Página 44 de 97
Página 1 de 97 IUPSM-Caracas Proyecto Estructural de Acero y Madera (Sección B E!E"CICI# $%& ('iro) *ISE+# *E ES,"UC,U"AS ME,A'ICAS-Estados ME,A'ICAS-Estados 'iites '".*/.ratelli0 Pág% 17 Una 2iga si3leente a3oyada de 05 de lu60 dee resistir una carga 3eranente de t8 y una 2ariale de $ t80 aas unioreente distriuidas% *eterine el oento teórico re:uerido% Calculo de la carga actori6ada)
Para otener la carga actori6ada se deen coinar las acciones :ue inciden sore la 2iga0 en este caso se tienen dos acciones :ue son) la carga 3eranente y la carga 2ariale% En la 3ág% 11 del 'iro de .ratelli0 se encuentran todos los casos (a3artado $%$0 3ara nuestro caso se escogerá el caso II% Siendo C;t < =% Para este caso0 3or lo :ue la ecuación :ueda as>) :u < &04C; ? &01 C; @ :u < &0 t8 ? &01 $ t8 < 105 t8 II &04C; ? &01 C; ? (=0 C;t :u < 105 t8 CP< t8 :u< C;< $ t8
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' CP< Acciones 3eranentes (cargas uertas deidas al 3eso 3ro3io de la estructura de acero0 losas0 3lacas0 3aredes0 cerraientos0 sore3isos0 cielorrasos0 aislaciones0 y todas las 3artes del ediicio aderidas a ellos en ora 3eranente y con carácter in2ariale en el tie3o% C;< Acciones 2ariales gra2itacionales (cargas 2i2as 3or uso ocu3acional de 3ersonas0 oDetos ó2iles0 ó2iles0 e:ui3aientos des3la6ales0 2e>culos0 incluyendo i3actos 3or co:ues o colisiones% :u< Suatoria total de las acciones :ue actan sore la estructura% C;t< Acciones 2ariales sore tecos y cuiertas (ecluyendo el agua 3lu2ial e3o6ada% :u < Carga actori6adas C;< Acciones 2ariales CP< Acciones 3eranentes
Página 2 de 97 IUPSM-Caracas
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Calculo del Moento áio)
Coo teneos una 2iga si3leente a3oyada0 se 3uede utili6ar la siguiente e3resión 3ara EMP#,"AMIEF,# EMP#,"AMIEF,# PE".EC,#% PE".EC,#% Mu < : % ' $ @ Mu < 105 t8 (05$ $ @ Mu < M3 < $501 t% 55 Calculo del oento teórico de la 2iga)
Para ello dee toarse en cuenta el actor inorante 3ara el caso de 2igas leadas (,ala $%&0 3ág% 1&% 'iro de .ratelli% G % Mt < M3 @ Mt < //M3/ @ Mt < //$501 t% @ Mt < &075t% G8 =09 G < =09 ,racción en ieros conectados ediante 3ernos o soldadura% ,racción o co3resión 3aralelas al eDe de las soldaduras de ilete% "esistencia teórica a leión% Corte en el ala de las 2igas leadas% :u< 105 t8 05 MP Mu < Moento Máio
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G< .actor inorante de resistencia Mt< Moento teórico re:uerido M3< Moento áio de la 2iga
Página 3 de 97 IUPSM-Caracas Proyecto Estructural de Acero y Madera (Sección B
Página 4 de 97 CAPI,U'# $ CA"HAS C"I,E"I#S *E *ISE+# EDe3lo $%$ *eterinar la coinación ás desa2orale de cargas actori6adas0 3ara una coluna de 3lanta aDa de un ediicio :ue so3orta las siguientes siguientes cargas C3<&$=,on C3<&$=,on C2< 5,on 5,on C;t<$$ ,on J<=,on Coinación de cargas actori6adas Ediicio ;ac>o0 sin 2iento ni siso) &%4 C3< &%4K&$=< &15 ,on Ediicio #cu3ado0 sin 2iento ni siso) &%$ C3?&%1 C2?=% C;t < $47%5 ,on ,on ) &%$ C3?&%1 C2?=% C2<$=5%$ ,on Ediicio con 2iento y concentración de gente en la a6otea) &%$ C3?&%1 C;t =%5J < $=%$ ,on
