Post on 06-Aug-2015
description
data plat dan beban:L = 4 mѵ = 0.3h= 12 mmq= 150 kg/m2E= 210000 N/mm2perletakan sederhana
==> kekakuan platD = 33230769.231 Nmm
Berat sendiri qbs = 0.003696 N/mm2q total = 0.005196 N/mm2
Mencari u, terlebih dahulu ordinat dari grafik 1 adalah dimana
= 0.00359744182
= 1.56 , dengan grafik 1 u= 0
1dari grafik 2
1
==> Lendutana Max dan Mmax
L (mm) u W (mm) M (Nm)
4000 0 1 1 521.20 10392
Log 104
f0 (u) =
ψ0 =
f0 ψ0
Lx
data plat dan beban:Lx = 4 mLy = 4 mq = 200 kg/m2h = 10 cmfc' = 25 Mpaperletakan jepit dikeempat sisinyaε = 1K = 0.500
Lx==> Beban mati (Wd)Berat sendiri plat = 0.250 kN/m2 Px 181.3Berat spesi (t=5cm)= 0.105 kN/m2
0.355 kN/m2
==> Beban hidup (WL)
2.00 kN/m2mx tumpua
3.626 kN/m2 362.6 kg/m2mx lapang 203.9625
I = 83333333.33 mm4
E = 30000 Mpa
==> Momen arah YPy = 181.3 Kg/mM tumpuan = 362.6 kg.mM lapangan = 203.9625 kg.m
==> Momen arah xPx = 181.3 Kg/mM tumpuan = 362.6 kg.mM lapangan = 203.9625 kg.m
==> kontrol lendutanδ = 0.001934 m
….. OKδ izin = 0.008333 m(ambil L dg momen terbesar)
WD =
WL=
WU=
My tumpuan362.6
181.3Ly Py my lapangan
203.9625
kg/m
362.6 kg.m
kg.m
BEBAN SINUSOIDAL
Data :h = 15 cma = 6 m Lxb = 5 m Lyy = 2.5 m
= 200v = 0.2E = 26833 N/mm2K = 20 Mpa
Jawaban :Menghitung Lendutan
x y DKoefisien
(m) (m) kgm0.00 2.50 786117.65 0.0006 0.0001.00 2.50 786117.65 0.0006 0.5002.00 2.50 786117.65 0.0006 0.8663.00 2.50 786117.65 0.0006 1.0004.00 2.50 786117.65 0.0006 0.8665.00 2.50 786117.65 0.0006 0.5006.00 2.50 786117.65 0.0006 0.000
Menghitung Momen Mx pada y = 2,5mx y
Koefisien(m) (m)0.00 2.50 157.983 0.000 11.00 2.50 157.983 0.500 1
qo kg/m2
Jenis perletakannya adalah perletakan sederhana.
2.00 2.50 157.983 0.866 13.00 2.50 157.983 1.000 14.00 2.50 157.983 0.866 15.00 2.50 157.983 0.500 16.00 2.50 157.983 0.000 1
Menghitung Momen My pada x = 3mx y
Koefisien(m) (m)3.00 0.00 201.158 1.000 0.0003.00 1.00 201.158 1.000 0.5883.00 2.00 201.158 1.000 0.9513.00 3.00 201.158 1.000 0.9513.00 4.00 201.158 1.000 0.5883.00 5.00 201.158 1.000 0.000
Menghitung Momen Mxy pada x = 0 x y
Koefisien(m) (m)3.00 0.00 7.981 0.000 1.0003.00 1.00 7.981 0.000 0.8093.00 2.00 7.981 0.000 0.3093.00 3.00 7.981 0.000 -0.3093.00 4.00 7.981 0.000 -0.8093.00 5.00 7.981 0.000 -1.000
Menghitung Momen Myx pada y = 0 x y
Koefisien(m) (m)0.00 1.50 7.981 1.000 0.5881.00 1.50 7.981 0.866 0.5881.50 1.50 7.981 0.707 0.5882.00 1.50 7.981 0.500 0.5883.00 1.50 7.981 0.000 0.5884.00 1.50 7.981 -0.500 0.5885.00 1.50 7.981 -0.866 0.5886.00 1.50 7.981 -1.000 0.588
