kg m
σTerjadiMX MY σprofilWX WX
kg/cm2
kg/cm2 kg/cm2
FXqTotal × cos α × L4 P × cos α × L3
FYqTotal × cos α × L4 P × cos α × L3
FX2 FY
2
Fizin
Fizin
MX1 q total × cos α × LX2 / 8
MY1 q total × sin α × LY2 / 8
)2
MX2a
MY2a
MX2b
MY2b
MX3 P × cos α × λX / 4
MY3 P × sin α × λY / 4
Track Stang
Ly
Lx
Gading Kap
Gading Kap
Sb.Y
Sb.X
Page 4
Kombinasi Momen• Akibat Muatan 1 + Muatan 2a (Angin Datang)
= ( 27.5713 + 4.2548 q ) + ( -86.1840 ) = ( -58.6127 + 4.2548 q ) kg m= ( 1.0548 + 0.1628 q ) + ( 0 ) = ( 1.0548 + 0.1628 q ) kg m
• Akibat Muatan 1 + Muatan 2b (Angin Pergi)= ( 27.5713 + 4.2548 q ) + ( -226.800 ) = ( -199.229 + 4.2548 q ) kg m= ( 1.0548 + 0.1628 q ) + ( 0 ) = ( 1.0548 + 0.1628 q ) kg m
• Akibat Muatan 1 + Muatan 3 (Muatan Tak Terduga)= ( 27.5713 + 4.2548 q ) + ( 141.828 ) = ( 169.399 + 4.2548 q ) kg m= ( 1.0548 + 0.1628 q ) + ( 16.2784 ) = ( 17.3332 + 0.1628 q ) kg m
Maka momen maksimum yang menentukan : = ( 169.399 + 4.2548 q ) kg m= ( 17.3332 + 0.1628 q ) kg m
Dicoba profil Channel Lips C 125×50×20×2.3Data: q = 4.51 kg/m Ix = 137 ix = 4.88 cm
Wx = 21.92 Iy = 20.6 iy = 1.89 cm
Wy = 6.22 F = 5.747 E = 2100000q total = ( 6.480 + 4.510 ) = 10.990 kg/m
Kontrol Tegangan
= + ≤
=( 16939.9 + 425.48 × 4.5 )
+( 1733.32 + 16.28 × 4.5 )
≤ 160021.92 6.22
1150.821 ≤ 1600 ….. OK
Kontrol Lendutan
=5
+1
384 E × Ix 48 E × Ix
=5 0.110 × cos 19 × 600 4
+1 100 × cos 19 × 600 3
384 2100000 × 137 48 2100000 × 137= 2.088 cm
=5
+1
384 E × Iy 48 E × Iy
=5 0.110 × cos 19 × ( 600 / 3
+1 100 × cos 19 × ( 600 / 3
384 2100000 × 20.6 48 2100000 × 20.6= 0.143 cm
F = + = 2.088 2 + 0.143 2 = 2.093 cm
=L
=600
= 3.333 cm180 180
F < ….. OK
Kesimpulan : Profil gording yang di pakai adalah Channel Lips C 125×50×20×2.3
h = 125 mmb = 50 mmd = 20 mmt = 2.3 mmF = 5.747q = 4.51 kg/mWx = 21.92
Wy = 6.22
Ix = 137
Iy = 20.6
Jumlah profil Channel Lips C yang diperlukan : n = ( Jumlah Lapangan Gording ) + 1 = 10 + 1 = 11 buah 9.989
MX Total
MY Total
MX Total
MY Total
MX Total
MY Total
MX Total
MY Total
cm4
cm3 cm4
cm3 cm2 kg/cm2
σTerjadiMX MY σprofilWX WX
kg/cm2
kg/cm2 kg/cm2
FXqTotal × cos α × LX
4 P × cos α × LX3
FYqTotal × cos α × LY
4 P × cos α × LY3
)4 )3
FX2 FY
2
Fizin
Fizin
cm2
cm3
cm3
cm4
cm4
h
Cx
X
Y
b
Cy
d
t
Page 5
2 m
2 m
2 m
a = ### mb = ### mBerat sendiri atap = ###Jarak batang tarik = 2 mBerat sendiri gording (q) = 5 kg/mBeban tak terduga = ### kg
Beban yang bekerjaA. Tipe 1 = Atap = 2.00 × 1.78 × 3.60 × sin 19 = 4.171 kg
Gording = 2.00 × 4.51 × sin 19 = 2.937 kgBeban Tak Terduga = 100 × sin 19 = 32.557 kg +
= 39.665 kg
A. Tipe 2 = Atap = 2.00 × 1.8 × 3.60 × sin 19 = 4.219 kgGording = 2.00 × 4.51 × sin 19 = 2.937 kgBeban Tak Terduga = 100 × sin 19 = 32.557 kg +
= 39.713 kg
Beban yang dipikul oleh track stang := + 9 = 397.080 kg
Dibutuhkan : ≤
≤ 1600A
≤ 1600
d ≥1600π/4
d ≥397.080
1600 × π / 4d ≥ 0.562 cm
Ambil : d = 6 mm
BAB IIDIMENSI BATANG TARIK (TRACK STANG)
kg/m2
N1
N2
NTotal N1 N2
σTerjadi σprofil
NTotal kg/cm2
NTotalkg/cm2
πd2/4
NTotal
aaaaaab
Page 6
A. Gelagar MelintangKoefisien kejut :
L diambil = 31 - 0.5 = 30.5 m
Menurut pedoman perencanaan untuk rumah dan gedung, koefisien kejut untuk beban yang membebani struktur :υ =
Dimana : v = Kecepatan angkat maksimum = 1.0 m/s= Koefisien kekakuan struktur keran induk = 0.6= Koefisien sifat mesin angkat dari keran angkat = 1.0
Maka : υ = 1 + (0.6) (1.0) (1.0) ≥ 1.15υ = 1.6
I. Merencanakan profil dasar= 5000 kg= = 1.6 × 5000 = 8000 kg
=8000
×30.5
= 61000 kg m = 6100000 kg cm2 2
= =6100000
= 3812.501600
Coba profil WF 700×300×15×28
Data : q = 215 kg/m = 6695
h = 708 mm = 854
b = 302 mm = 237000
= 15 mm = 12900
= 28 mm A = 273.6
8000+
1× 215 × 30.5 = 7278.750 kg
2 2
= 7278.75 ×30.5
-1
× 215 × ( 30.5 ) 2= 86000.469 kg m = 8600046.875 kg cm
2 2 2
= =8600046.875
= 1284.5 ≤ = 1600 ….. OK6695
BAB IIIDIMENSI GELAGAR MELINTANG
( 1 + K1 × K2 × v )
K1
K2
PTotal
PTotal υ × Pcrane
Mmax
WmaxMmax
cm3
σprofil
WX cm3
WY cm3
IX cm4
tw IY cm4
tf cm2
RVA =
Mmax
σTerjadiMmax
kg/cm2 σprofil kg/cm2
WX
Gelagar Melintang
P
Gelagar Memanjang
Crane
b
htw
tf
Page 7
Kontrol Kips
=L × h
=30500 × 708
= 2553.69> , maka
= ×302 × 28
=0.63 E
=0.63 × 2100000
= 826.875 =2553.69
× 0.701600 826.88
250 < < , maka= ( 1 - 0.3 × ) = 3458.966
= 1600 ( 1 - 0.3 ×2303.69 )576.875
= -316.83 < = 1284.5 ….. TIDAK OK
Jadi diperlukan pelat tepiII. Penambahan Pelat ( 5 × 287 )
287 = 2 × ( 0.5 × 28.7 × 0.00785= 0.225295 kg/cm= 22.5295 kg/m
5=
28.7 × 0.5 3+ 0.5 × 28.7 × 35.65
228 12
= 18238.0368= 2 × 18238.0368
= 36476.0737
= 36476.0737 + 237000
= 273476.074
708 718 = =2 × 273476.074
= 7617.717971.8
7278.75 +22.5295 × 30.5
= 7622.325 kg2
=7622.325 × 30.5
-215 + 22.5295
× 30.52
2 8= 88620.2271719 kg m
28 = 8862022.71719 kg cm5
= =8862022.717
= 1163.347617.718
< = 1600 ….. OK302
Kontrol Kipsh
=718
= 47.86667 < 75 ….. OK15
L≥
1.25 b===>
30500≥
1.25 × 302h 718 33
42.479 ≥ 11.43939 ….. OK
=L × h
=30500 × 718
= 2214.033( 302 × 28 ) + ( 287 × 5 )
=0.63 E
=0.63 × 2100000
= 826.8751600
> , maka= ×
250 < < , maka=
=826.875
× 0.70 × 1600 = 16002214.03
= 418.2865 < = 1163.34 ….. TIDAK OK = -34.2116
C1C1 C2
σkipsC2
0.70 σprofilb × tf C1
C2 σprofil
C1 C2σkips σprofil
C1 - 250 kg/cm2
C2 - 250
kg/cm2 σTerjadi kg/cm2
mm2
qbs pelat 1 kg/cm3 )
IX Pelat 1
cm4
IX 2 Pelat
cm4
IX Total
cm4
WX Total2 IX Total
cm3
hTotal
RVA =
Mmax
σTerjadiMmax
kg/cm2
WX
σTerjadi σprofil kg/cm2
tw
tf
C1 b × tf
C2 σprofil
C1 C2σkips
C20.70 σprofil
C1 C2σkips σprofil
C1
kg/cm2 σTerjadi kg/cm2
Page 8
Penambahan Pelat ( 5 × 267 )
267 = 2 × ( 0.5 × 26.7 × 0.00785= 0.209595 kg/cm= 20.9595 kg/m
5=
26.7 × 0.5 3+ 0.5 × 26.7 × 36.15
25 12
28 = 17446.3585
= 2 × 17446.3585
= 34892.7170
= 34892.7170 + 273476.074
= 308368.791
708 728 = =2 × 308368.791
= 8471.670172.8
7622.32 +20.9595 × 30.5
= 7941.957 kg2
=7941.957 × 30.5
-237.53 + 20.96
× 30.52
2 8= 91057.4240313 kg m
28 = 9105742.40313 kg cm5
= =9105742.403
= 1074.855 8471.670
< = 1600 ….. OK302
Kontrol Kipsh
=728
= 48.53333 < 75 ….. OK15
L≥
1.25 b===>
30500≥
1.25 × 302h 728 38
41.896 ≥ 9.934211 ….. OK
=L × h
=30500 × 728
= 1977.908( 302 × 28 ) + ( 287 × 5 ) + ( 267 × 5 )
=0.63 E
=0.63 × 2100000
= 826.8751600
> , maka= ×
250 < < , maka
=826.875
× 0.70 × 16001977.908
= 468.2219 < = 1074.85 ….. TIDAK OK
mm2
qbs pelat 2 kg/cm3 )
IX Pelat 2
cm4
IX 2 Pelat
cm4
IX Total
cm4
WX Total2 IX Total
cm3
hTotal
RVA =
Mmax
σTerjadiMmax
kg/cm2
WX
σTerjadi σprofil kg/cm2
tw
tf
C1 b × tf
C2 σprofil
C1 C2σkips
C20.70 σprofil
C1 C2σkips
C1
kg/cm2 σTerjadi kg/cm2
Page 9
Penambahan Pelat ( 5 × 247 )
247 = 2 × ( 0.5 × 24.7 × 0.00785= 0.193895 kg/cm
5 = 19.3895 kg/m5
=24.7 × 0.5 3
+ 0.5 × 24.7 × 36.42
5 1228 = 16363.5133
= 2 × 16363.5133
= 32727.0266
= 32727.0266 + 308368.791
= 341095.817
708 733 = =2 × 341095.817
= 9306.843673.3
7941.96 +19.3895 × 30.5
= 8237.647 kg2
=8237.647 × 30.5
-258.49 + 19.39
× 30.52
2 8= 93312.0593281 kg m
28 = 9331205.93281 kg cm5
= =9331205.933
= 1002.625 9306.844
5 < = 1600 ….. OK302
Kontrol Kipsh
=733
= 48.86667 < 75 ….. OK15
L≥
1.25 b===>
30500≥
1.25 × 302h 733 43
41.610 ≥ 8.77907 ….. OK
=L × h
=30500 × 733
= 1991.493( 302 × 28 ) + ( 287 × 5 ) + ( 267 × 5 ) + ( 247 × 5 )
=0.63 E
=0.63 × 2100000
= 826.8751600
> , maka= ×
=826.875
× 0.70 × 16001991.493
= 465.028 < = 1002.62 ….. TIDAK OK
Kontrol Lendutan= 215 + 22.5295 + 20.960 + 19.389 = 277.879 kg/m
=8000 × 3050 3
+5 × 277.879 × 3050 4
= 10.973 cm48 × ( 2100000 ) × ( 341095.817 ) 384 × ( 2100000 ) × ( 341095.817 ) × 100
=30500
= 122.000 mm 12.200 cm ≥ 10.973 cm ….. OK250
mm2
qbs pelat 2 kg/cm3 )
IX Pelat 2
cm4
IX 2 Pelat
cm4
IX Total
cm4
WX Total2 IX Total
cm3
hTotal
RVA =
Mmax
σTerjadiMmax
kg/cm2
WX
σTerjadi σprofil kg/cm2
tw
tf
C1 b × tf
C2 σprofil
C1 C2σkips
C20.70 σprofil
C1
kg/cm2 σTerjadi kg/cm2
qTotal
Ymax
Yizin
Page 10
III. Pemutusan Pelat• Pelat 3
P = 8000 kg
=( 30.5 - x )
x = x -1
30.5 30.5
= 215 + 22.529 + 20.960 + 19.389 = 277.879 kg/m
= 8000 ( x -1 ) +
30.5 ( x -1 ) × 277.879
30.5 2 30.5
= 8000 x -8000
+ 4237.65 x -4237.65
30.5 30.5
= 12237.647 x -12237.647
30.5= 12237.647 x - 401.234
× ≥1600 × 8471.6701 ≥ ( 12237.647 x - 401.234 ) × 100
0 ≤ 401.234 - 12237.647 x + 135546.721x ≤ ∞
Jadi yang menentukan adalah kips dan lendutan :× ≥
468.22 × 8471.6701 ≥ ( 12237.647 x - 401.234 ) × 100
0 ≤ 401.234 - 12237.647 x + 39666.213x ≤ 3.68704040501905 Ambil x = 3.00 m
• Pelat 2
P = 8000 kg
=( 30.5 - x )
x = x -1
30.5 30.5
=27.50
x30.5
=3.00
x30.5
= 215 + 22.529 + 20.960 = 258.489 kg/m= 19.389 kg
Y1 x2
qTotal
Mx x2 x2
x2 x2
x2
x2
σprofil WX Mx
x2
x2
σkips WX Mx
x2
x2
Y1 x2
Y2
Y3
qTotal
qPelat 3
x
Y1
x
P
Y1Y2
Y3
Page 11
= 8000 ( x -1 ) +
30.5 ( x -1 ) × 258.489 +
24.5 ( 27.50 + 3.00x ) × 19.389
30.5 2 30.5 2 30.5
= 8000 x -8000
+ 3941.96 x -3941.96
+ 237.521 x30.5 30.5
= 12179.479 x -11941.957
30.5= 12179.479 x - 391.540
Jadi yang menentukan adalah kips dan lendutan :× ≥
418.29 × 7617.7179 ≥ ( 12179.479 x - 391.540 ) × 100
0 ≤ 391.540 - 12179.479 x + 31863.882x ≤ 2.883484 m ==> Ambil x = 2.50 m
• Pelat 1
P = 8000 kg
=( 30.5 - x )
x = x -1
30.5 30.5
=28.00
x30.5
=27.50
x30.5
=3.00
x30.5
=2.50
x30.5
= 215 + 22.529 = 237.529 kg/m= 19.389 kg= 20.960 kg
= 8000 ( x -1 ) +
30.5 ( x -1 ) × 237.529 +
25.5 ( 28.00 + 2.50x ) × 20.960
30.5 2 30.5 2 30.524.5 ( 27.50 + 3.00
x ) × 19.3892 30.5
= 8000 x -8000
+ 3622.32 x -3622.32
+ 267.234 x + 237.521 x30.5 30.5
= 12127.080 x -11622.325
30.5= 12127.080 x - 381.060
Jadi yang menentukan adalah kips dan lendutan :× ≥
-316.83 × 6695.0000 ≥ ( 12127.080 x - 381.060 ) × 100
0 ≤ 381.060 - 12127.080 x + -21211.739x ≤ -1.6623 m ==> Ambil x = 1.50 m
Mx x2 x2
x2 x2
x2
x2
σkips WX Mx
x2
x2
Y1 x2
Y2
Y3
Y4
Y5
qTotal 2
qPelat 3
qPelat 2
Mx x2 x2
x2 x2
x2
x2
σkips WX Mx
x2
x2
xP
Y1Y2
Y3
Y4Y5
Page 12
30.5 m
27.5 m
