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MÉTODO PENDIENTE DEFLEXIÓN PARA UN POR

10000 3 400

V1

C1 C1

5000 2 1600

V1

C1 C1

1

8

SOLUCIÓN

Como las cuerdas 2 - 5 y 3 - 4 no giran :

Ψ12 = Ψ56 = Ψ1

Ψ23 = Ψ45 = Ψ2

Hallamos los M! en ca

#arra 1 - 2 #arra 2 - 5

M12 = 0 M25 = -8533$33

M21 = 0 M52 = 8533$33

scri"imos las ecuaciones sa"iendo %ue &1 = &6 = 0 en'onces

M12 = 2()* + , &2 - 3Ψ1 . M! M12 =M21 = 2()* + ,2&2 - 3Ψ1 . M! M21 =

M25 = 2()* + ,2&2 . &5 . M! M25 =

M52 = 2()* + ,&2 . 2&5 . M! M52 =

M23 = 2()* + ,2&2 . &3 - 3Ψ2 . M! M23 =

M32 = 2()* + ,&2 . 2&3 - 3Ψ2 . M! M32 =

M34 = 2()* + ,2&3 . &4 . M! M34 =

M43 = 2()* + ,&3 . 2&4 . M! M43 =

M45 = 2()* + ,2&4 . &5 - 3Ψ2 . M! M45 =

M54 = 2()* + ,&4 . 2&5 - 3Ψ2 . M! M54 =

M56 = 2()* + ,2&5 - 3Ψ1 . M! M56 =

M65 = 2()* + ,&5 - 3Ψ1 . M! M65 =

/M2 = 0 = M21 . M25 . M23 20634$8

/M3 = 0 = M32 . M34 5221$25

/M4 = 0 = M43 . M45 0

/M5 = 0 = M52 . M54 . M56 5380$0

/or H1 = - 1000 = ,M23 . M32)* . ,M45 . M54)* = -H1 15683$5

/or H2 = - 3000 = ,M12 . M21)* . ,M56 . M65)* = -,H1 . H2 11655$32

esoliendo las ecuaciones de manera ma'ricialmen'e o"'ene

&2 = 0$0000 0$0000

&3 = 0$0000 0$0000

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&4 = 0$0000 0$0000

&5 = 0$0000 0$0000

Ψ1 = 0$0000 0$0000

Ψ2 = 0$0000 0$0000

θ2 = 0$151

θ3= 0$058

θ4 = 0$054

θ5 = 0$080

Ψ1 = 0$185

Ψ2 = 0$134

Hallamos cor'an'es en cada "arra

#arra 1 - 2

V,1 6451$18 -6451$18 V,1

V,2 0 0 V,2

V12 = 6451$18 V21= -6451$18 V25 =

#arra 3 - 4

V,1 -2264$3 2264$3 V,1

V,2 1600 1600 V,2

V34 = -664$3 V43= 3864$3 V45 =

(77M7 M9M;9< !9 #77

#arra 1 - 2M+ = 6451$18 + -1580$04 M+ =

+ M+

0 -1580$04

0$4 -1328$5

0$8 -100$0

1$2 -8128$62

1$6 -5548$15

2 -26$6

2$4 -38$202$8 213$28

3$2 43$5

8/17/2019 Portico de 2 Pisos Final

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3$6 354$22

4 34$0

#arra 3 - 4

M+ = -664$3 + . $ +>)2 . 015$54

+ M+

0 015$54

0$8 6612$02

1$6 6464$51

2$4 653$00

3$2 63$4

4 55$

4$8 8434$465$6 566$5

6$4 1055$43

$2 125$2

8 14500$41

0 0$4 0$8 1$2 1$6 2 2$4 2$8 3$2 3$6 4

-20000$00

-15000$00

-10000$00

-5000$00

0$00

5000$00

10000$00

15000$00

0 0$80$00

10000$00

20000$00

30000$00

40000$00

50000$00

60000$00

0000$00

80000$00

0000$00

0 0$8 1$6 2$4 3$2 4 4$8 5$6 6$4 $2 80$00

2000$00

4000$00

6000$00

8000$00

10000$00

12000$00

14000$00

16000$00

0 0$3

-15000$00

-10000$00

-5000$00

0$00

5000$00

10000$00

15000$00

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ICO CON DESPLAZAMIENTOS LATERALES - CARLOS EDUARDO LÓPEZ SALGADO

4 ?@c = 280 Ag)cm>

V1 = 0$30 + 0$0

3C1 = 0$30 + 0$50

5 = 250801 Ag)m>

4Cál!l" #$ %&$'%(

V1 = " + B )12

6 " = 0$30

B = 0$0 A1 = V1 2()* = 5380$

i = 0$00

C1 = " + B )12

" = 0$30 A2 = C1 2()* = 3218$44

B = 0$50

i = 0$003 A3 = C2 2()* = 5221$25

  a "arra

#arra 2 - 3 #arra 3 - 4 #arra 4 - 5 #arra

M23 = 0 M34 = -2133$33 M45 = 0 M56 =

M32 = 0 M43 = 2133$33 M54 = 0 M65 =

:

&2 &3 &4 &5 Ψ1 Ψ2 M!