Vxy
KoefisienVx
(m) (kg/m)0.00 230.573 0.000 0.0001.00 230.573 0.588 135.5272.00 230.573 0.951 219.2883.00 230.573 0.951 219.2884.00 230.573 0.588 135.5275.00 230.573 0.000 0.0006.00 230.573 -0.588 -135.5277.00 230.573 -0.951 -219.2888.00 230.573 -0.951 -219.2889.00 230.573 -0.588 -135.527
10.00 230.573 0.000 0.000
Vyx
KoefisienVy
(m) (kg/m)
0.00 249.573 0.000 0.0001.00 249.573 0.500 124.7872.00 249.573 0.866 216.1373.00 249.573 1.000 249.5734.00 249.573 0.866 216.1375.00 249.573 0.500 124.7876.00 249.573 0.000 0.000
R = 235.502 Kg
0.5
w(m)
1 01 0.000281 0.000491 0.000571 0.000491 0.000281 0.00000
Mx(y = 2,5m)
078.991
0 1 2 3 4 5 6 70
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
x (m)
w (m
m)
0 1 2 3 4 5 6 70
200
400
600
800
1000
1200
x (m)
Mx (y
=5
m)
Grafik Momen Mx pada y = 5m
Grafik Lendutan dan x
136.817157.983136.81778.9910.000
My(x = 3m)
0.000118.238191.313191.313118.238
0.000
Mxy
0.0000.0000.0000.0000.0000.000
0 1 2 3 4 5 6 70
200
400
600
800
1000
1200
x (m)
Mx (y
=5
m)
Grafik Momen Mx pada y = 5m
0 2 4 6 8 10 120
100
200
300
400
500
600
y (m)
My (x=3m)
Grafik Momen My pada x = 3m
0 2 4 6 8 10 12
-20
-15
-10
-5
0
5
10
15
20
y (m)
Mxy (x=0)
Grafik Momen Mxy pada x = 0
Mxy
4.6914.0633.3172.3460.000-2.346-4.063-4.691
0 2 4 6 8 10 12
-20
-15
-10
-5
0
5
10
15
20
y (m)
Mxy (x=0)
Grafik Momen Mxy pada x = 0
0 1 2 3 4 5 6 7
-20
-15
-10
-5
0
5
10
15
20
x (m)
Myx (y=0)Grafik Momen Myx pada y = 0
0 1 2 3 4 5 6 70
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
x (m)
w (m
m)
0 1 2 3 4 5 6 70
200
400
600
800
1000
1200
x (m)
Mx (y
=5
m)
Grafik Momen Mx pada y = 5m
Grafik Lendutan dan x
0 1 2 3 4 5 6 70
200
400
600
800
1000
1200
x (m)
Mx (y
=5
m)
Grafik Momen Mx pada y = 5m
0 2 4 6 8 10 120
100
200
300
400
500
600
y (m)
My (x=3m)
Grafik Momen My pada x = 3m
0 2 4 6 8 10 12
-20
-15
-10
-5
0
5
10
15
20
y (m)
Mxy (x=0)
Grafik Momen Mxy pada x = 0
0 2 4 6 8 10 12
-20
-15
-10
-5
0
5
10
15
20
y (m)
Mxy (x=0)
Grafik Momen Mxy pada x = 0
0 1 2 3 4 5 6 7
-20
-15
-10
-5
0
5
10
15
20
x (m)
Myx (y=0)
Grafik Momen Myx pada y = 0
Data :h = 11 cm 110 mm 0.11 m
a = 5 m 5000 mm Lxb = 4.5 m 4500 mm Lyy = 2.25 m
= 200 300 N/m2
v = 0.2K = 300 30 N/m2E = 32863.35345 N/mm2 32863353450 N/m2D = 3796972.521 Nm
===> Lendutan
x (mm) y (mm) m n
