Resistencia de Materiales II

UNIVERSIDAD PRIVADA DE TACNA TACNA T ACNA -2016

RESISTENCIA DE MATERIALES II JUAN CAT CATA CORA SAGREDO

19

RESISTENCIA DE MATERIALES II. GRAFICO DEL PROTICO: (SOFTWARE) (SOFTWARE)

1000 +,

1000

2000

C

E

D

 2

2000

2

. 

*000



*926319

/

G

301963

142*.*6



10649 +,

*

2

649 A .194.

Grado de indeer!ina"i#n de$ %#ri"o& N' de rea""ione(& 6 N' de e")a"ione( de $a e(ai"a& * Grado de indeer!ina"i#n& *

DIAGRAMAS DE FUERZA CORTANTE, MOMENTO FLECTOR Y FUERZA AXIA AX IAL: L:

.194.

496413 *496413 203*241 194.

E

 C

DFC

D

-

-12000 -

-649

/

G

A

RESISTENCIA DE MATERIALES II

UNIVERSIDAD PRIVADA DE TACNA

19

140311 -

.01*39



-

D

C

E

DMF

23401

*4.3

9192443

-143.3.

G

/

A

C



D

E

DFA DFA -

142*.*6

-

G

-

/ A -.194.

VALORES MAXIMOS DIAGRAMA DE FUERZA CORTANTE: TRAMO A C C/ CD DG DE


VALORES MA5IMOS MA5IMOS -20649 .194. -12000 496413 0 -*926319


19

VALORES MA5IMOS DIAGRAMA DE MOMENTO /LECTOR& TRAMO A C C/ CD DG DE

VALORES MA5IMOS MA5IMOS -241*62 9192443 -2000 -140311* 0 *4.34

PUNTOS DE INFLEXION: VIGA BC: M ( X ) =−4281.364 + 5194.85 X −500 X

2

0

2

=−4281.364 + 5194.85 X −500 X

X =0.9

VIGA CD: M ( X ) =−5013.48 + 3896.817 X 0

=−5013.48 + 3896.817 X

X =1.96

UICACIN DE LOS PUNTOS DE IN/LE5ION&

ESFUERZOS POR CORTE Y POR FLEXIÓN:



A



19

C

/

E

D

G

DISEÑO PARA LAS VIGAS: Di(e7o de (e""i#n %ara e$ %#ri"o !o(rado& E(8)ero nor!a$ e "o!%re(i#n :11.0 +,"!2 a 1*.0 +,"!2; E(8)ero nor!a$ en ra""i#n :3.0 +,"!2 a 900 +,"!2; E(8)ero "orane :16 +,"!2 a 14 +,"!2; A()!iendo $a( (i,)iene( "ara"er<(i"a(& I =

b∗h 12

3

3

=

b∗(1.5 b ) 12

= 0.28 b

4

03. 1.=

03.

=

CALCULO DE = > ? PARA @UE SOPORTE LOS ES/UEROS POR TRACCION& M ∗c 1 σtrac = I σtrac =

24000 kg

−m∗0.75 b

0.28 b

4

∗100



19

σtrac =

24000 kg

−m∗0.75 b

0.28 b

4

∗100

b = 21 cm h = 32 cm

VERI/ICANDO A LOS ES/UEROS CORTANTES& VB12000 +, AB 21 "! 5 *2 "! >B4"! τ =

τ =

v∗Y ∗ A b∗ I

∗8∗21∗32 =53.57 kg / cm 21∗57344

12000

PROCEDEMOS A CORREGIR

∗ b∗0.75 b∗1.5 b b∗0.28 b

12000

=

18

4

b = 58 h = 87

Se endr $a !i(!a =a(e %ero $a iner"ia e( di8erene enon"e(&

VIGA BE: La i,a E iene 2I

= 6365529

2 I

6365529

=

b∗h

3

12

h =110

VIGA AB: La i,a E iene 1.I

= 4774147

1.5 I



19 3

4774147

=

b∗ h 12

h = 100

CALCULOS DE ESFUERZOS NORMALES: PARA LA VIGA AB:

.0 10 .0

.

