DISEÑO DE MIEMBROS A TRACCIÓN

DISEÑO DE MIEMBROS A TRACCIÓN SEGÚN COVENIN 1618-98 75

COVENIN – MINDUR 1618-9 ESTRUCTURAS DE ACERO PARA EDIFICACIONES

PARTE 3

DISEÑO DE MIEMBROS

CAPÍTULO 14 MIEMBROS A TRACCIÓN 14.1 ALCANCE Este Capítulo se aplicará a los miembros prismáticos solicitados por tracción normal causada por fuerzas que actúan a lo largo de su eje baricéntrico. Para miembros solicitados por tensiones combinadas de tracción normal y flexión, véase el Capítulo 15. Para las barras roscadas, véase el Capítulo 21. Para la resistencia por bloque de corte de las conexiones extremas de miembros traccionados, véase la Sección 21.14.3. Para la resistencia de diseño a tracción de los elementos conectores, véase el Artículo 21.15. Para el diseño por fatiga, véase el Apéndice D. 14.2 LONGITUD PARA EL DISEÑO A menos que en esta Norma se especifique de otra manera, la longitud de diseño de los miembros traccionados normalmente, L, será la longitud no arriostrada lateralmente, definida como la distancia entre los baricentros de los miembros que los restringen lateralmente.

14.3 RELACIÓN DE ESBELTEZ La relación de esbeltez de los miembros traccionados será su longitud no arriostrada, L, dividida por el correspondiente radio de giro, r, es decir L/r. La relación de esbeltez de los miembros traccionados distintos a las barras, preferentemente no excederá de 300. Este límite puede ser obviado cuando se disponen de otros medios para controlar la flexibilidad, el combamiento, la vibración y el aflojamiento que puedan ocurrir durante las condiciones de servicio de la estructura o cuando pueda demostrase que no perjudica el desempeño de la estructura o el conjunto del cual el miembro forma parte. 14.4 RESISTENCIA La resistencia minorada de los miembros sometidos a tracción, It Nt , será el menor valor que se obtenga de considerar los estados límite de cedencia en la sección del área total y de fractura en la sección del área neta efectiva. (1) Cedencia en la sección del área total It = 0.90 Nt = Fy A

(14-1)

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COVENIN - MINDUR 1618-98 ESTRUCTURAS DE ACERO PARA EDIFICACIONES

(2) Fractura en la sección del área neta efectiva It = 0.75 Nt = Fu Ae

(14-2)

donde: A = Área total de la sección transversal del miembro. Ae = Área neta efectiva, calculada según el Artículo 7.3. Nt = Resistencia teórica a tracción normal. It = Factor de minoración de la resistencia teórica. Para el diseño de los miembros sin perforaciones conectados completamente por medios de soldaduras, se utilizará la fórmula (14-2), usando como área neta efectiva el valor definido en el Artículo 7.3. Cuando existan agujeros en un miembro con conexiones soldadas, o cuando las conexiones soldadas sean soldaduras de tapón o de ranura, en la fórmula (14-2) se utilizará el área neta calculada a través de la sucesión de agujeros, tal como se definió en el Artículo 7.2. 14.5 MIEMBROS COMPUESTOS Los miembros traccionados constituidos por dos o más perfiles o planchas, separados unos de otros por planchas de relleno intermitentes, se conectarán entre sí en lo sitios donde se colocan los rellenos a intervalos tales que la relación de esbeltez de cada uno de los elementos componentes entre conectores no exceda de 300. La separación longitudinal de los conectores que conectan una plancha y un perfil en un miembro compuesto sometido a tracción, o dos planchas componentes en contacto entre será la indicada en los Artículos 22.4 y 22.5. En los lados abiertos de los miembros compuestos sometidos a tracción pueden utilizarse tanto planchas de cubierta con agujeros de acceso como presillas sin rejillas. Las presillas tendrán una longitud no menor que dos tercios de la distancia entre las líneas de conectores o soldaduras que los unen a los componentes del miembro, y su espesor no será inferior a 0.02 veces la distancia entre esas líneas. La separación longitudinal de sus conectores o soldaduras intermitentes no excederá de 150 mm. La separación de las presillas será tal que la relación de esbeltez de cualquier elemento componente entre ellas no sea superior a 300. 14.6 MIEMBROS CONECTADOS CON PASADORES El diseño de las bielas simples, constituidas por barras o planchas de espesor uniforme sin refuerzo en la zona del agujero para el pasador, cumplirá con los requisitos de la Sección 14.6.1. Las

