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There are no amended sections in this chapter.
This chapter shall apply to the design of nonprestressed and prestressed concrete structures assigned to Seismic Design Categories (SDC) B through F, including, where applicable:
(a) Structural systems designated as part of the seismic-force-resisting system, including diaphragms, moment frames, structural walls, and foundations
(b) Members not designated as part of the seismic-force-resisting system but required to support other loads while undergoing deformations associated with earthquake effects
Structures designed according to the provisions of this chapter are intended to resist earthquake motions through ductile inelastic response of selected members.
All structures shall be assigned to a SDC in accordance with 4.4.6.1.
Structures assigned to Seismic Design Category A shall satisfy requirements of Chapters 1 through 17 and 19 through 26; Chapter 18 does not apply. Structures assigned to Seismic Design Category B, C, D, E or F shall satisfy 18.2.1.3 through 18.2.1.7, as applicable. Except for structural elements of plain concrete complying with Section 1905.1.7 of the International Building Code, structural elements of plain concrete are prohibited in structures assigned to Seismic Design Category C, D, E or F.
Structures assigned to SDC B shall satisfy 18.2.2.
Structural systems designated as part of the seismic force-resisting system shall be restricted to those permitted by ASCE 7. Except for Seismic Design Category A, for which Chapter 18 does not apply, the following provisions shall be satisfied for each structural system designated as part of the seismic force-resisting system, regardless of the seismic design category:
- Ordinary moment frames shall satisfy 18.3.
- Ordinary reinforced concrete structural walls and ordinary precast structural walls need not satisfy any provisions in Chapter 18.
- Intermediate moment frames shall satisfy 18.4.
- Intermediate precast structural walls shall satisfy 18.5.
- Special moment frames shall satisfy 18.6 through 18.9.
- Special structural walls shall satisfy 18.10.
- Special structural walls constructed using precast concrete shall satisfy 18.11.
A reinforced concrete structural system not satisfying this chapter shall be permitted if it is demonstrated by experimental evidence and analysis that the proposed system will have strength and toughness equal to or exceeding those provided by a comparable reinforced concrete structure satisfying this chapter.
The interaction of all structural and nonstructural members that affect the linear and nonlinear response of the structure to earthquake motions shall be considered in the analysis.
Rigid members assumed not to be a part of the seismic-force-resisting system shall be permitted provided their effect on the response of the system is considered in the structural design. Consequences of failure of structural and nonstructural members that are not a part of the seismic-force-resisting system shall be considered.
Structural members extending below the base of structure that are required to transmit forces resulting from earthquake effects to the foundation shall comply with the requirements of Chapter 18 that are consistent with the seismic-force-resisting system above the base of structure.
Strength reduction factors shall be in accordance with Chapter 21.
Specified compressive strength of concrete in special moment frames and special structural walls shall be in accordance with the special seismic systems requirements of Table 19.2.1.1.
Reinforcement in special moment frames and special structural walls shall be in accordance with the special seismic systems requirements of 20.2.2.
Except for Type 2 mechanical splices on Grade 60 reinforcement, mechanical splices shall not be located within a distance equal to twice the member depth from the column or beam face for special moment frames or from critical sections where yielding of the reinforcement is likely to occur as a result of lateral displacements beyond the linear range of behavior. Type 2 mechanical splices on Grade 60 reinforcement shall be permitted at any location, except as noted in 18.9.2.1(c).
Welded splices in reinforcement resisting earthquake-induced forces shall conform to 25.5.7 and shall not be located within a distance equal to twice the member depth from the column or beam face for special moment frames or from critical sections where yielding of the reinforcement is likely to occur as a result of lateral displacements beyond the linear range of behavior.
Welding of stirrups, ties, inserts, or other similar elements to longitudinal reinforcement required by design shall not be permitted.
This section shall apply to ordinary moment frames forming part of the seismic-force-resisting system.