/IGURA 1

AREA .400

> .0

A> 290000

CALCULO DE LOS ES/UEROS NORMALES& σc =

M ∗c I

Para )n !o!eno !Fi!o de 241*62 +,-! σc =

4281.362

4833333

σc = 4.43

σt =

∗50

kg cm 2

4281.362

∗50

4833333

σt =4.43

∗100

∗100

kg cm 2

2 RESISTENCIA=DE MATERIALES II


19

=

2

Paa !a "#$a BE:

.. 11 ..

.

/IGURA AREA > 1 6*40 .. Para )n !o!eno !Fi!o de 140311* +,-! σc =

14807.113

6433167

σc =12.66

σt =

∗55

∗100

kg cm 2

∗

14807.113 55 6433167

σt =12.66

A> *.0900

∗100

kg cm 2

=

2



19

=

2

Paa !a "#$a CF:

*. 43 *

.

/IGURA 1

AREA .06

> *.

A> 219.01

Para )n !o!eno !Fi!o de 2000 +,-! σc =

∗ 43.5

24000

3182765

σc =32.802

σt =

kg cm 2

∗43.5

24000

3182765

σt =32.802

∗100

∗100

kg cm 2


=

2


19

=

2

CALCULOS DE ESFUERZOS CORTANTES: VIGA AB:



19

11

Para )n a$or !Fi!o de 8)era "orane de 20649 +, τ =

V ∗Q I ∗b

Core 1-1& τ 1− 1=0

Core 2-2&

?

=

4833333 cm

( ¿¿ 4 )( 58 cm )=0.223

AB

kg cm

2

2

( 2046.894 kg )( 841 cm )( 36.25 cm ) Τ − = ¿ 2

2



19 6433167 cm

(¿ ¿ 4 )( 58 cm )=0.561

BE

kg 2 cm

( 5194.85 kg ) ( 966.86 cm ) ( 41.665 cm ) Τ − = ¿ 2

2

2

3182165 cm

(¿¿ 4 )( 58 cm)=−3.168 kg

2

CF

cm

2

(−12 000 kg )( 1063.14 cm )( 45.835 cm ) Τ − = ¿ 2

2

Core *-*&

?

= 4833333 cm

kg 2 cm (2046.894 kg )( 1682 cm2)( 29 cm )

(¿¿ 4 )( 58 cm )=0.356

AB Τ 3 −3 =

¿

6433167 cm

kg 2 cm ( 5194.85 kg ) ( 1933.72 cm2 ) (33.34 cm )

(¿¿ 4 )( 58 cm)= 0.896

BE Τ 3 −3 =

¿

3182165 cm

(¿¿ 4 )( 58 cm )=−5.068

CF

kg 2 cm 2

(−12 000 kg )( 2126.28 cm )( 36.66 cm) Τ − = ¿ 3

3

Core -& RESISTENCIA DE MATERIALES II


19

?

=

4833333 cm

(¿ ¿ 4 )( 58 cm )=0.401 kg

AB

cm

2

2

Τ 4−4

( 2046.894 kg )( 2523 cm )( 21.75 cm) = ¿ 6433167 cm

(¿¿ 4 )( 58 cm )=1.009 kg

2

BE

Τ 4− 4 =

cm ( 5194.85 kg ) ( 2900 cm2 ) ( 25 cm )

¿

3182165 cm

(¿¿ 4 )( 58 cm)=−5.704 kg

CF

cm

2

2

Τ 4− 4

(−12000 kg )( 3190 cm )( 27.5 cm) = ¿

Core .-.&

?

=



19 4833333 cm

kg 2 cm ( 2046.894 kg )( 3364 cm2 )( 14.5 cm)

(¿¿ 4 )( 58 cm)= 0.356

AB Τ 5 −5 =

¿ 6433167 cm

kg 2 cm

(¿¿ 4 )( 58 cm)= 0.897

BE

( 5194.85 kg ) ( 3867.44 cm ) ( 16 .665 cm ) Τ − = ¿ 2

5

5

3182165 cm

(¿¿ 4 )( 58 cm )=−5.069 kg

CF

cm

2

2

(−12 000 kg )( 4252.56 cm )( 18.335 cm) Τ − = ¿ 5

5

Core 6-6&

?

