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TUGAS MEKANIKA REKAYASA 5

GRID SYSTEM 

oleh:

 NANANG HIDAYATULLAH 1407164182

M. ADITHYA H RANGKUTI 1407164193

GIRI PRAYOGO 1407164211

KAIRON WIKA RS 1407164256

EKA CANDRA SARI!AL 1407164313

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1. GLO'LAL STI$$NESS MATRI(  

Elemen Batang 1 (1-2)

 A = 8,000 G = 76,925 Mpa

Iy = 3,000,000 L = 6,000 mm

Ix = 300,000 E = 200,000 MPa

a = 90

3,846,250 0 0 -3,846,250 0 0

0 400,000,000 -100,000 0 200,000,000 100,000

0 -100,000 33 0 -100,000 -33

-3,846,250 0 0 3,846,250 0 0

0 200,000,000 -100,000 0 400,000,000 100,000

0 100,000 -33 0 100,000 33

 

0 1 0 0 0 0

-1 0 0 0 0 00 0 1 0 0 0

mm2

mm4

mm4

o

!l" =

#" =

 A = 8$000 mm2

Iy = 3$000$000 mm4

Ix = 300$000 mm4

6 m

7 Kn

Z

11

2

2 8 m

3

X

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0 0 0 0 1 0

0 0 0 -1 0 0

0 0 0 0 0 1

0 -1 0 0 0 0

1 0 0 0 0 0

0 0 1 0 0 0

0 0 0 0 -1 0

0 0 0 1 0 0

0 0 0 0 0 1

 

#"# =

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0 -1 0 0 0 0 3,846,250

1 0 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 0 -1 0 -3,846,2500 0 0 1 0 0 0

0 0 0 0 0 1 0

0 -400,000,000 100,000 0 -200,000,000 -100,000 0

3,846,250 0 0 -3,846,250 0 0 -1

0 -100,000 33 0 -100,000 -33 0

0 -200,000,000 100,000 0 -400,000,000 -100,000 0

-3,846,250 0 0 3,846,250 0 0 0

0 100,000 -33 0 100,000 33 0

400,000,000 0 100,000 200,000,000 0 -100,000

0 3,846,250 0 0 -3,846,250 0

100,000 0 33 100,000 0 -33

200,000,000 0 100,000 400,000,000 0 -100,000

0 -3,846,250 0 0 3,846,250 0

-100,000 0 -33 -100,000 0 33

Elemen Batang 2  A = 10,000 G = 76,925 Mpa

Iy = 5,000,000 L = 8,000 mm

Ix = 500,000 E = 200,000 MPa

a = 0

4,807,812$5 0 0 -4,807,812$5 0 0

0 500,000,000 -93,750 0 250,000,000 93,750

0 -93,750 23$4 0 -93,750 -23$4

-4,807,812$5 0 0 4,807,812$5 0 0

0 250,000,000 -93,750 0 500,000,000 93,750

0 93,750 -23$4 0 93,750 23$4

!%"1 = #"# !l" #"

!%"1 =

!%"1 =

qx1 qy1 &1 qx2 qy2 &2

qx1

qy1

!%"1 = &1

qx2

qy2

&2

mm2

mm4

mm4o

!l" =

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1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

 

#" =

#"# =

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1 0 0 0 0 0 4,807,813

0 1 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 1 0 0 -4,807,8130 0 0 0 1 0 0