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133

21.14.2 Resistencia a la rotura por tracción La resistencia minorada a lo largo del plano de tracción en los elementos afectados de los miembros conectados será igual a I Rt , donde : Rt = Fu Ant

¡Importante! Actualizado con AISC 360-10

(21-2)

Ant = Área neta sometida a tracción I = 0.75 21.14.3 Resistencia por rotura en el bloque de corte Se verificará el estado límite de agotamiento resistente por rotura en el bloque de corte en las conexiones de los extremos de las vigas cuya ala superior haya sido cortada y desmembrada y situaciones similares, en los miembros traccionados y en las planchas usadas como cartelas ( planchas de nodos). La resistencia minorada a la rotura por bloque de corte, I Rbs , estará determinada por el mecanismo que controle el modo de falla: (a) Cuando Fu Ant t 0.6 Fu Anv , el mecanismo de falla es de cedencia por corte y fractura por tracción I Rbs = I [0.6 Fy Av + Fu Ant]

(21-3a)

(b) Cuando 0.6 Fu Anv > Fu Ant, el mecanismo de falla es de cedencia por tracción y fractura por corte I Rbs = I [ 0.6 Fu Anv + Fy At ]

(21-3b)

(c) En todos los casos I Rbs d I [ 0.6 Fu Anv + Fy Ant ] En las fórmulas (21-3), Ant = Área neta traccionada. Anv = Área neta sometida a corte. At = Área total traccionada. Av = Área total sometida a corte. I

= 0.75.

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C-139

A pesar de que actualizamos esta sección con el AISC 360-10, estas figuras siguen siendo válidas

FIGURA C-21.5

Ejemplos de falla por ruptura en el bloque de corte (zona sombreada)

FIGURA C-21.6

Mecanismo de ruptura por bloque de corte.

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C-140


FIGURA C-21.7

Definición de variables para el cálculo del bloque de corte.

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35


CAPÍTULO 7 ÁREAS TOTALES, NETAS Y EFECTIVAS 7.1 ÁREA TOTAL El área de la sección transversal total, A, en un punto cualquiera de un miembro se determinará sumando las áreas obtenidas al multiplicar el espesor y el ancho de cada uno de los elementos componentes, debiéndose medir los anchos perpendicularmente al eje del miembro. En los perfiles angulares el ancho total es igual a la suma de los anchos de los dos lado menos el espesor. 7.2

ÁREA NETA

El área de la sección neta, An , se determinará sumando las áreas obtenidas al multiplicar el espesor y el ancho neto de cada uno de los elementos componentes , calculado el ancho neto como se indica a continuación: Al calcular las áreas netas de los elementos en tracción y corte, los diámetros de los agujeros , da , se considerarán 2 milímetros (1/16 plg.) mayores que la dimensión nominal del agujero, dh, o 3 mm (1/8”)mayores que el diámetro nominal del perno, d. da = dh + 2 mm = d + 3 mm

(7-1)

En el caso de una sucesión de agujeros que se extienda a través de una parte del miembro según una línea cualquiera diagonal o en zigzag, el ancho neto de esa parte se obtendrá al restar del ancho total la suma de los diámetros de todas los agujeros circulares o alargados (definidos en el Artículo 22.3) en la sucesión considerada y añadiendo para cada espacio entre los agujeros de la sucesión la cantidad. En esta expresión la separación longitudinal medida centro a centro entre dos agujeros consecutivos cualesquiera y medida paralelamente al eje del miembro, se le denomina paso, s. La separación transversal centro a centro entre los mismos dos agujeros, medida perpendicularmente al eje del miembro; se le denomina gramil, g. En los perfiles L, la separación transversal o gramil, g ,entre agujeros que estén situados en lados opuestos será la suma de las separaciones transversales medidas desde el borde exterior del ángulo menos el espesor. Al determinar el área neta a través de soldaduras de tapón o de canal, el metal de aporte de la soldadura no se considera como contribuyente al área neta. 7.3 ÁREA NETA EFECTIVA EN MIEMBROS SOLICITADOS EN TRACCIÓN El área neta efectiva, Ae , en miembros traccionados se calculará como se indica a continuación: 7.3.1 Cuando la solicitación de tracción se transmite directamente a todos y cada uno de los elementos de la sección transversal por medio de pernos o soldadura, el área neta efectiva será igual al área neta, es decir, Ae = An.