Beams shall have at least two continuous bars at both top and bottom faces. Continuous bottom bars shall have area not less than one-fourth the maximum area of bottom bars along the span. These bars shall be anchored to develop f_{y} in tension at the face of support.
Columns having unsupported length ℓ_{u} ≤ 5c_{1} shall have ϕV_{n} at least the lesser of (a) and (b):
(a) The shear associated with development of nominal moment strengths of the column at each restrained end of the unsupported length due to reverse curvature bending. Column flexural strength shall be calculated for the factored axial force, consistent with the direction of the lateral forces considered, resulting in the highest flexural strength.
(b) The maximum shear obtained from design load combinations that include E, with Ω_{o}E substituted for E.
This section shall apply to intermediate moment frames including two-way slabs without beams forming part of the seismic-force-resisting system.
Beams shall have at least two continuous bars at both top and bottom faces. Continuous bottom bars shall have area not less than one-fourth the maximum area of bottom bars along the span. These bars shall be anchored to develop f_{y} in tension at the face of support.
The positive moment strength at the face of the joint shall be at least one-third the negative moment strength provided at that face of the joint. Neither the negative nor the positive moment strength at any section along the length of the beam shall be less than one-fifth the maximum moment strength provided at the face of either joint.
ϕV_{n} shall be at least the lesser of (a) and (b):
(a) The sum of the shear associated with development of nominal moment strengths of the beam at each restrained end of the clear span due to reverse curvature bending and the shear calculated for factored gravity and vertical earthquake loads
(b) The maximum shear obtained from design load combinations that include E, with E taken as twice that prescribed by the general building code
At both ends of the beam, hoops shall be provided over a length of at least 2h measured from the face of the supporting member toward midspan. The first hoop shall be located not more than 2 in. from the face of the supporting member. Spacing of hoops shall not exceed the smallest of (a) through (d):
(a) d/4
(b) Eight times the diameter of the smallest longitudinal bar enclosed
(c) 24 times the diameter of the hoop bar
(d) 12 in.
Transverse reinforcement spacing shall not exceed d/2 throughout the length of the beam.
ϕV_{n} shall be at least the lesser of (a) and (b):
(a) The shear associated with development of nominal moment strengths of the column at each restrained end of the unsupported length due to reverse curvature bending. Column flexural strength shall be calculated for the factored axial force, consistent with the direction of the lateral forces considered, resulting in the highest flexural strength
(b) The maximum shear obtained from factored load combinations that include E, with Ω_{o}E substituted for E
At both ends of the column, hoops shall be provided at spacing s_{o} over a length ℓ_{o} measured from the joint face. Spacing s_{o} shall not exceed the least of (a) through (c):
(a) For Grade 60, the smaller of 8d_{b} of the smallest longitudinal bar enclosed and 8 in.
(b) For Grade 80, the smaller of 6d_{b} of the smallest longitudinal bar enclosed and 6 in.
(c) One-half of the smallest cross-sectional dimension of the column
Length ℓ_{o} shall not be less than the longest of (d), (e), and (f):
(d) One-sixth of the clear span of the column
(e) Maximum cross-sectional dimension of the column
(f) 18 in.
Outside of length ℓ_{o}, spacing of transverse reinforcement shall be in accordance with 10.7.6.5.2.
Columns supporting reactions from discontinuous stiff members, such as walls, shall be provided with transverse reinforcement at the spacing s_{o} in accordance with 18.4.3.3 over the full height beneath the level at which the discontinuity occurs if the portion of factored axial compressive force in these members related to earthquake effects exceeds A_{g}f_{c}'/10. If design forces have been magnified to account for the overstrength of the vertical elements of the seismic-force-resisting system, the limit of A_{g}f_{c}'/10 shall be increased to A_{g}f_{c}'/4. Transverse reinforcement shall extend above and below the column in accordance with 18.7.5.6(b).