3218$44 0 0 0 -11655$3 0 08436$88 0 0 0 -11655$3 0 0

10615$40 0 0 5380$68 0 0 -8533$333

5380$0 0 0 10615$4 0 0 8533$333

104582$50 5221$251 0 0 0 -15683$8 0

5221$25 104582$503 0 0 0 -15683$8 0

0 10615$36 5380$68 0 0 0 -2133$333

0 5380$68 10615$36 0 0 0 2133$333

0 0 104582$503 5221$252 0 -15683$8 0

0 0 5221$251 104582$5 0 -15683$8 0

0 0 0 8436$8 -11655$3 0 0

0 0 0 3218$43 -11655$3 0 0

5221$25 0 5380$68 -11655$32 -15683$8

+

&2

2121$0 5380$68 0 0 -15683$8 &3

5380$0 2121$8 5221$251 0 -15683$8 &4

0 5221$251 20634$ -11655$32 -15683$8 &5

15683$548 15683$55 15683$55 0 -6245 Ψ1

0 0 11655$316 -40621$26 0 Ψ2

os:

0$0000 0$0000 0$0000 0$0000 8533$3333

0$0000 0$0000 0$0000 0$0000 2133$3333

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0$0000 0$0000 0$0000 0$0000+

-2133$333

0$0000 0$0000 0$0000 0$0000 -8533$333

0$0000 0$0000 0$0000 0$0000 -30000

0$0000 0$0000 0$0000 0$0000 -60000

M12 = -1580$04

M21 = -34$0

M25 = 1205$2

M52 = 25288$6

M23 = -2124$58

M32 = -015$54

M34 = 015$54

M43 = 110$5

M45 = -110$5

M54 = -60$2M5) = -15528$38

M)5 = -18666$88

#arra 2 - 5 #arra 2 - 3

-4668$4 4668$4 V,1 3046$1 -3046$

6400 6400 V,2 0 0

131$51 V52= 11068$4 V23 = 3046$1 V32= -3046$

#arra 4 - 5 #arra 5 - 6

653$2 -653$2 V,1 8548$82 -8548$8

0 0 V,2 0 0

653$2 V54= -653$2 V56 = 8548$82 V65= -8548$8

#arra 2 - 5 #arra131$51 + . 1205$2 M+ = 3046$1

+ M+ +

0 1205$2 0

0$8 1356$48 0$3

1$6 168$68 0$6

2$4 20822$8 0$

3$2 252$10 1$2

4 3185$30 1$5

4$8 38802$51 1$85$6 46843$1 2$1

6$4 5508$2 2$4

 eemlamo los giros y los delaamien'os la'erales o"'enidos en las ecuaciones arlos momen'os Dnales:

$ +>)2 .

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$2 658$12 2$

8 111$33 3

#arra 4 - 5 #arra

M+ = 653$2 + -110$5 M+ = 8548$82

+ M+ +

0 -110$5 0

0$3 -013$60 0$4

0$6 -62$62 0$8

0$ -4841$63 1$2

1$2 -255$64 1$6

1$5 -66$65 2

1$8 1416$34 2$42$1 3502$33 2$8

2$4 5588$31 3$2

2$ 64$30 3$6

3 60$2 4

$6 2$4 3$2 4 4$8 5$6 6$4 $2 8

0 0$3 0$6 0$ 1$2 1$5

-4000$00

-2000$00

0$00

2000$00

4000$00

6000$00

8000$00

0$6 0$ 1$2 1$5 1$8 2$1 2$4 2$ 30 0$4 0$8 1$2 1$6 2

-20000$0

-15000$0

-10000$0

-5000$0

0$0

5000$0

10000$0

15000$0

20000$0

25000$0

8/17/2019 Portico de 2 Pisos Final

7/9

 5 - 6

0

0

= 8533$3333

= 2133$3333

= -2133$333

= -8533$333

= -30000

= -60000

8/17/2019 Portico de 2 Pisos Final

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 2 - 3+ -2124$58

M+

-2124$58

-1210$5

-26$56

61$46

1531$4

2445$48

335$4423$50

518$51

  o"'ener

8/17/2019 Portico de 2 Pisos Final

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6101$53

015$54

  5 - 6

+ -15528$4

M+

-15528$4

-12108$

-868$3

-526$8

-1850$3

156$3

488$88408$3

1182$8

1524$4

18666$

1$8 2$1 2$4 2$ 3

$4 2$8 3$2 3$6 4