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COVENIN - MINDUR 1618-98 ESTRUCTURAS DE ACERO PARA EDIFICACIONES

7.3.2 Cuando la solicitación de tracción se transmite por medio de pernos a través de algunos, pero no de todos los elementos de la sección transversal del miembro, el área neta efectiva se obtendrá al multiplicar el área A, definida a continuación para cada tipo de conexión, por el factor de reducción del área, IA , calculado según la fórmula (7-2) o tomando los valores dados para las conexiones soldadas en la Subsección 7.3.2.2: Ae = IA A

(7-2)

_

IA = 1 - ( x / L) d 0.9

(7-3)

En la fórmula (7-3): L = Longitud de la conexión medida en la dirección de la carga. _

x = Excentricidad de la conexión.

Cuando se justifiquen por ensayos u otros criterios racionales se permitirán valores mayores del factor de reducción del área, IA. 7.3.3 Cuando la fuerza de tracción se transmite solamente por medios de pernos, el área será igual al área neta del miembro, es decir, A = An. 7.3.4 Cuando la fuerza de tracción se transmite solamente por soldaduras transversales, el valor del factor de reducción del área, IA, se tomará igual a la unidad y el área A será el área de los elementos directamente conectados. 7.3.5 Cuando la solicitación de tracción se transmite directamente a los miembros solamente por soldaduras longitudinales o por medio de una combinación de soldaduras longitudinales y transversales, el área A será igual al área total del miembro. 7.3.6 Cuando la fuerza de tracción se transmite a una plancha por medio de soldaduras longitudinales a lo largo de ambos bordes del extremo de la misma, el área A se tomará igual al área de la plancha, Ap. La longitud de la soldadura, L, no será menor al ancho de la plancha o separación entre soldaduras, w, es decir, L t w: Para L t 2w........................................ IA = 1.00 Para 2w > L t 1.5w........................................ IA = 0.87 Para 1.5w > L t w .. ..................................... IA = 0.75 Las planchas de empalme, las cartelas y otros elementos de conexión solicitados a tracción se diseñarán en concordancia con la Sección 21.15.1, donde se define su área efectiva.

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Alternativamente al uso de la fórmula (7-3), pueden emplearse los siguientes valores del factor de

reduccción del área, IA: (a)

En perfiles con alas de anchos superiores a 2/3 de la altura y las tes estructurales cortadas de estos perfiles, siempre que la conexión se haga en las alas y que no tenga menos de 3 medios de unión por línea en la dirección de la tracción.................................................................................................. IA = 0.90

(b)

En perfiles que no cumplan con las condiciones del literal anterior, las tes estructurales cortadas de estos perfiles y cualquier otro perfil, incluyendo los ensamblados, siempre que la conexión no tenga menos de 3 medios de unión por línea en la dirección de la tracción.................................................. IA = 0.85

(c)

En todos los elementos con conexiones empernadas o soldadas que tengan solamente dos medios de unión por línea en la dirección de la tracción............................................................................................................ IA = 0.75

Cuando la carga de tracción es transmitida por soldadura de filete a algunos pero no todos los elementos de una sección transversal, la resistencia de la soldadura controlará el diseño.

¡Atención! Esta sección la actualizamos con el AISC 360-10

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C-34


FIGURA C-7.1. Ejemplos de cálculo de área neta

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C-35

FIGURA C-7.2. Determinación de la excentricidad de la conexión, X para el cálculo de coeficiente de reducción IA

FIGURA C-7.3. Agujeros en tres bolillos

FIGURA C-7.4. Soldaduras longitudinales y transversales.

