taller 1 analisis de estructuras

 ANAL ISIS DE ESTRUC ESTRUCTURAS TURAS I

MARLON MANRIQUE MEDINA 7302975

UNIVERSIDAD MILITAR NUEVA GRANADA FAEDIS PROGRAMA PROGRAMA INGENIERIA INGENIERIA CIVIL  AGOSTO 2017

MARLON MANRIQUE MEDINA

CODIGO. 7302975

 ANAL ISIS ESTRUCTURAS I TALLER 1

Darwin Mora Villota Ingeniero civil MSC

UNIVERSIDAD MILITAR NUEVA GRANADA FAEDIS PROGRAMA INGENIERIA CIVIL  AGOSTO 2017

B

DIAGRMA DE CUERPO LIBRE

   



ECUACIONES ESTÁTICAS (EE)

∑ = 0 ∑ = 0 ∑ = 0 =3 INCOGNITAS (I)

     =3 ==3    Á A

B

C

D

DIAGRMA DE CUERPO LIBRE

    





 



=8 ECUACIONES ESTÁTICAS (EE)

∑ = 0 ∑ = 0 ∑ = 0 =3 < =−=8−3=5    Á  5     ó

DIAGRMA DE CUERPO LIBRE



   









 

 =1 0 ECUACIONES ESTÁTICAS (EE)

∑ = 0 ∑ = 0 ∑ = 0 =3 < =−=10−3=7    Á  7     ó



B







C





D

A

INCOGNITAS (I)

1 = 4 1 = 5 1 = 6  =1 5 ECUACIONES ESTÁTICAS (EE)

3 = 9 2 = 6 =15  = = 15    Á B





 A

C

  D

INCOGNITAS (I)

2 = 10 1 = 6  =1 6 ECUACIONES ESTÁTICAS (EE)

3 = 9 2 = 6

=15 < =−=16−15=1    Á  1     ó     







INCOGNITAS (I)

1 = 3 1 = 4 3 = 15  =2 2 ECUACIONES ESTÁTICAS (EE)

5 = 15 2 = 4 1 = 3 =22  = = 22    Á     

   



  

INCOGNITAS (I)

 



   

8 = 40 4 = 24  =6 4 ECUACIONES ESTÁTICAS (EE)

12 = 36 3 = 6 5 = 15 =57 < =−=64−57=7    Á  7     ó 

   



  







 

INCOGNITAS (I)

2 = 8 5 = 25 2 = 12  =4 5 ECUACIONES ESTÁTICAS (EE)

9 = 27 3 = 6 3 = 9 =45  = = 45    Á







 

  

 

INCOGNITAS (I)

5 = 25  =2 5 ECUACIONES ESTÁTICAS (EE)

5 = 15 2 = 4 2 = 6 =25  = = 25    Á          



INCOGNITAS (I)

2 = 8 5 = 25  =3 3 ECUACIONES ESTÁTICAS (EE)

7 = 21 3 = 6 2 = 6

 

=33  = = 33    Á  











 

INCOGNITAS (I)

1 = 3 4 = 16  =1 9 ECUACIONES ESTÁTICAS (EE)

5 = 15 4 = 8 =23 >  =  − = 23 −1 9 =4    Á  4     

  

 

INCOGNITAS (I)

2 = 6 1 = 4



 

3 = 15  =2 5 ECUACIONES ESTÁTICAS (EE)

6 = 18 2 = 4 2 = 6 =28 >  =  − = 28 −2 5 =3    Á  3   

DIAGRAMA DE CUERPO LIBRE

160

80

192

   

 2

2

2

2

∑ = 0 −160∗2−80∗4−192∗6+ ∗ 8  = 0  = 320+320+1152 =224 8

 =224 ∑ = 0   =0 ∑ = 0 160+80+192−−  = 0   =160+80+192−224=208   =208 DESPIECE

160

80 48/

 

 224

208 DIAGRAMA DE FUERZA CORTANTE

 0  = 208   0  2  = 208  2  = 208   = 208 − 160 = 48   2  4  = 48  4  = 48   = 48 − 80 = −32   4  8  = −32 − 48( − 4)  8  = −32 − 48(4) =−224  =−224+224=0 ()

208 416 1

2

48 96 3

32

4

5

6 7 512

8

()

224

DIAGRAMA DE MOMENTO FLECTOR

 0  3  4  8 ()

 = 0  = 208 ∗ 2 = 416  = 416 + 48 ∗ 2 = 512 )4 = 024 + 224 = 0  = 512 − (32+224 2 512 416

1

2

4

3

5

6

8

7

()

DIAGRAMA DE CUERPO LIBRE

270

72

180 108

   

 3

3

1

2

3

∑ = 0 −270∗3−180∗6−108∗7+ ∗9−72∗12=0  = 810+1080+756+864 =390 9

 =390 ∑ = 0   =0 ∑ = 0 270+180+108+72−390−  = 0   =270+180+108+72−390=240   =240 DESPIECE

270

180 108

240

72

390

DIAGRAMA DE FUERZA CORTANTE

 0  = 240   0  6  = 240 − (45/) =0 0=240−45 = 240 45 =5.33  6  = 240 − 45 ∗ 6 = −30   = −30 − 180 = −210   6  7  = −210  7  = −210   = −210 − 108 = −318   7  9  = −318  9  = −318   = −318 + 390 = 72   9  12  = 72  12  = 72   = 72 − 72 = 0

() 240 72 640 1

2

3

5.33 4 5 306 7 10 210

8

216 9 10 11 12

()

9 10 11 12

()

636

210 318

DIAGRAMA DE MOMENTO FLECTOR

 0  = 0  5.33  = 640  6  = 640 − 10 = 630  7  = 630 − 210 = 420  9  = 420 − 636 = −216  12  = −216 + 216 = 0 () 240

640 630 420

1

2

3

4

5.33 5 6

7

8

216

DIAGRAMA DE CUERPO LIBRE

256 120 2 2  4

    

48

         2

     

 

 

∑ = 0 −48∗2−256∗4−120∗6+ ∗ 8  = 0  = 96+1024+760 =230 8  =230 ∑ = 0   =48 ∑ = 0 256+120−230− = 0

  =256+120−230=146   =146 DESPIECE Columna AB



 ′ 

48 48   146

∑ = 0 −48+48− = 0  =0 ∑ = 0  =146 ∑ = 0 −48∗2+ +0∗4 =0 ′ =96 Viga BC





96

146

256 120 ′  



∑ = 0  =  =0 ∑ = 0  =256+120−146=230

 =230 ∑′ = 0 −96−256∗4−120∗6−  +230∗8=0  =0 Columna CD

 

′ 

 230

∑ = 0  =0 ∑ = 0  =230 ∑′ = 0 ′ =0



32/ 96

146 146 

120  2306

96

230

48 48  

230

146 NODO B

146 96

NODO C

230 96 146

230

DIAGRAMA DE FUERZA CORTANTE

 

192 136 146

333

 48



33

96

4.56 46 166

 

396

230 

DIAGRAMA DE MOMENTO FLECTOR

 

429 96 

396 

4.56

96  



FUERZA NORMAL

 



146  

 -

-

230 