Retrofit of Steel Moment Frame Connections: Current Testing Program

TEORIA A COMPRESION1Desarrollado por: Scott CivjanUniversity of Massachusetts, Amherst

Traducido al Espaol: Por Fidel Copa Pineda, IC/UNSAAISC 2010LRFD/ASD1COLUMNA INDIVIDUAL2Initially its easiest to describe behavior of an individual column, then introduce the role and analysis of a column within an entire structure. The full structure can be conceptualized as varying the end conditions of individual columns.2CargasHasta completa fluencia de la seccin transversal33Cuando una columna corta es cargada la seccin transversal entra a la fluencia en forma completa.

En ausencia de esfuerzos residuales, Todas las fibras de la seccin fluyen simultneamente P/A=Fy.DFyAeyL0PPDL04PCrushing is often called the squash load, the load at which the entire cross section would yield.4La reduccin de rigidez efectiva de la seccin transversal da como resultado una curva, pero la carga ultima no sufre cambios.La reduccin de la rigidez efectiva puede influir en la aparicin de pandeo.5ESFUERZOS RESIDUALES5Con esfuerzos residuales, el patn fluye primero aP/A + esfuerzos residual = FyLa seccin transversal fluye gradualmente.

La rigidez se reduce en la primera fluencia.DFyAeyL0ESFUERZO RESIDUAL(Fy-Fres)AEfectos de esfuerzos Residuales6Sin esfuerzo residualPMaximum achieved load is therefore still P=AFy, but the load deflection curve is very different, stiffness is reduced.6Con esfuerzos residuales, el patn fluye primero aP/A + esfuerzos residual = FyLa seccin transversal fluye gradualmente.

La rigidez se reduce en la primera fluencia.DFyAeyL0ESFUERZO RESIDUAL(Fy-Fres)A1= Fluencia del acero1Efectos de esfuerzos Residuales7Sin esfuerzo residualPMaximum achieved load is therefore still P=AFy, but the load deflection curve is very different, stiffness is reduced.7Con esfuerzos residuales, el patn fluye primero aP/A + esfuerzos residual = FyLa seccin transversal fluye gradualmente.

La rigidez se reduce en la primera fluencia.DFyAeyL0ESFUERZO RESIDUAL(Fy-Fres)A1= Fluencia del acero122Efectos de esfuerzos Residuales8Sin esfuerzo residualPMaximum achieved load is therefore still P=AFy, but the load deflection curve is very different, stiffness is reduced.8Con esfuerzos residuales, el patn fluye primero aP/A + esfuerzos residual = FyLa seccin transversal fluye gradualmente.

La rigidez se reduce en la primera fluencia.DFyAeyL0ESFUERZO RESIDUAL(Fy-Fres)A1= Fluencia del acero12233Efectos de esfuerzos Residuales9Sin esfuerzo residualPMaximum achieved load is therefore still P=AFy, but the load deflection curve is very different, stiffness is reduced.9Con esfuerzos residuales, el patn fluye primero aP/A + esfuerzos residual = FyLa seccin transversal fluye gradualmente.

La rigidez se reduce en la primera fluencia.DFyAeyL0ESFUERZO RESIDUAL(Fy-Fres)A1= Fluencia del acero12233Efectos de esfuerzos Residuales104Sin esfuerzo residualP4Maximum achieved load is therefore still P=AFy, but the load deflection curve is very different, stiffness is reduced.10Pandeo de Euler1111Asunciones:La columna es articulada en sus extremos.La columna es inicialmente perfectamente recta.La carga est en centroide.El material es elstico lineal (sin fluencia).Curvas miembros sobre eje principal (sin torcer).Secciones planas permanecen planas.Teora pequea deflexin.12Pandeo de EulerA handout from any structural analysis text is worthwhile to show the derivation of the Euler Buckling Equation.12esEDP

Equilibrio EstablePunto de BifurcacinDPandeo de EulerP13At the bifurcation point the member is mathematically indifferent between carrying additional load with no deflection or deflecting with no additional load strength. However, any actual member will have some perturbation (slight out of straightness or imperfect end conditions, etc.) which will make additional load impossible. It is also important to note that while the load deflection plots are typically shown as above, the theory is only valid for small deflections. Therefore the plot does not accurately describe actual column behavior.13

Dependiente de Imin y L2.Independiente de Fy.LPE

Eje Menor al PandeoFor similar unbraced length in each direction, minor axis (Iy in a W-shape) will control strength.14Eje Mayor al PandeoPandeo de EulerEuler Buckling plot of strength versus column length for a W-shape note that each axis has a different strength the lowest controls. Often a demonstration of buckling of an I-shape foam beam or slender ruler is effective. Students intuitively understand the controlling buckling axis-this plot provides a descriptive justification.14PE = divide by A, PE/A = , then with r2 = I/A,PE/A = FE =FE=Esfuerzo de Pandeo de Euler elsticoL/r=Relacin de Esbeltez

Rescrito en trminos de Esfuerzos:15Pandeo de Euler15

Buckling controlled by largest value of L/r. Most slender section buckles first.L/rFE