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=%9 C3-&% J< 19 ,on 'a coinación :ue controla el diseLo es la segunda y la carga actori6ada es de $47%5 ,on0 la resistencia teorica re:uerida resuelta% Ft< $47%58=%5< $9&% $9&% ,on ,on < =%5 tala $%&
Página 5 de 97 IUPSM-Caracas Proyecto Estructural de Acero y Madera (Sección B E!E"CICI# $%$ ('iro) *ISE+# *E ES,"UC,U"AS ME,A'ICAS-Estados ME,A'ICAS-Estados 'iites '".*/.ratelli0 Pág% 15 *eterinar la coinación ás desa2orale de cargas actori6adas0 3ara una coluna de 3lanta aDa de un ediicio :ue so3orta las siguientes siguientes cargas de ser2icio) CP< &$=t C;< 5t C;t< $$t J< =t Coinaciones de cargas actori6adas)
&%- Ediicio 2ac>o0 sin 2iento ni siso) &04CP $%- Ediicio ocu3ado0 sin 2iento ni siso) &0$CP ? &01C; ? =0 C;t %- Ediicio con 2iento y concentración de gente en la a6otea) &0$CP ? &01C;t ? =05J
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Calculo de cargas actori6adas)
&%- &04CP < &04 &$= < &15t $%- &0$CP ? &01C; ? =0 C;t < &0$ &$=t ? &01 5t ? =0 $$< $4705t &0$ &$=t ? &01 5t - =0 $$< $=50$t %- &0$CP ? &01C;t ? =05J< &0$ &$=t ? &01 $$t ? =05 =t< $=0$t 4%- &0$CP ? &0J ? =0(C; ? C;t< &0$ &$=t ? &0 =t ? =0 (5?$$t< $$t %- =09CP ? &0J< =09 &$=t ? &0 =t< &47t =09 &$=t - &0 =t< 19t 'a coinación :ue controla el diseLo es la segunda0 y la carga actori6ada es de $4705t% 'a resistencia teórica re:uerida resulta) Ft< :u 8 G G< Se otiene de la tala $%& CP< Acciones 3eranentes (cargas uertas deidas al 3eso 3ro3io de la estructura de acero0 losas0 3lacas0 3aredes0 cerraientos0 sore3isos0 cielorrasos0 aislaciones0 y todas las 3artes del ediicio aderidas a ellos en ora 3eranente y con carácter in2ariale en el tie3o% C;< Acciones 2ariales gra2itacionales (cargas 2i2as 3or uso ocu3acional de 3ersonas0 oDetos ó2iles0 ó2iles0 e:ui3aientos des3la6ales0 2e>culos0 incluyendo i3actos 3or co:ues o colisiones% C;t< Acciones 2ariales sore tecos y cuiertas (ecluyendo el agua 3lu2ial e3o6ada% J< Acción del 2iento% Ft < Moento Máio
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Página 6 de 97 IUPSM-Caracas Proyecto Estructural de Acero y Madera (Sección B Ft< $4705t 8 =05 < $9&0 $9&0 t
Página 7 de 97 IUPSM-Caracas Proyecto Estructural de Acero y Madera (Sección B E!E"CICI# $% ('iro) *ISE+# *E ES,"UC,U"AS ME,A'ICAS-Estados ME,A'ICAS-Estados 'iites '".*/.ratelli0 Pág% 15 Es el iso eDe3lo $%$0 3ero agregando una carga P< $5t0 3or 3osiilidad de e3o6aiento de agua en la a6otea% En este caso0 cuando las ecuaciones incluyan la carga 2i2a actori6ada en la a6otea0 su 2alor se co3ara con el de &0$P y se ado3ta la ayor de las cargas% 'as ecuaciones resultan) &%- &04CP < &04 &$= < &15t