2.5 2.5 1 1 1.318943E-06 1 0.984808 0.04002.5 2.5 3 3 1.318943E-06 -1 -0.866025 0.36002.5 2.5 5 5 1.318943E-06 1 0.642788 1.0000
===> Mx di x=0-5, y=2,5
x (mm) y (mm) m n Wmn
0 2.5 1 1 0.0001650893 0 0.984808 0.04000 2.5 3 3 2.264599E-07 0 -0.866025 0.36000 2.5 5 5 1.056571E-08 0 0.642788 1.0000
x (mm) y (mm) m n Wmn
1 2.5 1 1 0.0001650893 0.587785252 0.984808 0.04001 2.5 3 3 2.264599E-07 0.951056516 -0.866025 0.36001 2.5 5 5 1.056571E-08 1.224647E-16 0.642788 1.0000
x (mm) y (mm) m n Wmn
2 2.5 1 1 0.0001650893 0.951056516 0.984808 0.04002 2.5 3 3 2.264599E-07 -0.587785252 -0.866025 0.36002 2.5 5 5 1.056571E-08 -2.44929E-16 0.642788 1.0000
x (mm) y (mm) m n Wmn
3 2.5 1 1 0.0001650893 0.951056516 0.984808 0.0400
qo kg/m2
3 2.5 3 3 2.264599E-07 -0.587785252 -0.866025 0.36003 2.5 5 5 1.056571E-08 3.67394E-16 0.642788 1.0000
x (mm) y (mm) m n Wmn
4 2.5 1 1 0.0001650893 0.587785252 0.984808 0.04004 2.5 3 3 2.264599E-07 0.951056516 -0.866025 0.36004 2.5 5 5 1.056571E-08 -4.89859E-16 0.642788 1.0000
x (mm) y (mm) m n Wmn
5 2.5 1 1 0.0001650893 1.224647E-16 0.984808 0.04005 2.5 3 3 2.264599E-07 3.67394E-16 -0.866025 0.36005 2.5 5 5 1.056571E-08 6.123234E-16 0.642788 1.0000
===> Mx di x=2,5, y=0-5
x (mm) y (mm) m n Wmn
2.5 0 1 1 0.0001650893 1 0 0.04002.5 0 3 3 2.264599E-07 -1 0 0.36002.5 0 5 5 1.056571E-08 1 0 1.0000
x (mm) y (mm) m n Wmn
2.5 1 1 1 0.0001650893 1 0.642788 0.04002.5 1 3 3 2.264599E-07 -1 0.866025 0.36002.5 1 5 5 1.056571E-08 1 -0.34202 1.0000
x (mm) y (mm) m n Wmn
2.5 2 1 1 0.0001650893 1 0.984808 0.04002.5 2 3 3 2.264599E-07 -1 -0.866025 0.36002.5 2 5 5 1.056571E-08 1 0.642788 1.0000
x (mm) y (mm) m n Wmn
2.5 3 1 1 0.0001650893 1 0.866025 0.04002.5 3 3 3 2.264599E-07 -1 -2.45E-16 0.36002.5 3 5 5 1.056571E-08 1 -0.866025 1.0000
x (mm) y (mm) m n Wmn
2.5 4 1 1 0.0001650893 1 0.34202 0.04002.5 4 3 3 2.264599E-07 -1 0.866025 0.36002.5 4 5 5 1.056571E-08 1 0.984808 1.0000
x (mm) y (mm) m n Wmn
2.5 5 1 1 0.0001650893 1 -0.34202 0.04002.5 5 3 3 2.264599E-07 -1 -0.866025 0.36002.5 5 5 5 1.056571E-08 1 -0.984808 1.0000
===> My di x=0-5, y=2,5
x (mm) y (mm) m n Wmn
0 2.5 1 1 0.0001650893 0 0.984808 0.04000 2.5 3 3 2.264599E-07 0 -0.866025 0.36000 2.5 5 5 1.056571E-08 0 0.642788 1.0000
x (mm) y (mm) m n Wmn
1 2.5 1 1 0.0001650893 0.587785252 0.984808 0.04001 2.5 3 3 2.264599E-07 0.951056516 -0.866025 0.36001 2.5 5 5 1.056571E-08 1.224647E-16 0.642788 1.0000
x (mm) y (mm) m n Wmn