Fy16Pandeo de EulerFor a given column length, the maximum value of L/r will occur when r is a minimum.For a given column shape, the maximum value of L/r will occur when L is a maximum16SUPOSICIONES de EULER (COMPORTAMIENTO ACTUAL)17170 = Deflexin inicial en el centro de LuzDeformada inicial / Fuera de la rectaPPM = PDoDo18DoFirst, what are the effects of a column that is not perfectly straight as expected by the Euler Buckling derivation? ASTM limits are noted to show that these are expected in an actual shape. The ASTM limits may change in the future, but the concept is the same regardless of the limiting value. An initial displacement D0, causes an initial moment along the length of the section, Pd. This is greatest at the location of maximum deflection. Elastic theory then predicts the solid line in the plot to the right. Actual behavior, shown as the dashed line, is due to the additional effects of inelastic behavior. Yielding occurs from a combination of stresses due to moment and axial loads.18DP

Do= 0Do19Deformada inicial / Fuera de la recta19DP

Do= 0DoElastic theory20Deformada inicial / Fuera de la recta20DP

Do= 0DoTeora Elstica21Comportamiento ActualDeformada inicial / Fuera de la recta21Pandeo no es instantneo.ASTM limite de 0=L/1000 0.25 en 20 piesValores Tpicos son 0=L/1500 0.15 en 20 piesEsfuerzos adicionales debido a la flexin de la columna,P/A Mc/I.Suponiendo la teora de material elstico (nunca fluye), P se aproxima a PE.En Realidad, Algunas Perdidas de Resistencia Pequeo 0 => perdidas de resistencia pequea Grande 0 => la perdida de resistencia es importante22Deformada inicial / Fuera de la rectaThe first of these (along with the ductility of steel shapes) usually allows for some warning prior to a column failure. It also means that a column limited by buckling does not exhibit the classical instantaneaous buckling failure at a bifurcation point.22DPeLDCarga Excntrica23DP

Do= 0Teora ElsticaAn initial load eccentricity, e, causes an initial moment along the length of the section, (Pe at the top). This is a similar effect to that of an initial out-of-straightness, namely the introduction of a moment in addition to the purely axial loading. Elastic theory then predicts the solid line in the plot to the right. Actual behavior, shown as the dashed line, is due to the additional effects of inelastic behavior. Yielding occurs from a combination of stresses due to moment and axial loads.23DPeLDCarga Excntrica24DP

Do= 0Teora ElsticaComportamiento ActualAn initial load eccentricity, e, causes an initial moment along the length of the section, (Pe at the top). This is a similar effect to that of an initial out-of-straightness, namely the introduction of a moment in addition to the purely axial loading. Elastic theory then predicts the solid line in the plot to the right. Actual behavior, shown as the dashed line, is due to the additional effects of inelastic behavior. Yielding occurs from a combination of stresses due to moment and axial loads.24Si el momento "significativo" la seccin debe ser diseada como un miembro sometido a cargas combinadas.El Pandeo no es Instantneo.Esfuerzos adicionales debido a la flexin de la columna, P/A Mc/I.Suponiendo la teora de material elstico (nunca fluye), P se aproxima a PE.En Realidad, Algunas Perdidas de Resistencia: Pequeo e=> pequea perdida de resistencia Grandee=> perdida de resistencia sustancial25Carga ExcntricaNote that significant moment is difficult to define. Most computer software design all members as beam-columns. The latter slides on columns address analysis methods where sections are analyzed as beam-columns for all cases. It is good to have students start thinking about the effects of moment on axial member design so they understand the concepts when beam-columns are introduced.25

Similar a pin-pin, con L = L/2.Carga de Soporte = 4 veces mas grande.EJEMPLOKLSe resuelve por equilibrio y de manera similar a la derivacin del pandeo de Euler. Determine un factor KExtremos Restringidos (Fijos)26A derivation of the above example is provided in many structural analysis texts subsequent to the Euler Buckling strength derivation, and is found similarly. Charts of effective lengths and K-factors can be found in steel design texts and the AISC code as well. 26Longitud equivalente con extremos con pines columna con similar carga de pandeo elstico,Longitud Efectiva = KLExtremos Restringidos (Fijos)Distancia entre puntos de inflexin en el perfil deformado.2727Ver Folleto sobre factores K:EquivalentLength.pdf

2828KL/r

Efectos Material Inelsticos29Compression TheoryElastic BehaviorInelastic action reduces column strength for lower values of KL/r. The maximum possible strength is the crushing limit, where all of the cross section attains Fy. Using tangent modulus theory, we can use a reduced modulus of elasticity, Et in the Euler Buckling equation. Et is obtained from a Stub Column (very short section in compression) test as shown on the previous page. Alternatively, one could assume that the entire cross section continues to have a material property, E, but that all yielded portions of the cross section are no longer effective, reducing I. In other words, ET = (Ie/I)E where Ie = I of non-yielded cross section. The end result is similar, as it is the combined stiffness parameter EI that controls the buckling strength. 29FyET= Modulo TangenteE(Fy-Fres)esResultados de pruebas de Columnas axialmente cargados30Efectos Material InelsticoInelastic material effects occur whenever axial stress in any portion of the cross section exceeds the first yield of the material (including residual stresses). This also compounds effects of out of straightness and load eccentricity, as the bending moment term introduced also results in longitudinal stresses.30KL/r

s31Compression TheoryFy-FresFy

Inelstico

ElsticoEfectos Material InelsticoInelastic action reduces column strength for lower values of KL/r. The maximum possible strength is the crushing limit, where all of the cross section attains Fy. Using tangent modulus theory, we can use a reduced modulus of elasticity, Et in the Euler Buckling equation. Et is obtained from a Stub Column (very short section in compression) test as shown on the previous page. Alternatively, one could assume that the entire cross section continues to have a material property, E, but that all yielded portions of the cross section are no longer effective, reducing I. In other words, ET = (Ie/I)E where Ie = I of non-yielded cross section. The end result is similar, as it is the combined stiffness parameter EI that controls the buckling strength. 31KL/r