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DISEÑO DE MIEMBROS A TRACCIÓN SEGÚN AISC 360-10

16.1–26

CHAPTER D DESIGN OF MEMBERS FOR TENSION

This chapter applies to members subject to axial tension caused by static forces acting through the centroidal axis. The chapter is organized as follows: D1. D2. D3. D4. D5. D6.

Slenderness Limitations Tensile Strength Effective Net Area Built-Up Members Pin-Connected Members Eyebars

¡Estos dos puntos son muy importantes! En la práctica, lo indicado en la sección J4.3 controla típicamente el diseño de los miembros a tracción

User Note: For cases not included in this chapter the following sections apply: • B3.11 Members subject to fatigue • Chapter H Members subject to combined axial tension and flexure • J3 Threaded rods • J4.1 Connecting elements in tension • J4.3 Block shear rupture strength at end connections of tension members

D1.

SLENDERNESS LIMITATIONS There is no maximum slenderness limit for members in tension. User Note: For members designed on the basis of tension, the slenderness ratio L /r preferably should not exceed 300. This suggestion does not apply to rods or hangers in tension.

D2.

TENSILE STRENGTH The design tensile strength, φt Pn, and the allowable tensile strength, Pn /Ωt, of tension members shall be the lower value obtained according to the limit states of tensile yielding in the gross section and tensile rupture in the net section. (a) For tensile yielding in the gross section: Pn = Fy Ag φt = 0.90 (LRFD)

(D2-1)

Ωt = 1.67 (ASD)

(b) For tensile rupture in the net section: Pn = Fu Ae φt = 0.75 (LRFD)

(D2-2)

Ωt = 2.00 (ASD)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Page 11 of 22

Sect. D4.]

BUILT-UP MEMBERS

16.1–27

where Ae = effective net area, in.2 (mm2) Ag = gross area of member, in.2 (mm2) Fy = specified minimum yield stress, ksi (MPa) Fu = specified minimum tensile strength, ksi (MPa) When members without holes are fully connected by welds, the effective net area used in Equation D2-2 shall be as defined in Section D3. When holes are present in a member with welded end connections, or at the welded connection in the case of plug or slot welds, the effective net area through the holes shall be used in Equation D2-2.

D3.

EFFECTIVE NET AREA The gross area, Ag, and net area, An, of tension members shall be determined in accordance with the provisions of Section B4.3. The effective net area of tension members shall be determined as follows: Ae = AnU

(D3-1)

where U, the shear lag factor, is determined as shown in Table D3.1. For open cross sections such as W, M, S, C or HP shapes, WTs, STs, and single and double angles, the shear lag factor, U, need not be less than the ratio of the gross area of the connected element(s) to the member gross area. This provision does not apply to closed sections, such as HSS sections, nor to plates. User Note: For bolted splice plates Ae = An ≤ 0.85Ag, according to Section J4.1.

D4.

BUILT-UP MEMBERS For limitations on the longitudinal spacing of connectors between elements in continuous contact consisting of a plate and a shape or two plates, see Section J3.5. Either perforated cover plates or tie plates without lacing are permitted to be used on the open sides of built-up tension members. Tie plates shall have a length not less than two-thirds the distance between the lines of welds or fasteners connecting them to the components of the member. The thickness of such tie plates shall not be less than one-fiftieth of the distance between these lines. The longitudinal spacing of intermittent welds or fasteners at tie plates shall not exceed 6 in. (150 mm). User Note: The longitudinal spacing of connectors between components should preferably limit the slenderness ratio in any component between the connectors to 300.



Page 12 of 22

16.1–28

BUILT-UP MEMBERS

[Sect. D4.

TABLE D3.1 Shear Lag Factors for Connections to Tension Members Case 1

2

3

4

Description of Element

Shear Lag Factor, U

All tension members where the tension load is transmitted directly to each of the cross-sectional elements by fasteners or welds (except as in Cases 4, 5 and 6). All tension members, except plates and HSS, where the tension load is transmitted to some but not all of the crosssectional elements by fasteners or longitudinal welds or by longitudinal welds in combination with transverse welds. (Alternatively, for W, M, S and HP, Case 7 may be used. For angles, Case 8 may be used.) All tension members where the tension load is transmitted only by transverse welds to some but not all of the cross-sectional elements. Plates where the tension load is transmitted by longitudinal welds only.