25.5 m
24.5 m
1.50 m
2.50 m
3.00 m
27.50 m
28.00 m
29.00 m
8000 ( 30.5 - x ) +215 × 30.5
+22.529 × 27.5
+20.960 × 25.5
+19.389 × 24.5
30.5 2 2 2 2
= 8000 ( 30.5 - x ) + 4093.285630.5
Untuk x = 1.50 m=
= { 8000 ( 30.5 - 1.50 ) + 4093.2856 } × 1.50 -215 × 1.50 2
30.5 2= 17307.8895031 kg m= 1730788.95031 kg cm
= =1730788.95031
= 258.520≤ = 1600 ….. OK
6695 ≤ = -316.83 ….. TIDAK OK
Untuk x = 2.50 m= - 1.50
= { 8000 ( 30.5 - 2.50 ) + 4093.2856 } × 2.50 -215 × 2.50 2
-22.5295 × 1.00 2
30.5 2 2= 27910.7300502 kg m= 2791073.00502 kg cm
= =2791073.00502
= 366.392≤ = 1600 ….. OK
7617.7179 ≤ = 418.2865 ….. OK
RVA =
Mx RVA × X - qprofil × X2 / 2
σTerjadiMX
kg/cm2σprofil kg/cm2
WX σkips kg/cm2
Mx RVA × X - qprofil × X2 / 2 - qpelat1 ( X )2 / 2
σTerjadiMX
kg/cm2σprofil kg/cm2
WX σkips kg/cm2
Page 13
Untuk x = 3.00 m= - 1.50 - 2.50
= { 8000 ( 30.5 - 3.00 ) + 4093.2856 } × 3.00 -215 × 3.00 2
-22.5295 × 1.50 2
30.5 2 2
-20.9595 × 0.50 2
2= 32923.7355123 kg m= 3292373.55123 kg cm
= =3292373.55123
= 388.633≤ = 1600 ….. OK
8471.6701 ≤ = 468.2219 ….. OK
IV. Kontrol Lendutan• Akibat Berat Sendiri + Pelat
= 4093.2856 kg• Untuk x = 1.50 m
= 4093.2856 × 1.50 - 215 × 1.50 2= 5898.053437 kg m
• Untuk x = 2.50 m= 4093.2856 × 2.50 - 215 × 2.50 2 - 22.5295 × ( 2.50 - 1.50 2= 9550.074312 kg m
• Untuk x = 3.00 m= 4093.2856 × 3.00 - 215 × 3.00 2 - 22.5295 × ( 3.00 - 1.50 2
- 20.9595 × ( 3.00 - 2.50 2= 11284.39125 kg m
• Untuk x = 15.25 m= 4093.2856 × 15.25 - 215 × 15.25 2 - 22.5295 × ( 15.25 - 1.50 2
- 20.9595 × ( 15.25 - 2.50 2 - 19.3895 × ( 15.25 - 3.00 2= 32133.96245 kg m
1.50
2.50
3.00
= 2 / 3 × 1.50 ×= 2 / 3 × 1.50 × 5898.053437= 5898.053437
= ( 2.50 - 1.50 ) ×= ( 2.50 - 1.50 ) × 5898.053437= 5898.053437
= 2 / 3 × ( 2.50 - 1.50 ) × ( - )= 2 / 3 × ( 2.50 - 1.50 ) × ( 9550.074312 - 5898.053437 )= 2434.681
Mx RVA × X - qprofil × X2 / 2 - qpelat1 ( X )2 / 2 - qpelat2 ( X )2 / 2
σTerjadiMX
kg/cm2σprofil kg/cm2
WX σkips kg/cm2
RVA
M12 /
M22 / )2/
M32 / )2/
)2/
M42 / )2/
)2/ )2/
L1 M1
kg m2
L2 M1
kg m2
L3 M2 M1
kg m2
1 2
34
5
6
7
X1
X2
X3
X4
X5
X6
X7
L1 L2L3 L4L5 L6 L7
L
X
Page 14
= ( 3.00 - 2.50 ) ×= ( 3.00 - 2.50 ) × 9550.074312= 4775.037156
= 2 / 3 × ( 3.00 - 2.50 ) × ( - )= 2 / 3 × ( 3.00 - 2.50 ) × ( 11284.39125 - 9550.074312 )= 578.106
= ( 15.25 - 3.00 ) ×= ( 15.25 - 3.00 ) × 11284.39125= 138233.793
= 2 / 3 × ( 15.25 - 3.00 ) × ( - )= 2 / 3 × ( 15.25 - 3.00 ) × ( 32133.96245 - 11284.39125 )= 170271.498
ΣL = + + + + + += 5898.053437 + 5898.053437 + 2434.681 + 4775.037156 + 578.106 + 138233.793 + 170271.498= 19583.930
= 5 / 8 × 1.50 = 0.93750 m= 1.50 + ( 2.50 - 1.50 ) / 2 = 2.00000 m= 1.50 + 5 / 8 × ( 2.50 - 1.50 ) = 2.12500 m= 2.50 + ( 3.00 - 2.50 ) / 2 = 2.7500 m= 2.50 + 5 / 8 × ( 3.00 - 2.50 ) = 2.8125 m= 3.00 + ( 15.25 - 3.00 ) / 2 = 9.1250 m= 3.00 + 5 / 8 × ( 15.25 - 3.00 ) = 10.6563 m= × + × + × + × + × + × + ×
ΣL= 158.9617 m
Lendutan :• Untuk x = 1.50 m
M = 19583.930 × 1.50 - 5898.053437 × ( 1.50 - )= 19583.930 × 1.50 - 5898.053437 × ( 1.50 - 0.93750 )= 26058.24
y =26058.24 × 10 6
+8000 × 1.50 2 × ( 30.5 - 1.50 × 10 6
2100000 × 237000 3 × 30.5 × 2100000 × 237000= 0.3848 cm < 12.200 cm ….. OK
• Untuk x = 2.50 mM = 19583.930 × 2.50 - 5898.053437 × ( 2.50 - ) - 5898.053437 × ( 2.50 - ) - 2434.681 × ( 2.50 -
= 19583.930 × 2.50 - 5898.053437 × ( 2.50 - 0.93750 ) - 5898.053437 × ( 2.50 - 2.00000 )- 2434.681 × ( 2.50 - 2.12500 )
= 35882.09
y =35882.09 × 10 6
+8000 × 2.50 2 × ( 30.5 - 2.50 × 10 6
2100000 × 273476.074 3 × 30.5 × 2100000 × 273476.074= 0.8085 cm < 12.200 cm ….. OK
• Untuk x = 3.00 mM = 19583.930 × 3.00 - 5898.053437 × ( 3.00 - ) - 5898.053437 × ( 3.00 - ) - 2434.681 × ( 3.00 -
- 4775.037156 × ( 3.00 - ) - 578.106 × ( 3.00 -= 19583.930 × 3.00 - 5898.053437 × ( 3.00 - 0.93750 ) - 5898.053437 × ( 3.00 - 2.00000 )
- 2434.681 × ( 3.00 - 2.12500 ) - 4775.037156 × ( 3.00 - 2.7500 )- 578.106 × ( 3.00 - 2.8125 )
= 37256.50
y =37256.50 × 10 6
+8000 × 3.00 2 × ( 30.5 - 3.00 × 10 6
2100000 × 308368.791 3 × 30.5 × 2100000 × 308368.791= 0.9765 cm < 12.200 cm ….. OK
L4 M2
kg m2
L5 M3 M2
kg m2
L6 M3
kg m2
L7 M4 M3
kg m2
L1 L2 L3 L4 L5 L6 L7
kg m2
X1
X2
X3
X4
X5
X6
X7
XΣ L1 X1 L2 X2 L3 X3 L4 X4 L5 X5 L6 X6 L7 X7
X1
kg m3
)2
X1 X2 X3 )
kg m3
)2
X1 X2 X3 )X4 X5 )
kg m3
)2
Page 15
• Untuk x = 15.25 mM = 19583.930 × 15.25 - 19583.930 × ( 15.25 - )
= 19583.930 × 15.25 - 19583.930 × ( 15.25 - 158.9617 )= 3113095.51
y =3113095.51 × 10 6
+8000 × 30.5 10 6
2100000 × 341095.817 48 × 2100000 × 341095.817= 10.9477 cm < 12.200 cm ….. OK
V. Kontrol Lintang== 4093.2856 + 8000= 12093.2856 kg
Sx = b × × ( h - ) + × ( h- ) 1
2 2 2
= 30.2 × 2.8 × ( 70.8 - 2.8 ) + 1.5 × ( 70.8- 2.8 ) 1
2 2 2= 3672.11
= =12093.2856 × 3672.11
= 124.917 ≤ = 928 ….. OK1.5 × 237000
VI. Sambungan30.5 m27.5 m25.5 m24.5 m
9.25 m 12 m 9.25 m
1.50 m2.50 m
3.00 m
Mutu las = 2400
a. Sambungan Profil Dasar1. Sayap (Flens)
= 4093.2856 kg
= 4093.2856 + ( 30.5 - 9.25 ) 8000 = 9667.0561 kg30.5
M = 9667.0561 × 9.25 - 215 × 9.25 2 - 22.5295 × ( 9.25 - 1.5
- 20.9595 × ( 9.25 - 2.50 - 19.3895 × ( 9.25 - 3.00= 78689.527 kg m= 7868952.7 kg cm
=7868952.7
= 845.50189306.8436
XΣ
kg m3
3 ×
Dmax RVA (x=0)
tftf tw tf
2 ×
2 ×
cm3
τterjadiDmax SX
kg/cm2 0.58 σprofil kg/cm2
tw IX
kg/cm2
RVA akibat berat sendiri + pelat
RA
2 / )2 / 2
)2 / 2 )2 / 2
σTerjadi kg/cm2
Page 16
Lebar flens = 30.2 cmTebal flens = 2.8 cmLebar pelat atas = 28.7 cmTebal pelat atas = 0.5 cmLebar pelat bawah = 28.7 cm
≤b × ≤ 0.5 × 28.7 + 28.7 × × 2
30.2 × 2.8 ≤ 14.35 + 57.4
84.560 ≤ 14.35 + 57.4
≥ 70.210 / 57.4≥ 1.223171 cm
Ambil tebal pelat bawah = 5 mm
Sambungan Las
=340.0
×369
369 =340.0
× 845.5018340.0
369= 779.0531
= ×= 779.0531 × 2.8 × 30.2= 65876.73135 kg
• Las 1α = 45 ˚
c =1
= 0.707( + 3
= Lebar pelat = 28.7 + 2 × 28.7 = 86.1 cmAmbil tebal las : = 0.2 cm
= 2400 × 0.707 × 0.2 × 86.1 × 0.707= 20664 kg
• Las 2= = ( 65876.73135 - 20664 ) / 2 = 22606.366 kg
α = 0 ˚
c =1
= 0.577( + 3
Ambil tebal las : = 0.5 cm=
22606.366 = 2400 × 0.707 × 0.5 × × 0.577= 46.145 cm
= + 3a = 46.145 + 3 × 0.707 × 0.5 = 47.206 cm= 30 cm
Kesimpulan :Untuk sambungan flens digunakan pelat : 2 / ( 60 × 28.7 × 0.5 )
4 / ( 60 × 28.7 × 0.5 )
Aflens Apelat
tf tp
tp
tp
tp
tp
σf σTerjadi
kg/cm2
Pflens σf Af
sin2α cos2α )0.5
L1
tlas
Plas = σlas × Ageser × c
P2 ( P - P1 ) / 2
sin2α cos2α )0.5
tlas
P2 σlas × Ageser × cL2
L2
L2 perlu L2
Ambil L2
cm3
cm3
Terjadi
f
2
1
2
P2P2
P1
L2
L2
L1
Page 17
2. Badan (Web)
369 =326.0
×326
369
=326.0
× 845.5018369
= 746.9745
5 mm≤
1.5 × 65.2 12 ≤ 2 × 0.5 × 12
≥ 415751.712
≥ 74.6 cm ( tetapi harus lebih kecil dari 65.2 cm )= 20 cm
= 2 × 0.5 × 20 3 / 12 = 666.6666667
Garis pengaruh D= 8000 kg
3.00 m0.696721
2.50 m
1.50 m
9.25= 0.303279
30.5
9.25 m 21.25 m
=1.50
× 0.303279 = 0.04918 =3.00
× 0.696721 = 0.098369.25 21.25
=2.50
× 0.303279 = 0.08197 =2.50
× 0.696721 = 0.081979.25 21.25
=3.00
× 0.303279 = 0.09836 =1.50
× 0.696721 = 0.049189.25 21.25
= 8000 × 0.696721 + 215 × 21.25 × 0.696721 / 2+ 22.529 × ( 21.25 - 1.50 ) × ( 0.696721 + ) / 2+ 20.960 × ( 21.25 - 2.50 ) × ( 0.696721 + ) / 2+ 19.389 × ( 21.25 - 3.00 ) × ( 0.696721 + ) / 2- 19.389 × ( 9.25 - 3.00 ) × ( 0.303279 + ) / 2- 20.960 × ( 9.25 - 2.50 ) × ( 0.303279 + ) / 2- 20.960 × ( 9.25 - 1.50 ) × ( 0.303279 + ) / 2
= 7544.759 kg
= ×= 746.9745 × 66.67= 49798.30 kg cm= 497.9830 kg m
σw σTerjadi
kg/cm2
Ambil tebal pelat penyambung badan tp =IX badan IX pelat
3 / hp3 /
hp3
hp
Ambil tinggi pelat penyambung badan hp
Maka Ix pelat cm4
Y1 Y4
Y2 Y5
Y3 Y6
Dmaks
Y6
Y5
Y4
Y3
Y2
Y1
Mpelat σw Wx pelat
Terjadi
w
y1 y2 y3
y4
y5 y6
x
Page 18
20 cm
60 cm 60 cmLas dianggap 1 satuan
X =60 × 30 + 60 × 30
= 25.71429 cm20 + 60 + 60
= { 1 × 60 12 + ( 60 × 1 ) × ( 60 - 25.71429 } × 2
+ { 20 × 1 12 + ( 20 × 1 ) × ( 25.71429 }
= 190287.381
= { 60 × 1 12 + ( 60 × 1 ) × ( 10 } × 2 + { 1 × 20 12 }
= 12676.667
+ = 190287.381 + 12676.667 = 202964.048
= × ( 60 - 25.71429 ) / 2 = 7544.759 × 17.1429 = 129338.717 kg cm = 1293.38717 kg m= M + = 49798.297 + 129338.717 = 179137.014 kg cm = 1791.37014 kg m
=× ( 60 - 25.71429 )
=179137.01444 × 34.28571
= 30.26073202964.048
=× ( 20 / 2 )
=179137.01444 × 10
= 8.82605202964.048
=D / 2
=7544.759 / 2
= 26.9455760 + 60 + 20
2 + ( + = 8.82605 2 + ( 30.26073 + 26.94557
= 57.88315 ≤ = 1440
a = =57.88315
= 0.040197 cm1440
a=
0.040197= 0.056847 cm ≤ 0.5 cm ….. OK
0.707 0.707Ambil tebal las : t = 0.5 mmUntuk sambungan web digunakan pelat : 2 / ( 120 × 20 × 5 )
b. Sambungan Pelat
=357
× =367
×369 369
=357
× 845.5018 =367
× 845.5018356.5 361.5 366.5 369 369 369
= 816.8601 = 839.7734
=362
×369
=362
× 845.5018369
= 828.3168
Tebal las seluruhnya diambil t = 2 mm= × = 816.8601 × 0.5 × 28.7 = 11721.942 kg= × = 828.3168 × 0.5 × 26.7 = 11058.029 kg= × = 839.7734 × 0.5 × 24.7 = 10371.202 kg
Ilas X3 / )2
3 / )2
cm4
Ilas Y3 / )2 3 /
cm4
Ilas Total = Ilas X Ilas Y cm4
MS Dmax
MT MS
τVMT
kg/cm2
Ilas Total
τHMT
kg/cm2
Ilas Total
τD kg/cm2
Alas
τlas = τH τV τD )2 )2
kg/cm2 0.6 σlas kg/cm2
τlas
0.6 σlas
tlas =
cm3
σ1 σTerjadi σ3 σTerjadi
kg/cm2 kg/cm2
σ2 σTerjadi
kg/cm2
P1 σ1 A1
P2 σ2 A2
P3 σ3 A3
x
Terjadi
2
3
1
Page 19
• Pelat 1= × α = 45 ˚= 0.707 × 2400 × 0.707 × 0.2 × 26.7
c =1
= 0.707= 6408 kg ( + 3
= - α = 0 ˚= ( 11721.942 - 6408 ) / 2
c =1
= 0.577= 2656.971 kg ( + 3
= ×2656.971 = 0.577 × 2400 × 0.707 × 0.2 ×2656.971 = 195.959 ×
= 13.559 cm
= + 30 = 13.559 + 30 = 43.559 cm ==> Ambil = 36 cm
Untuk sambungan pelat 1 digunakan pelat : 2 / ( 72 × 26.7 × 0.5 )
60 cm = Sambungan antar flens72 cm = Sambungan antar pelat 1
• Pelat 2= × α = 45 ˚= 0.707 × 2400 × 0.707 × 0.2 × 24.7
c =1
= 0.707= 5928 kg ( + 3
= - α = 0 ˚= ( 11058.029 - 5928 ) / 2
c =1
= 0.577= 2565.014 kg ( + 3
= ×2565.014 = 0.577 × 2400 × 0.707 × 0.2 ×2565.014 = 195.959 ×
= 13.090 cm