0 0 0 0 0 1 0

4,807,813 0 0 -4,807,813 0 0 1

0 500,000,000 -93,750 0 250,000,000 93,750 0

0 -93,750 23 0 -93,750 -23 0

-4,807,813 0 0 4,807,813 0 0 0

0 250,000,000 -93,750 0 500,000,000 93,750 0

0 93,750 -23 0 93,750 23 0

4,807,813 0 0 -4,807,813 0 0

0 500,000,000 -93,750 0 250,000,000 93,750

0 -93,750 23 0 -93,750 -23

-4,807,813 0 0 4,807,813 0 0

0 250,000,000 -93,750 0 500,000,000 93,750

0 93,750 -23 0 93,750 23

2. O%ERALL STI$$NESS MATRI( 

=

400000000 0 100000 200000000 0

0 3846250 0 0 -3846250

100000 0 33 100000 0

200000000 0 100000 404807813 0

0 -3846250 0 0 503846250

-100000 0 -33 -100000 -93750

0 0 0 -4807813 0

!%"2 = #"# !l" #"

!%"2 =

!%"2 =

qx2 qy2 &2 qx3 qy3 &3

qx2

qy2

!%"2 = &2

qx3

qy3

&3

'2 = 5 () = 5000 )

qx1 qy1 &1 qx2 qy2

M*1

M+1

'1

M*2 = 0

M+2 = 0

'2 = -5000

M*3

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0 0 0 0 250000000

0 0 0 0 93750

!. REARRAGEMENT

0

=

404807813 0 -100000 200000000 0

0 0 503846250 -93750 0 -3846250

-5000 -100000 -93750 57 -100000 0

200000000 0 -100000 400000000 0

0 -3846250 0 0 -3846250

100000 0 -33 100000 0

-4807813 0 0 0 0

0 250000000 -93750 0 0

0 93750 -23 0 0

M+3

'3

qx2 qy2 &2 qx1 qy1

M*1

M+1

'1

M*3

M+3

'3

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. UNKNO)N DISPLA*EMENT AND REA*TIONS

0

=

404807813 0 -100000

0 0 503846250 -93750

-5000 -100000 -93750 57

404,807,813 0 -100,000 0

0 503,846,250 -93,750 0

-100,000 -93,750 57 -5,000

1$0000 0$0000 -0$0002 0$0000

0$0000 503,846,250 -93,750$0000000 0$0000

1$0000 0$9375 -0$0006 0$0500

1$0000 0$0000 -0$0002 0$0000

0$0000 503,846,250 -93,750$0000 0$0000

0$0000 0$9375 -0$0003 0$0500

1$0000 0$0000 -0$0002 0$0000

0$0000 1$0000 -0$0002 0$0000

0$0000 1$0000 -0$0003 0$0533

1$0000 0$0000 -0$0002 0$0000

0$0000 1$0000 -0$0002 0$0000

0$0000 0$0000 0$0002 -0$0533

-341$908038856mm

0$000000000 -0$063618373 = -0$063618373 a

0$000000000 -0$084461818 0$000000000 = -0$084461818 a

=

200000000 0 -100000 -0$08446

=

0 -3846250 0 -0$06362

100000 0 -33 -341$90804

-4807813 0 0

0 250000000 -93750

0 93750 -23

qx2

qy2

&2

&2 =

qy2 =

qx2 =

M(1

MY1

+1

M(!

MY!

+!