Example

U = 1.0

U = 1− x l

U = 1.0 and An = area of the directly connected elements / ≥ 2w…U = 1.0 2w > / ≥ 1.5w…U = 0.87 1.5w > / ≥ w…U = 0.75

5

Round HSS with a single concentric gusset plate

/ ≥ 1.3D…U = 1.0

D ≤ l < 1.3D …U = 1− x l x =D π

6

Rectangular HSS

with a single concentric gusset plate

l ≥ H …U = 1− x l

with two side gusset plates

l ≥ H …U = 1− x l

x=

B 2 + 2BH 4(B + H )

x= 7

8

W, M, S or HP Shapes or Tees cut from these shapes. (If U is calculated per Case 2, the larger value is permitted to be used.)

Single and double angles (If U is calculated per Case 2, the larger value is permitted to be used.)

with flange connected with 3 or more fasteners per line in the direction of loading with web connected with 4 or more fasteners per line in the direction of loading with 4 or more fasteners per line in the direction of loading with 3 fasteners per line in the direction of loading (With fewer than 3 fasteners per line in the direction of loading, use Case 2.)

B2 4(B + H )

bf ≥ 2/3d…U = 0.90 bf < 2/3d…U = 0.85

U = 0.70

U = 0.80

U = 0.60

l = length of connection, in. (mm); w = plate width, in. (mm); x– = eccentricity of connection, in. (mm); B = overall width of rectangular HSS member, measured 90° to the plane of the connection, in. (mm); H = overall height of rectangular HSS member, measured in the plane of the connection, in. (mm)



Page 13 of 22

16.1–282

CHAPTER D DESIGN OF MEMBERS FOR TENSION

The provisions of Chapter D do not account for eccentricities between the lines of action of connected assemblies.

D1.

SLENDERNESS LIMITATIONS The advisory upper limit on slenderness in the User Note is based on professional judgment and practical considerations of economics, ease of handling, and care required so as to minimize inadvertent damage during fabrication, transport and erection. This slenderness limit is not essential to the structural integrity of tension members; it merely assures a degree of stiffness such that undesirable lateral movement (“slapping” or vibration) will be unlikely. Out-of-straightness within reasonable tolerances does not affect the strength of tension members. Applied tension tends to reduce, whereas compression tends to amplify, out-of-straightness. For single angles, the radius of gyration about the z-axis produces the maximum L/r and, except for very unusual support conditions, the maximum KL /r.

D2.

TENSILE STRENGTH Because of strain hardening, a ductile steel bar loaded in axial tension can resist without rupture a force greater than the product of its gross area and its specified minimum yield stress. However, excessive elongation of a tension member due to uncontrolled yielding of its gross area not only marks the limit of its usefulness but can precipitate failure of the structural system of which it is a part. On the other hand, depending upon the reduction of area and other mechanical properties of the steel, the member can fail by rupture of the net area at a load smaller than required to yield the gross area. Hence, general yielding of the gross area and rupture of the net area both constitute limit states. The length of the member in the net area is generally negligible relative to the total length of the member. Strain hardening is easily reached in the vicinity of holes and yielding of the net area at fastener holes does not constitute a limit state of practical significance. Except for HSS that are subjected to cyclic load reversals, there is no information that the factors governing the strength of HSS in tension differ from those for other structural shapes, and the provisions in Section D2 apply. Because the number of different end connection types that are practical for HSS is limited, the determination of the effective net area, Ae, can be simplified using the provisions in Chapter K.

D3.

EFFECTIVE NET AREA Section D3 deals with the effect of shear lag, applicable to both welded and bolted tension members. Shear lag is a concept used to account for uneven stress distribuSpecification for Structural Steel Buildings, June 22, 2010


Page 14 of 22

Comm. D3.]