= 4833333 cm

kg 2 cm (2046.894 kg )( 4205 cm2)( 7.25 cm )

(¿¿ 4 )( 58 cm)= 0.223

A B Τ 6 −6 =

¿

6433167 cm

kg 2 cm (5194.85 kg ) ( 4834.3 cm2 ) ( 8.33 cm)

(¿¿ 4 )( 58 cm )=0.561

BE Τ 6 −6 =


¿


19 3182165 cm

(¿¿ 4 )( 58 cm)=−3.169

CF

kg 2 cm 2

(−12000 kg )( 5315.7 cm )( 9.17 cm ) Τ − = ¿ 6

6

Core 3-3& τ 7− 7 =0

DIAGRAMA DE LOS ESFUERZOS CORTANTES: VIGA A& T1-1& 0 T2-2& 022* T*-*& 0*.6 T-& 001 T.-.& 0*.6 T6-6& 022* T3-3& 0

VIGA E& T1-1& 0 T2-2& 0.61 T*-*& 0493 T-& 1009 T.-.& 0493 T6-6& 0.61 T3-3& 0

VIGA C/&



19

T1-1& 0 T2-2& -*169 T*-*& -.069 T-& -.30 T.-.& -.069 T6-6& -*169 T3-3& 0

CALCULO DE LOS DESPLAZAMIENTOS DE NUDOS: 1000 +,

1000

2000

C

E

D

 2

. 2000

*

2

10649 +,

2 *000







*926319

/

G

301963

142*.*6

649 A .194.

DESPLAAMIENTO DE NUDOS& :SO/TARE; NUDO  C D


DESPLAAMIENTO 00314 "! 006. "! 00239 "!


19

II. METODO DE COMPATIBILIDAD (MANUAL): PORTICO ORIGINAL& 1000

1000 C

2000 D

E

 2000 *000 /

G

A

PORTICO ACOMODADO PARA SER ISOSTATICO VIRTUALES&

1000

1000

5

5

> PORTICO CON CARGAS

2000 E

5 

5

C

D

5

2000 *000

5

5

/

5

G

A



19

Pori"o "on "ar,a ir)a$ de 1000 +, en GH 1000 +,

1000 +,

Pori"o "on "ar,a ir)a$ de 1000 +, en EH

1000 +,

Pori"o "on "ar,a ir)a$ de 1000 +, en EF

ELASTICA DE LOS PORTICOS& :EN ORDEN RESPECTIVO A LAS PORTICOS;



19



19

CALCULO DE DESPLAAMIENTOS& E")a"ione( de aria"i#n de$ %#ri"o i(o(i"o "on "ar,a ir)a$ en GH& ECUACIO N 51

LIMIT E 0-

52

PORTICO

CARGA VIRTUAL

M ( X )=14000 X

m ( x )= 0

0-2

M ( X )=12000 X + 56000

m ( x )= 0

5*

0-.

M ( X )=80000 −15700 X −500 X

m ( x )= 0.8 X

5

0-

M ( X )=−1500 X

m ( x )= 0

5.

0-2

M ( X )=7000 X − 35000

m ( x )= 4 − X

56

0-2

M ( X )=6000 X −21000

m ( x )=2 − X

53

0-

M ( X )=0

m ( x )= 0

54

0-*

M ( X )=6000 X −9000−1000 X

(∫ (

2

2

2

5

∆ Gy =

m ( x )= 0

2

80000

2

−15700 X −500 X ) ( 0.8 X ) dx +∫ (7000 X −35000 ) ( 4 − X ) dx +∫ ( 6000 X −21000 ) ( 2 − X ) 2

0

0

0

∆ Gy =0.4167 cm

E")a"ione( de aria"i#n de$ %#ri"o i(o(i"o "on "ar,a ir)a$ en EH& ECUACIO N 51

LIMIT E 0-

PORTICO M ( X )=14000 X


CARGA VIRTUAL m ( x )= 0


19

52

0-2

M ( X )=12000 X + 56000

5*

0-.

M ( X )=80000−15700 X −500 X

m ( x )=1.4 X

5

0-

M ( X )=−1500 X

m ( x )= 0

5.