= + 36 = 13.090 + 36 = 49.090 cm ==> Ambil = 66 cm
Untuk sambungan pelat 1 digunakan pelat : 2 / ( 132 × 24.7 × 5 )
Plas 1 σlas Ageser
sin2α cos2α )0.5
2 Plas 2 P1 Plas 1
Plas 2
sin2α cos2α )0.5
Plas 2 σlas Ageser
L2'L2'
L2'
L2 L2' L2
cm3
Plas 1 σlas Ageser
sin2α cos2α )0.5
2 Plas 2 P1 Plas 1
Plas 2
sin2α cos2α )0.5
Plas 2 σlas Ageser
L2'L2'
L2'
L2 L2' L2
cm3
Pelat 1Flens
Pelat 2Pelat 1Flens
Page 20
60 cm = Sambungan antar flens72 cm = Sambungan antar pelat 1
132 cm = Sambungan antar pelat 2
• Pelat 3= × α = 45 ˚= 0.707 × 2400 × 0.707 × 0.2 × 22.7
c =1
= 0.707= 5448 kg ( + 3
= - α = 0 ˚= ( 10371.202 - 5448 ) / 2
c =1
= 0.577= 2461.601 kg ( + 3
= ×2461.601 = 0.577 × 2400 × 0.707 × 0.2 ×2461.601 = 195.959 ×
= 12.562 cm
= + 66 = 12.562 + 66 = 78.562 cm ==> Ambil = 72 cm
Untuk sambungan pelat 1 digunakan pelat : 2 / ( 144 × 22.7 × 5 )
60 cm = Sambungan antar flens72 cm = Sambungan antar pelat 1
132 cm = Sambungan antar pelat 2144 cm = Sambungan antar pelat 3
Berat pelat = 4 × { 0.00785 × ( 72 × 26.7 × 0.5 + 132 × 24.7 × 5 + 144 × 22.7 × 5 ) }= 1055.26608 kg= 1056 kg
Plas 1 σlas Ageser
sin2α cos2α )0.5
2 Plas 2 P1 Plas 1
Plas 2
sin2α cos2α )0.5
Plas 2 σlas Ageser
L2'L2'
L2'
L2 L2' L2
cm3
Pelat 2Pelat 1Flens
Pelat 3Pelat 2Pelat 1Flens
Page 21
A. Gelagar MelintangKoefisien kejut :
L diambil = 31 - 0.5 = 30.5 m
Menurut pedoman perencanaan untuk rumah dan gedung, koefisien kejut untuk beban yang membebani struktur :υ =
Dimana : v = Kecepatan angkat maksimum = 1.0 m/s= Koefisien kekakuan struktur keran induk = 0.6= Koefisien sifat mesin angkat dari keran angkat = 1.0
Maka : υ = 1 + (0.6) (1.0) (1.0) ≥ 1.15υ = 1.6= 5000 kg= = 1.6 × 5000 = 8000 kg
I. Merencanakan profil dasaruntuk x = 4 m
P = 8000 kg
4
Ra = ( 26.5 ) 8000 = 6950.82 kg30.5
M = 6950.82 x 4 = 27803.28 kgm
Wx =27803.28
= 1737.7051600
Coba profil WF 400×400×11×18Data : q = 147 kg/m = 2848
h = 394 mm = 950b = 398 mm = 56100
= 11 mm = 18900= 18 mm A = 186.8
6951 +1
× 147 × 30.5 = 9192.57 kg2
= 9192.57 × 4 -1
× 147 × 42
= 35594.32
== 3559427.869 =
1249.8 ≤ = 1600 ….. OK2848
Kontrol Kips
=L × h
=30500 × 394
= 1677.41398 × 18
=0.63 E
=0.63 × 2100000
= 826.8751600
250 < < , maka= ( 1 - 0.3 × )= 1600 ( 1 - 0.3 ×
1427.41 )576.875= 412.2919 < = 1249.8 ….. TIDAK OK
untuk x = 8 m > , maka= ×
P
=1677.41
× 0.70 × 1600826.88
8 = 2272.054 > = 1249.80 ….. OK
Ra = ( 22.5 ) 8000 +1
x 147 x 30.5 = 8143.38930.5 2
Mx = 8143.389 x 8 -1
x 147 x 82
= 60443.112
== 6044311.475 =
2122.3 ≤ = 1600 ….. TIDAK OK2848
Jadi diperlukan pelat tepiII. Penambahan Pelat ( 13 × 398 )
= 2 × ( 1.3 × 39.8 × 0.00785398 = 0.812318 kg/cm
= 81.2318 kg/m
=39.8 × 1.3 3
+ 1.3 × 39.8 × 20.352
13 1218 = 21433.9849
= 2 × 21433.98
= 42868.0
= 42867.970 + 56100= 98967.970
394 420 = 8143.389 x -1
1.472
4556800 = 8143.389 x - 0.7350.735 - 8143.389 x + 4556800 = 0
maka, x = 591.107 cmx = 5.9 m= = 2 × 98967.970 = 4712.7605
18 4213
8143.39+ ( 147 ( 30.5 - 2 x 5.9 ) =
9516.212kg
BAB IIIDIMENSI GELAGAR MELINTANG
( 1 + K1 × K2 × v )
K1
K2
PTotal
PTotal υ × Pcrane
cm3
WX cm3
WY cm3
IX cm4
tw IY cm4
tf cm2
RVA =
Mmax
σTerjadiMmax
kg/cm2 σprofil kg/cm2
WX
C1 b × tf
C2 σprofil
C1 C2σkips σprofil
C1 - 250C2 - 250
kg/cm2 σTerjadi kg/cm2
C1 C2σkips
C20.70 σprofil
C1
kg/cm2 σTerjadi kg/cm2
σTerjadiMmax
kg/cm2 σprofil kg/cm2
WX
mm2
qbs pelat 1 kg/cm3 )
IX Pelat 1
cm4
IX 2 Pelat
cm4
IX Total
cm4
σwx x2
x2
x2
WX Total 2 IX Total cm3
hTotal
RVA =
Gelagar Melintang
P
Gelagar Memanjang
Crane
b
htw
tf
Page 22
8143.392
9516.212
= 9516.21 x 8 - 147 x 8 2 - 81 ( 8 - 2.1398 2 2
Kontrol Kips = 70006.546 kg mh
=420
= 38.18182 < 75 ….. OK= 7000654.635622 kg cm
11 = = 7000654.636 =1485.47
4712.760L
≥1.25 b
===>30500
≥1.25 × 398
h 420 1872.619 ≥ 27.63889 ….. OK
< = 1600 ….. OK
=L × h
=30500 × 420
= 1038.256( 398 × 18 ) + ( 398 × 13 )
=0.63 E
=0.63 × 2100000
= 826.8751600
Mmax )2
tw σTerjadi Mmax kg/cm2
WX
tf
σTerjadi σprofil kg/cm2
C1 b × tf
C2 σprofil
Page 23
> , maka= ×
=1038.26
× 0.70 × 1600826.88
= 1406.315 < = 1485.47 ….. TIDAK OK
untuk x = 11.5 m
P
11.5
Ra = ( 19 ) 8000 +1
x 147 x 30.5 +1
x 81.23 x ( 30.5 - 2 x 5.9 ) = 7983.974630.5 2 2
Mx = 7983.975 x 11.5 -1
x 147 x 11.52
-1
x 81.2 ( 11.5 - 5.9 = 80826.652 2
== 8082664.957 =
2838.0 ≤ = 1600 ….. TIDAK OK2848
Jadi diperlukan pelat tepi
Penambahan Pelat ( 13 × 378 )
378 = 2 × ( 1.3 × 37.8 × 0.00785= 0.771498 kg/cm= 77.1498 kg/m
13=
37.8 × 1.3 3+ 1.3 × 37.8 × 19.05
213 1218 = 17839.9494
= 2 × 17839.95
= 35679.9
= 35679.899 + 98967.970
= 134647.869
394 394 = =2 × 134647.869
= 6834.917239.4
= 7983.975 x -1
1.47 -1
### ( x - 591.12 2
4556800 = 7983.975 x - 0.735 - 0.406 ( - 591.1 x + 349407.5 )1.141 - 8224.058 x + 4698715 = 0
maka, x = 625.6538 cm18 x = 6.3 m
137983.97
+ ( 77.15 ( 30.5 - 2 x 6.3 ) = 8677.818 kg
13 2=
8677.82x
11.5- 147 x 11.5 2 - 81.23 ( 11.5 - 5.6 - 77.1 ( 11.5 - 5.2
398 2 2 2Kontrol Kips = 87145.401 kg mh
=394
= 21.88889 < 75 ….. OK= 8714540.056095 kg cm
18 = = 8714540.056 = 1275.00
6834.917
L≥
1.25 b===>
30500≥
1.25 × 398 < = 1600 ….. OK
h 394 1377.411 ≥ 38.26923 ….. OK
=L × h
=30500 × 394
= 696.557( 398 × 18 ) + ( 398 × 13 ) + ( 378 × 13 )
=0.63 E
=0.63 × 2100000
= 826.8751600
250 < < , maka= ( 1 - 0.3 × )= 1600 ( 1 - 0.3 ×
446.56 )576.875= 1228.434 < = 1275.0 ….. TIDAK OK
Kontrol Lendutan= 147 + 81.232 + 77.150 = 305.382 kg/m
=8000 × 3050 3
+5 × 305.382 × 3050 4
= 28.893 cm48 × ( 2100000 ) × ( 134647.869 ) 384 × ( 2100000 ) × ( 134647.869 ) × 100
=30500
= 122.000 mm 12.200 cm ≥ 28.893 cm ….. TIDAK OK250
Pemutusan Plat• Pelat 2
=( 30.5 - x )
x = x -1
30.5 30.5
= 147 + 81.232 + 77.150 = 305.382 kg/m
= 8000 ( x -1 ) +
30.5 ( x -1 ) × 305.382
30.5 2 30.5
= 8000 x -8000
+ 4657.07 x -4657.07
30.5 30.5
= 12657.069 x -12657.069
30.5= 12657.069 x - 414.986
× ≥1600 × 2848 ≥ ( 12657.069 x - 414.986 ) × 100
0 ≤ 414.986 - 12657.069 x + 45568.000x ≤ ∞
Jadi yang menentukan adalah kips dan lendutan :× ≥
0.00 × 2848.0000 ≥ ( 12657.069 x - 414.986 ) × 100
0 ≤ 414.986 - 12657.069 x + 0.000x ≤ 0 Ambil x = 2.00 m
• Pelat 1
=( 30.5 - x )
x = x -1
30.5 30.5
=28.5
x30.5
=2.00
x30.5
= 147 + 81.232 = 228.232 kg/m= 77.150 kg
C1 C2 σkipsC2 0.70 σprofilC1
kg/cm2 σTerjadi kg/cm2
)2
σTerjadiMmax
kg/cm2 σprofil kg/cm2
WX
mm2
qbs pelat 2 kg/cm3 )
IX Pelat 2
cm4
IX 2 Pelat
cm4
IX Total
cm4
WX Total2 IX Total
cm3
hTotal
σwx x2 )2
x2 x2
x2
RVA =
Mmax )2 )2
tw σTerjadi Mmax kg/cm2
WX
σTerjadi σprofil kg/cm2
tf
C1 b × tf
C2 σprofil
C1 C2σkips σprofil
C1 - 250C2 - 250
kg/cm2 σTerjadi kg/cm2
qTotal
Ymax
Yizin
Y1 x2
qTotal
Mx x2 x2
x2 x2
x2
x2
σprofil WX Mx
x2
x2
σkips WX Mx
x2
x2
Y1 x2
Y2
Y3
qTotal
qPelat 3
Page 24
= 8000 ( x -1 ) +
30.5 ( x -1 ) × 228.232 +
26.5 ( 28.50 + 2.00x ) × 77.150
30.5 2 30.5 2 30.5
= 8000 x -8000
+ 3480.53 x -3480.53
+ 1022.235 x30.5 30.5
= 12502.770 x -11480.535
30.5= 12502.770 x - 376.411
Jadi yang menentukan adalah kips dan lendutan :× ≥
2272.05 × 2848.0000 ≥ ( 12502.770 x - 376.411 ) × 100
0 ≤ 376.411 - 12502.770 x + 64708.097x ≤ 6.414085 m ==> Ambil x = 1.00 m
8000 ( 30.5 - x ) +147 × 30.5
+81.232 × 28.5
+77.150 × 19.00
30.5 2 2 2
= 8000 ( 30.5 - x ) + 4132.226330.5
Untuk x = 1.00 m=
= { 8000 ( 30.5 - 1.00 ) + 4132.2263 } × 1.00 -147 × 1.00 2
30.5 2= 11796.43116803 kg m= 1179643.116803 kg cm
= =1179643.116803
= 414.201≤ = 1600 ….. OK
2848 ≤ = 2272.054 ….. OK
Untuk x = 2.00 m= - 1.00
= { 8000 ( 30.5 - 2.00 ) + 4132.2263 } × 2.00 -147 × 2.00 2
-81.2318 × 1.00 2
30.5 2 2= 22880.65627213 kg m= 2288065.627213 kg cm
= =2288065.627213
= 803.394≤ = 1600 ….. OK
2848 ≤ = 0 ….. TIDAK OK
IV. Kontrol Lendutan• Akibat Berat Sendiri + Pelat
= 4132.2263 kg• Untuk x = 1.00 m
= 4132.2263 × 1.00 - 147 × 1.00 2= 4058.72625 kg m
• Untuk x = 2.00 m= 4132.2263 × 2.00 - 147 × 2.00 2 - 81.2318 × ( 2.00 - 1.00 2= 7929.8366 kg m
• Untuk x = 15.25 m= 4132.2263 × 15.25 - 147 × 15.25 2 - 81.2318 × ( 15.25 - 1.00 2
- 77.1498 × ( 15.25 - 2.00 2= 30903.23449 kg m
= 2 / 3 × 1.00 ×= 2 / 3 × 1.00 × 4058.72625= 2705.8175
= ( 2.00 - 1.00 ) ×= ( 2.00 - 1.00 ) × 4058.72625= 4058.72625
= 2 / 3 × ( 2.00 - 1.00 ) × ( - )= 2 / 3 × ( 2.00 - 1.00 ) × ( 7929.8366 - 4058.72625 )= 2580.740
= ( 15.25 - 2.00 ) ×= ( 15.25 - 2.00 ) × 7929.8366= 105070.3349
= 2 / 3 × ( 15.25 - 2.00 ) × ( - )= 2 / 3 × ( 15.25 - 2.00 ) × ( 30903.23449 - 7929.8366 )= 202931.681
ΣL = + + + += 2705.8175 + 4058.72625 + 2580.740 + 105070.3349 + 202931.681= 317347.300
= 5 / 8 × 1.00 = 0.62500 m= 1.00 + ( 2.00 - 1.00 ) / 2 = 1.50000 m= 1.00 + 5 / 8 × ( 2.00 - 1.00 ) = 1.62500 m= 2.00 + ( 15.25 - 2.00 ) / 2 = 8.6250 m= 2.00 + 5 / 8 × ( 15.25 - 2.00 ) = 10.2813 m= × + × + × + × + ×
ΣL= 9.4678 m
Lendutan :• Untuk x = 1.00 m
M = 317347.300 × 1.00 - 2705.8175 × ( 1.00 - )= 317347.300 × 1.00 - 2705.8175 × ( 1.00 - 0.62500 )= 316332.62
y =316332.62 × 10 6
+8000 × 1.00 2 × ( 30.5 - 1.00 × 10 6
2100000 × 56100 3 × 30.5 × 2100000 × 56100= 3.3310 cm < 12.200 cm ….. OK
• Untuk x = 2.00 mM = 317347.300 × 2.00 - 2705.8175 × ( 2.00 - ) - 4058.72625 × ( 2.00 - ) - 2580.740 × ( 2.00 -
= 317347.300 × 2.00 - 2705.8175 × ( 2.00 - 0.62500 ) - 4058.72625 × ( 2.00 - 1.50000 )- 2580.740 × ( 2.00 - 1.62500 )
= 627976.96
y =627976.96 × 10 6
+0 × 2.00 2 × ( 30.5 - 2.00 × 10 6
2100000 × 98967.970 3 × 30.5 × 2100000 × 98967.970= 3.0215 cm < 12.200 cm ….. OK
• Untuk x = 15.25 mM = 317347.300 × 15.25 - 2705.8175 × ( 15.25 - ) - 4058.72625 × ( 15.25 - ) - 2580.740 × ( 15.25 -
- 105070.3349 × ( 15.25 - ) - 202931.681 × ( 15.25 -= 317347.300 × 15.25 - 2705.8175 × ( 15.25 - 0.62500 ) - 4058.72625 × ( 15.25 - 1.50000 )
- 2580.740 × ( 15.25 - 1.62500 ) - 105070.3349 × ( 15.25 - 8.6250 )- 202931.681 × ( 15.25 - 10.2813 )
= 3004595.92
y =3004595.92 × 10 6
+0 × 15.25 2 × ( 30.5 - 15.25 × 10 6
2100000 × 134647.869 3 × 30.5 × 2100000 × 134647.869= 10.6259 cm < 12.200 cm ….. OK