s32Fy-FresFy

InelsticoElsticoEfectos Material InelsticoInelastic action reduces column strength for lower values of KL/r. The maximum possible strength is the crushing limit, where all of the cross section attains Fy. Using tangent modulus theory, we can use a reduced modulus of elasticity, Et in the Euler Buckling equation. Et is obtained from a Stub Column (very short section in compression) test as shown on the previous page. Alternatively, one could assume that the entire cross section continues to have a material property, E, but that all yielded portions of the cross section are no longer effective, reducing I. In other words, ET = (Ie/I)E where Ie = I of non-yielded cross section. The end result is similar, as it is the combined stiffness parameter EI that controls the buckling strength. 32Pandeo Elstico: ET = E No hay fluencia antes de pandeoFe Fy-Fres(max)Fe = Pandeo predicho (PANDEO DE EULER)Dos Clases de Pandeo: Pandeo Inelstico :Alguna fluencia/prdida de rigidez antes de pandeoFe > Fy-Fres(max)Fc = Pandeo predicho (PANDEO INELASTICO)33Efectos Material Inelstico33FyKL/r

Datos ExperimentalesResistencia total Columna34In general, the differences observed in testing of columns from Euler Buckling predicted capacities are as follows: Columns of low slenderness ratios are governed by inelastic buckling, and limited by crushing capacities. Columns of high slenderness ratios are limited by out of straightness effects. Columns of intermediate slenderness ratios see a combination of these effects.34FyKL/r

Experimental DataEfectos materiales inelsticosIncluyendo los esfuerzos residualesFuera de RectitudResistencia total Columna35In general, the differences observed in testing of columns from Euler Buckling predicted capacities are as follows: Columns of low slenderness ratios are governed by inelastic buckling, and limited by crushing capacities. Columns of high slenderness ratios are limited by out of straightness effects. Columns of intermediate slenderness ratios see a combination of these effects.35Los principales factores que determinan la resistencia:1) esbeltez (L/r).2) La restriccin de los extremos factores K).3) curvatura inicial o la excentricidad de la carga.4) Antes de Esfuerzos fluencia o residual.Resistencia total ColumnaLos ltimos 2 artculos son muy variables entre muestras.3636PANDEO LOCAL3737Pandeo local se relaciona con el pandeo de placaEl ala es restringida por una arista del almaLa falla es localizada en reas de alto esfuerzo(mximo momento) o imperfecciones..38Restriccin Parcial del Alma38Pandeo local se relaciona con el pandeo de placaEl ala es restringida por una arista del almaLa falla es localizada en reas de alto esfuerzo(mximo momento) o imperfecciones.39Restriccin Parcial del Alma39Pandeo local se relaciona con el pandeo de placaEl ala es restringida por una arista del alma.40La falla es localizada en reas de alto esfuerzo(mximo momento) o imperfecciones.Restriccin Parcial del Alma40Pandeo local se relaciona con el pandeo de placaLa falla es localizada en reas de alto esfuerzo(mximo momento) o imperfecciones.El alma es restringida por las aristas del ala.41Restriccin Parcial del AlaRestriccin Parcial del Ala41Pandeo local se relaciona con el pandeo de placaLa falla es localizada en reas de alto esfuerzo(mximo momento) o imperfecciones.El alma es restringida por las aristas del ala.42Restriccin parcial del las alasPandeo predicho Restriccin parcial del las alas42Pandeo local se relaciona con el pandeo de placaLa falla es localizada en reas de alto esfuerzo(mximo momento) o imperfecciones.El alma es restringida por las aristas del ala.43

