plat & cangkang

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

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)


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)


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 Lendutan dan x

0 1 2 3 4 5 6 70

200

400

600

800

1000

1200

x (m)

Mx (y

=5

m)


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)


0 2 4 6 8 10 12

-20

-15

-10

-5

0

5

10

15

20

y (m)

Mxy (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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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

plat & cangkang

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