V. Kontrol Lintang== 4132.2263 + 8000= 12132.2263 kg
Sx = b × × ( h - ) + × ( h- ) 1
2 2 2
= 39.8 × 1.8 × ( 39.4 - 1.8 ) + 1.1 × ( 39.4- 1.8 ) 1
Mx x2 x2
x2 x2
x2
x2
σkips WX Mx
x2
x2
RVA =
Mx RVA × X - qprofil × X2 / 2
σTerjadiMX
kg/cm2σprofil kg/cm2
WX σkips kg/cm2
Mx RVA × X - qprofil × X2 / 2 - qpelat1 ( X )2 / 2
σTerjadiMX
kg/cm2σprofil kg/cm2
WX σkips kg/cm2
RVA
M12 /
M22 / )2/
M32 / )2/
)2/
L1 M1
kg m2
L2 M1
kg m2
L3 M2 M1
kg m2
L4 M2
kg m2
L5 M3 M2
kg m2
L1 L2 L3 L4 L5
kg m2
X1
X2
X3
X4
X5
XΣ L1 X1 L2 X2 L3 X3 L4 X4 L5 X5
X1
kg m3
)2
X1 X2 X3 )
kg m3
)2
X1 X2 X3 )X4 X5 )
kg m3
)2
Dmax RVA (x=0)
tftf tw tf
2 ×
2 ×
Page 25
= 39.8 × 1.8 × ( 2 ) + 1.1 × ( 2- 1.8 ) 2
= 1523.0575
= =12132.2263 × 1523.0575
= 299.434 ≤ = 928 ….. OK1.1 × 56100
2 ×
cm3
τterjadiDmax SX
kg/cm2 0.58 σprofil kg/cm2
tw IX
Page 26
VI. Sambungan
Mutu las = 2400
a. Sambungan Profil Dasar1. Sayap (Flens)
= 4132.2263 kg
= 4132.2263 + ( 30.5 - 5.5 ) 8000 = 10689.6033 kg30.5
M = 10689.6033 × 5.5 - 147 × 5.5 2 - 81.2318 × ( 5.5 - 1
- 77.1498 × ( 5.5 - 2.00= 55274.429 kg m= 5527442.9 kg cm
=5527442.9
= 808.7066 ≤ = 1600 ….. OK6834.9172
≤b × ≤ 1.3 × 39.8 + 6 × × 2
39.8 × 1.8 ≤ 51.74 + 1271.640 ≤ 51.74 + 12
≥ 19.900 / 12≥ 1.7 cm
Ambil tebal pelat bawah = 10 mm
Sambungan Las
=188.0
×223
223 =188.0
× 808.7066188.0
223= 681.78
= ×= 681.78 × 1.8 × 39.8= 48842.68934 kg
• Las 1α = 45 ˚
c =1
= 0.707( + 3
= Lebar pelat = 39.8 + 2 × 6 = 51.8 cmAmbil tebal las : = 0.2 cm
= 2400 × 0.707 × 0.2 × 51.8 × 0.707= 12432 kg
• Las 2= = ( 48842.68934 - 12432 ) / 2 = 18205.345 kg
α = 0 ˚
c =1
= 0.577( + 3
Ambil tebal las : = 0.2 cm=
18205.345 = 2400 × 0.707 × 0.2 × × 0.577= 92.904 cm
= + 3a = 92.904 + 3 × 0.707 × 0.2 = 93.328 cm= 15 cm
Kesimpulan :Untuk sambungan flens digunakan pelat : 2 / ( 30 × 39.8 × 1.3 )
2 / ( 30 × 6 × 1 )
2. Badan (Web)
223 =179.0
×179
223
=179.0
× 808.7066223
= 649.1412
20 mm≤
1.1 × 35.8 12 ≤ 2 × 2 × 12
≥ 12617.7458
≥ 23.3 cm ( tetapi harus lebih kecil dari 35.8 cm )= 25 cm
= 2 × 2 × 25 3 / 12 = 5208
Garis pengaruh D= 8000 kg
0.00 m0.819672
2.00 m
1.00 m
5.5= 0.180328
30.5
5.5 m 25.00 m
=1.00
× 0.180328 = 0.033 =0.00
× 0.819672 = 0.0005.5 25.00
=2.00
× 0.180328 = 0.066 =2.00
× 0.819672 = 0.0665.5 25.00
=0.00
× 0.180328 = 0.000 =1.00
× 0.819672 = 0.0335.5 25.00
= 8000 × 0.819672 + 147 × 25.00 × 0.819672 / 2+ 81.232 × ( 25.00 - 1.00 ) × ( 0.819672 + ) / 2+ 77.150 × ( 25.00 - 2.00 ) × ( 0.819672 + ) / 2- 77.150 × ( 5.50 - 2.00 ) × ( 0.180328 + ) / 2- 81.232 × ( 5.50 - 1.00 ) × ( 0.180328 + ) / 2
= 9607.745 kg
kg/cm2
RVA akibat berat sendiri + pelat
RA
2 / )2 / 2
)2 / 2
σTerjadi kg/cm2 σprofil kg/cm2
Aflens Apelat
tf tp
tp
tp
tp
tp
σf σTerjadi
kg/cm2
Pflens σf Af
sin2α cos2α )0.5
L1
tlas
Plas = σlas × Ageser × c
P2 ( P - P1 ) / 2
sin2α cos2α )0.5
tlas
P2 σlas × Ageser × cL2
L2
L2 perlu L2
Ambil L2
cm3
cm3
σw σTerjadi
kg/cm2
Ambil tebal pelat penyambung badan tp =IX badan IX pelat
3 / hp3 /
hp3
hp
Ambil tinggi pelat penyambung badan hp
Maka Ix pelat cm4
Y1 Y4
Y2 Y5
Y3 Y6
Dmaks
Y4
Y3
Y2
Y1
Terjadi
f
2
1
2
P2P2
P1
L2
L2
L1
Terjadi
w
y1 y2 y3
y4
y5 y6
Page 27
= ×= 649.1412 × 416.67= 270475.50 kg cm= 2704.7550 kg m
Mpelat σw Wx pelat
Page 28
25 cm
30 cm 30 cmLas dianggap 1 satuan
X =30 × 15 + 30 × 15
= 10.58824 cm25 + 30 + 30
= { 1 × 30 12 + ( 30 × 1 ) × ( 30 - 10.58824 } × 2
+ { 25 × 1 12 + ( 25 × 1 ) × ( 10.58824 }
= 29913.848
= { 30 × 1 12 + ( 30 × 1 ) × ( 12.5 } × 2 + { 1 × 30 12 }
= 11630.000
+ = 29913.848 + 11630.000 = 41543.848
= × ( 30 - 10.58824 ) / 2 = 9607.745 × 9.7059 = 93251.644 kg cm = 932.51644 kg m= M + = 270475.500 + 93251.644 = 363727.144 kg cm = 3637.27144 kg m
=× ( 30 - 10.58824 )
=363727.14402 × 19.41176
= 169.9550341543.848
=× ( 25 / 2 )
=3637.27144 × 12.5
= 1.0944141543.848
=D / 2
=9607.745 / 2
= 56.5161530 + 30 + 25
2 + ( + = 1.09441 2 + ( 169.95503 + 56.51615
= 226.47382 ≤ = 1440
a = =226.47382
= 0.157273 cm1440
a=
0.157273= 0.222418 cm ≤ 2 cm ….. OK
0.707 0.707Ambil tebal las : t = 0.5 mmUntuk sambungan web digunakan pelat : 2 / ( 60 × 25 × 2 )
b. Sambungan Pelat
=204
×223
=204
× 808.7066203.5 216.5 223 223
= 737.9901
=217
×223
=217
× 808.7066223
= 785.1345
Tebal las seluruhnya diambil t = 2 mm= × = 737.9901 × 1.3 × 39.8 = 38183.610 kg= × = 785.1345 × 1.3 × 37.8 = 38581.508 kg
• Pelat 1= × α = 45 ˚= 0.707 × 2400 × 0.707 × 0.2 × 37.8
c =1
= 0.707= 9072 kg ( + 3
= - α = 0 ˚= ( 38183.610 - 9072 ) / 2
c =1
= 0.577= 14555.805 kg ( + 3
= ×14555.805 = 0.577 × 2400 × 0.707 × 0.2 ×14555.805 = 195.959 ×
= 74.280 cm
= + 15 = 74.280 + 15 = 89.280 cm ==> Ambil = 30 cm
Untuk sambungan pelat 1 digunakan pelat : 2 / ( 60 × 37.8 × 1.3 )
30 cm = Sambungan antar flens60 cm = Sambungan antar pelat 1
• Pelat 3= × α = 45 ˚= 0.707 × 2400 × 0.707 × 0.2 × 35.8
c =1
= 0.707= 8592 kg ( + 3
= - α = 0 ˚= ( 38581.508 - 8592 ) / 2
c =1
= 0.577= 14994.754 kg ( + 3
= ×14994.754 = 0.577 × 2400 × 0.707 × 0.2 ×14994.754 = 195.959 ×
= 76.520 cm
= + 30 = 76.520 + 30 = 106.520 cm ==> Ambil = 54 cm
Untuk sambungan pelat 1 digunakan pelat : 2 / ( 108 × 35.8 × 1.3 )
Ilas X3 / )2
3 / )2
cm4
Ilas Y3 / )2 3 /
cm4
Ilas Total = Ilas X Ilas Y cm4
MS Dmax
MT MS
τVMT
kg/cm2
Ilas Total
τHMT
kg/cm2
Ilas Total
τD kg/cm2
Alas
τlas = τH τV τD )2 )2
kg/cm2 0.6 σlas kg/cm2
τlas
0.6 σlas
tlas =
cm3
σ1 σTerjadi
kg/cm2
σ2 σTerjadi
kg/cm2
P1 σ1 A1
P2 σ2 A2
Plas 1 σlas Ageser
sin2α cos2α )0.5
2 Plas 2 P1 Plas 1
Plas 2
sin2α cos2α )0.5
Plas 2 σlas Ageser
L2'L2'
L2'
L2 L2' L2
cm3
Plas 2 σlas Ageser
sin2α cos2α )0.5
2 Plas 3 P2 Plas 2
Plas 3
sin2α cos2α )0.5
Plas 2 σlas Ageser
L2'L2'
L2'
L2 L2' L2
cm3
x
Terjadi
2
3
1
Pelat 1Flens
Pelat 3Pelat 2Pelat 1Flens
Page 29
30 cm = Sambungan antar flens60 cm = Sambungan antar pelat 1
108 cm = Sambungan antar pelat 20 cm = Sambungan antar pelat 3
Berat pelat = 4 × { 0.00785 × ( 60 × 37.8 × 1.3 + 108 × 35.8 × 1.3 ) }= 250.406208 kg= 251 kg
Pelat 3Pelat 2Pelat 1Flens
Page 30
6 m
Beban terpusat = = 8000 + += 8000 + 4093.2856 + 1056 / 2= 12621.2856 kg
Digunakan rel baja No.2
37 mmW = 95.7
I = 52.8
110 mmF = 32.3
q = 25.7510 mm
90 mm
1. Dimensi Profil Memanjang
= × λ / 4 + q × / 8= 12621.2856 × 6 / 4 + 25.75 × 6 2 / 8= 19047.80344 kg m
6 m= 1904780.344 kg cm
1904780.344= 1190.488
1600Coba profil WF 400×200×8×13Data : q = 66 kg/m = 1185
h = 400 mm = 174
b = 200 mm = 23700
= 8 mm = 1740
= 13 mm A = 84.12
= 19047.80344 + 66 × 6 2 / 8= 19344.80344 kg m= 1934480.344 kg cm
=1934480.344
= 1632.47 ≤ = 1600 ….. TIDAK OK1185
BAB IVDIMENSI GELAGAR MEMANJANG
PA Rakibat berat sendiri + pelat Rpelat penyambung
cm3
cm3
cm3
cm3
PA Mmax PA λ2
Wx perlu = cm3
WX cm3
WY cm3
IX cm4
tw IY cm4
tf cm2
Mmax
σterjadi kg/cm2 σprofil kg/cm2
b
htw
tf
Page 31
Kontrol lendutan
y = +48 E I 384 E I
=12621.2856 × 600 3
+5 × ( 0.660 + 0.258 ) × 600 4
48 × 2100000 × 23700 48 × 2100000 × 23700= 1.390 cm
λ=
600= 2.4 cm > 1.390 cm ….. OK
250 250
2. Hubungan Antara Rel, Gelagar Memanjang, dan Konsol
Rel Baja110 mm No.2
60 mm400 mm
WF 400×200×8×13
200 mm
25 cm
50 cm
Hubungan Rel Dengan Gelagar Memanjang• Gaya yang dipikul 1 rel = + × λ / 2
P' = 12621.2856 + 25.75 × 6 / 2= 12698.5356 kg
• Gaya rem = P' / 15 = 12698.5356 / 15 = 846.5690 kg• 846.5690 × 11 / 6 = 1552.0432 kg• Direncanakan 2 baut
σ = ≤2 × π × / 4
1552.0432≤ 0.6 × 2400
2 × π × / 4
≥1440 × π
1552.0432 × 2d ≥ 1.207228 cm
Ambil diameter baut d = 15 mm
Hubungan Gelagar Memanjang Dengan Konsol• = P' + × λ / 2
= 12698.5356 + 66 × 6 / 2= 12896.5356 kg
• Gaya rem = / 15 = 12896.5356 / 15 = 859.7690 kg• 859.7690 × 40 / 20 = 1719.5381 kg
PA λ3 5 (qbs + qrel) λ4
yizin =
PA qrel
Rpk =
Rpkσbaut
d2
d2
d2
Ptotal qgel.memanjang
Ptotal
Rpk =
Page 32
• Direncanakan 2 baut
σ = ≤2 × π × / 4
1719.5381≤ 0.6 × 2400
2 × π × / 4
≥1440 × π
1719.5381 × 2d ≥ 1.146926 cm
Ambil diameter baut d = 15 mm
3. Dimensi Plat KonsolM = × 25
= 12896.5356 × 25= 322413.391 kg cm
M=
322413.391= 201.5084
1600
Coba profil WF 200×200×8×12Data : q = 50 kg/m = 472
h = 200 mm = 160
b = 200 mm = 4720
= 8 mm = 1600
= 12 mm A = 63.53
50 50 50 50Ambil diameter baut d = 22 mm
a =2 × π × / 4
×40 s
=2 × π × 2.2 4
×2400
60 6 1600200 = 1.901 cm
60
x =h ×
=20 × ( 1.901
= 4.713 cm40 + ( 1.901 + ( 20.0
200= b × x 3 / 3 + a × ( h - x / 3
= 20 × 4.713 3 + 1.901 × ( 20 - 4.713
= 2961.257784
=2961.258
= 193.707h - x 20 - 4.713
200 =2961.258
= 628.358x 4.713
M=
322413.391= 1664.44
193.707
τ =D
× =12896.5356
×1600
= 376.96n F 6 × π × 2.2 4 2400
= + 3 = 1664.44 3 × 376.96 3
= 1787.919 ≤ = 1600 ….. TIDAK OK
Rpkσbaut
d2
d2
d2
Ptotal
WX = cm3
σprofil
WX cm3
WY cm3
IX cm4
tw IY cm4
tf cm2
d2 σbaut
σprofil
2 /
(a)0.5 )0.5
(a)0.5 (b)0.5 )0.5 )0.5
IX )3
3 / ) 3 / 3
cm4
Wxa =IX cm3
Wxb =IX cm3
σmax = kg/cm2
Wxa
σprofilkg/cm2
σbaut2 /
σi σ2 τ2 2 +
kg/cm2 σprofil kg/cm2
b
htw
tf
x
h-x
Page 33
Tebal Pelat Penyambung
q = 50P = A ×
=π ×
× ×g = 50 4
=π × 2.2 2
× 1787.919 ×2400
g = 50 4 1600= 10194.6983 kg
q = 50M = 0.6 { P ( g - / 2 ) }
= 0.6 { 10194.6983 ( 5 - 0.8 / 2 ) }= 28137.367304 kg cm
T = P { 1 + ( g - / 2 ) / q }= 10194.6983 { 1 + ( 5 - 0.8 / 2 ) / 5 }= 19573.8207332 kg
σ =M
=28137.3673040326
=28137.3673
W 6 × / 6
τ =T
=19573.8207332
=3262.3035
s t 6 × t t≥ + 3
2400 2 ≥ ( 28137.3673 ) 2+ 3 ( 3262.3035 ) 2
t
2400 2 ≥791711438.80
+31927871.508
0 ≤ 5760000 - 31927871.508 - 791711438.80
0 ≤ - 5.543 - 137.450
misalkan = a
0 ≤ - 5.543 a - 137.450a ≥ 14.819t ≥ 3.849 cm
Ambil tebal pelat t = 35 mmMaka dipakai pelat / ( 21 × 20 × 3.5 )
Las Pada Sambungan Pelat dan Profil12 mm Tebal las dianggap 1 satuan
Luasan las• = 20 × 1 = 20.00
8 mm• = ( 20 - 0.8 ) / 2 × 1 = 9.6
200• = 1 × ( 20 - 2 × 1.2 ) = 17.60
2 + 4 + 2= 2 × 20.00 + 4 × 9.60 + 2 × 17.60= 113.6
y = 10 cmx = 10 cm
200
Inersia las arah x• = 20 × 1 3 / 12 + 20.00 × 10 2 = 2001.667
