Ejercicio de Emparrillado Plano

8/19/2019 Ejercicio de Emparrillado Plano

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Datos:

a = 3 m , b = 6m , EI = 40·107 kN·m2, GIt = 3·106 kN·m2, Py = 60 kN, Mx=60 kN·m.

Sol!"#$:

%a&&as 'a&al(las al ()( *

EI = 40.00 +Nm2

GIt = 3.00 +Nm2

Py = 60.00 +N

- = 3.00 m 1.00

a$lo = 0 / = 0.00

'l"!a$o (l Mtoo ( ""(, &(sol5(& la (st&!t&a ( la "&a ba)o las !a&as ( s( "$"!a$. -a &"

to&s"#$ GIt ( las ba&&as so$ !o$sta$t(s.

-a &(sol!"#$ ( la (st&!t&a !om"($a 'o& la $m(&a!"#$ ( los $os y ( las ba&&as. -a $m(&a!"#$ (l

!o&&(s'o$"($t(s ()(s ( &(8(&($!"a lobal(s y lo!al(s ( la (st&!t&a s( m(st&a$ ($ la "&a

S( !al!la$, a !o$t"$a!"#$, las mat&"!(s ( &""( ( las '"(as ($ !oo&($aas lo!al(s . S" b"($ la &""

ba&&as (s !o$sta$t(, al 5a&"a& la lo$"t ( las ba&&as s( obt($&$ mat&"!(s ( &""( (l(m($tal "8(



!os = 1.00 0.00

s($ = 0.00

G;- = 1.00 Mat&" <&a$s8oma!"#$

= 177.7

= 266.67

= >33.33

= 266.67

1

= 0

0

1

= 0

0

Mat&" ( &""( ($ !oo&($aas Global(

1.00

K = 0.00

0.00

%a&&as 'a&al(las al ()( ?

EI = 40.00 +Nm2

GIt = 3.00 +Nm2

Py = 60.00 +N

- = 6.00 m 0.>0

a$lo = @0 / = 0.00

!os = 0.00 0.00

s($ = 1.00

G;- = 0.>0 Mat&" <&a$s8oma!"#$

= 22.22

= 66.67

= 266.67

= 133.33

0

= 0

1

0



= 0

-1

Mat&" ( &""( ($ !oo&($aas Global(

266.67

K = A66.67

0.00

A60 266.67 A66.67 0.

60 = A66.67 377.7 0.

0 0.00 0.00 106

(ms 'o& obl( s"m(t&9a (l '&obl(ma, '(( (s!&"b"&s(:

El s"st(ma ( (!a!"o$(s ( '(&m"t( obt($(& (l 5alo& ( los mo5"m"($tos "$!#$"ta, (s (!"&, los aso!"a

-a mat&" ( &""( lobal ( la (st&!t&a s( obt"($( '&o!(so ( ($sambla)( . S" s( t"($( ($ !($ta la

( la !a&a, s( (!( ( los mo5"m"($tos ( los $os (b($ s(& s"mt&"!os y 'o& ta$to, basta !o$o!(&

'a&a &(sol5(& (l '&obl(ma. S( (l"(, (l $o 3 y s( 'la$t(a la !o$"!"#$ ( ("l"b&"o ($t&( 8(&as (xt(&

"$t(&$os ($ los (xt&(mos ( las ba&&as ( !o$!&&($ a l, '(( (s!&"b"&s(:



-a sol!"#$ (l s"st(ma a$t(&"o& '(&m"t( obt($(&:

A4.>317

= = 6.7>17

2.2>14

Do$( (l (s'laam"($to s( (x'&(sa ($ m(t&os y los "&os ($ &a"a$(s

Cálculo de las reacciones

8 = +8s . D8 B Ps Ps8 C8(&as ( 8")

0.4>317

= A60

A120

o$( la 8(&a s( (x'&(sa ($ kN y los mom($tos ($ kN·m. -as

&(a!!"o$(s ($ los $os '&(s!&"tos &(sta$t(s so$ "al(s ($ 5alo&

absolto y ss s"$os s( (!($ 'o& la !o$"!"#$ ( obl( s"m(t&9a.

l!los ( los (s8(&os ($ las ba&&as

-os (s8(&os ($ los (xt&(mos ( las ba&&as s( !al!la$ a 'a&t"& ( los

mo5"m"($tos m("a$t( las (!a!"o$(s C2.24 (l a'9tlo 2. s9, 'o&

()(m'lo, los (s8(&os ($ (l (xt&(mo a ( la ba&&a 13 C 13 0F = , so$:

<($"($o ($ !($ta ( los ()(s lo!al(s ( la ba&&a !o"$!"($ !o$ (l

s"st(ma ( &(8(&($!"a lobal y ( los mo5"m"($tos (l $o 1 so$

$los, s( obt"($(:

(!'(&a$o (l s"st(ma ( (!a!"o$(s !om'l(to, s( !al!la$ las &(a!!"o$(s "$!#$"tas ($ los $os !o$ mo5"m"($tos1, 2, 7 y . <amb"$ ($ (st( !aso, 'o& s"m(t&9a, basta !o$ !o$o!(& las &(a!!"o$(s ($ $o s#lo ( los $os '&(s!&"tos

N#t(s( ( al (x"st"& s#lo !a&as ($ los $os, (l t&m"$o ( !o&&(s'o$( a la &(a!!"#$ ( (m'ot&am"($to (s $lo.

&(a!!"o$(s &(sta$t(s, s( obt"($(:



<($"($o ($ !($ta ( los ()(s lo!al(s ( la ba&&a !o"$!"($ !o$ (l

s"st(ma ( &(8(&($!"a lobal y ( los mo5"m"($tos (l $o 1 so$

$los, s( obt"($(:

&(sol5"($o

0.4>317

A60

A120

o$( los mom($tos s( (x'&(sa$ ($ kN·m y la 8(&a ($ kN. N#t(s( (

los (s8(&os ($ (l (xt&(mo 1 ( la ba&&a 13 !o"$!"($ !o$ (l 5alo& ( las

&(a!!"o$(s ($ (l $o 1. ('"t"($o (l '&o!("m"($to s( obt"($($ los

&(sta$t(s 5alo&(s 'a&a los (s8(&os ($ los (xt&(mos ( las ba&&as:

0.4>3 0

A60 0

A120 60.4>3A0.4>3 0

60 0

A60 A60.4>3



0.00 0.00 A1.00 0.00

177.7 266.67 = 0.00 A177.7

"( a 8l(x"#$ EI y la &""( a

("a, as9 !omo los

a 8l(x"#$ y a to&s"#$ ( las

($t(s.



266.67 >33.33 0.00 A266.67

0 0

1 0

0 1

0 0

1 0

0 1

0.00 0.00 A1.00 0.00

177.7 266.67 K = 0.00 A177.7

266.67 >33.33 0.00 A266.67

0.00 0.00 A0.>0 0.00

22.22 66.67 = 0.00 A22.22

66.67 266.67 0.00 A66.67

0 -1

1 0

0 0

0 1



1 0

0 0

A66.67 0.00 133.33 66.67

22.22 0.00 K = A66.67 A22.22

0.00 0.>0 0.00 0.00

0 133.33 66.67 0.00 -1.00

0 -66.67 -22.22 0.00 0.00

.17 0.00 0.00 -0.50 0.00

os al $o 3

obl( s"m(t&9a ( la (st&!t&a y

los mo5"m"($tos ( $o ( (llos

$as ($ (l $o y (s8(&os



!"#$ : (sta$ s(&$ o&""$aas 'o& las !a&as (xt(&$as ( so$ a'l"!aas a !aa (l(m($to ( la (st&!t

&(s!&"tos C$os

('"t"($o (l '&o!("m"($to 'a&a las



0

0

600

0

A60



0.00 A1.00 0.00 0.00

266.67 = 0.00 A177.7 A266.67



266.67 0.00 266.67 266.67

0.00 A1.00 0.00 0.00

266.67 K = 0.00 A177.7 A266.67

266.67 0.00 266.67 266.67

0.00 A0.>0 0.00 0.00

66.67 = 0.00 A22.22 A66.67

133.33 0.00 66.67 133.33



0.00 133.33 A66.67 0.00

0.00 K = 66.67 A22.22 0.00

A0.>0 0.00 0.00 A0.>0

0.00 0.00 Hx

-177.78 266.67 5

-266.67 266.67 H



&a.



1.00 0.00 0.00

= 0.00 177.7 A266.67



0.00 A266.67 >33.33

1.00 0.00 0.00

K = 0.00 177.7 A266.67

0.00 A266.67 >33.33

0.>0 0.00 0.00

= 0.00 22.22 A66.67

0.00 A66.67 266.67



266.67 66.67 0.00

K = 66.67 22.22 0.00

0.00 0.00 0.>0

Ejercicio de Emparrillado Plano

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