EFFECTIVE NET AREA

16.1–283

tion in connected members where some but not all of their elements (flange, web, leg, etc.) are connected. The reduction coefficient, U, is applied to the net area, An, of bolted members and to the gross area, Ag, of welded members. As the length of the connection, l, is increased, the shear lag effect diminishes. This concept is expressed empirically by the equation for U. Using this expression to compute the effective area, the estimated strength of some 1,000 bolted and riveted connection test specimens, with few exceptions, correlated with observed test results within a scatterband of ±10% (Munse and Chesson, 1963). Newer research provides further justification for the current provisions (Easterling and Gonzales, 1993). For any given profile and configuration of connected elements, x– is the perpendicular distance from the connection plane, or face of the member, to the centroid of the member section resisting the connection force, as shown in Figure C-D3.1. The length, l, is a function of the number of rows of fasteners or the length of weld. The length, l, is illustrated as the distance, parallel to the line of force, between the first and last row of fasteners in a line for bolted connections. The number of bolts in a line, for the purpose of the determination of l, is determined by the line with the maximum number of bolts in the connection. For staggered bolts, the out-to-out dimension is used for l, as shown in Figure C-D3.2.

Fig. C-D3.1. Determination of x– for U. Specification for Structural Steel Buildings, June 22, 2010


Page 15 of 22

16.1–284

EFFECTIVE NET AREA

[Comm. D3.

From the definition of the plastic section modulus, Z = ∑| Ai di |, where Ai is the area of a cross-sectional element and di is the perpendicular distance from the plastic neutral axis to the center of gravity of the element; x– for cases like that shown on the right hand side of Figure C-D3.1(c) is Zy /A. Because the section shown is symmetric about the vertical axis and that axis is also the plastic neutral axis, the first moment of the area to the left is Zy /2, where Zy is the plastic section modulus of the entire section. The area of the left side is A/2; therefore, by definition ⫺ x = Zy /A. For ⫺ the case shown on the right hand side of Figure C-D3.1(b), x = d/2 ⫺ Zx /A. Note that the plastic neutral axis must be an axis of symmetry for this relationship to apply. There is insufficient data for establishing a value of U if all lines have only one bolt, but it is probably conservative to use Ae equal to the net area of the connected element. The limit states of block shear (Section J4.3) and bearing (Section J3.10), which must be checked, will probably control the design. The ratio of the area of the connected element to the gross area is a reasonable lower bound for U and allows for cases where the calculated U based on (1–x– / l ) is very small, or nonexistent, such as when a single bolt per gage line is used and l = 0. This lower bound is similar to other design specifications, for example the AASHTO Standard Specifications for Highway Bridges (AASHTO, 2002), which allow a U based on the area of the connected portion plus half the gross area of the unconnected portion. The effect of connection eccentricity is a function of connection and member stiffness and may sometimes need to be considered in the design of the tension connection or member. Historically, engineers have neglected the effect of eccentricity in both the member and the connection when designing tension-only bracing. In Cases 1a and 1b shown in Figure C-D3.3, the length of the connection required to resist the axial loads will usually reduce the applied axial load on the bolts to a negligible value. For Case 2, the flexibility of the member and the connections will allow the member to deform such that the resulting eccentricity is relieved to a considerable extent.

Fig. C-D3.2. Determination of l for U of bolted connections with staggered holes.



Page 16 of 22

Comm. D3.]

EFFECTIVE NET AREA

16.1–285

For welded connections, l is the length of the weld parallel to the line of force as shown in Figure C-D3.4 for longitudinal and longitudinal plus transverse welds. For welds with unequal lengths, use the average length. End connections for HSS in tension are commonly made by welding around the perimeter of the HSS; in this case, there is no shear lag or reduction in the gross area.

Case 1a. End Rotation Restrained by Connection to Rigid Abutments

Case 1b. End Rotation Restrained by Symmetry

Case 2. End Rotation Not Restrained—Connection to Thin Plate Fig. C-D3.3. The effect of connection restraint on eccentricity.



Page 17 of 22

16.1–286

EFFECTIVE NET AREA

[Comm. D3.