• = ( 20 - 0.8 ) / 2 × 1 3 / 12 + 9.6 × ( 10 - 1.2 ) 2 = 744.224
• = 1 × ( 20 - 2 × 1.2 ) 3 / 12 = 454.315
= 2 + 4 + 2 = 2 × 2001.667 + 4 × 744.224 + 2 × 454.315 = 7888.859
σi
tw d2
σiσbaut
σprofil
tw
tw
t2 t2
σizin σ2 τ2
t2
t4 t2
t4 t2
t4 t2
t2
a2
cm3
F1 cm2
F2 cm2
F3 cm2
Flas = F1 F2 F3
cm2
IX1 cm4
IX2 cm4
IX3 cm4
IX Total IX1 IX2 IX3 cm4
y
1
2
3
1
2
x
Page 34
Inersia las arah y• = 1 × 20 3 / 12 = 666.667
• = 1 × { ( 20 - 0.8 ) / 2 } 3 / 12 + 9.6 × { ( 10 - 0.8 ) / 4 + 0.8 / 2 } 2
= 143.712
• = ( 20 - 2 × 1.2 ) × 1 3 / 12 + 17.60 × ( 0.8 / 2 ) 2 = 4.283
= 2 + 4 + 2 = 2 × 666.667 + 4 × 143.712 + 2 × 4.283 = 1916.747
= + = 7888.859 + 1916.747 = 9805.605
=M y
=322413.391 × 10.00
= 328.8059805.605
=D'
=12896.53563
= 113.526113.600
= 2 + ( = 328.805 2 + ( 113.526 = 347.8519
Tebal las = × 1 = × 1 =347.8519
× 1 = 0.242 cmτ 1440
Ambil tebal las t = 2 mm
Iy1 cm4
Iy2
cm4
Iy3 cm4
Iy Total Iy1 Iy2 Iy3 cm4
ITotal IX Total Iy Total cm4
τX kg/cm2
ITotal
τY' kg/cm2
Flas
τi' τX τY' )2 )2 kg/cm2
τi' τi'
0.6 σlas
Tugas Struktur Baja Tipe A
Page 35
α = 19 °
A. Beban Atap• Panjang L miring =
= 2 × ( 1.586 + 16.39312 )= 35.959 m
• Berat gording == 4.51 × 6 × 22= 595.32 kg
• Berat atap == 3.60 × 6 × 35.959= 776.7166 kg
• Berat w = 595.32 + 776.7166= 1372.037 kg
• Berat penyambung dan lain-lain = 25% × Berat w= 25 % × 1372.037= 343.009 kg
• Berat total = Berat w + Berat penyambung dan lain-lain= 1372.037 + 343.009= 1715.046 kg
• = 1715.046 / 35.96 = 47.694 kg/m
B. Beban Angin• Angin Kiri
BAB VPERHITUNGAN BEBAN YANG BEKERJA
2 ( Z1 + Z2 )
qgording × λ × Jumlah Gording
qatap × λ × L
qekivalen
D
E
F
A
B
C
H
IG
q4
q3q2
q1
Tugas Struktur Baja Tipe A
Page 36
q4
q3q2
q1
Tugas Struktur Baja Tipe A
Page 37
Beban Angin = 70Jarak kuda-kuda = 6.0 mBeban : = 0.9 × × λ = 0.9 × 70 × 6.0 = 378 kg/m
= ( 0.02 α - 0.4 ) × × λ = ( 0.02 × 19 - 0.4 ) × 70 × 6.0 = -8.4 kg/m= -0.4 × × λ = -0.4 × 70 × 6.0 = -168 kg/m= -0.4 × × λ = -0.4 × 70 × 6.0 = -168 kg/m
• Angin Kanan
Beban : = -168 kg/m= -168 kg/m= -8.4 kg/m= 378 kg/m
C. Beban P
• P di kiriA = 12896.53563 + 50 × 0.5 = 12921.53563 kg
12921.53563 × 0.25 + 50 × 0.5 2 = 3236.633906 kg mB = 12921.53563 - 8000 = 4921.535625 kg
4921.535625 × 0.25 + 50 × 0.5 2 = 1236.633906 kg m
• P di kananA = 4921.535625 kg
1236.633906 kg mB = 12921.53563 kg
3236.633906 kg m
kg/cm2
q1 qa
q2 qa
q3 qa
q4 qa
q1
q2
q3
q4
MA = 2 /
MB = 2 /
MA =
MB =
q4
q3q2
q1
q4
q3
q2
q1
A B
Tugas Struktur Baja Tipe A
Page 38
• Matriks kekakuan terhadap Sumbu lokalSetiap elemen memiliki sumbu lokal masing-masing
Hubungan antara gaya dengan perpindahan adalah :{ fe } = [ k ] { d }dimana : { fe } = gaya
[ k ] = matriks kekakuan{ d } = perpindahan
{ fe } = { d } =dan
Sedangkan matriks kekakuan adalah sebagai berikut :
[ k ] =
E A0 0
- E A0 0
=
L L
012 E I 6 E I
0- 12 E I 6 E I
06 E I 4 E I
0- 6 E I 4 E I
L L- E A
0 0E A
0 0L L
0- 12 E I - 6 E I
012 E I - 6 E I
06 E I 4 E I
0- 6 E I 4 E I
L L
• Matriks kekakuan terhadap Sumbu global
BAB VIPERHITUNGAN SAP
Secara konvensional dalam mencari gaya-gaya batang di dalam sistem portal dapat diselesaikan dengan metode cleperon, metode slope deflection, metode cross, metode energi, dan lain-lain. Tetapi juga dapat digunakan metode matriks kekakuan yang disebut juga dengan metode displacement (metode perpindahan).
SX1 u1
SY1 v1
MZ1 χ1
SX2 u2
SY2 v2
MZ2 χ2
L3 L2 L3 L2
k11 k12L2 L2
k21 k22
L3 L2 L3 L2
L2 L2
z
Sy
z
Sx
Sy
z
Sx
L
Y
X
Sy1
Sx1
Sy2Sx2
1
2
Mz2
Mz1
Tugas Struktur Baja Tipe A
Page 39
Untuk simpul 1
= =cos α - sin α 0sin α cos α 0
0 0 1= [ T ] … (1)
Untuk simpul 2 berlaku juga seperti simpul 1
Dengan demikian maka untuk satu elemen berlaku :{ fe } = [ Te ] { fe }
Te = [ T 0 ]0 T … (2)
Untuk displacement vektor{ de } = [ Te ] { de } … (3)
Dari persamaan (1), (2), dan (3)
dimana : [ ke ] = [ Te ] [ ke ]
= [ Te ] [ ke ]
keterangan : = ==> karena [ Te ] adalah matriks ortogonal
Maka untuk batang miring
dengan : s = sin αc = cos α
Degree Of Freedom (DOF)
Nodal RestraintSendi (Hinge) δx, δy, δzRol (Rollers) δzJepit (Fixed) δx, δy, δz, θx, θy, θz
f1
SX1 SX1
SY1 SY1
MZ1 MZ1
{ f1 }
[ Te ]-1 { fe } = [ ke ] [ Te ]-1 { de }
{ fe } = [ Te ] [ ke ] [ Te ]-1 { de } = [ ke ] { de }
[ Te ]-1
[ Te ]T
[ Te ]-1 [ Te ]T
Joint atau nodal memiliki peranan penting pada pemodelan analisa struktur. Nodal merupakan titik dimana elemen-elemen batang bertemu sehingga mempunyai bentuk yang bermakna yaitu geometri struktur itu sendiri.
Degree of freedom (DOF) adalah derajat kebebasan suatu titik nodal untuk mengalami deformasi yang dapat berupa translasi (perpindahan) maupun rotasi terhadap tiga sumbu ruang.
Jadi untuk suatu nodal dapat terjadi 6 bentuk deformasi jika berada pada suatu kondisi bebas yakni 3 translasi (δx, δy, δz) dan 3 rotasi (θx, θy, θz). Suatu nodal tidak bebas berdeformasi (tertahan) karena diberi restraint atau disebut juga sebagai tumpuan.
Tugas Struktur Baja Tipe A
Page 40
HASIL OUTPUT ANALISIS DENGAN SAP
Frame Titik N (kg) D (kg) M (kg cm)
1JJ (A) 11990.36 2208.46 0Lap 11990.36 1439.15 492985JK (B) 11990.36 1034.15 809523
2JJ (B) 333.37 1034.15 1027870Lap 333.37 899.15 1049816JK (C) 333.37 764.15 1043284
3JJ (D) 11990.35 2208.46 0Lap 11990.35 1439.15 492985JK (E) 11990.35 1034.15 809523
4JJ (E) 333.37 1034.15 1027870Lap 333.37 899.15 1049816JK (F) 333.37 764.15 1043284
5JJ (C) 34.74 112.23 8802Lap 17.37 56.11 2200JK (G) 0.00 0.00 0
6JJ (C) 763.15 463.34 1037029Lap 612.59 808.96 632177JK (H) 462.04 1154.59 62676
7JJ (F) 763.15 463.34 1037029Lap 612.59 808.96 632177JK (H) 462.04 1154.59 62676
8JJ (F) 34.74 112.23 8802Lap 17.37 56.11 2200JK (I) 0.00 0.00 0
Dari kombinasi pembebanan pada tiap frame didapat Mmax, Dmax, Nmax
Tugas Struktur Baja Tipe A
Page 41
A. KolomUkuran kolom AC dan DF disamakan (Frame 1, 2, 3, 4)
= 1049816 kg cm= 2208.46 kg= 11990.36 kg
Untuk komponen struktur tertekan (kolom) yang lebih menentukan adalah faktor tekuk
• Menurut peraturan PPBBI 1983 untuk struktur seperti tampang pada gambar di samping :Lk = 2 L
= 2 × 800= 1600 cm
•λ =
Lk≤ 200
=Lk
200
=1600200
= 8 cm
Coba profil WF 300×300×12×12Data : q = 85 kg/m = 1150
h = 294 mm = 16900
b = 302 mm = 12.5
= 12 mm = 7.16
= 12 mm A = 107.7
Kontrol Kelangsingan• Arah y
=Lk
=1600
= 223.4637 ≤ 200 ….. TIDAK OK7.16
= πE
= π2100000
= 111.07210.7 fy 0.7 × 2400
= =223.4637
= 2.012111.0721
Faktor tekuk ω = 1 untuk ≤ 0.183
=1.41
untuk 0.183 < < 1
= untuk ≥ 1
Maka : = 9.637
• Arah x
=Lk
=1600
= 127.6935 ≤ 200 ….. OK12.5
= πE
= π2100000
= 111.07210.7 fy 0.7 × 2400
= =127.6935
= 1.150111.0721
Faktor tekuk ω = 1 untuk ≤ 0.183
=1.41
untuk 0.183 < < 1
= untuk ≥ 1
Maka : = 3.147
BAB VIIDIMENSI PROFIL
Mmax
Dmax
Nmax
imin
imin perlu
WX cm3
IX cm3
iX cm4
tw iY cm4
tf cm2
λY iY
λg
λsλY
λg
λs
λs1.593 - λs
2.381 λs2 λs
ωY
λX iX
λg
λsλX
λg
λs
λs1.593 - λs
2.381 λs2 λs
ωX
L
b
htw
tf
Tugas Struktur Baja Tipe A
Page 42
Kontrol Tegangan Geser
• = +2 2
=( 30.2 × 1.2 ) × ( 29.4 - 1.2 )
+1.2 × ( 29.4 / 2 - 1.2 ) 2
2 2= 620.334
• τ = =2208.4600 × 620.334
= 67.553 ≤ = 928 ….. OK1.2 × 16900
Kontrol Tegangan Desak• Momen pada ujung : 0
1049816 kg cm
• = 0.6 + 0.4 = 0.6
• = 127.6935 --> = 3.147
• = =π 2100000 × 107.7
= 11.41711990.36 × 127.6935 2
• σ =N
+ ×A - 1
= 3.147 ×11990.36
+ 0.6 ×11.417
×1049816
107.7 11.417 - 1 1150= 950.660 < = 1600 ….. OK
• σ =N
+A
= 9.637 ×11990.36
+1049816
107.7 1150= 1985.835 < = 1600 ….. TIDAK OK
• σ =NA
= 9.637 ×11990.36
107.7= 1072.951 < = 1600 ….. OK
• = + 3
= 1985.83 3 × 67.553 3
= 1989.279 ≤ = 1600 ….. TIDAK OK
B. BalokUkuran kolom GC, CH, HF dan FI disamakan (Frame 5, 6, 7, 8)Balok GC dan FI digunakan profil WF yang dipotong seperti terlihat pada gambar berikut :
= 1037029 kg cm= 1154.59 kg= 763.15 kg
M=
1037029= 648.1431
1600
SX( b × tf ) ( h - tf ) tw ( h/2 - tf )2
cm3
Dmax SXkg/cm2 0.58 σprofil kg/cm2
tw IX
MX1 =MX2 =
βXMX1
MX2
λX ωX
nXπ2 E A 2 ×
N λX2
ωX βXnX MX
nX WX
kg/cm2 σprofil kg/cm2
ωYMX
WX
kg/cm2 σprofil kg/cm2
ωY
kg/cm2 σprofil kg/cm2
σi σ2 τ2
2 +
kg/cm2 σprofil kg/cm2
Mmax
Dmax
Nmax
WX Perlu = cm3
σprofil
GC
Kolom
Profil WF
Tugas Struktur Baja Tipe A
Page 43
Untuk keadaan tertekan maka :
• Menurut peraturan PPBBI 1983 untuk struktur seperti tampang pada gambar di atas :Lk = L
= 1639= 1639 cm
•λ =
Lk≤ 200
=Lk
=1639 = 8.19656 cm
200 200
Coba profil WF 250×250×9×14Data : q = 72 kg/m = 864
h = 250 mm = 10800
b = 250 mm = 10.8
= 9 mm = 6.29
= 14 mm A = 92.18
Kontrol Kelangsingan• Arah y
=Lk
=1639
= 260.6219 ≤ 200 ….. TIDAK OK6.29
= πE
= π2100000
= 111.07210.7 fy 0.7 × 2400
= =260.6219
= 2.346111.0721
Faktor tekuk ω = 1 untuk ≤ 0.183
=1.41
untuk 0.183 < < 1
= untuk ≥ 1
Maka : = 13.109
• Arah x
=Lk
=1639
= 151.5076 ≤ 200 ….. OK10.8
= πE
= π2100000
= 111.07210.7 fy 0.7 × 2400
= =151.5076
= 1.364111.0721
Faktor tekuk ω = 1 untuk ≤ 0.183
=1.41
untuk 0.183 < < 1
= untuk ≥ 1
Maka : = 4.430
Kontrol Tegangan Geser
• = +2 2
=( 25 × 1.4 ) × ( 25 - 1.4 )
+0.9 × ( 25 / 2 - 1.4 ) 2
2 2= 468.4445
imin
imin perlu
WX cm3
IX cm3
iX cm4
tw iY cm4
tf cm2
λY iY
λg
λsλY
λg
λs
λs1.593 - λs
2.381 λs2 λs
ωY
λX iX
λg
λsλX
λg
λs
λs1.593 - λs
2.381 λs2 λs
ωX
SX( b × tf ) ( h - tf ) tw ( h/2 - tf )2
cm3
b
htw
tf
P P
L
Tugas Struktur Baja Tipe A
Page 44
• τ = =1154.5900 × 468.4445
= 55.644 ≤ = 928 ….. OK0.9 × 10800
Kontrol Tegangan Desak
• σ =N
+A
= 4.430 ×763.15
+1037029
92.18 864= 1236.942 < = 1600 ….. OK
• σ =N
+A
=763.15
+1037029
92.18 864= 1208.544 < = 1600 ….. OK
• σ =NA
= 13.109 ×763.1592.18
= 108.529 < = 1600 ….. OK
• = + 3
= 1236.94 3 × 55.644 3
= 1240.691 ≤ = 1600 ….. OK
Dmax SXkg/cm2 0.58 σprofil kg/cm2
tw IX
ωXMX
WX
kg/cm2 σprofil kg/cm2
MX
WX
kg/cm2 σprofil kg/cm2
ωY
kg/cm2 σprofil kg/cm2
σi σ2 τ2
2 +
kg/cm2 σprofil kg/cm2
Tugas Struktur Baja Tipe A
Page 45