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5. MEM'ER $OR*ES

Elemen Batang 1

#" !%" ./

0 1 0 0 0 0 400,000,000$0

-1 0 0 0 0 0 0$0

0 0 1 0 0 0 100,000$0

0 0 0 0 1 0 200,000,000$0

0 0 0 -1 0 0 0$0

0 0 0 0 0 1 -100,000$0

0 3,846,250 0 0 -3,846,250 0 0

-400,000,000 0 -100,000 -200,000,000 0 100,000 0

100,000 0 33 100,000 0 -33 0

0 -3,846,250 0 0 3,846,250 0 -0$08446

-200,000,000 0 -100,000 -400,000,000 0 100,000 -0$06362

-100,000 0 -33 -100,000 0 33 -341$90804

2,&92.17 N  

#17,29-,0.2 N  

2,950.75 N  

#2,&92.17 N  

#0&,07&.59 N  

#2,950.75 N  

mx1

my1h1

mx2

my2

h2

mx1

my1

h1

mx2

my2

h2

mx1

my1

h1

mx2

my2

h2

1

/1

1

2

/2

2

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Elemen Batang 2 

#" !%" ./

1 0 0 0 0 0 4,807,813

0 1 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 1 0 0 -4,807,813

0 0 0 0 1 0 0

0 0 0 0 0 1 0

4,807,813 0 0 -4,807,813 0 0 -0$08446

0 500,000,000 -93,750 0 250,000,000 93,750 -0$06362

0 -93,750 23 0 -93,750 -23 -341$90804

-4,807,813 0 0 4,807,813 0 0 0

0 250,000,000 -93,750 0 500,000,000 93,750 0

0 93,750 -23 0 93,750 23 0

#0&,07&.59 N  

2,&92.17 N  

#2,09.25 N  

0&,07&.59 N  

1&,19,2-5.0 N  

2,09.25 N  

mx2

my2

h2

mx3

my3

h3

mx2

my2

h2

mx3

my3

h3

mx2

my2

h2

mx3

my3

h3

2

/2

2

!

/!

!

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0 0 -3,846,250 0 0 0 1 0 0 0 0

400,000,000 -100,000 0 200,000,000 100,000 -1 0 0 0 0 0

-100,000 33 0 -100,000 -33 0 0 1 0 0 0

0 0 3,846,250 0 0 0 0 0 0 1 0

200,000,000 -100,000 0 400,000,000 100,000 0 0 0 -1 0 0

100,000 -33 0 100,000 33 0 0 0 0 0 1

 

1 0 0 0 0

0 0 0 0 0

0 1 0 0 0

0 0 0 1 0

0 0 -1 0 0

0 0 0 0 1

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0 0 -4,807,813 0 0 1 0 0 0 0 0

500,000,000 -93,750 0 250,000,000 93,750 0 1 0 0 0 0

-93,750 23 0 -93,750 -23 0 0 1 0 0 0

0 0 4,807,813 0 0 0 0 0 1 0 0

250,000,000 -93,750 0 500,000,000 93,750 0 0 0 0 1 0

93,750 -23 0 93,750 23 0 0 0 0 0 1

 

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

 

-100000 0 0 0 0

0 0 0 0 0

-33 0 0 0 0

-100000 -4807813 0 0

-93750 0 250000000 93750

57 0 -93750 -23

0 4807813 0 0 0

&2 qx3 qy3 &3

qx1

qy1

&1

qx2 qx2

qy2 qy2

&2 &2

qx3

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-93750 0 500000000 93750 0

-23 0 93750 23 0

 

100000 -4807813 0 00 0 250000000 93750

-33 0 -93750 -23

100000 0 0 0 0

0 0 0 0 0

-33 0 0 0 0

0 4807813 0 0 0

0 0 500000000 93750 0

0 0 93750 23 0

qy3

&3

&1 qx3 qy3 &3

qx2 qx2qy2 qy2

&2 &2

qx1

qy1

&1

qx3

qy3

&3

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1729-0.2!& N  

2&92.1&7 N

2950.75! N  

0&07&.5-& N  

1&192-5.05 N  

209.27 N  

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0$0 100,000$0 200,000,000 0$0 -100,000$0 0

3,846,250$0 0$0 0$0 -3,846,250$0 0$0 0

0$0 33$3 100,000$0 0$0 -33$3 0

0$0 100,000$0 400,000,000 0$0 -100,000$0 -0$0845-3,846,250$0 0$0 0$0 3,846,250$0 0$0 -0$0636

0$0 -33$3 -100,000$0 0$0 33$3

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0 0 -4,807,813 0 0 -0$0845

500,000,000 -93,750 0 250,000,000 93,750 -0$0636

-93,750 23 0 -93,750 -23

0 0 4,807,813 0 0 0

250,000,000 -93,750 0 500,000,000 93,750 0

93,750 -23 0 93,750 23 0