43COMPORTAMIENTO ESTRUCTURAL COMPLETO44Compression TheoryColumn within a full structure will first be described as affecting the end conditions of a single column. Next the approach of full structure behavior including nominal forces (Direct Analysis Method) is introduced. This is covered in more detail in the Beam-Column design module.44NOMOGRAMAOMETODOS ANALISIS DIRECTO45Compression TheoryThe instructor must decide how they wish to proceed here both methods are presented and the instructor can select one or the other as their primary method. The alignment chart is a more classical method, wherein structural interactions are included as end restraint on individual columns. Column design then proceeds as for an individual column but with a revised K factor. This is the more traditional approach and is covered in most text books.Alternatively, Direct Analysis Methods are more common in international codes and are now introduced in AISC publications, with the likelihood of being the dominant design method in the future. This method is also easier to program for analysis and design in typical software packages. In this method, all members are designed as beam-columns with a K factor of 1.0. However, to account for structure interaction a series of notional loads are applied to the structure to develop moments in all columns, and these combined forces are calibrated to column capacities with K=1. As will be shown in beam-column modules these loads are based on rational principles, but require a slight leap of faith from the students to accept their values. If this method is chosen for instruction, it may be preferable to skip to beam-column design directly after addressing single column behavior and design.Ideally both methods would be introduced, with an assignment comparing results for students to determine acceptability of the notional load values. Alignment chart procedures are often simpler for students to grasp conceptually while Direct Analysis methods easier for them to apply in a design.45Acaso no redistribuir la restriccin de momentos en trabes / vigas.CARTA DE ALINEAMIENTOMetodo TradicionalDetermine la longitud efectiva, KL, para cada columna.Bases para el diseo similar a las columnas individuales.46The alignment chart is a more classical method, wherein structural interactions are included as end restraint on individual columns. Column design then proceeds as for an individual column but with a revised K factor. This is the more traditional approach and is covered in most text books.46METODO DE ANALISIS DIRECTOAnlisis Estructural de interaccin completa.Incluye cargas Laterales NocionesTodos los elementos deben ser evaluados bajo el efecto combinado de flexin y carga.No son requeridos los valores K.Reduce la rigidez de la estructura.47Alternatively, Direct Analysis Methods are more common in international codes and are now introduced in AISC publications, with the likelihood of being the dominant design method in the future. This method is also easier to program for analysis and design in typical software packages. In this method, all members are designed as beam-columns with a K factor of 1.0. However, to account for structure interaction a series of notional loads are applied to the structure to develop moments in all columns, and these combined forces are calibrated to column capacities with K=1. As will be shown in beam-column modules these loads are based on rational principles, but require a slight leap of faith from the students to accept their values. If this method is chosen for instruction, it may be preferable to skip to beam-column design directly after addressing single column behavior and design.47CARTA DE ALINEAMIENTOSe utiliza para los siguientes diapositivas48Compression TheoryThe instructor must decide how they wish to proceed here both methods are presented and the instructor can select one or the other as their primary method. The alignment chart is a more classical method, wherein structural interactions are included as end restraint on individual columns. Column design then proceeds as for an individual column but with a revised K factor. This is the more traditional approach and is covered in most text books.Alternatively, Direct Analysis Methods are more common in international codes and are now introduced in AISC publications, with the likelihood of being the dominant design method in the future. This method is also easier to program for analysis and design in typical software packages. In this method, all members are designed as beam-columns with a K factor of 1.0. However, to account for structure interaction a series of notional loads are applied to the structure to develop moments in all columns, and these combined forces are calibrated to column capacities with K=1. As will be shown in beam-column modules these loads are based on rational principles, but require a slight leap of faith from the students to accept their values. If this method is chosen for instruction, it may be preferable to skip to beam-column design directly after addressing single column behavior and design.Ideally both methods would be introduced, with an assignment comparing results for students to determine acceptability of the notional load values. Alignment chart procedures are often simpler for students to grasp conceptually while Direct Analysis methods easier for them to apply in a design.48CARTA DE ALINEAMIENTOMtodo TradicionalDetermine longitud efectiva, KL, para cada columna.Bases para el diseo similar a columna individual.Acaso no redistribuir la restriccin de momentos en trabes / vigas.49The alignment chart is a more classical method, wherein structural interactions are included as end restraint on individual columns. Column design then proceeds as for an individual column but with a revised K factor. This is the more traditional approach and is covered in most text books.49K-FACTORS FOR END CONSTRAINTSNo Joint Translation Allowed Sidesway Inhibited0.5 K 1.0Joint Translation Allowed Sidesway Uninhibited1.0 K 50Compression Theory50K-FACTORES DE RESTRICCIONES DE EXTREMOComportamiento individual de una columna sin cambios.(Marco se limita a establecer las condiciones finales).Dos categoras:Prtico Arriostrado, 0.5 K 1.0Marco sin arriostrar, K 1.05151Los Pisos no se trasladan entre s en el plano.Normalmente, los miembros estn conectados con articulaciones para ahorrar costes.52Portico Arriostrado52Compression Theory53

Supongamos trabe / viga infinitamente rgida o flexible en comparacin con columnas a los resultados limitesK=0.7K=0.5K=1K=0.754Prticos Arriostrados54Shear WallIdealizadoEquivalente55Prticos ArriostradosNote that even a brace or shear wall braces all attached nodes within the story if they are connected and therefore act as bracing to linked columns.55Shear WallIdealizadoEquivalente56Prticos ArriostradosNote that even a brace or shear wall braces all attached nodes within the story if they are connected and therefore act as bracing to linked columns.56Shear WallIdealizadoEquivalente57Compression TheoryPrticos ArriostradosNote that even a brace or shear wall braces all attached nodes within the story if they are connected and therefore act as bracing to linked columns.57Por lo general, los miembros estn articulados en sus extremos para ahorrar costes (K = 1).Si los miembros incluyen conexiones rgidas,Mtodo Carta Alineamiento para explicar la restriccin de rotacin para ahorrar costes (K < 1).El Diseo tpico asumir K=1 como lmite superior conservador (real K0.8 no hay mucha diferencia de K=1 en el diseo).58Prticos Arriostrados58Los pisos pueden trasladarse con respecto el uno al otro en el plano.Suficientes miembros estn fijados para proporcionar estabilidad.Nmero de marcos momento escogido para proporcionar una distribucin razonable de la fuerza y la redundancia.59Prticos No Arriostrados59Supongamos trabe / viga infinitamente rgida o flexible en comparacin con columnas a los resultados limites.K=2K=1K = K=260Compression TheoryPrticos No Arriostrados60Portico a momentos61Compression TheoryPrticos No ArriostradosNote that even a single moment frame braces all attached nodes within the story if they are connected though the rest of the structure is just along for the ride.6162Compression TheoryPortico a momentosPrticos No ArriostradosNote that even a single moment frame braces all attached nodes within the story if they are connected though the rest of the structure is just along for the ride.6263Compression TheoryPortico a momentosPrticos No ArriostradosNote that even a single moment frame braces all attached nodes within the story if they are connected though the rest of the structure is just along for the ride.63Calcular G superior e inferior de la columna (GA y GB).G es inversamente proporcional al grado de restriccin de rotacin en los extremos de columna.I=momento de inercia de los miembrosL=longitude de los miembros entre nudos

