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ACI-318-11
Longitud de desarrollo de varillas corrugadas a tensión Proyecto: Fy = 59684 f 'c = 3013 yt = 1 ye = 1 diám. = 1 l= 1 Fy yt ye ye / l(f l(f 'c) 'c)^. ^.5 5= caso = 2 0 20
fecha: psi psi
4200 212
Sep-13
kg/cm^2 kg/cm^2
in conc. Peso normal 1087 1087.3 .39 9 0 d= usar
0
20
54.37 diámetros 44
diámetros
ACI 12.2.2
CASO
1
CASO 3
CASO 2
CASO 4
Factors for Use in the Expressions for Determining Required Development Lengths for Deformed Bars and Deformed Wires in Tension (ACI ( ACI 12.2.4) 12.2.4) (1) ψt = reinforcement location factor Horizontal reinforcement so placed that more than 12 in. of fresh concrete is cast in the member below the development length or splice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Other reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 (2) ψe = coating factor Epoxy-coated bars or wires with cover less than 3db, or clear spacing less than 6db . . . . . . . . . . . 1.5 All other epoxy-coated epoxy-coated bars or wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Uncoated and zinc-coated reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 However, the product of ψtψe need not be taken as greater than 1.7.
Para aplicar la fórmula 12-1, seguir el siguiente procedimiento: (3) ψs = reinforcement size factor
No. 6 and smaller bars and deformed wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8 No. 7 and larger bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 In SI units No. 19 and smaller bars and deformed wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8 No. 22 and larger bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 (4) λ (lambda) = lightweight aggregate concrete factor When lightweight aggregate concrete is used, λ shall not exceed . . . . . . . . . . . . . . . . . . . . . . . . . 0.75 However, when fct is specified, λ shall be permitted to be taken as 6.7 * f ' c / fct fct = resistencia promedio a la tensión (tracción)
It’s
f ' c / 1.8 fct
in SI
but not greater than . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 When normal weight concrete is used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 (5) cb = spacing or cover dimension, in. Use the smaller of either the distance from the center of the bar or wire to the nearest concrete surface, or one-half the center-to-center spacing of the bars or wires being developed. In the following paragraphs, all of the terms in ACI Equation 12-1 that have not previously been introduced are described. their values for different situations were given in the previous page. 1. Location of reinforcement—Horizontal bars that have a least 12 in.[3] of fresh concrete placed beneath them do not bond as well to concrete as do bars placed nearer the bottom of the concrete. These bars are referred to as top bars. During the placing and vibration of the concrete, some air an d excess water tend to rise toward the top of the concrete, and some portion may be caught under the higher bars. In addition, there may be some settlement of the concrete below. As a result, the reinforcement does not bond as well to the concrete underneath, and increased development lengths will be needed. To account for this effect, the reinforcement location factor, ψt, is used. 2. Coating of bars—Epoxy-coated reinforcing bars are frequently used today to protect the steel from severe corrosive situations, such as where deicing chemicals are used. Bridge decks and parking garage slabs in the colder states fit into this class. When bar coatings are used, bonding is reduced and development lengths must be increased. To account for this fact, the term ψe—the coating factor—is used in the equation. 3. Sizes of reinforcing—If small bars are used in a member to obtain a certain total crosssectional area, the total surface area of the bars will be appreciably larger than if fewer but larger bars are used to obtain the same total bar area. As a result, the required development lengths for smaller bars with their larger surface bonding areas (in proportion to their cross-sectional areas) are less than those required for larger-diameter bars. This factor is accounted for with the reinforcement size factor, ψs. 4. Lightweight aggregates—The dead weight of concrete can be substantially reduced by substituting lightweight aggregate for the regular stone aggregate. The use of such aggregates (expanded clay or shale, slag, etc.) generally results in lower-strength concretes. Such concretes have lower splitting strengths, and so development lengths will have to be larger. In the equation, λ is the lightweight concrete modification factor d iscussed in Section 1.12. 