2 2.5 1 1 0.0001650893 0.951056516 0.984808 0.04002 2.5 3 3 2.264599E-07 -0.587785252 -0.866025 0.36002 2.5 5 5 1.056571E-08 -2.44929E-16 0.642788 1.0000
x (mm) y (mm) m n Wmn
3 2.5 1 1 0.0001650893 0.951056516 0.984808 0.04003 2.5 3 3 2.264599E-07 -0.587785252 -0.866025 0.36003 2.5 5 5 1.056571E-08 3.67394E-16 0.642788 1.0000
x (mm) y (mm) m n Wmn
4 2.5 1 1 0.0001650893 0.587785252 0.984808 0.04004 2.5 3 3 2.264599E-07 0.951056516 -0.866025 0.36004 2.5 5 5 1.056571E-08 -4.89859E-16 0.642788 1.0000
x (mm) y (mm) m n Wmn
5 2.5 1 1 0.0001650893 1.224647E-16 0.984808 0.04005 2.5 3 3 2.264599E-07 3.67394E-16 -0.866025 0.36005 2.5 5 5 1.056571E-08 6.123234E-16 0.642788 1.0000
===> My di x=2,5, y=5
x (mm) y (mm) m n Wmn
2.5 0 1 1 0.0001650893 1 0 0.04002.5 0 3 3 2.264599E-07 -1 0 0.36002.5 0 5 5 1.056571E-08 1 0 1.0000
x (mm) y (mm) m n Wmn
2.5 1 1 1 0.0001650893 1 0.642788 0.04002.5 1 3 3 2.264599E-07 -1 0.866025 0.36002.5 1 5 5 1.056571E-08 1 -0.34202 1.0000
x (mm) y (mm) m n Wmn
2.5 2 1 1 0.0001650893 1 0.984808 0.04002.5 2 3 3 2.264599E-07 -1 -0.866025 0.36002.5 2 5 5 1.056571E-08 1 0.642788 1.0000
x (mm) y (mm) m n Wmn
2.5 3 1 1 0.0001650893 1 0.866025 0.04002.5 3 3 3 2.264599E-07 -1 -2.45E-16 0.36002.5 3 5 5 1.056571E-08 1 -0.866025 1.0000
x (mm) y (mm) m n Wmn
2.5 4 1 1 0.0001650893 1 0.34202 0.04002.5 4 3 3 2.264599E-07 -1 0.866025 0.36002.5 4 5 5 1.056571E-08 1 0.984808 1.0000
x (mm) y (mm) m n Wmn
2.5 5 1 1 0.0001650893 1 -0.34202 0.04002.5 5 3 3 2.264599E-07 -1 -0.866025 0.36002.5 5 5 5 1.056571E-08 1 -0.984808 1.0000
===> Mxy
x (mm) y (mm) m n Wmn
2.5 0 1 1 0.0006677147 0 1 0.00202.5 0 3 3 9.159324E-07 0 1 0.16002.5 0 5 5 4.273374E-08 0 1 1.2346
Mxy t
x (mm) y (mm) m n Wmn
2.5 1 1 1 0.0006677147 0 0.766044 0.00202.5 1 3 3 9.159324E-07 0 -0.5 0.16002.5 1 5 5 4.273374E-08 0 -0.939693 1.2346
Mxy t
x (mm) y (mm) m n Wmn
2.5 2 1 1 0.0006677147 0 0.173648 0.00202.5 2 3 3 9.159324E-07 0 -0.5 0.16002.5 2 5 5 4.273374E-08 0 0.766044 1.2346
Mxy t
x (mm) y (mm) m n Wmn
2.5 3 1 1 0.0006677147 0 -0.5 0.00202.5 3 3 3 9.159324E-07 0 1 0.16002.5 3 5 5 4.273374E-08 0 -0.5 1.2346
Mxy t
x (mm) y (mm) m n Wmn
2.5 4 1 1 0.0006677147 0 -0.939693 0.00202.5 4 3 3 9.159324E-07 0 -0.5 0.1600
2.5 4 5 5 4.273374E-08 0 0.173648 1.2346Mxy t
x (mm) y (mm) m n Wmn
2.5 5 1 1 0.0006677147 0 -0.939693 0.00202.5 5 3 3 9.159324E-07 0 -0.5 0.16002.5 5 5 5 4.273374E-08 0 0.173648 1.2346
Mxy t