0-2

M ( X )=7000 X − 35000

m ( x )=7 − X

56

0-2

M ( X )=6000 X −21000

m ( x )=5 − X

53

0-

M ( X )=0

m ( x )= 0

54

0-*

M ( X )=6000 X −9000 −1000 X

(∫ (

2

2

m ( x )=3 − X

2

5

∆ Ey =

m ( x )= 0

2 2

80000−15700 X −500 X

2

) ( 1.4 X ) dx +∫ ( 7000 X −35000 ) ( 7 − X ) dx +∫ ( 6000 X −21000 ) ( 5 − X )

0

0

0

∆ Ey =−6.118 cm

E")a"ione( de aria"i#n de$ %#ri"o i(o(i"o "on "ar,a ir)a$ en EF& ECUACIO N 51

LIMIT E 0-

52

PORTICO

CARGA VIRTUAL

M ( X )=14000 X

m ( x )= X

0-2

M ( X )=12000 X + 56000

m ( x )= 4 + X

5*

0-.

M ( X )=80000−15700 X −500 X

m ( x )=6 − 1.2 X

5

0-

M ( X )=−1500 X

m ( x )= 0

5.

0-2

M ( X )=7000 X − 35000

m ( x )= 0

56

0-2

M ( X )=6000 X −21000

m ( x )= 0

53

0-

M ( X )=0

m ( x )= 0

54

0-*

M ( X )=6000 X −9000 −1000 X

(

∆ Ex =

4

2

2

2

∫ ( 14000 X ) ( X ) dx +∫ ( 12000 X +56000 ) ( 4 + X ) dx 0

m ( x )= 0

2

0


)

6

10

+

E 1.5 I

(

5

∫ ( 80000 −15700 X −500 X ) ( 6 −1.2 2

0


19

∆ Ex =116.211 cm

E")a"ione( de aria"i#n de$ %#ri"o "on 1000 +, en GH H "ar,a ir)a$ en GH& ECUACIO N 51

LIMIT E 0-

M ( X )=0

m ( x )= 0

52

0-2

M ( X )=0

m ( x )= 0

5*

0-.

M ( X )=800 X

m ( x )= 0.8 X

5

0-

M ( X )=0

m ( x )= 0

5.

0-2

M ( X )=4000 −1000 X

m ( x )= 4 − X

56

0-2

M ( X )=2000− 1000 X

m ( x )=2 − X

53

0-

M ( X )=0

m ( x )= 0

54

0-*

M ( X )=0

m ( x )= 0

(∫ 5

f 11=

PORTICO

2

CARGA VIRTUAL

2

( 800 X ) ( 0.8 X ) dx +∫ ( 4000−1000 X ) ( 4 − X ) dx +∫ ( 2000 −1000 X ) ( 2− X ) dx

0

0

0

)

6

10

E 2 I

f 11= 2.66 cm

E")a"ione( de aria"i#n de$ %#ri"o "on 1000 +, en GH H "ar,a ir)a$ en EH& ECUACIO N 51

LIMIT E 0-

PORTICO M ( X )=0

m ( x )= 0

52

0-2

M ( X )=0

m ( x )= 0

5*

0-.

M ( X )=800 X

m ( x )=1.4 X

5

0-

M ( X )=0

m ( x )= 0


CARGA VIRTUAL


19

5.

0-2

M ( X )=4000 −1000 X

m ( x )=7 − X

56

0-2

M ( X )=2000− 1000 X

m ( x )=5 − X

53

0-

M ( X )=0

m ( x )= 0

54

0-*

M ( X )=0

m ( x )=3 − X

f 21=

(

5

2

2

3

0

0

0

0

f 21= 5.11 cm

E")a"ione( de aria"i#n de$ %#ri"o "on 1000 +, en GH H "ar,a ir)a$ en EF& ECUACIO N 51

LIMIT E 0-

M ( X )=0

m ( x )= X

52

0-2

M ( X )=0

m ( x )= 4 + X

5*

0-.

M ( X )=800 X

m ( x )=6 − 1.2 X

5

0-

M ( X )=0

m ( x )= 0

5.