A. Sambungan di Titik C (Kanan) dan di Titik F (Kiri)
WF 250×250×9×14
WF 300×300×12×12
= 1037029 kg cm= 463.34 kg= 763.15 kg
Rencana baut : ≤≤
2 d ≤ 15% × 30.2d ≤ 2.265 cm
Pakai diameter baut d = 16 mm
Data-data profil dan sambungan : b = 250 mm = 25 mmh = 250 mm = 25 mmH = 450 mm L = 200 mm
= 9 mm g = 70 mm= 14 mm q = 55 mm
s = 50 mm --> 1.5d ≤ S1 ≤ 3d atau 6t --> 40 ≤ s ≤ 112 ….. OK= 25 mm --> 2.5d ≤ S ≤ 7d atau 14t --> 24 ≤ ≤ 48 ….. OK
Luasan pengganti :a =
2 × π × / 4× =
2 × π × 1.6 4×
2400= 1.206 cm
s 5 1600
x =H ×
=45 × ( 1.206
= 8.105 cm+ ( 1.206 + ( 25.0
= b × x 3 / 3 + a × ( H - x / 3
= 25 × 8.105 3 + 1.206 × ( 45 - 8.105
= 24632.743
Gaya-gaya yang bekerja : D' = D cos α - N sin α = 463.34 cos 19 - 763.15 sin 19 = 189.639 kgN' = D sin α + N cos α = 463.34 sin 19 + 763.15 cos 19 = 872.421 kgM' = M + N' (H - x - h/2) = 1037029 + 872.421 × ( 45 - 8.105 - 12.5 / 2 ) = 1063765 kg cm
Tegangan yang terjadi : M' (H - x)=
1063765 × ( 45 - 8.105 )= 1593.32
24632.743
=N'
× =872.4212
×1600
= 16.071n F 18 × π × 1.6 4 2400
τ =D'
× =189.6392
×1600
= 3.493n F 18 × π × 1.6 4 2400
= + 3 ( + τ ) 2 = 1593.32 3 × ( 16.071 + 3.493
BAB VIIIPERENCANAAN SAMBUNGAN
Mmax
Dmax
Nmax
Flob 15% Fbruto
2 d tf 15% b tf
s2
s3
tw
tf
s1 s1
d2 σbaut2 /
σprofil
(a)0.5 )0.5
(a)0.5 (b)0.5 )0.5 )0.5
IX )3
3 / ) 3 / 3
cm4
σmax = kg/cm2
IX
σNσprofil
kg/cm2
σbaut2 /
σprofilkg/cm2
σbaut2 /
σi σ2 σN2 + )2
b
H
L
h
x
h-x
D
N
M s1
sssss2s3
ssss1
q g g qa
b
Tugas Struktur Baja Tipe A
Page 46
= 1593.680 ≤ = 1600 ….. OKkg/cm2 σprofil kg/cm2
Tugas Struktur Baja Tipe A
Page 47
Rencana pelat penyambung :
q = 55• P = A ×
=π ×
× ×g = 70 4
=π × 1.6 2
× 1593.680 ×2400
g = 70 4 1600= 4806.4259 kg
q = 55• M = 0.6 { P ( g - / 2 ) }
= 0.6 { 4806.4259 ( 7 - 0.9 / 2 ) }= 18889.2535962 kg cm
• T = P { 1 + ( g - / 2 ) / q }= 4806.4259 { 1 + ( 7 - 0.9 / 2 ) / 5.5 }= 10530.4420927 kg
• σ =M
=18889.253596152
=22667.10432
W 5 × / 6
• τ =T
=10530.4420927
=210.6088
s t 50 × t t• ≥ + 3
2400 2 ≥ ( 22667.10432 ) 2+ 3 ( 210.6088 ) 2
t
2400 2 ≥513797618.04
+133068.253
0 ≤ 5760000 - 133068.253 - 513797618.04
0 ≤ - 0.023 - 89.201
misalkan = a
0 ≤ - 0.023 a - 89.201a ≥ 9.456t ≥ 3.075 cm
Ambil tebal pelat t = 32 mm• Maka dipakai pelat / ( 46 × 25 × 3.2 )
Sambungan las antara pelat dan profil :
Data-data profil dan las :• h = 250 mm• L = 200 mm• b = 250 mm• = 14 mm• = 9 mm• = 450 mm• = 436 mm• = 325 mm• = 214 mm• = 200 mm• = 107 mm• = 14 mm• = 0 mm• = 4.5 mm• = 64.75 mm
σi
tw d2
σiσbaut
σprofil
tw
tw
t2 t2
σizin σ2 τ2
t2
t4 t2
t4 t2
t4 t2
t2
a2
cm3
tf
tw
y1
y2
y3
y4
y5
y6
y7
y8
x1
x2
L
h
2
3
1
4
5
6
7
8
y
wt
ft
b
6y
7y
5y 4y
3y
2y 1y
1x2x
Tugas Struktur Baja Tipe A
Page 48
• Tebal las dianggap 1 satuan• Luasan las :
• = 25 × 1 = 25.0
• = ( 25 - 0.9 ) / 2 × 1 = 12.05 × 1 = 12.1
• = 1 × ( 25 - 2 × 1.4 ) = 1 × 22.2 = 22.2
• = = 12.05 × 1 = 12.1
• = = 12.05 × 1 = 12.1
• = 1 × ( 20 - 1.4 ) = 1 × 18.6 = 18.6
• = = 12.05 × 1 = 12.1
• = = 25 × 1 = 25.0
+ 2 + 2 + 2 + 2 + 2 + 2 += 25.0 + 2 ( 12.1 + 22.2 + 12.1 + 12.1 + 18.6 + 12.1 ) + 25.0= 228.0
• Garis netral :
• y =× + 2 ( × + × + × + × + × + × ) + ×
= 22.142 cm• x = b / 2
= 12.500 cm
• Inersia las arah x• = 25 × 1 3 / 12 + 25.00 × ( 45 - 22.142 ) 2 = 13064.769
• = 12.05 × 1 3 / 12 + 12.05 × ( 43.6 - 22.142 ) 2 = 5549.593
• = 1 × 22.2 3 / 12 + 22.20 × ( 32.5 - 22.142 ) 2 = 2381.991
• = 12.05 × 1 3 / 12 + 12.05 × ( 22.142 - 21.4 ) 2 = 7.631
• = 12.05 × 1 3 / 12 + 12.05 × ( 22.142 - 20 ) 2 = 56.270
• = 1 × 18.6 3 / 12 + 18.60 × ( 22.142 - 10.7 ) 2 = 2971.159
• = 12.05 × 1 3 / 12 + 12.05 × ( 22.142 - 1.4 ) 2 = 5185.072
• = 25 × 1 3 / 12 + 25.00 × ( 22.142 - 0 ) 2 = 12258.321
= + 2 + 2 + 2 + 2 + 2 + 2 += 13064.769 + 2 ( 5549.593 + 2381.991 + 7.631 + 56.270 + 2971.159 + 5185.072 )
+ 12258.321= 57626.522
• Inersia las arah y• = 1 × 25 3 / 12 = 1302.083
• = 1 × 12.05 3 / 12 + 12.05 × 6.475 2 = 651.011
• = 22.2 × 1 3 / 12 + 22.20 × 0.45 2 = 6.345
• = 1 × 12.05 3 / 12 + 12.05 × 6.475 2 = 651.011
• = 1 × 12.05 3 / 12 + 12.05 × 6.475 2 = 651.011
• = 18.6 × 1 3 / 12 + 18.60 × 0.45 2 = 5.317
• = 1 × 12.05 3 / 12 + 12.05 × 6.475 2 = 651.011
• = 1 × 25 3 / 12 = 1302.083
= + 2 + 2 + 2 + 2 + 2 + 2 += 1302.083 + 2 ( 651.011 + 6.345 + 651.011 + 651.011 + 5.317 + 651.011 )
+ 1302.083= 7835.581
• = + = 57626.522 + 7835.581 = 65462.103
• Tegangan yang terjadi pada las :
=M' y
=1063764.549 × 22.14
= 359.80265462.103
=N'
=872.421
= 3.826
F1 cm2
F2 cm2
F3 cm2
F4 F2 cm2
F5 F2 cm2
F6 cm2
F7 F2 cm2
F8 F1 cm2
Flas = F1 F2 F3 F4 F5 F6 F7 F8
cm2
F1 y1 F2 y2 F3 y3 F4 y4 F5 y5 F6 y6 F7 y7 F8 y8
Flas
IX1 cm4
IX2 cm4
IX3 cm4
IX4 cm4
IX5 cm4
IX6 cm4
IX7 cm4
IX8 cm4
IX Total IX1 IX2 IX3 IX4 IX5 IX6 IX7 IX8
cm4
IY1 cm4
IY2 cm4
IY3 cm4
IY4 cm4
IY5 cm4
IY6 cm4
IY7 cm4
IY8 cm4
IY Total IY1 IY2 IY3 IY4 IY5 IY6 IY7 IY8
cm4
ITotal IX Total Iy Total cm4
τX kg/cm2
ITotal
τX' kg/cm2
L
h
2
3
1
4
5
6
7
8
y
wt
ft
b
6y
7y
5y 4y
3y
2y 1y
1x2x
Tugas Struktur Baja Tipe A
Page 49
= =228.000
= 3.826
=D'
=189.639
= 0.832228.000
= 2 + ( + = 0.832 2 + ( 359.802 + 3.826 = 363.6298
Tebal las = × 1 = × 1 =363.6298
× 1 = 0.253 cmτ 1440
Ambil tebal las t = 2 mm
B. Sambungan di Titik H (Tengah)
WF 250×250×9×14 WF 250×250×9×14
= 62676 kg cm= 1154.59 kg= 462.04 kg
Rencana baut : ≤≤
2 d ≤ 15% × 30.2d ≤ 2.265 cm
Pakai diameter baut d = 16 mm
Data-data profil dan sambungan : b = 250 mm = 25 mmh = 250 mm = 25 mmH = 400 mm L = 150 mm
= 9 mm g = 70 mm= 14 mm q = 55 mm
s = 50 mm --> 1.5d ≤ S1 ≤ 3d atau 6t --> 40 ≤ s ≤ 112 ….. OK= 25 mm --> 2.5d ≤ S ≤ 7d atau 14t --> 24 ≤ ≤ 48 ….. OK
Luasan pengganti :a =
2 × π × / 4× =
2 × π × 1.6 4×
2400= 1.206 cm
s 5 1600
x =H ×
=40 × ( 1.206
= 7.204 cm+ ( 1.206 + ( 25.0
= b × x 3 / 3 + a × ( H - x / 3
= 25 × 7.204 3 + 1.206 × ( 40 - 7.204
= 17300.363
Gaya-gaya yang bekerja : D' = D cos α - N sin α = 1154.59 cos 19 - 462.04 sin 19 = 941.261 kgN' = D sin α + N cos α = 1154.59 sin 19 + 462.04 cos 19 = 812.765 kgM' = M + N' (H - x - h/2) = 62676 + 812.765 × ( 40 - 7.204 - 12.5 / 2 ) = 84251 kg cm
Tegangan yang terjadi : M' (H - x)=
84251 × ( 40 - 7.204 )= 159.713
17300.363
=N'
× =812.7651
×1600
= 16.843n F 16 × π × 1.6 4 2400
τ =D'
× =941.2608
×1600
= 19.506n F 16 × π × 1.6 4 2400
= + 3 ( + τ ) 2 = 159.713 3 × ( 16.843 + 19.506
= 171.674 ≤ = 1600 ….. OK
τX' kg/cm2
Flas
τY' kg/cm2
Flas
τi' τY' τX τX' )2 )2 kg/cm2
τi' τi'0.6 σlas
Mmax
Dmax
Nmax
Flob 15% Fbruto
2 d tf 15% b tf
s2
s3
tw
tf
s1 s1
d2 σbaut2 /
σprofil
(a)0.5 )0.5
(a)0.5 (b)0.5 )0.5 )0.5
IX )3
3 / ) 3 / 3
cm4
σmax = kg/cm2
IX
σNσprofil
kg/cm2
σbaut2 /
σprofilkg/cm2
σbaut2 /
σi σ2 σN2 + )2
kg/cm2 σprofil kg/cm2
x
h-x
NM
b
H
L
h
s1
sssss2s3
ss
q g g q
s1
a
b
Tugas Struktur Baja Tipe A
Page 50
Rencana pelat penyambung :
q = 55• P = A ×
=π ×
× ×g = 70 4
=π × 1.6 2
× 171.674 ×2400
g = 70 4 1600= 517.7569 kg
q = 55• M = 0.6 { P ( g - / 2 ) }
= 0.6 { 517.7569 ( 7 - 0.9 / 2 ) }= 2034.78467455 kg cm
• T = P { 1 + ( g - / 2 ) / q }= 517.7569 { 1 + ( 7 - 0.9 / 2 ) / 5.5 }= 1134.35833117 kg
• σ =M
=2034.78467454747
=2441.741609
W 5 × / 6
• τ =T
=1134.35833117
=22.6872
s t 50 × t t• ≥ + 3
2400 2 ≥ ( 2441.741609 ) 2+ 3 ( 22.6872 ) 2
t
2400 2 ≥5962102.087
+1544.123
0 ≤ 5760000 - 1544.123 - 5962102.087
0 ≤ - 0.000 - 1.035
misalkan = a
0 ≤ - 0.000 a - 1.035a ≥ 1.018t ≥ 1.009 cm
Ambil tebal pelat t = 10 mm• Maka dipakai pelat / ( 41 × 25 × 1 )
Sambungan las antara pelat dan profil :
Data-data profil dan las :• h = 250 mm• L = 150 mm• b = 250 mm• = 14 mm• = 9 mm• = 400 mm• = 386 mm• = 275 mm• = 164 mm• = 150 mm• = 82 mm• = 14 mm• = 0 mm• = 4.5 mm• = 64.75 mm
σi
tw d2
σiσbaut
σprofil
tw
tw
t2 t2
σizin σ2 τ2
t2
t4 t2
t4 t2
t4 t2
t2
a2
cm3
tf
tw
y1
y2
y3
y4
y5
y6
y7
y8
x1
x2
L
h
2
3
1
4
5
6
7
8
y
wt
ft
b
6y
7y
5y 4y
3y
2y 1y
1x2x
Tugas Struktur Baja Tipe A
Page 51
• Tebal las dianggap 1 satuan• Luasan las :
• = 25 × 1 = 25.0
• = ( 25 - 0.9 ) / 2 × 1 = 12.05 × 1 = 12.1
• = 1 × ( 25 - 2 × 1.4 ) = 1 × 22.2 = 22.2
• = = 12.05 × 1 = 12.1
• = = 12.05 × 1 = 12.1
• = 1 × ( 15 - 1.4 ) = 1 × 13.6 = 13.6
• = = 12.05 × 1 = 12.1
• = = 25 × 1 = 25.0
+ 2 + 2 + 2 + 2 + 2 + 2 += 25.0 + 2 ( 12.1 + 22.2 + 12.1 + 12.1 + 13.6 + 12.1 ) + 25.0= 218.0
• Garis netral :
• y =× + 2 ( × + × + × + × + × + × ) + ×
= 19.104 cm• x = b / 2
= 12.500 cm
• Inersia las arah x• = 25 × 1 3 / 12 + 25.00 × ( 40 - 19.104 ) 2 = 10917.636
• = 12.05 × 1 3 / 12 + 12.05 × ( 38.6 - 19.104 ) 2 = 4580.904
• = 1 × 22.2 3 / 12 + 22.20 × ( 27.5 - 19.104 ) 2 = 1564.756
• = 12.05 × 1 3 / 12 + 12.05 × ( 19.104 - 16.4 ) 2 = 89.141
• = 12.05 × 1 3 / 12 + 12.05 × ( 19.104 - 15 ) 2 = 204.009
• = 1 × 13.6 3 / 12 + 13.60 × ( 19.104 - 8.2 ) 2 = 1826.770
• = 12.05 × 1 3 / 12 + 12.05 × ( 19.104 - 1.4 ) 2 = 3778.067
• = 25 × 1 3 / 12 + 25.00 × ( 19.104 - 0 ) 2 = 9126.627
= + 2 + 2 + 2 + 2 + 2 + 2 += 10917.636 + 2 ( 4580.904 + 1564.756 + 89.141 + 204.009 + 1826.770 + 3778.067 )
+ 9126.627= 44131.558
• Inersia las arah y• = 1 × 25 3 / 12 = 1302.083
• = 1 × 12.05 3 / 12 + 12.05 × 6.475 2 = 651.011
• = 22.2 × 1 3 / 12 + 22.20 × 0.45 2 = 6.345
• = 1 × 12.05 3 / 12 + 12.05 × 6.475 2 = 651.011
• = 1 × 12.05 3 / 12 + 12.05 × 6.475 2 = 651.011
• = 13.6 × 1 3 / 12 + 13.60 × 0.45 2 = 3.887
• = 1 × 12.05 3 / 12 + 12.05 × 6.475 2 = 651.011
• = 1 × 25 3 / 12 = 1302.083
= + 2 + 2 + 2 + 2 + 2 + 2 += 1302.083 + 2 ( 651.011 + 6.345 + 651.011 + 651.011 + 3.887 + 651.011 )
+ 1302.083= 7832.723
• = + = 44131.558 + 7832.723 = 51964.281
• Tegangan yang terjadi pada las :
=M' y
=84251.468 × 19.10
= 30.97551964.281
=N'
=812.765
= 3.728
F1 cm2
F2 cm2
F3 cm2
F4 F2 cm2
F5 F2 cm2
F6 cm2
F7 F2 cm2
F8 F1 cm2
Flas = F1 F2 F3 F4 F5 F6 F7 F8
cm2
F1 y1 F2 y2 F3 y3 F4 y4 F5 y5 F6 y6 F7 y7 F8 y8
Flas
IX1 cm4
IX2 cm4
IX3 cm4
IX4 cm4
IX5 cm4
IX6 cm4
IX7 cm4
IX8 cm4
IX Total IX1 IX2 IX3 IX4 IX5 IX6 IX7 IX8