64Carta de Alineamiento64Carta de AlineamientoCartas para Prticos con desplazamiento lateral inhibido y desinhibido

Sidesway Inhibited (desplazamiento lateral inhibido) (Braced Frame) Portico ArriostradoSidesway UnInhibited (desplazamiento lateral desinhibido) (Sway Frame) Portico Arriostrado6565

66GtopXGInferiorXGsuperiorXGInferiorXSidesway Inhibited (desplazamiento lateral inhibido) (Braced Frame) Portico ArriostradoSidesway Inhibited (desplazamiento lateral inhibido) (Braced Frame) Portico ArriostradoCarta de AlineamientoCartas para desplazamiento lateral: inhibido y desinhibido66Carta de Alineamiento

67KKSidesway Inhibited (desplazamiento lateral inhibido) (Braced Frame) Portico ArriostradoSidesway Inhibited (desplazamiento lateral inhibido) (Braced Frame) Portico ArriostradoGsuperiorXGInferiorXGsuperiorXGInferiorXCartas para desplazamiento lateral inhibido y desinhibido67Usando la rigidez En-PLANO Ix si el eje de la direccin es mayor, Iy si el eje es menor. Trabes/Vigas son tpicamente flexin alrededor de Ix cuando la restriccin de la columna es considerada.Slo se incluyen los miembros con nudos rgidos (miembros con extremos articulados no estn incluidos en los clculos de G).Si la base es articulada tericamente G = . AISC recomienda usar 10.Si la base es empotrada tericamente G = 0. AISC recomienda usar 1.68Carta de Alineamiento68CARTA DE ALINEAMIENTO HIPOTESIS:El comportamiento es puramente elstico.Todos los miembros tienen una seccin transversal constante.Todas las juntas son rgidas.Desplazamiento lateral inhibida (Braced) - curvatura simple flexin de vigas.Desplazamiento lateral desinhibido (Sway) - curvatura inversa flexin de vigas.Parmetro de rigidez de todas las columnas es igual.Restriccin del nudo se distribuye a las columnas superior e inferior del nudo en proporcin al EI/L de las columnas.Todas las columnas pandean simultneamente.Ninguna fuerza de compresin axial significativa existe en las vigas.69Carta de Alineamiento69Vamos a evaluar las hiptesis.70Carta de Alineamiento70CARTA DE ALINEAMIENTO HIPOTESIS:El comportamiento es puramente elstico.Todos los miembros tienen una seccin transversal constante.Todas las juntas son rgidas.Desplazamiento lateral inhibida (Braced) - curvatura simple flexin de vigas.Desplazamiento lateral desinhibido (Sway) - curvatura inversa flexin de vigas.Parmetro de rigidez de todas las columnas es igual.Restriccin del nudo se distribuye a las columnas superior e inferior del nudo en proporcin al EI/L de las columnas.Todas las columnas pandean simultneamente.Ninguna fuerza de compresin axial significativa existe en las vigas.71Carta de Alineamiento71Si el comportamiento de la columna es inelstica,La fluencia disminuye la rigidez de la columna.Las vigas aumentan la restriccin relativa del nudo .Por lo tanto, G disminuye, como lo hace K.Si decrece suele ser poco.Conservadoramente ignore los efectos.Pueden considerarse los efectos mediante el uso de un factor de reduccin de rigidez, t, veces G.(SRF Tabla 4-21, pag 4-317)72Carta de Alineamiento7273Carta de AlineamientoCARTA DE ALINEAMIENTO HIPOTESIS:El comportamiento es puramente elstico.Todos los miembros tienen una seccin transversal constante.Todas las juntas son rgidas.Desplazamiento lateral inhibida (Braced) - curvatura simple flexin de vigas.Desplazamiento lateral desinhibido (Sway) - curvatura inversa flexin de vigas.Parmetro de rigidez de todas las columnas es igual.Restriccin del nudo se distribuye a las columnas superior e inferior del nudo en proporcin al EI/L de las columnas.Todas las columnas pandean simultneamente.Ninguna fuerza de compresin axial significativa existe en las vigas.73Estas condiciones se pueden considerar directamente, pero en general se evitan en el diseo.Restriccin parcial de las conexiones y de los miembros no uniformes cambiar la rigidez rotacional efectiva en las conexiones.Slo se incluyen los miembros con nudos rgidos (miembros con extremos articulados no estn incluidos en los clculos de G).74Carta de Alineamiento7475Carta de AlineamientoCARTA DE ALINEAMIENTO HIPOTESIS:El comportamiento es puramente elstico.Todos los miembros tienen una seccin transversal constante.Todas las juntas son rgidas.Desplazamiento lateral inhibida (Braced) - curvatura simple flexin de vigas.Desplazamiento lateral desinhibido (Sway) - curvatura inversa flexin de vigas.Parmetro de rigidez de todas las columnas es igual.Restriccin del nudo se distribuye a las columnas superior e inferior del nudo en proporcin al EI/L de las columnas.Todas las columnas pandean simultneamente.Ninguna fuerza de compresin axial significativa existe en las vigas.75Clculo de G representa la restriccin rigidez rotacional en cada nudo basado en una presunta flexin.