w (mm)
0.049382716 0.16258120.444444444 0.00002181.234567901 0.0000003
w maks 0.1626032
Mx (kg.m)
0.049382716 0.00000000.444444444 0.00000001.234567901 0.0000000
Mx t 0.0000000
Mx (kg.m)
0.049382716 178.43582000.444444444 -3.13446801.234567901 0.0000000
Mx t 175.3013520
Mx (kg.m)
0.049382716 288.71522150.444444444 1.93720771.234567901 0.0000000
Mx t 290.6524293
Mx (kg.m)
0.049382716 288.7152215
0.444444444 1.93720771.234567901 0.0000000
Mx t 290.6524293
Mx (kg.m)
0.049382716 178.43582000.444444444 -3.13446801.234567901 0.0000000
Mx t 175.3013520
Mx (kg.m)
0.049382716 0.00000000.444444444 0.00000001.234567901 0.0000000
Mx t 0.0000000
Mx (kg.m)
0.049382716 0.00000000.444444444 0.00000001.234567901 0.0000000
Mx t 0.0000000
Mx (kg.m)
0.049382716 198.14330080.444444444 -3.29577471.234567901 -0.1686878
Mx t 194.6788384
Mx (kg.m)
0.049382716 303.57314900.444444444 3.29577471.234567901 0.3170293
Mx t 307.1859529
Mx (kg.m)
0.049382716 266.95774700.444444444 0.00000001.234567901 -0.4271324
Mx t 266.5306146
Mx (kg.m)
0.049382716 105.42984820.444444444 -3.29577471.234567901 0.4857170
Mx t 102.6197906
Mx (kg.m)
0.049382716 -105.42984820.444444444 3.29577471.234567901 -0.4857170
Mx t -102.6197906
My (kg.m)
0.049382716 0.00000000.444444444 0.00000001.234567901 0.0000000
Mx t 0.0000000
My (kg.m)
0.049382716 205.28952750.444444444 -3.60618991.234567901 0.0000000
Mx t 201.6833377
My (kg.m)
0.049382716 332.16543310.444444444 2.22874791.234567901 0.0000000
Mx t 334.3941810
My (kg.m)
0.049382716 332.16543310.444444444 2.22874791.234567901 0.0000000
Mx t 334.3941810
My (kg.m)
0.049382716 205.28952750.444444444 -3.60618991.234567901 0.0000000
Mx t 201.6833377
My (kg.m)
0.049382716 0.00000000.444444444 0.00000001.234567901 0.0000000
Mx t 0.0000000
My (kg.m)
0.049382716 0.00000000.444444444 0.00000001.234567901 0.0000000
Mx t 0.0000000
My (kg.m)
0.049382716 227.96288660.444444444 -3.79177241.234567901 -0.1940744
Mx t 223.9770398
My (kg.m)
0.049382716 349.25940510.444444444 3.79177241.234567901 0.3647406
Mx t 353.4159181
My (kg.m)
0.049382716 307.13356630.444444444 0.00000001.234567901 -0.4914137
Mx t 306.6421526
My (kg.m)
0.049382716 121.29651850.444444444 -3.79177241.234567901 0.5588150
Mx t 118.0635611
My (kg.m)
0.049382716 -121.29651850.444444444 3.79177241.234567901 -0.5588150
Mx t -118.0635611
Mxy (kg.m)
0.00000000.00000000.00000000.0000000
Mxy (kg.m)
0.00000000.00000000.00000000.0000000