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'a "esistencia teórica es) Ft< :u 8 G G< Se otiene de la tala $%& Ft< $7=04t 8 =05 < &50&t &50&t Ft < Moento Máio :u< Carga sore la 2iga G< 'ongitud de la 2iga Por ser la ás alta es la :ue controla el diseLo CP< Acciones 3eranentes (cargas uertas deidas al 3eso 3ro3io de la estructura de acero0 losas0 3lacas0 3aredes0 cerraientos0 sore3isos0 cielorrasos0 aislaciones0 y todas las 3artes del ediicio aderidas a ellos en ora 3eranente y con carácter in2ariale en el tie3o% C;< Acciones 2ariales gra2itacionales (cargas 2i2as 3or uso ocu3acional de 3ersonas0 oDetos ó2iles0 e:ui3aientos des3la6ales0 2e>culos0 incluyendo i3actos 3or co:ues o colisiones% colisiones% P< Cargas deidas al e3o6aiento de aguas 3lu2iales C;t< Acciones 2ariales sore tecos y cuiertas (ecluyendo el agua 3lu2ial e3o6ada% J< Acción del 2iento%
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Proyecto Estructural de Acero y Madera (Sección B E!E"CICI# $%4 ('iro) *ISE+# *E ES,"UC,U"AS ME,A'ICAS-Estados ME,A'ICAS-Estados 'iites '".*/.ratelli0 Pág% 19 *eterine la carga actori6ada de diseLo de una coluna de PB del ediicio donde unciona una central elctrica uicada en una 6ona s>sica ontaLosa0 con aDa concentración de ocu3antes% El ediicio es de acero0 con ora 3risática sin 2olados y con 3órticos r>gidos% 'a coluna :ue se anali6a so3orta las siguientes cargas de ser2icio0 incluyendo la carga de nie2e CF sore el teco) CP< &&t 8 C;< 15t 8 J< $$t 8 CF< $5t SeDeN< 1=t 8 SeDe< 4t 8 SO< $0t Calculo de las acciones (sin siso)
&04CP< &04 &&t < &1&, &0$CP ? &01C; ? =0CF< &0$ &&t &01 15t ? =0 $5t< $1=05, &0$CP ? &01CF ? =0C;< &0$ &&t ? &01 $5t ? = 15t< $&105t CP ? &01CF ? =05J< &0$ &&t ? &01 $5t ? =05 $$t< $==04t &0$CP ? &0J ? =0C; ? =0CF< &0$ &&t ? &0 $$t ? =0 15t ? =0 $5t< $&401t =09CP ? &0J< =09 &&t ? &0 $$t< &$0&t
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i3actos 3or co:ues o colisiones% C;t< Acciones 2ariales sore tecos y cuiertas (ecluyendo el agua 3lu2ial e3o6ada% J< Acción del 2iento% CF< Carga de nie2e% SeDeN< Modulo de sección en N% SeDe< Modulo de sección en %
Página 10 de 97 IUPSM-Caracas Proyecto Estructural de Acero y Madera (Sección B Cálculo de la acción del siso)
Para ello dee toarse en cuenta el 3orcentaDe de acción 2ariale @ < =0$ Para toar en consideración la acción del siso se a3lican las ecuaciones del EDercicio $%$ (1 y 7% &0$ CP ? C; ? SeDeN< &0$&& ? =0$15 ? 1= ? =04< $$50t < &0$&& ? =0$15 ? 4 ? =01=< $&5t < &0$&& ? =0$15 Q (1=?=04< 5&0t =09 CP ? S < =09&& ? 1= ? =04< &77t
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estructura% 'a coinación ás desa2orale corres3onde al caso II0 con una acción actori6ada de carga 3eranente0 carga 2ariale y nie2e sore el teco del ediicio0 donde no inluye ni la acción del 2iento no del siso% $%- Coo el ediicio no tiene 2oladi6os ori6ontales0 no corres3onde a3licar las ecuaciones :ue toan en cuenta ese caso% Cuando la Fora lo re:uiera0 se a3licaran los criterios sisoresistentes del EDercicio $%$ (9 y &=0 sin incluir los eectos ortogonales de las co3onentes s>sicas% Se ado3tará) R= < &0$ CP ? C; ? R=SO< &0$&& ? =0$15 ? $0< $$0t < &0$&& ? =0$15 - $0< 70t =09 CP ? R=SO < =09&& ? $0< $=&t < =09&& - $0< 1t Se concluye :ue) ,a3oco ,a3oco eiste tracción en la coluna ni 3eligro de 2olcaiento en la estructura%