0-2

M ( X )=4000 −1000 X

m ( x )= 0

56

0-2

M ( X )=2000− 1000 X

m ( x )= 0

53

0-

M ( X )=0

m ( x )= 0

54

0-*

M ( X )=0

m ( x )= 0

(∫

PORTICO

5

f 31=

)

∫ ( 800 X ) ( 1.4 X ) dx +∫ ( 4000 −1000 X ) ( 7− X ) dx +∫ ( 2000 −1000 X ) ( 5− X ) dx +∫ ( 0 ) ( 3 − X ) dx E102

( 800 X ) ( 6 −1.2 x ) dx

0

)

CARGA VIRTUAL

6

10

E 2 I

f 31= 1.11 cm



19

E")a"ione( de aria"i#n de$ %#ri"o "on 1000 +, en EH H "ar,a ir)a$ en GH& ECUACIO N 51

LIMIT E 0-

M ( x )=0

m ( x )= 0

52

0-2

M ( x )=0

m ( x )= 0

5*

0-.

M ( x )=1400 X

m ( x )= 0.8 x

5

0-

M ( x )=0

m ( x )= 0

5.

0-2

M ( x )=7000 −1000 X

m ( x )= 4 − X

56

0-2

M ( x )=5000 −1000 X

m ( x )=2 − X

53

0-

M ( x )=0

m ( x )= 0

54

0-*

M ( x )=3000 −1000 X

m ( x )= 0

(∫ 5

f 12=

PORTICO

2

CARGA VIRTUAL

2

( 1400 X ) ( 0.8 X ) dx +∫ ( 7000 −1000 X ) ( 4 − X ) dx +∫ ( 5000 −1000 X ) ( 2 − X ) dx

0

0

0

)

6

10

E 2 I

f 12= 5.11 cm

E")a"ione( de aria"i#n de$ %#ri"o "on 1000 +, en EH H "ar,a ir)a$ en EH& ECUACIO N 51

LIMIT E 0-

PORTICO M ( x )=0

m ( x )= 0

52

0-2

M ( x )=0

m ( x )= 0

5*

0-.

M ( x )=1400 X

m ( x )=1.4 X

5

0-

M ( x )=0

m ( x )= 0


CARGA VIRTUAL


19

5.

0-2

M ( x )=7000 −1000 X

m ( x )=7 − X

56

0-2

M ( x )=5000 −1000 X

m ( x )=5 − X

53

0-

M ( x )=0

m ( x )= 0

54

0-*

M ( x )=3000 −1000 X

m ( x )=3 − X

(∫ 5

f 22=

2

2

3

( 1400 X ) ( 1.4 X ) dx +∫ ( 7000−1000 X ) ( 7 − X ) dx +∫ ( 5000−1000 X ) ( 5− X ) dx +∫ (3000−1000 X

0

0

0

0

f 22= 10.89 cm

E")a"ione( de aria"i#n de$ %#ri"o "on 1000 +, en EH H "ar,a ir)a$ en EF& ECUACIO N 51

LIMIT E 0-

M ( x )=0

m ( x )= X

52

0-2

M ( x )=0

m ( x )= 4 + X

5*

0-.

M ( x )=1400 X

m ( x )=6 − 1.2 X

5

0-

M ( x )=0

m ( x )= 0

5.

0-2

M ( x )=7000 −1000 X

m ( x )= 0

56

0-2

M ( x )=5000 −1000 X

m ( x )= 0

53

0-

M ( x )=0

m ( x )= 0

54

0-*

M ( x )=3000 −1000 X

m ( x )= 0

(∫

PORTICO

5

f 32=

( 1400 X ) ( 6−1.2 X ) dx

0

)

10

CARGA VIRTUAL

6

E 2 I

f 32= 1.94 cm

E")a"ione( de aria"i#n de$ %#ri"o "on 1000 +, en EF H "ar,a ir)a$ en EH& ECUACIO N 51

LIMIT E 0-

PORTICO M ( x )=1000 X


CARGA VIRTUAL m ( x )= 0


19

52

0-2

M ( x )= 4000 + 1000 X

m ( x )= 0

5*

0-.

M ( x )=6000 −1200 X

m ( x )= 0.8 x

5

0-

M ( x )=0

m ( x )= 0

5.