Para otras condiciones de incluir un factor de correccin "m" para dar cuenta de la rigidez de rotacin real de la viga en el nudo.76Carta de Alineamiento76Extremo lejano articuladoRigidez a la Flexion=Rigidez a la Flexion =Rigidez a la Flexion =Desplazamiento lateral inhibido (Braced) ArriostradoAsuncin: curvatura simple flexin de la viga.Extremo lejano empotrado77

m = (3EI/L)/(2EI/L) = 1.5m = (4EI/L)/(2EI/L) = 2

Carta de Alineamiento77Extremo articuladoDesplazamiento lateral Sin restriccin (Sway)Asuncin: curvatura inversa a la flexin de la viga.Extremo empotradoRigidez por flexion =Rigidez por flexion= Rigidez por flexion =78

m = (3EI/L)/(6EI/L) = 1/2

m = (4EI/L)/(6EI/L) = 2/3Carta de Alineamiento7879Carta de AlineamientoCARTA DE ALINEAMIENTO HIPOTESIS:El comportamiento es puramente elstico.Todos los miembros tienen una seccin transversal constante.Todas las juntas son rgidas.Desplazamiento lateral inhibida (Braced) - curvatura simple flexin de vigas.Desplazamiento lateral desinhibido (Sway) - curvatura inversa flexin de vigas.Parmetro de rigidez de todas las columnas es igual.Restriccin del nudo se distribuye a las columnas superior e inferior del nudo en proporcin al EI/L de las columnas.Todas las columnas pandean simultneamente.Ninguna fuerza de compresin axial significativa existe en las vigas (Trabes).79Diseo general se comprueba para cada piso independientemente, con base en estas suposiciones.En general, las columnas se eligen para ser de un tamao similar para ms de un piso. Para cada seccin de la columna esto resulta en secciones con resistencia adicional en plantas superiores, y cerca de su resistencia en los pisos inferiores.Las condiciones actuales se pueden registran directamente, pero en general son ignorados en el diseo.80Carta de Alineamiento8081Carta de AlineamientoCARTA DE ALINEAMIENTO HIPOTESIS:El comportamiento es puramente elstico.Todos los miembros tienen una seccin transversal constante.Todas las juntas son rgidas.Desplazamiento lateral inhibida (Braced) - curvatura simple flexin de vigas.Desplazamiento lateral desinhibido (Sway) - curvatura inversa flexin de vigas.Parmetro de rigidez de todas las columnas es igual.Restriccin del nudo se distribuye a las columnas superior e inferior del nudo en proporcin al EI/L de las columnas.Todas las columnas pandean simultneamente.Ninguna fuerza de compresin axial significativa existe en las vigas (Trabes).81Este caso se abordar en primer lugar, con el concepto vlido para condiciones generales, as.En un entrepiso no todas las columnas sern cargadas a su plena capacidad.Algunas estn dispuestas a pandear, mientras que otros tienen una resistencia adicional.Un caso extremo de esto es una columna Leaner (Delgada).82Carta de Alineamiento82COLUMNASDelgadasLEANER83Compression Theory83Columnas LeanerPara obtener esta estructura observe que las columnas de la derecha se articulan en cada conexin, y no proporcionan ninguna restriccin por flexin.84Portico MomentosLeaner Columnas84Tericamente, la columna tiene un KL infinita.Por lo tanto, la fuerza debe ser cero.

Para Columnas Leaner:

G top = InfinitoG bottom= Infinito

Por lo tanto K= Infinito

KL= Infinito

As que la columna no tiene resistencia de acuerdo al nomograma85Columnas LeanerNomograma prtico no arriostrado 85Prtico a MomentosColumnasLeanerConsidere aplicar slo una pequea carga a las columnas de la derecha86Columnas Leaner86Prtico a MomentosColumnasLeanerConsidere aplicar slo una pequea carga a las columnas de la derecha87Columnas LeanerSin duda, una carga pequea se puede aplicar sin causar inestabilidad! (Debido a la conexin con el resto de la estructura).87PA K = infinitofPn=ceroPA K< infinitofPn>ceroCondicin RealCartaA condicin de que el marco momento no se ha cargado a su total capacidad, que puede proporcionar una cierta restriccin lateral a las columnas ms delgadas. Esto se indica por el resorte en la figura arriba.88Columnas Leaner88PTenga en cuenta que el resultado de una fuerza vertical tratando de trasladarse a travs del desplazamiento, D, es una carga lateral de valor PD/H aplicada al sistemaDPD/HHPD/HP89Columnas Leaner89leaner1234P1P2P3P4P = PeP=P1+P2+P3+P4Pe=P1e+P2e+P3e+P4e=P1e+P4eEn el estado del rango elstico, el concepto Sumatoria de Fuerzas da la capacidad total de las columnas y pueden ser re-distribuidas.90Columnas Leaner90leaner1234P1P2P3P4Si: P2 = P2eAlcanzar la falla, incluso siP < Pe Sin embargo, la carga total en una columna ms delgada an no debe exceder la resistencia de prtico arriostrado.91Leaner Columns91Se debe considerar un sistema de columnas para cada piso.Diseo actual considera el comportamiento inelstico de las secciones, pero el concepto bsico es el mismo.La resistencia de piso es la carga que hara que todas las columnas se balanceen.de una columna individual es la carga que sera hacer que Pandee en el modo y sin desplazamiento (K=1).92Columnas Leaner92VER VIDEOSDE EJEMPLO DEMOSTRATIVOS DE YURA9393En general, cada piso es un sistema de columnas que se cargan a grados variables de su resistencia limite.

Los que tienen resistencia adicional pueden proporcionar soporte lateral a los que estn en su resistencia al pandeo desplazamiento lateral.