Página 11 de 97 *iseLar una arra de oDo de acero AE$ :ue so3orta las siguientes cargas
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d3 < $ $9 T < &9% c a < < $= c V 4 d< = 4 T < $$% c Correcto d < $9%=1 c W d3 ? =%5 < $9%=5 c t < = X &$
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II ,racción en área neta eecti2a ∅t < =%7 Anco eecti2o) e < $t ? &1 < &&%1 c Yrea neta eecti2a) ee cti2a) Ane < $et < $&&%1 < &&1 c$ Ft < =%1 As.y < &&17== &&17== < 4$9%$t 4$9%$t ∅tFt < =%74$9%$ < $&%9t X Pu < $4=t III Corte en el área eecti2a ∅s < =%7 EDe3lo %&% *iseLo de Barra de #Do Autor) *a2id #coa
Página 12 de 97 Yrea Eecti2a) As < $t(a ? d3 $ T < $&&%1 $&&%1 < &&1 &&1 c$ Ft < =%1 As.y < =%14$== =%14$== < &7% ∅sFt < =%7$49%$$&%9 t X Pu < $4=t
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resistente% Para los 3ernos) d < &%9 c A < $%5 c$ (de la tala %&= Para el 3eril) < = c t < &%7 c t[ < & c I < & c Se ado3ta) a < 7% c < 7 c 'as cargas actori6adas son) Pu < &%$5%5 ? &%1&= < $1%1t En cada 3erno) . < $1%1 4 < 1%14 t *e la tala %9 se lee) ∅t < =%7 .t < 1= g8c$ En cada 3erno) ∅t"t < ∅t.tA < =%71=$%5 < &% t X 1%14 t Correcto Se calcula a continuación la uer6a \ deida al eecto de 3alanca) \<] &==7&%9
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Página 14 de 97 Controla M&% Por lo tanto M$ < $%47 tc y el es3esor >nio del ala del 3eril conectado será) t < ` 1Mn '=%9.y <` 1$47= &=%9$== < $%& c X &%7 c Insuiciente Por lo tanto0 3ara rigidi6ar la coneión se colocara una 3lanca interedia de reuer6o de coo uestra la igura
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"esulta) A %5 c$ Por lo tanto0 de la ,ala %&= se escogen los 3ernos) 785Z (con %579 c$ Controla Caso II Co3ortaiento aDo cargas actori6adas a ctori6adas Pu < &%$$$ ? &%1&4%5 < = t b2 < & < =% Por ser Su3ericie Clase B0 la ca3acidad resistente noinal se otiene) "ser < &%&=% ,4$ ====g *ee cu3lirse) , &&=1$ g En consecuencia0 se selecciona de la tala %4 el 3erno A $ $ cuyo , sea igual o su3erior al re:uerido0 y resulta el 84Z con , < &$7== g *e las diensiones de los 3ernos otenidos se deduce :ue controla el diseLo el estado l>ite aDo cargas de ser2icio0 3or lo cual los 3ernos a colocar serán los de 785Z% EDe3lo % Autor) *a2id #coa
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Por lo tanto) ∅2Pi2n < =%7$&51$ < &9$%44 t X &55 t Correcto EDe3lo %4 Autor) *a2id #coa
Página 18 de 97 EDe3lo % Elaorado 3or Angel SanoDa ;erii:ue si la unión de las 3lancas sola3adas de la igura0 en acero AE con ordes cortados a la laa y 1 3ernos de de T4Z es resistente al a3lastaiento0 aDo la acción de una carga) Pu< &1= t
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"n en cada 3erno) G3 "n< $04 d t .u < =07 $04 &09 %== < $5%$& g% En los 1 3ernos) G3 "n < $50$& 1< &19%$9= g X Pu < &1=%=== g (Correcto B 'a deoración en las 3eroraciones alrededor de los 3ernos no es una consideración de diseLo% Para cada 3erno cercano al orde0 segn ecuación) ] "n< 'e t .u W d t .u_ ecuación %$ Sustituye) "n< 'e t .u< 4 &0 =%== < %=== g W d t .u< &09&0 %==< 47%=$ g