0-2

M ( x )=0

m ( x )= 4 − X

56

0-2

M ( x )=0

m ( x )=2 − X

53

0-

M ( x )=0

m ( x )= 0

54

0-*

M ( x )=0

m ( x )= 0

(∫ 5

f 13 =

( 6000 −1200 X ) ( 0.8 X ) dx

0

)

6

10

E 2 I

f 13 =1.11 cm

E")a"ione( de aria"i#n de$ %#ri"o "on 1000 +, en EF H "ar,a ir)a$ en EH& ECUACIO N 51

LIMIT E 0-

52

PORTICO

CARGA VIRTUAL

M ( x )=1000 X

m ( x )= 0

0-2

M ( x )= 4000 + 1000 X

m ( x )= 0

5*

0-.

M ( x )=6000 −1200 X

m ( x )=1.4 X

5

0-

M ( x )=0

m ( x )= 0

5.

0-2

M ( x )=0

m ( x )=7 − X

56

0-2

M ( x )=0

m ( x )=5 − X

53

0-

M ( x )=0

m ( x )= 0

54

0-*

M ( x )=0

m ( x )=3 − X

(∫ 5

f 23 =

( 6000 −1200 X ) ( 1.4 X ) dx

0

)

6

10

E 2 I

f 23 = 1.94 cm

E")a"ione( de aria"i#n de$ %#ri"o "on 1000 +, en EF H "ar,a ir)a$ en EF& ECUACIO N 51

LIMIT E 0-

PORTICO M ( x )=1000 X


CARGA VIRTUAL m ( x )= X


19

52

0-2

M ( x )= 4000 + 1000 X

m ( x )= 4 + X

5*

0-.

M ( x )=6000 −1200 X

m ( x )=6 − 1.2 X

5

0-

M ( x )=0

m ( x )= 0

5.

0-2

M ( x )=0

m ( x )= 0

56

0-2

M ( x )=0

m ( x )= 0

53

0-

M ( x )=0

m ( x )= 0

54

0-*

M ( x )=0

m ( x )= 0

(∫ 4

f 33 =

2

( 1000 X ) ( X ) dx +∫ ( 4000 + 1000 X ) ( 4 + X ) dx

0

0

)

10

(∫ 5

6

+

E 1.5 I

( 6000 −1200 X ) ( 6−1.2 X ) dx

0

f 33 =8.67 cm

Veri"a"i#n "on (o8are& CALCULO MANUAL

CALCULO SO/ARE

∆ Gy =0.4167 cm

∆ Gy =0.195525 cm

∆ Ey =−6.118 cm

∆ Ey =−6.434516 cm

∆ Ex = 116.211 cm

∆ Ex =116.445204 cm

f 11=2.66 cm

f 11=2.683094 cm

f 21= 5.11 cm

f 21=5.129443 cm

f 31=1.11 cm

f 31=1.099509 cm

f 12= 5.11 cm

f 12=5.129443 cm

f 22=10.89 cm

f 22=10.914604 cm

f 32= 1.94 cm

f 32=1.927141 cm

f 13 =1.11 cm

f 13 =1.099509 cm

f 23 = 1.94 cm

f 23 = 1.927141 cm

f 33 =8.67 cm

f 33 =8.685732 cm

( (

f 11 f 12 f 21 f 22 f 31 f 32

)( ) ( ) )( ) ( )

f 13 Gy ∆ Gy f 23 Ey = ∆ Ey f 33 Ex ∆ Ex

2.66

5.11

1.11

5.11

10.89

1.94

1.11

1.94

8.67

−0.4167 Gy Ey = 6.118 −116.211 Ex



)

6

10

E 2 I

19

( )( ( )(

) )

−1.840613 Gy ∗1000 3.9279 Ey = −14.047064 Ex −1840.613 Gy 3927.9 Ey = −14047.064 Ex

PORTICO ORIGINAL& 1000

1000 C

2000 E

D



10306

2000

*9239 *000 G

/

14061* +, A

CALCULO DE LAS OTRAS REACCIONES&

∑ X =0 FyA + 2000 + 12000 =14047.064 FxA = 47.064 kg

∑ MA = 0 FyD =4729.667 kg FyA =5183.046 kg

PORTICO CON TODAS LAS REACCIONES > DIAGRAMAS DE MOMENTO /LECTOR > /UERA CORTANTE&

1000

RESISTENCIA DE MATERIALES II 2000 *000

2000


19

1000 C 

E

D

10306 *9239

306

/

G

329663

14061* +

A .14*06

.14*06

91231* *91231* 20321 14*06

-

-12000 -*9239

-306



19 140311 -

.01*39 -

23401 9192443

*4.3

-143.3.