Mxy (kg.m)
0.00000000.00000000.00000000.0000000
Mxy (kg.m)
0.00000000.00000000.00000000.0000000
Mxy (kg.m)
0.00000000.0000000
0.00000000.0000000
Mxy (kg.m)
0.00000000.00000000.00000000.0000000
Data :h = 12 cm 120a = 9 m 9000b = 4 m 4000y = 2 m
= 250 2500v = 0.2c = 300 30 N/m2E = 32863.35345 N/mm2 32863353450
D = 4929503.018 Nm
===> Lendutan
x (m) y (m) m
4.5 2 1 4.2348912287 14.5 2 3 4.2348912287 0.00411522634.5 2 5 4.2348912287 0.00032
===> Mx di x=4.5
x (mm) y (mm) m
4.5 0 1 2531.25 410062.54.5 0 3 2531.25 410062.54.5 0 5 2531.25 410062.5
===> My di x=4.5
x (mm) y (mm) m
4.5 0 1 0.2 2531.254.5 0 3 0.2 2531.254.5 0 5 0.2 2531.25
qo kg/m2
1
m54 qa4
π5 D
q x (a−x )2
qa2 x2
q x (a−x )2
ν
w=4 qa4
π5 D∑
m=1,3,5
∞ 1m5 (1−
αm tanh αm+2
2 coshαm
cosh2 αm y
b+
2 αm
2 cosh αm
2 yb
sinh2 αm y
b ) sinmπx
a
Mx y=0=qx (a−x )
2−qa2 π2 ∑
m=1,3,5
∞m2 [2νBm−(1−ν ) Am ] sin
mπxa
My y=0=νqx (a−x )
2−qa2 π2 ∑
m=1,3,5
∞m2 [2νBm+(1−ν ) Am ] sin
mπxa
Data :mm 0.12 m
mm Lxmm Ly
N/m2 3.14285714285714
N/m2 0.55343237290762.23
-0.698412698412698 -0.00425647529116624 0.00851295058233252-2.0952380952381 -0.038293106984064 0.0765862139681278
-3.49206349206349 -0.106285580348876 0.212571160697753
-0.0130993324299534 0.00652190588373131 1-5.57006371632682E-05 2.68231758395576E-05 9-4.60943704872223E-06 2.0832943728999E-06 25
410062.5 -0.0130448000385012 0.00652239025244662410062.5 -5.36822257043871E-05 2.68411128514668E-05410062.5 -4.17432987066285E-06 2.08716493533104E-06
π=
αm=−mπb2 a
1−αm tanh αm+2
2 coshαm
cosh2 αm y
b2 α m
2cosh αm
2 yb
sinh2 αm y
b
Am=−2 (αm tanh αm+2)
π 5 m5 cosh αm
Bm=2
π5 m5 cosh αmm2
qa2 x2Am=−
2 (αm tanh αm+2)
π 5 m5 cosh αm
Bm=2
π5 m5 cosh αm
w=4 qa4
π5 D∑
m=1,3,5
∞ 1m5 (1−
αm tanh αm+2
2 coshαm
cosh2 αm y
b+
2 αm
2 cosh αm
2 yb
sinh2 αm y
b ) sinmπx
a
Mx y=0=qx (a−x )
2−qa2 π2 ∑
m=1,3,5
∞m2 [2 νBm−(1−ν ) Am ] sin
mπxa
My y=0=νqx (a−x )
2−qa2 π2 ∑
m=1,3,5
∞m2 [2 νBm+(1−ν ) Am ] sin
mπxa
w (m)
1.0000 0.0180257-1.0000 -0.00066741.0000 0.0001440
0.0175024
Mx (kg.m)
0.0026 -0.010479465943963 2.30129890231 -9819.8021.07E-05 -4.456050973061E-05 55.6543975994 -8825.0518.33E-07 -3.687549638978E-06 1287.9850542 -57161.647
-75806.500
Mx (kg.m)
1 0.0130 -0.01043584003 2.301298902307 -1955.7469 0.0001 -4.2945781E-05 55.65439759942 -1698.973
25 0.0000 -3.3394639E-06 1287.985054197 -10517.203-14171.922
sinmπx
a
2 υ Bm (1−ν ) Am sinhmπx
a
m22 Bm (1−ν ) Am sinh
mπxa