Una vez alcanzado el lmite de restriccin contra el pandeo lateral, el piso completo mostrar desplazamiento lateral de pandeo.94Carta de Alineamiento9495CARTA DE ALINEAMIENTO HIPOTESIS:El comportamiento es puramente elstico.Todos los miembros tienen una seccin transversal constante.Todas las juntas son rgidas.Desplazamiento lateral inhibida (Braced) - curvatura simple flexin de vigas.Desplazamiento lateral desinhibido (Sway) - curvatura inversa flexin de vigas.Parmetro de rigidez de todas las columnas es igual.Restriccin del nudo se distribuye a las columnas superior e inferior del nudo en proporcin al EI/L de las columnas.Todas las columnas pandean simultneamente.Ninguna fuerza de compresin axial significativa existe en las vigas (Trabes).Carta de Alineamiento95La Carga axial reduce la rigidez a la flexin de una seccin.

En vigas, se cuenta para ello con una factor de reduccin de EI/L. 96Carta de Alineamiento96Si la carga de flexin predomina, considere el miembros de una "viga" con la reduccin de la rigidez rotacional en la junta (reduccin de la carga axial).Si la carga axial domina, considere miembros de una "columna" con resistencia adicional para evitar que el entrepiso se pandee (suma de las fuerzas de aproximacin).Es til pensar en trminos de los miembros controlados por la fuerza axial o de flexin, en lugar de "vigas" y "columnas".97Carta de Alineamiento97METODO de ANALISIS DIRECTO ES USADO PARA LOS SIGUIENTE SLIDES9898METODO de ANALISIS DIRECTO (analisis estructural de segundo orden)Analisis completo de la Interaccion de la estructura.Incluye cargas laterales.No requiere hallar valores de K.Reduce la rigidez de la estructura.99Alternatively, Direct Analysis Methods are more common in international codes and are now introduced in AISC publications, with the likelihood of being the dominant design method in the future. This method is also easier to program for analysis and design in typical software packages. In this method, all members are designed as beam-columns with a K factor of 1.0. However, to account for structure interaction a series of notional loads are applied to the structure to develop moments in all columns, and these combined forces are calibrated to column capacities with K=1. As will be shown in beam-column modules these loads are based on rational principles, but require a slight leap of faith from the students to accept their values. If this method is chosen for instruction, it may be preferable to skip to beam-column design directly after addressing single column behavior and design.99METODO de ANALISIS DIRECTOUna evaluacin ms profunda de este mtodo se incluye en el mdulo sobre "cargas combinadas."100Traducido al EspaolPor: Fidel Copa Pineda, IC/UNSA

100Compression Manual

AISC 14 Edicion101Miembros a Compresin:Captulo E: Resistencia a la compresin.Captulo I: Fuerza de Miembros Compuestos.Parte 4: Diseo Grficos y Tablas.Captulo C: Anlisis de Temas.102102Compression AISC Manual 14th EdPandeo Local:Los criterios de la Tabla B4.1.Resistencia en el Captulo E: Los miembros con elementos esbeltos.103103Compression AISC Manual 14th Ed

Criterios de Pandeo LocalEsbeltez del ala y el alma, l, se utilizan como criterios para determinar si el pandeo local puede controlar en el rango elstico o inelstico, de lo contrario controlan los criterios globales de pandeo.

Criterios r se basan en la teora de pandeo placa.Para Perfiles WFLB, = bf /2tf rf = WLB, = h/tw rw =

104Depends on 2 variables:1)Width to thickness ratio of flange and/or web and 2)FyValues are more stringent from those provided for beams, as the entire section is under full compression, and therefore less likely to provide restraint to the adjacent sections. In a W-shape beam bent about the major axis, only part of the web is in compression, and the value is minimal near the centroid, allowing the web to provide additional restraint to the flanges. Also, the web in such a beam is only partially under compression, so is much less likely to buckle than in a compressive member.104Compression AISC Manual 14th Ed > r elemento esbelto

Falla por pandeo local, se presenta.Cubierto en la Seccin E7Muchas secciones W-perfiles rolados estn dimensionados de tal manera que los controlan a todos los criterios globales.105Pandeo LocalIn general practically all W-shapes are non-slender as compression members, so this is covered as an advanced topic only.May control if high Fy, welded shapes, shapes not generally used for compression (such as angles, WT, etc.)105Compression AISC Manual 14th EdCaptulo E:Resistencia a la Compresin106106Compression AISC Manual 14th Edfc= 0.90 (Wc= 1.67)107Resistencia a la compresin107Compression AISC Manual 14th EdEspecificacin considera las siguientes condiciones:pandeo por flexinpandeo torsionalPandeo por flexin-torsin108Resistencia a la compresinNote that for W-shape and tube members, only global flexural buckling needs to be checked108Compression AISC Manual 14th EdResistencia a la compresin109109Compression AISC Manual 14th EdLas siguientes diapositivas asumen:Patn no esbelto y secciones del almaMiembros con simetra doble110Resistencia a la compresinThis corresponds to simply supported beams which include a floor slab. The majority of beams fall into this easy to design category.110Compression AISC Manual 14th EdDado que los miembros no son esbeltos y doblemente simtrico,a la flexin (global de) pandeo es la ms probable modo de fallo potencial antes de alcanzar la carga al pandeo.Resistencia de pandeo depende de la esbeltez de la seccin, que se define como KL/r.Resistencia se define como Pn= FcrAg Ecuacin E-3.1111Resistencia a la compresinEquation E3-1 defines the strength as an effective critical stress times the gross area of the cross section. Fcr is therefore limited to Fy, which would indicate the squash load.111Compression AISC Manual 14th EdFe = esfuerzo pandeo elstico (Euler), ecuacin E3-4 Si , luego Fcr = 0.877Fe

Ecuacin E3-3 Esto define el lmite de pandeo "elstico"con un factor de reduccin, 0.877, veces el lmite terico. Si, a continuacin, la Ecuacin E3-2define el lmite de pandeo "inelstico".