5. Spacing of bars or cover dimensions—Should the concrete cover or the clear spacing between the bars be too small, the concrete may very well split, as was previously shown in Figure 7.6. This situation is accounted for with the (cb Ktr)/db term in the development length expression. It is called the confinement term. In the equation, cb
represents the smaller of the distance from the center of the tension bar or wire to the nearest concrete surface, or one-half the center-to-center spacing of the reinforcement. In this expression, Ktr is a factor called the transverse reinforcement index. It is used to account for the contribution of confining reinforcing (stirrups or ties) across possible splitting planes. Ktr = 40Atr / sn where: Atr = the total cross-sectional area of all transverse reinforcement having the center-to-center spacing s and a yield strength fyt n = the number of bars or wires being developed along the plane of splitting. If steel is in two layers, n is the largest number of bars in a single layer. s = center-to-center spacing of transverse reinforcing The code in Section 12.2.3 conservatively permits the use of Ktr = 0 to simplify the calculations, even if transverse reinforcing is present. ACI 12.2.3 limits the value of (cb + Ktr)/db used in the equation to a maximum value of 2.5. (It has been found that if values larger than 2.5 are used, the shorter development lengths resulting will increase the danger of pullout-type failures.) The calculations involved in applying ACI Equation 12-1 are quite simple, as is illustrated in Example 7.2.(del libro de Mcormac y Brown, 9a edición) In SI units, Ktr = Atr fyt / 10sn
diámetro de estribos = ramas verticales = Atr = db = cb = ys = espaciam. Entre estribos 's' =
3/8 in 2
0.221 in^2 1 in acero longitudinal 1.5 in recub. o dist a c-c de vrs long. 1 8 in 3 cant de vrs long 'n' = Ktyr = 40 Atr/sn = 0.368 Fy yt ye ys / l(f 'c)^.5 = 1087.3945 (cb+Ktr/db) = 1.87 in o.k. debe ser =< 2.5 d=
44
diámetros
ACI-318-11, 12.3
Longitud de desarrollo de varillas corrugadas a compresión Proyecto:
fecha:
= Fy = f 'c = diam de varillas = 12.3.2
1 411.85 35 1.5
eq. 1
SI (0.24fy / (f´c)^.5 )db
eq. 2
(0.043fy)db db =
38 eq. 1 635
Sep-13
Concreto de peso normal Mpa Mpa in
mm eq. 2 673
mm
Esta longitud puede ser multiplicada por: rel= As req./As real rel 0.7 0.75 0.8 0.85 0.9 12.3.1
L dc 471 mm 505 mm 538 mm 572 mm 606 mm L dc no debe ser menor de 200 mm
12.2.3 Si el ref está confinado por una espiral de diámetro. => 6 mm y una separación =<100 mm o estribos de 13 mm espaciados a no mas de 100 mm multiplique por: 0.75 L dc = 505 mm
Longitud de desarrollo de varillas corrugadas a tensión Proyecto: Fy = 59684 f 'c = 3013 yt = 1 ye = 1 diám. = 1 l= 1 Fy yt ye ye / l(f l(f 'c) 'c)^. ^.5 5= caso = 2 0 20
fecha: psi psi
4200 212
Sep-13
kg/cm^2 kg/cm^2
in conc. Peso normal 1087 1087.3 .39 9 0 d= usar
0
20
54.37 diámetros 44
diámetros
ACI 12.2.2
CASO
1
CASO 3
CASO 2
CASO 4
Factors for Use in the Expressions for Determining Required Development Lengths for Deformed Bars and Deformed Wires in Tension (ACI ( ACI 12.2.4) 12.2.4) (1) ψt = reinforcement location factor Horizontal reinforcement so placed that more than 12 in. of fresh concrete is cast in the member below the development length or splice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Other reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 (2) ψe = coating factor Epoxy-coated bars or wires with cover less than 3db, or clear spacing less than 6db . . . . . . . . . . . 1.5 All other epoxy-coated epoxy-coated bars or wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Uncoated and zinc-coated reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 However, the product of ψtψe need not be taken as greater than 1.7.