Alternatively, an end connection with gusset plates can be used. Single gusset plates may be welded in longitudinal slots that are located at the centerline of the cross section. Welding around the end of the gusset plate may be omitted for statically loaded connections to prevent possible undercutting of the gusset and having to bridge the gap at the end of the slot. In such cases, the net area at the end of the slot is the critical area as illustrated in Figure C-D3.5. Alternatively, a pair of gusset plates can be welded to opposite sides of a rectangular HSS with flare bevel groove welds with no reduction in the gross area. For end connections with gusset plates, the general provisions for shear lag in Case 2 of Table D3.1 can be simplified and the connection eccentricity can be explicitly defined as in Cases 5 and 6. In Cases 5 and 6 it is implied that the weld length, l, should not be less than the depth of the HSS. This is consistent with the weld length requirements in Case 4. In Case 5, the use of U = 1 when l ≥ 1.3D is based on research (Cheng and Kulak, 2000) that shows rupture occurs only in short connections and in long connections the round HSS tension member necks within its length and failure is by member yielding and eventual rupture. The shear lag factors given in Cases 7 and 8 of Table D3.1 are given as alternate U values to the value determined from 1 ⫺ ⫺ x /l given for Case 2 in Table D3.1. It is permissible to use the larger of the two values.

Fig. C-D3.4. Determination of l for calculation of U for connections with longitudinal and transverse welds.

Fig. C-D3.5. Net area through slot for a single gusset plate. Specification for Structural Steel Buildings, June 22, 2010


Page 18 of 22

Sect. J4.]

AFFECTED ELEMENTS OF MEMBERS AND CONNECTING ELEMENTS

φ = 0.75 (LRFD)

16.1–129

Ω = 2.00 (ASD)

where Ae = effective net area as defined in Section D3, in.2 (mm2); for bolted splice plates, Ae = An ≤ 0.85Ag. User Note: The effective net area of the connection plate may be limited due to stress distribution as calculated by methods such as the Whitmore section.

2.

Strength of Elements in Shear The available shear strength of affected and connecting elements in shear shall be the lower value obtained according to the limit states of shear yielding and shear rupture: (a) For shear yielding of the element: Rn = 0.60Fy Agv φ = 1.00 (LRFD)

(J4-3)

Ω = 1.50 (ASD)

where Agv = gross area subject to shear, in.2 (mm2) (b) For shear rupture of the element: Rn = 0.60Fu Anv φ = 0.75 (LRFD)

(J4-4)

Ω = 2.00 (ASD)

where Anv = net area subject to shear, in.2 (mm2)

3.

Block Shear Strength The available strength for the limit state of block shear rupture along a shear failure path or paths and a perpendicular tension failure path shall be taken as Rn = 0.60Fu Anv + Ubs Fu Ant ≤ 0.60Fy Agv + Ubs Fu Ant φ = 0.75 (LRFD)

(J4-5)

Ω = 2.00 (ASD)

where Ant = net area subject to tension, in.2 (mm2) Where the tension stress is uniform, Ubs = 1; where the tension stress is nonuniform, Ubs = 0.5. User Note: Typical cases where Ubs should be taken equal to 0.5 are illustrated in the Commentary.

4.

Strength of Elements in Compression The available strength of connecting elements in compression for the limit states of yielding and buckling shall be determined as follows: Specification for Structural Steel Buildings, June 22, 2010


Page 19 of 22

Comm. J4.]

12.

AFFECTED ELEMENTS OF MEMBERS

16.1–411

Tension Fasteners With any connection configuration where the fasteners transmit a tensile force to the HSS wall, a rational analysis must be used to determine the appropriate limit states. These may include a yield-line mechanism in the HSS wall and/or pull-out through the HSS wall, in addition to applicable limit states for the fasteners subject to tension.

J4.

AFFECTED ELEMENTS OF MEMBERS AND CONNECTING ELEMENTS

1.

Strength of Elements in Tension Tests have shown that for bolted splice plates yielding will occur on the gross section before the tensile strength of the net section is reached if the ratio An /Ag is greater than or equal to 0.85 (Kulak et al., 1987). Since the length of connecting elements is small compared to the member length, inelastic deformation of the gross section is limited. Hence, the effective net area, Ae, of the connecting element is limited to 0.85Ag in recognition of the limited capacity for inelastic deformation, and to provide a reserve capacity. Tests have also shown than Ae may be limited by the ability of the stress to distribute in the member. Analysis procedures such as the Whitmore section should be used to determine Ae in these cases.

2.