cm4
IY1 cm4
IY2 cm4
IY3 cm4
IY4 cm4
IY5 cm4
IY6 cm4
IY7 cm4
IY8 cm4
IY Total IY1 IY2 IY3 IY4 IY5 IY6 IY7 IY8
cm4
ITotal IX Total Iy Total cm4
τX kg/cm2
ITotal
τX' kg/cm2
Tugas Struktur Baja Tipe A
Page 52
= =218.000
= 3.728
=D'
=941.261
= 4.318218.000
= 2 + ( + = 4.318 2 + ( 30.975 + 3.728 = 34.97062
Tebal las = × 1 = × 1 =34.97062
× 1 = 0.024 cmτ 1440
Ambil tebal las t = 1 mm
C. Sambungan di Titik C (Kir) dan di Titik F (Kanan)
WF 250×250×9×14
WF 300×300×12×12
= 8802 kg cm= 112.23 kg= 34.74 kg
Rencana baut : ≤≤
2 d ≤ 15% × 30.2d ≤ 2.265 cm
Pakai diameter baut d = 18 mm
Data-data profil dan sambungan : b = 250 mm h = 250 mmH = 236 mm g = 70 mm
= 9 mm q = 48 mm= 14 mm
s = 45 mm --> 1.5d ≤ S1 ≤ 3d atau 6t --> 45 ≤ s ≤ 126 ….. OK= 28 mm --> 2.5d ≤ S ≤ 7d atau 14t --> 27 ≤ ≤ 54 ….. OK
Luasan pengganti :a =
2 × π × / 4× =
2 × π × 1.8 4×
2400= 1.696 cm
s 4.5 1600
x =h ×
=23.6 × ( 1.696
= 4.877 cm+ ( 1.696 + ( 25.0
= b × x 3 / 3 + a × ( H - x / 3
= 25 × 4.877 3 + 1.696 × ( 23.6 - 4.877
= 4678.161
Gaya-gaya yang bekerja : D' = D cos α - N sin α = 112.23 cos 19 - 34.74 sin 19 = 94.805 kgN' = D sin α + N cos α = 112.23 sin 19 + 34.74 cos 19 = 69.386 kgM' = M + N' (H - x - h/2) = 8802 + 69.386 × ( 23.6 - 4.877 - 25 / 2 ) = 9234 kg cm
Tegangan yang terjadi : M' (H - x)=
9234 × ( 23.6 - 4.877 )= 36.955
4678.161
=N'
× =69.3858
×1600
= 1.818n F 10 × π × 1.8 4 2400
τX' kg/cm2
Flas
τY' kg/cm2
Flas
τi' τY' τX τX' )2 )2 kg/cm2
τi' τi'0.6 σlas
Mmax
Dmax
Nmax
Flob 15% Fbruto
2 d tf 15% b tf
tw
tf
s1 s1
d2 σbaut2 /
σprofil
(a)0.5 )0.5
(a)0.5 (b)0.5 )0.5 )0.5
IX )3
3 / ) 3 / 3
cm4
σmax = kg/cm2
IX
σNσprofil
kg/cm2
σbaut2 /
H
x
h-x
b
q g g q
ssss
s1
s1
D
N
M
b
a
Tugas Struktur Baja Tipe A
Page 53
τ =D'
× =94.8053
×1600
= 2.484n F 10 × π × 1.8 4 2400
σprofilkg/cm2
σbaut2 /
Tugas Struktur Baja Tipe A
Page 54
= + 3 ( + τ ) 2 = 36.955 3 × ( 1.818 + 2.484
= 37.699 ≤ = 1600 ….. OK
Rencana pelat penyambung :
q = 48• P = A ×
=π ×
× ×g = 70 4
=π × 1.8 2
× 37.699 ×2400
g = 70 4 1600= 143.8971 kg
q = 48• M = 0.6 { P ( g - / 2 ) }
= 0.6 { 143.8971 ( 7 - 0.9 / 2 ) }= 565.51571225 kg cm
• T = P { 1 + ( g - / 2 ) / q }= 143.8971 { 1 + ( 7 - 0.9 / 2 ) / 4.8 }= 340.256750108 kg
• σ =M
=565.515712249663
=754.0209497
W 4.5 × / 6
• τ =T
=340.256750108
=7.5613
s t 45 × t t• ≥ + 3
2400 2 ≥ ( 754.0209497 ) 2+ 3 ( 7.5613 ) 2
t
2400 2 ≥568547.593
+171.518
0 ≤ 5760000 - 171.518 - 568547.593
0 ≤ - 0.000 - 0.099
misalkan = a
0 ≤ - 0.000 a - 0.099a ≥ 0.314t ≥ 0.561 cm
Ambil tebal pelat t = 6 mm• Maka dipakai pelat / ( 25 × 25 × 0.6 )
Sambungan las antara pelat dan profil :Data-data profil dan las :• h = 236 mm• b = 250 mm• = 14 mm• = 9 mm• = 236 mm• = 222 mm• = 111 mm• = 4.5 mm• = 64.75 mm
• Tebal las dianggap 1 satuan• Luasan las :
• = 25 × 1 = 25.0
• = ( 25 - 0.9 ) / 2 × 1 = 12.05 × 1 = 12.1
• = 1 × ( 23.6 - 1.4 ) = 1 × 22.2 = 22.2
+ 2 + 2= 25.0 + 2 ( 12.1 + 22.2 )
σi σ2 σN2 + )2
kg/cm2 σprofil kg/cm2
σi
tw d2
σiσbaut
σprofil
tw
tw
t2 t2
σizin σ2 τ2
t2
t4 t2
t4 t2
t4 t2
t2
a2
cm3
tf
tw
y1
y2
y3
x1
x2
F1 cm2
F2 cm2
F3 cm2
Flas = F1 F2 F3
h
2
3
1
ywt
ft
3y
2y 1y
1x2x
x
Tugas Struktur Baja Tipe A
Page 55
= 93.5 cm2
Tugas Struktur Baja Tipe A
Page 56
• Garis netral :
• y =× + 2 ( × + × )
= 17.303 cm• x = b / 2
= 12.500 cm
• Inersia las arah x• = 25 × 1 3 / 12 + 25.00 × ( 23.6 - 17.303 ) 2 = 993.289
• = 12.05 × 1 3 / 12 + 12.05 × ( 22.2 - 17.303 ) 2 = 289.933
• = 1 × 22.2 3 / 12 + 22.20 × ( 17.303 - 11.1 ) 2 = 1766.035
= + 2 + 2= 993.289 + 2 ( 289.933 + 1766.035 )= 5105.226
• Inersia las arah y• = 1 × 25 3 / 12 = 1302.083
• = 1 × 12.05 3 / 12 + 12.05 × 6.475 2 = 651.011
• = 22.2 × 1 3 / 12 + 22.20 × 0.45 2 = 6.346
= + 2 + 2= 1302.083 + 2 ( 651.011 + 6.346 )= 2616.797
• = + = 5105.226 + 2616.797 = 7722.023
• Tegangan yang terjadi pada las :
=M' y
=9233.773 × 17.30
= 20.6917722.023
=N'
=69.386
= 0.74293.500
=D'
=94.805
= 1.01493.500
= 2 + ( + = 1.014 2 + ( 20.691 + 0.742 = 21.45687
Tebal las = × 1 = × 1 =21.45687
× 1 = 0.015 cmτ 1440
Ambil tebal las t = 1 mm
F1 y1 F2 y2 F3 y3
Flas
IX1 cm4
IX2 cm4
IX3 cm4
IX Total IX1 IX2 IX3
cm4
IY1 cm4
IY2 cm4
IY3 cm4
IY Total IY1 IY2 IY3
cm4
ITotal IX Total Iy Total cm4
τX kg/cm2
ITotal
τX' kg/cm2
Flas
τY' kg/cm2
Flas
τi' τY' τX τX' )2 )2 kg/cm2
τi' τi'0.6 σlas
Nama Profil h b d t F q Cx Cy
mm mm mm mm kg/m cm cmC 200×75×20×3.2 200 75 20 3.2 11.810 9.27 10.00 2.27C 150×75×20×4.5 150 75 20 4.5 13.970 11.00 7.50 2.50C 150×65×20×3.2 150 65 20 3.2 9.567 7.51 7.50 2.11C 150×50×20×4.5 150 50 20 4.5 11.720 9.20 7.50 1.54C 150×50×20×3.2 150 50 20 3.2 8.607 6.76 7.50 1.54C 150×50×20×2.3 150 50 20 2.3 6.322 4.96 7.50 1.55C 125×50×20×4.5 125 50 20 4.5 10.590 8.32 6.25 1.68C 125×50×20×4.0 125 50 20 4.0 9.548 7.50 6.25 1.68C 125×50×20×3.2 125 50 20 3.2 7.807 6.13 6.25 1.68C 125×50×20×2.3 125 50 20 2.3 5.747 4.51 6.25 1.69C 100×50×20×4.5 100 50 20 4.5 9.469 7.43 5.00 1.86C 100×50×20×4.0 100 50 20 4.0 8.548 6.71 5.00 1.86C 100×50×20×3.2 100 50 20 3.2 7.007 5.50 5.00 1.86C 100×50×20×2.6 100 50 20 2.6 5.796 4.55 5.00 1.86C 100×50×20×2.3 100 50 20 2.3 5.172 4.06 5.00 1.86C 100×50×20×1.6 100 50 20 1.6 3.672 2.88 5.00 1.87C 75×45×15×2.3 75 45 15 2.3 4.137 3.25 3.75 1.72C 75×45×15×1.6 75 45 15 1.6 2.952 2.32 3.75 1.72C 60×30×10×2.3 60 30 10 2.3 2.872 2.25 3.00 1.06C 60×30×10×1.6 60 30 10 1.6 2.072 1.53 3.00 1.06
Nama Profil h b F q r Ix
mm mm mm mm kg/m cmWF 900×300×18×34 912 302 18 34 364.0 286 28 498000WF 900×300×16×28 900 300 16 28 309.8 243 28 411000WF 900×300×15×23 890 299 15 23 270.9 213 28 345000WF 800×300×16×30 808 302 16 30 307.6 241 28 339000WF 800×300×14×26 800 300 14 26 267.4 210 28 292000WF 800×300×14×22 792 300 14 22 243.4 191 28 254000WF 700×300×15×28 708 302 15 28 273.6 215 28 237000WF 700×300×13×24 700 300 13 24 235.5 185 28 201000WF 700×300×13×20 692 300 13 20 211.5 166 28 172000WF 600×300×14×23 594 302 14 23 222.4 175 28 137000WF 600×300×12×20 588 300 12 20 192.5 151 28 118000WF 600×300×12×17 582 300 12 17 174.5 137 28 103000WF 600×200×13×23 612 202 13 23 170.7 134 22 103000WF 600×200×12×20 606 201 12 20 152.5 120 22 90400WF 600×200×11×17 600 200 11 17 134.4 106 22 77600WF 600×200×10×15 596 199 10 15 120.5 95 22 68700WF 500×300×11×18 488 300 11 18 163.5 128 26 71000WF 500×300×11×15 482 300 11 15 145.5 114 26 60400WF 500×200×11×19 506 201 11 19 131.3 103 20 56500WF 500×200×10×16 500 200 10 16 114.2 90 20 47800WF 500×200×9×14 496 199 9 14 101.3 80 20 41900WF 450×300×11×18 440 300 11 18 157.4 124 24 56100WF 450×300×10×15 434 299 10 15 135.0 106 24 46800WF 450×200×9×14 450 200 9 14 96.76 76 18 33500WF 450×200×8×12 446 199 8 12 84.30 66 18 28700WF 400×400×45×70 498 432 45 70 770.1 605 22 298000WF 400×400×30×50 458 417 30 50 528.6 415 22 187000WF 400×400×20×35 428 407 20 35 360.7 283 22 119000WF 400×400×18×28 414 405 18 28 295.4 232 22 92800WF 400×400×16×24 406 403 16 24 254.9 200 22 78000WF 400×400×21×21 400 408 21 21 250.7 197 22 70900
cm2
tw tf
cm2 cm4
WF 400×400×13×21 400 400 13 21 218.7 172 22 66600WF 400×400×18×18 394 405 18 18 214.4 168 22 59700WF 400×400×11×18 394 398 11 18 186.8 147 22 56100WF 400×400×15×15 388 402 15 15 178.5 140 22 49000WF 400×300×10×16 390 300 10 16 136.0 107 22 38700WF 400×300×9×14 386 299 9 14 120.1 94 22 33700WF 400×200×8×13 400 200 8 13 84.12 66 16 23700WF 400×200×7×11 396 199 7 11 72.16 57 16 20000WF 350×350×14×22 356 352 14 22 202.0 159 20 47600WF 350×350×19×19 350 357 19 19 198.4 156 20 42800WF 350×350×12×19 350 350 12 19 173.9 137 20 40300WF 350×350×16×16 344 354 16 16 166.6 131 20 35300WF 350×350×10×16 344 348 10 16 146.0 115 20 33300WF 350×350×13×13 338 351 13 13 135.3 106 20 28200WF 350×250×9×14 340 250 9 14 101.5 80 20 21700WF 350×250×8×12 336 249 8 12 88.15 69 20 18500WF 350×175×7×11 350 175 7 11 63.14 50 14 13600WF 350×175×6×9 346 174 6 9 52.68 41 14 11100WF 300×300×11×17 304 301 11 17 134.8 106 18 23400WF 300×300×15×15 300 305 15 15 134.8 106 18 21500WF 300×300×10×15 300 300 10 15 119.8 94 18 20400WF 300×300×9×14 298 299 9 14 110.8 87 18 18800WF 300×300×12×12 294 302 12 12 107.7 85 18 16900WF 300×200×9×14 298 201 9 14 83.36 65 18 13300WF 300×200×8×12 294 200 8 12 72.38 57 18 11300WF 300×150×6.5×9 300 150 6.5 9 46.78 37 13 7210WF 300×150×5.5×8 298 149 5.5 8 40.80 32 13 6320WF 250×250×14×14 250 255 14 14 104.7 82 16 11500WF 250×250×9×14 250 250 9 14 92.18 72 16 10800WF 250×250×8×13 248 249 8 13 84.70 66 16 9930WF 250×250×11×11 244 252 11 11 82.06 64 16 8790WF 250×175×7×11 244 175 7 11 56.24 44 16 6120WF 250×125×6×9 250 125 6 9 37.66 30 12 4050WF 250×125×5×8 248 124 5 8 32.68 26 12 3540WF 200×200×10×16 208 202 10 16 83.69 66 13 6530WF 200×200×12×12 200 204 12 12 71.53 56 13 4980WF 200×200×8×12 200 200 8 12 63.53 50 13 4720WF 200×150×6×9 194 150 6 9 39.01 31 13 2690WF 200×100×5.5×8 200 100 5.5 8 27.16 21 11 1840WF 200×100×4.5×7 198 9 4.5 7 23.18 18 11 1580WF 175×175×7.5×11 175 175 7.5 11 51.21 40 12 2880WF 175×125×5.5×8 169 125 5.5 8 29.65 23 12 1530WF 175×90×5×8 175 90 5 8 23.04 18 9 1210WF 150×150×7×10 150 150 7 10 40.14 32 11 1640WF 150×100×6×9 148 100 6 9 26.84 21 11 1020WF 150×75×5×7 150 75 5 7 17.85 14 8 866WF 125×125×6.5×9 125 125 6.5 9 30.31 24 10 847WF 125×60×6×8 125 6 6 8 16.84 13 9 413WF 100×100×6×8 100 100 6 8 21.90 17 10 383WF 100×50×5×7 100 50 5 7 11.85 9 8 187
Ix Iy ix iy Wx Wy
cm cm721 87.5 7.81 2.72 72.1 16.7489 99.2 5.92 2.66 65.2 19.8332 53.8 5.89 2.37 44.3 12.3368 35.7 5.60 1.75 49.1 10.3280 28.3 5.70 1.81 37.3 8.2210 21.9 5.76 1.86 28.0 6.4238 33.5 4.74 1.78 38.1 10.1217 33.1 4.77 1.86 34.7 10.0181 26.6 4.82 1.85 29.0 8.0137 20.6 4.88 1.89 21.9 6.2139 30.9 3.83 1.81 27.8 9.8127 28.7 3.85 1.83 25.4 9.1107 24.5 3.91 1.87 21.4 7.8