PUNTOS DE INFLEXION: VIGA BC: M ( X ) =−4281.364 + 5194.85 X −500 X

2

0

2

=−4281.364 + 5194.85 X −500 X

X =0.9

VIGA CD: M ( X ) =−5013.48 + 3896.817 X 0

=−5013.48 + 3896.817 X

X =1.96

UICACIN DE LOS PUNTOS DE IN/LE5ION&

ESFUERZOS POR CORTE Y POR FLEXIÓN:

C



/

A RESISTENCIA DE MATERIALES II

E

D

G


19

III METODO DE CROSS& PORTICO ORIGINAL& 1000 +,



19

1000

2000 C

E

D

 2000

2

.

2

*

2



*000



G

/



A

COLOCACION DE TOPE PARA EVITAR DESPLAAMIENTO DE NUEDOS& 1000

1000 +, C



2000 D E

2000 *000

/ G

A

CALCULO DE LAS RIGIDECES& ab= ba=

bc= cb =

1.5 I 6

2 I 5

8

=  I = k 3

=

16 15

k

I 2 cf = fc = = k = dg= gd 4

dc= cd =

d!= !d =

3

2 I

4

4

3

2 I 3

= k =

16 9

k



19

/ACTORES DE DISTRIUCION& NUDO A& Dab =0

NUDO & ba 5 Dba= = ba + bc 7 Dbc=

bc 2 = ba + bc 7

NUDO C& Dcb=

cb 8 = cb+ cd + cf 23

cd 10 = Dcd = cb + cd + cf 2 3 5 cf = Dcf = cb + cd + cf 23

NUDO /& Dfc =0

NUDO D& Ddc=

dc 6 = dc + d! + dg 17

Dd!=

8 d! = dc + d! + dg 17

Ddg=

3 dg = dc + d! + dg 17

NUDO G& Dgd= 0

NUDO E& D!d =0



19

EMPOTRAMIENTO& TRAMO A& Ma=

Mab =

2000

− "a b #

2

2

M=a

2

"ab =−888.89 Mba = 2 =1777.78 #

TRAMO C& M="

M"=

1000

Mbc =

−$ % 12

2

=−2083.33 Mcb =

%$2

12

=2083.33

TRAMO C/& M"8


M8"


19

*000

2

2

$% −$ % Mcf = =−4000 Mfc = = 4000 12

12

TRAMO DE& Mde

Med 2000

M d! =

−$ % 12

2

=−1500 M !d =

%$2

12

=1500

TRAMO CD& M"d

Md" 1000

"# "# =−500 M dc = =500 M cd = 8

8

CALCULO DE MOMENTOS :E5CEL;



19

TRAMO A& 92.0 2000

1303

Fb =1463.22 kg Fa =536.78 kg

TRAMO C& 1303

244** 1000

Fb=2264.081 kg Fc= 2735.919 kg



19

TRAMO C/& *902

2.44 *000

Ff =6191.16 kg Fc= 5808.84 kg

TRAMO DE& 12696*

161.14 2000

Fd =2884.818 kg F!=3115.182 kg

TRAMO CD& 60.90.

1142.* 1000



19

Fd =644.157 kg Fc= 355.843 kg

DIAGRAMAS DE FUERZA CORTANTE, MOMENTO FLECTOR Y FUERZA AXIAL:



19

.194.

496413 *496413 203*241 194.

E

 C

DFC

D

-

-12000 -

/

-649

G

A

140311 

.01*39 -

D

C

E

DMF

23401 9192443

-143.3.

/

*4.3

G

A



Resistencia de Materiales II

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