Strength of Elements in Shear Prior to 2005, the resistance factor for shear yielding had been 0.90, which was equivalent to a safety factor of 1.67. In ASD Specifications, the allowable shear yielding stress was 0.4Fy, which was equivalent to a safety factor of 1.5. To make the LRFD approach in the 2005 Specification consistent with prior editions of the ASD Specification, the resistance and safety factors for shear yielding became 1.0 and 1.5, respectively. The resulting increase in LRFD design strength of approximately 10% is justified by the long history of satisfactory performance of ASD use.

3.

Block Shear Strength Tests on coped beams indicated that a tearing failure mode (rupture) can occur along the perimeter of the bolt holes as shown in Figure C-J4.1 (Birkemoe and Gilmor, 1978). This block shear mode combines tensile failure on one plane and shear failure on a perpendicular plane. The failure path is defined by the centerlines of the bolt holes. The block shear failure mode is not limited to coped ends of beams; other examples are shown in Figures C-J4.1 and C-J4.2. The block shear failure mode must also be checked around the periphery of welded connections. This Specification has adopted a conservative model to predict block shear strength. The mode of failure in coped beam webs and angles is different than that of gusset plates because the shear resistance is present on only one plane, in which case there must be some rotation of the block of material that is providing the total resistance. Specification for Structural Steel Buildings, June 22, 2010


Page 20 of 22

16.1–412

AFFECTED ELEMENTS OF MEMBERS

[Comm. J4.

Fig. C-J4.1. Failure surface for block shear rupture limit state.

(a) Cases for which Ubs = 1.0

(b) Cases for which Ubs = 0.5 Fig. C-J4.2. Block shear tensile stress distributions.



Page 21 of 22

Comm. J7.]

BEARING STRENGTH

16.1–413

Although tensile failure is observed through the net section on the end plane, the distribution of tensile stresses is not always uniform (Ricles and Yura, 1983; Kulak and Grondin, 2001; Hardash and Bjorhovde, 1985). A reduction factor, Ubs, has been included in Equation J4-5 to approximate the nonuniform stress distribution on the tensile plane. The tensile stress distribution is nonuniform in the two row connection in Figure C-J4.2(b) because the rows of bolts nearest the beam end pick up most of the shear load. For conditions not shown in Figure C-J4.2, Ubs may be taken as (1 ⫺ e/l ) where e/l is the ratio of the eccentricity of the load to the centroid of the resistance divided by the block length. This fits data reported by Kulak and Grondin (2001), Kulak and Grondin (2002), and Yura et al. (1982). Block shear is a rupture or tearing phenomenon, not a yielding limit state. However, gross yielding on the shear plane can occur when tearing on the tensile plane commences if 0.6Fu Anv exceeds 0.6Fy Agv. Hence, Equation J4-5 limits the term 0.6Fu Anv to not greater than 0.6Fy Agv (Hardash and Bjorhovde, 1985). Equation J45 is consistent with the philosophy in Chapter D for tension members where the gross area is used for the limit state of yielding and the net area is used for the limit state of rupture.

4.

Strength of Elements in Compression To simplify connection calculations, the nominal strength of elements in compression when the element slenderness ratio is not greater than 25 is Fy Ag. This is a very slight increase over that obtained if the provisions of Chapter E are used. For more slender elements, the provisions of Chapter E apply.

J5.

FILLERS As noted in Commentary Section J3.8, research reported in Borello et al. (2009) resulted in significant changes in the design of bolted connections with fillers. In the 2010 Specification, bearing connections with fillers over 3/4-in. thick are no longer required to be developed provided the bolts are designed by multiplying the shear strength by a 0.85 factor. Slip-critical connections with a single filler of any thickness with proper surface preparation may be designed without any reduction in slip resistance. Slip-critical connections with multiple fillers may be designed without any reduction in slip resistance provided the joint has either all faying surfaces with Class B surfaces or Class A surfaces with turn-of-nut tensioning. This provision for multiple fillers is based on the additional reliability of Class B surface or on the higher pretension achieved with the turn-of-nut tensioning. Filler plates may be used in lap joints of welded connections that splice parts of different thickness, or where there may be an offset in the joint.

J7.

BEARING STRENGTH In general, the bearing strength design of finished surfaces is governed by the limit state of bearing (local compressive yielding) at nominal loads. The nominal bearing



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DISEÑO DE MIEMBROS A TRACCIÓN

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