89.7 21.0 3.93 1.90 17.9 6.780.7 19.0 3.95 1.92 16.1 6.158.4 14.0 3.99 1.95 11.7 4.537.1 11.8 2.99 1.69 9.9 4.227.1 8.71 3.03 1.72 7.2 3.115.6 3.32 2.33 1.08 5.2 1.711.6 2.56 2.37 1.11 3.9 1.3
Iy ix iy Wx Wy
cm cm15700 37.0 6.57 10921 104012600 36.4 6.38 9133 84010300 35.7 6.17 7753 68913800 33.2 6.70 8391 91411700 33.1 6.61 7300 780
9930 32.3 6.39 6414 66212900 29.4 6.87 6695 85410800 29.2 6.77 5743 720
9020 28.5 6.53 4971 60110600 24.8 6.90 4613 702
9020 24.8 6.85 4014 6017670 24.3 6.63 3540 5113180 24.6 4.32 3366 3152720 24.4 4.22 2983 2712280 24.0 4.12 2587 2281980 23.9 4.05 2305 1998110 20.8 7.04 2910 5416760 20.4 6.82 2506 4512580 20.7 4.43 2233 2572140 20.5 4.33 1912 2141840 20.3 4.26 1690 1858110 18.9 7.18 2550 5416690 18.6 7.04 2157 4471870 18.6 4.40 1489 1871580 18.5 4.33 1287 159
94400 19.7 11.1 11968 437060500 18.8 10.7 8166 290239400 18.2 10.5 5561 193631000 17.7 10.2 4483 153126200 17.5 10.1 3842 130023800 16.8 9.74 3545 1167
cm4 cm4 cm3 cm3
cm4 cm3 cm3
22400 17.5 10.1 3330 112020000 16.7 9.66 3030 98818900 17.3 10.1 2848 95016300 16.6 9.56 2526 811
7210 16.9 7.28 1985 4816240 16.8 7.21 1746 4171740 16.8 4.55 1185 1741450 16.7 4.48 1010 146
16000 15.4 8.90 2674 90914400 14.7 8.52 2446 80713600 15.2 8.84 2303 77711800 14.6 8.42 2052 66711200 15.1 8.76 1936 644
9380 14.4 8.33 1669 5343650 14.6 6.00 1276 2923090 14.5 5.92 1101 248
984 14.7 3.95 777 112792 14.5 3.88 642 91.0
7730 13.2 7.57 1539 5147100 12.6 7.26 1433 4666750 13.1 7.51 1360 4506240 13.0 7.50 1262 4175520 12.5 7.16 1150 3661900 12.6 4.77 893 1891600 12.5 4.70 769 160
508 12.4 3.30 481 67.7442 12.5 3.29 424 59.3
3880 10.5 6.09 920 3043650 10.8 6.29 864 2923350 10.8 6.29 801 2692940 10.4 5.99 720 233
984 10.4 4.18 502 112294 10.4 2.79 324 47.0255 10.4 2.79 285 41.1
2200 8.83 5.13 628 2181700 8.34 4.88 498 1671600 8.62 5.02 472 160
507 8.30 3.61 277 67.6134 8.23 2.22 184 26.8114 8.26 2.22 160 253984 7.50 4.38 329 112261 7.18 2.97 181 41.8
97.5 7.25 2.06 138 22.0563 6.39 3.75 219 75.0151 6.16 2.37 138 30.0
49.5 6.97 1.67 115 13.0293 5.29 3.11 136 47.0
29.2 4.95 1.32 66 97.0134 4.18 2.47 77 27.0
14.8 3.97 1.12 37.0 5.92
TABLE: Element Forces - FramesFrame Station OutputCase CaseType P V2 V3 TText m Text Text Kgf Kgf Kgf Kgf-m
1 0 COMB1 Combination -11581.23 2208.46 0 01 2.8125 COMB1 Combination -11581.23 1297.21 0 01 5.625 COMB1 Combination -11581.23 385.96 0 01 0 COMB2 Combination -3735.07 2208.46 0 01 2.8125 COMB2 Combination -3735.07 1297.21 0 01 5.625 COMB2 Combination -3735.07 385.96 0 01 0 COMB3 Combination -11990.36 -1844.15 0 01 2.8125 COMB3 Combination -11990.36 -1439.15 0 01 5.625 COMB3 Combination -11990.36 -1034.15 0 01 0 COMB4 Combination -4144.2 -1844.15 0 01 2.8125 COMB4 Combination -4144.2 -1439.15 0 01 5.625 COMB4 Combination -4144.2 -1034.15 0 02 0 COMB1 Combination 333.37 385.96 0 02 0.9375 COMB1 Combination 333.37 82.21 0 02 1.875 COMB1 Combination 333.37 -221.54 0 02 0 COMB2 Combination 179.53 385.96 0 02 0.9375 COMB2 Combination 179.53 82.21 0 02 1.875 COMB2 Combination 179.53 -221.54 0 02 0 COMB3 Combination -75.75 -1034.15 0 02 0.9375 COMB3 Combination -75.75 -899.15 0 02 1.875 COMB3 Combination -75.75 -764.15 0 02 0 COMB4 Combination -229.6 -1034.15 0 02 0.9375 COMB4 Combination -229.6 -899.15 0 02 1.875 COMB4 Combination -229.6 -764.15 0 03 0 COMB1 Combination -4144.2 1844.15 0 03 2.8125 COMB1 Combination -4144.2 1439.15 0 03 5.625 COMB1 Combination -4144.2 1034.15 0 03 0 COMB2 Combination -11990.35 1844.15 0 03 2.8125 COMB2 Combination -11990.35 1439.15 0 03 5.625 COMB2 Combination -11990.35 1034.15 0 03 0 COMB3 Combination -3735.08 -2208.46 0 03 2.8125 COMB3 Combination -3735.08 -1297.21 0 03 5.625 COMB3 Combination -3735.08 -385.96 0 03 0 COMB4 Combination -11581.23 -2208.46 0 03 2.8125 COMB4 Combination -11581.23 -1297.21 0 03 5.625 COMB4 Combination -11581.23 -385.96 0 04 0 COMB1 Combination -229.6 1034.15 0 04 0.9375 COMB1 Combination -229.6 899.15 0 04 1.875 COMB1 Combination -229.6 764.15 0 04 0 COMB2 Combination -75.75 1034.15 0 04 0.9375 COMB2 Combination -75.75 899.15 0 04 1.875 COMB2 Combination -75.75 764.15 0 0
4 0 COMB3 Combination 179.53 -385.96 0 04 0.9375 COMB3 Combination 179.53 -82.21 0 04 1.875 COMB3 Combination 179.53 221.54 0 04 0 COMB4 Combination 333.37 -385.96 0 04 0.9375 COMB4 Combination 333.37 -82.21 0 04 1.875 COMB4 Combination 333.37 221.54 0 05 0 COMB1 Combination 34.74 -79.76 0 05 0.78427 COMB1 Combination 17.37 -39.88 0 05 1.56854 COMB1 Combination -3.652E-09 -1.695E-10 0 05 0 COMB2 Combination 34.74 -79.76 0 05 0.78427 COMB2 Combination 17.37 -39.88 0 05 1.56854 COMB2 Combination -3.885E-09 -1.931E-10 0 05 0 COMB3 Combination 34.74 112.23 0 05 0.78427 COMB3 Combination 17.37 56.11 0 05 1.56854 COMB3 Combination 7.295E-11 -9.38E-11 0 05 0 COMB4 Combination 34.74 112.23 0 05 0.78427 COMB4 Combination 17.37 56.11 0 05 1.56854 COMB4 Combination -1.599E-10 -1.175E-10 0 06 0 COMB1 Combination -79.65 463.34 0 06 6.797 COMB1 Combination 70.91 808.96 0 06 13.59399 COMB1 Combination 221.46 1154.59 0 06 0 COMB2 Combination -124.63 316.22 0 06 6.797 COMB2 Combination 25.93 661.84 0 06 13.59399 COMB2 Combination 176.48 1007.46 0 06 0 COMB3 Combination -718.17 38.74 0 06 6.797 COMB3 Combination -567.61 -447.58 0 06 13.59399 COMB3 Combination -417.06 -933.91 0 06 0 COMB4 Combination -763.15 -108.38 0 06 6.797 COMB4 Combination -612.59 -594.71 0 06 13.59399 COMB4 Combination -462.04 -1081.04 0 07 0 COMB1 Combination -763.15 -108.38 0 07 6.797 COMB1 Combination -612.59 -594.71 0 07 13.59399 COMB1 Combination -462.04 -1081.04 0 07 0 COMB2 Combination -718.17 38.74 0 07 6.797 COMB2 Combination -567.61 -447.58 0 07 13.59399 COMB2 Combination -417.06 -933.91 0 07 0 COMB3 Combination -124.63 316.22 0 07 6.797 COMB3 Combination 25.93 661.84 0 07 13.59399 COMB3 Combination 176.48 1007.46 0 07 0 COMB4 Combination -79.65 463.34 0 07 6.797 COMB4 Combination 70.91 808.96 0 07 13.59399 COMB4 Combination 221.46 1154.59 0 08 0 COMB1 Combination 34.74 112.23 0 08 0.78427 COMB1 Combination 17.37 56.11 0 08 1.56854 COMB1 Combination 7.302E-11 -3.374E-11 0 0
8 0 COMB2 Combination 34.74 112.23 0 08 0.78427 COMB2 Combination 17.37 56.11 0 08 1.56854 COMB2 Combination -4.339E-11 -3.556E-11 0 08 0 COMB3 Combination 34.74 -79.76 0 08 0.78427 COMB3 Combination 17.37 -39.88 0 08 1.56854 COMB3 Combination 3.798E-09 -2.212E-11 0 08 0 COMB4 Combination 34.74 -79.76 0 08 0.78427 COMB4 Combination 17.37 -39.88 0 08 1.56854 COMB4 Combination 3.682E-09 -2.394E-11 0 0
M2 M3 FrameElem ElemStationKgf-m Kgf-m Text m Nmax N min D max D min M max
0 -7.276E-12 1 0 0.00 -11990.36 2208.46 -1844.15 0.000 -4929.85 1 2.8125 0.00 -11990.36 1297.21 -1439.15 4617.150 -7296.8 1 5.625 0.00 -11990.36 385.96 -1034.15 8095.230 -6.366E-12 1 00 -4929.85 1 2.81250 -7296.8 1 5.6250 0 1 00 4617.15 1 2.81250 8095.23 1 5.6250 9.095E-13 1 00 4617.15 1 2.81250 8095.23 1 5.6250 -10278.7 2 0 333.37 -229.60 385.96 -1034.15 7113.330 -10498.16 2 0.9375 333.37 -229.60 82.21 -899.15 8019.560 -10432.84 2 1.875 333.37 -229.60 0.00 -764.15 8799.240 -8278.7 2 00 -8498.16 2 0.93750 -8432.84 2 1.8750 5113.33 2 00 6019.56 2 0.93750 6799.24 2 1.8750 7113.33 2 00 8019.56 2 0.93750 8799.24 2 1.8750 -9.095E-13 3 0 0.00 -11990.35 1844.15 -2208.46 0.000 -4617.15 3 2.8125 0.00 -11990.35 1439.15 -1297.21 4929.850 -8095.23 3 5.625 0.00 -11990.35 1034.15 -385.96 7296.800 -9.095E-13 3 00 -4617.15 3 2.81250 -8095.23 3 5.6250 -9.095E-13 3 00 4929.85 3 2.81250 7296.8 3 5.6250 -9.095E-13 3 00 4929.85 3 2.81250 7296.8 3 5.6250 -7113.33 4 0 333.37 -229.60 1034.15 -385.96 10278.700 -8019.56 4 0.9375 333.37 -229.60 899.15 -82.21 10498.160 -8799.24 4 1.875 333.37 -229.60 764.15 0.00 10432.840 -5113.33 4 00 -6019.56 4 0.93750 -6799.24 4 1.875
0 8278.7 4 00 8498.16 4 0.93750 8432.84 4 1.8750 10278.7 4 00 10498.16 4 0.93750 10432.84 4 1.8750 -62.55 6 0 34.74 0.00 112.23 -79.76 88.020 -15.64 6 0.78427 17.37 0.00 56.11 -39.88 22.000 8.952E-11 6 1.56854 0.00 0.00 0.00 0.00 0.000 -62.55 6 00 -15.64 6 0.784270 1.084E-10 6 1.568540 88.02 6 00 22 6 0.784270 7.908E-11 6 1.568540 88.02 6 00 22 6 0.784270 9.798E-11 6 1.568540 10370.29 5 0 0.00 -763.15 463.34 -108.38 10370.290 6046.37 5 6.797 70.91 -612.59 808.96 -594.71 6046.370 -626.76 5 13.59399 221.46 -462.04 1154.59 -1081.04 0.000 8370.29 5 00 5046.37 5 6.7970 -626.76 5 13.593990 -6711.22 5 00 -5321.77 5 6.7970 -626.76 5 13.593990 -8711.22 5 00 -6321.77 5 6.7970 -626.76 5 13.593990 -8711.22 7 0 0.00 -763.15 463.34 -108.38 10370.290 -6321.77 7 6.797 70.91 -612.59 808.96 -594.71 6046.370 -626.76 7 13.59399 221.46 -462.04 1154.59 -1081.04 0.000 -6711.22 7 00 -5321.77 7 6.7970 -626.76 7 13.593990 8370.29 7 00 5046.37 7 6.7970 -626.76 7 13.593990 10370.29 7 00 6046.37 7 6.7970 -626.76 7 13.593990 88.02 8 0 34.74 0.00 112.23 -79.76 88.020 22 8 0.78427 17.37 0.00 56.11 -39.88 22.000 6.495E-11 8 1.56854 0.00 0.00 0.00 0.00 0.00
0 88.02 8 00 22 8 0.784270 6.416E-11 8 1.568540 -62.55 8 00 -15.64 8 0.784270 -4.701E-11 8 1.568540 -62.55 8 00 -15.64 8 0.784270 -4.78E-11 8 1.56854
M min N Ekstrem D EkstremM Ekstrem0.00 11990.36 2208.46 0.00
-4929.85 11990.36 1439.15 4929.85-7296.80 11990.36 1034.15 8095.23
333.37 1034.15 10278.70333.37 899.15 10498.16333.37 764.15 10432.84
11990.35 2208.46 0.0011990.35 1439.15 4929.8511990.35 1034.15 8095.23
333.37 1034.15 10278.70333.37 899.15 10498.16333.37 764.15 10432.84
-10278.70 34.74 112.23 88.02-10498.16 17.37 56.11 22.00-10432.84 0.00 0.00 0.00
763.15 463.34 10370.29612.59 808.96 6321.77462.04 1154.59 626.76763.15 463.34 10370.29612.59 808.96 6321.77462.04 1154.59 626.76
34.74 112.23 88.0217.37 56.11 22.00
0.00 0.00 0.000.00
-4617.15-8095.23
-7113.33-8019.56-8799.24
-62.55-15.64
0.00
-8711.22-6321.77
-626.76
-8711.22-6321.77
-626.76
-62.55-15.64
0.00