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ordes cortados a la laa y 1 3ernos de de T4Z es resistente al a3lastaiento0 aDo la acción de una carga) Pu< &1= t "esistencia >nia de agotaiento en tracción AE0 .u< %== g8c$ (,ala (,ala &%$ *iáetro de los Pernos) d< &09= c% *istancia de los ordes) 'e< 4 c X &0=d < $05 c Paso) s< d < 07 c ay ás de dos 3ernos en la isa dirección de la uer6a% Corres3onde0 en consecuencia0 al caso I% Se anali6aran las consideraciones A y B%
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"n< 'e t .u< 4 &0 =%== < %=== g W d t .u< &09&0 %==< 47%=$ g Para los deás 3ernos0 segn ecuación)
Página 23 de 97 EDe3lo) % ] "n< (s - =0= d t .u W d t .u_ ecuación % Sustituyo) "n< (s - =0= d t .u < (07 Q =0 &09= &0= %== < 9%&55 W 47%=$ g (Bien
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=09 $= &0$ %$== < 19%&$= g 'a ca3acidad resistente 3ara el área gruesa del 3eril resulta) =09 &705 4%$== < 17%$54 g
Página 25 de 97 CAPI,U'# $ CA"HAS C"I,E"I#S *E *ISE+# EDe3lo $%$ *eterinar la coinación ás desa2orale de cargas actori6adas0 3ara una coluna de
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Página 26 de 97 E!EMP'# %5 PAH%& CAPACI*A* "ESIS,EF,E A ,"ACCIfF EF Y"EA FE,A Oallar la ca3acidad resistente 3or tracción en are neta0 e la coneión de las 3lancas sola3adas de la igura% 'a 3lanca su3erior es de acero *IF S, 4$ con .u < 4%$==
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Placa inerior B) A < $$ &05 < 901 c$ =05 A < 011 c$
Página 27 de 97 ,rayectoria 4) An4 < 901 Q $0 &05 < $10& c$ 011 c$ Bien
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At< árera total soetida a tracción Ant<área neta soetida a tracción
Página 29 de 97 En cada caso) A2<' ht An2<(' h-(F-=%dat -(F-=%dat *a
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e < 0 c 'e < & ,racción en area gruesa Para el 3eril) t Ft < t .y A < =09 $%== 05 < &$&0= t 5= t Para las 3lacas) t < t .y A < =09 %1== & &0 $ < &405 t 5= t $ Corte 3or a3lastaiento de los 3ernos
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t Ft& < t .u Ae < =07 %$== 01 < && t 5= t 4 A3lastaiento en los uecos de los 3ernos Se estia :ue la deoración en los aguDes es una consideración de diseLo% En este caso se cu3le) 'e < 4 c &0 d < &0 &01 < $04 c s < d ay 4 3ernos 3or ila
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a ;eriicación ;eriicación de la ca3acidad resistente a tracción de las 3lancas%
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*e ec% 4%$$) 3ara *e ,ala ,ala &%$)
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Ps< =%7 (7==K$=K&%$?=%1K$==K$K&$K&%$<99 ,on X 7% ,on
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Se ado3ta ' < && c 3ues se desestia la colaoración del retorno en la resistencia de
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