Para aplicar la fórmula 12-1, seguir el siguiente procedimiento: (3) ψs = reinforcement size factor
No. 6 and smaller bars and deformed wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8 No. 7 and larger bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 In SI units No. 19 and smaller bars and deformed wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8 No. 22 and larger bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 (4) λ (lambda) = lightweight aggregate concrete factor When lightweight aggregate concrete is used, λ shall not exceed . . . . . . . . . . . . . . . . . . . . . . . . . 0.75 However, when fct is specified, λ shall be permitted to be taken as 6.7 * f ' c / fct fct = resistencia promedio a la tensión (tracción)
It’s
f ' c / 1.8 fct
in SI
but not greater than . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 When normal weight concrete is used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 (5) cb = spacing or cover dimension, in. Use the smaller of either the distance from the center of the bar or wire to the nearest concrete surface, or one-half the center-to-center spacing of the bars or wires being developed. In the following paragraphs, all of the terms in ACI Equation 12-1 that have not previously been introduced are described. their values for different situations were given in the previous page. 1. Location of reinforcement—Horizontal bars that have a least 12 in.[3] of fresh concrete placed beneath them do not bond as well to concrete as do bars placed nearer the bottom of the concrete. These bars are referred to as top bars. During the placing and vibration of the concrete, some air an d excess water tend to rise toward the top of the concrete, and some portion may be caught under the higher bars. In addition, there may be some settlement of the concrete below. As a result, the reinforcement does not bond as well to the concrete underneath, and increased development lengths will be needed. To account for this effect, the reinforcement location factor, ψt, is used. 2. Coating of bars—Epoxy-coated reinforcing bars are frequently used today to protect the steel from severe corrosive situations, such as where deicing chemicals are used. Bridge decks and parking garage slabs in the colder states fit into this class. When bar coatings are used, bonding is reduced and development lengths must be increased. To account for this fact, the term ψe—the coating factor—is used in the equation. 3. Sizes of reinforcing—If small bars are used in a member to obtain a certain total crosssectional area, the total surface area of the bars will be appreciably larger than if fewer but larger bars are used to obtain the same total bar area. As a result, the required development lengths for smaller bars with their larger surface bonding areas (in proportion to their cross-sectional areas) are less than those required for larger-diameter bars. This factor is accounted for with the reinforcement size factor, ψs. 4. Lightweight aggregates—The dead weight of concrete can be substantially reduced by substituting lightweight aggregate for the regular stone aggregate. The use of such aggregates (expanded clay or shale, slag, etc.) generally results in lower-strength concretes. Such concretes have lower splitting strengths, and so development lengths will have to be larger. In the equation, λ is the lightweight concrete modification factor d iscussed in Section 1.12. 5. Spacing of bars or cover dimensions—Should the concrete cover or the clear spacing between the bars be too small, the concrete may very well split, as was previously shown in Figure 7.6. This situation is accounted for with the (cb Ktr)/db term in the development length expression. It is called the confinement term. In the equation, cb
represents the smaller of the distance from the center of the tension bar or wire to the nearest concrete surface, or one-half the center-to-center spacing of the reinforcement. In this expression, Ktr is a factor called the transverse reinforcement index. It is used to account for the contribution of confining reinforcing (stirrups or ties) across possible splitting planes. Ktr = 40Atr / sn where: Atr = the total cross-sectional area of all transverse reinforcement having the center-to-center spacing s and a yield strength fyt n = the number of bars or wires being developed along the plane of splitting. If steel is in two layers, n is the largest number of bars in a single layer. s = center-to-center spacing of transverse reinforcing The code in Section 12.2.3 conservatively permits the use of Ktr = 0 to simplify the calculations, even if transverse reinforcing is present. ACI 12.2.3 limits the value of (cb + Ktr)/db used in the equation to a maximum value of 2.5. (It has been found that if values larger than 2.5 are used, the shorter development lengths resulting will increase the danger of pullout-type failures.) The calculations involved in applying ACI Equation 12-1 are quite simple, as is illustrated in Example 7.2.(del libro de Mcormac y Brown, 9a edición) In SI units, Ktr = Atr fyt / 10sn
diámetro de estribos = ramas verticales = Atr = db = cb = ys = espaciam. Entre estribos 's' =
3/8 in 2
0.221 in^2 1 in acero longitudinal 1.5 in recub. o dist a c-c de vrs long. 1 8 in 3 cant de vrs long 'n' = Ktyr = 40 Atr/sn = 0.368 Fy yt ye ys / l(f 'c)^.5 = 1087.3945 (cb+Ktr/db) = 1.87 in o.k. debe ser =< 2.5 d=
44
diámetros
ACI-318-11, 12.3
Longitud de desarrollo de varillas corrugadas a compresión Proyecto:
fecha:
= Fy = f 'c = diam de varillas = 12.3.2
1 411.85 35 1.5
eq. 1
SI (0.24fy / (f´c)^.5 )db
eq. 2
(0.043fy)db db =
38 eq. 1 635
Sep-13
Concreto de peso normal Mpa Mpa in
mm eq. 2 673
mm
Esta longitud puede ser multiplicada por: rel= As req./As real rel 0.7 0.75 0.8 0.85 0.9 12.3.1
L dc 471 mm 505 mm 538 mm 572 mm 606 mm L dc no debe ser menor de 200 mm
12.2.3 Si el ref está confinado por una espiral de diámetro. => 6 mm y una separación =<100 mm o estribos de 13 mm espaciados a no mas de 100 mm multiplique por: 0.75 L dc = 505 mm
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