112112Compression AISC Manual 14th EdKL/r

s113Comportamiento ElsticoEfectos de Material InelsticoInelastic action reduces column strength for lower values of KL/r. The maximum possible strength is the crushing limit, where all of the cross section attains Fy. Using tangent modulus theory, we can use a reduced modulus of elasticity, Et in the Euler Buckling equation. Et is obtained from a Stub Column (very short section in compression) test as shown on the previous page. Alternatively, one could assume that the entire cross section continues to have a material property, E, but that all yielded portions of the cross section are no longer effective, reducing I. In other words, ET = (Ie/I)E where Ie = I of non-yielded cross section. The end result is similar, as it is the combined stiffness parameter EI that controls the buckling strength. 113Compression AISC Manual 14th EdKL/r

s114Fy-FresFy

InelsticoElsticoEfectos de Material InelsticoInelastic action reduces column strength for lower values of KL/r. The maximum possible strength is the crushing limit, where all of the cross section attains Fy. Using tangent modulus theory, we can use a reduced modulus of elasticity, Et in the Euler Buckling equation. Et is obtained from a Stub Column (very short section in compression) test as shown on the previous page. Alternatively, one could assume that the entire cross section continues to have a material property, E, but that all yielded portions of the cross section are no longer effective, reducing I. In other words, ET = (Ie/I)E where Ie = I of non-yielded cross section. The end result is similar, as it is the combined stiffness parameter EI that controls the buckling strength. 114Compression AISC Manual 14th EdKL/r

s115Fy-FresFy

InelsticoElsticoEfectos de Material InelsticoInelastic action reduces column strength for lower values of KL/r. The maximum possible strength is the crushing limit, where all of the cross section attains Fy. Using tangent modulus theory, we can use a reduced modulus of elasticity, Et in the Euler Buckling equation. Et is obtained from a Stub Column (very short section in compression) test as shown on the previous page. Alternatively, one could assume that the entire cross section continues to have a material property, E, but that all yielded portions of the cross section are no longer effective, reducing I. In other words, ET = (Ie/I)E where Ie = I of non-yielded cross section. The end result is similar, as it is the combined stiffness parameter EI that controls the buckling strength. 115Compression AISC Manual 14th EdKL/r

s116FyInelsticoElsticoEfectos de Material Inelstico

0.44FyInelastic action reduces column strength for lower values of KL/r. The maximum possible strength is the crushing limit, where all of the cross section attains Fy. Using tangent modulus theory, we can use a reduced modulus of elasticity, Et in the Euler Buckling equation. Et is obtained from a Stub Column (very short section in compression) test as shown on the previous page. Alternatively, one could assume that the entire cross section continues to have a material property, E, but that all yielded portions of the cross section are no longer effective, reducing I. In other words, ET = (Ie/I)E where Ie = I of non-yielded cross section. The end result is similar, as it is the combined stiffness parameter EI that controls the buckling strength. 116COMPRESION AISC Manual 14 Edicion117Developed by Scott CivjanUniversity of Massachusetts, Amherst

Traducido por: Fidel Copa Pineda, iC/UNSA117Compression AISC Manual 14th EdDesign AidsTable 4-22fcFcr as a function of KL/rTables 4-1 to 4-20fcPn as a function of KLyUseful for all shapes.Larger KL/r value controls.Can be applied to KLx by dividing KLy by rx/ry.118118Compression AISC Manual 14th EdCriterios de esbeltez119Note KL/r=slenderness parameterThis criteria is mostly based on erection and shipping concerns rather than safety issues.

119Compression AISC Manual 14th Ed

Segn la Seccin E.2

Recomienda proporcionar KL / r menor que 200120120Compression AISC Manual 14th EdCarta de alineamiento Temas

121Note KL/r=slenderness parameterThis criteria is mostly based on erection and shipping concerns rather than safety issues.

121Compression AISC Manual 14th Ed

Para tomar en cuenta los efectos de columna inelstico,factores de reduccin de la rigidez, ta,utilizado para reducir IE de las columnas,Factores de reduccin de Rigidez Tabla 4-21Carta de alineamiento122122Si las vigas tienen considerable carga axial,que proporcionan menor restriccin de rotacin.1-Q/QcrQ= carga axial Qcr= resistencia al pandeo en el plano con K=1Reducir componente de rigidez rotacional (EI/L) de las vigas con la modificacinEsto es vlido para "columnas" con nudos (varios pisos), que llevan la carga axial mnima en comparacin con resistencia.123Carta de alineamiento123Compression AISC Manual 14th Ed

Para tomar en cuenta el concepto de pandeo de piso, todas las columnas deben alcanzar su capacidad para permitir la falla de piso.Revisar K para tener en cuenta los efectos los pisos.

Kn2=K factores directamente del mapa de alineacinPr= Carga en la columna (factor de LRFD)K2 de la ecuacin C-A-7-8124Carta de alineamiento124