If a beam framing into the joint and generating joint shear has depth exceeding twice the column depth, analysis and design of the joint shall be based on the strut-and-tie method in accordance with Chapter 23 and (a) and (b) shall be satisfied:
(a) Design joint shear strength determined in accordance with Chapter 23 shall not exceed ϕV_{n} calculated in accordance with 15.4.2.
Longitudinal reinforcement terminated in a joint shall extend to the far face of the joint core and shall be developed in tension in accordance with 18.8.5 and in compression in accordance with 25.4.9.
Spacing of joint transverse reinforcement s shall not exceed the lesser of 18.4.3.3(a) through (c) within the height of the deepest beam framing into the joint.
Where the top beam longitudinal reinforcement consists of headed deformed bars that terminate in the joint, the column shall extend above the top of the joint a distance at least the depth h of the joint. Alternatively, the beam reinforcement shall be enclosed by additional vertical joint reinforcement providing equivalent confinement to the top face of the joint.
Slab-column joints shall satisfy transverse reinforcement requirements of 15.3.2. Where slab-column joint transverse reinforcement is required, at least one layer of joint transverse reinforcement shall be placed between the top and bottom slab reinforcement.
ϕ shall be in accordance with 21.2.1 for shear.
Reinforcement placed within the effective width given in 8.4.2.2.3 shall be designed to resist γ_{f}M_{sc}. Effective slab width for exterior and corner connections shall not extend beyond the column face a distance greater than c_{t} measured perpendicular to the slab span.
At least one-half of the reinforcement in the column strip at the support shall be placed within the effective slab width given in 8.4.2.2.3.
At least one-fourth of the top reinforcement at the support in the column strip shall be continuous throughout the span.
Continuous bottom reinforcement in the column strip shall be at least one-third of the top reinforcement at the support in the column strip.
At least one-half of all bottom middle strip reinforcement and all bottom column strip reinforcement at midspan shall be continuous and shall develop f_{y} at the face of columns, capitals, brackets, or walls.
At discontinuous edges of the slab, all top and bottom reinforcement at the support shall be developed at the face of columns, capitals, brackets, or walls.
At the critical sections for columns defined in 22.6.4.1, two-way shear stress caused by factored gravity loads without moment transfer shall not exceed 0.4ϕv_{c} for nonprestressed slab-column connections and 0.5ϕv_{c} for unbonded post-tensioned slab-column connections with f_{pc} in each direction meeting the requirements of 8.6.2.1, where v_{c} shall be calculated in accordance with 22.6.5. This requirement need not be satisfied if the slab-column connection satisfies 18.14.5.
This section shall apply to intermediate precast structural walls forming part of the seismic-force-resisting system.
In connections between wall panels, or between wall panels and the foundation, yielding shall be restricted to steel elements or reinforcement.
Connections that are designed to yield shall be capable of maintaining 80 percent of their design strength at the deformation induced by the design displacement or shall use Type 2 mechanical splices.
In structures assigned to SDC D, E or F, wall piers shall be designed in accordance with 18.10.8 or 18.14 in ACI 318.
This section shall apply to beams of special moment frames that form part of the seismic-force-resisting system and are proportioned primarily to resist flexure and shear.
Beams shall have at least two continuous bars at both top and bottom faces. At any section, for top as well as for bottom reinforcement, the amount of reinforcement shall be at least that required by 9.6.1.2, and the reinforcement ratio ρ shall not exceed 0.025 for Grade 60 reinforcement and 0.02 for Grade 80 reinforcement.
Positive moment strength at joint face shall be at least one-half the negative moment strength provided at that face of the joint. Both the negative and the positive moment strength at any section along member length shall be at least one-fourth the maximum moment strength provided at face of either joint.
Lap splices of deformed longitudinal reinforcement shall be permitted if hoop or spiral reinforcement is provided over the lap length. Spacing of the transverse reinforcement enclosing the lap-spliced bars shall not exceed the lesser of d/4 and 4 in. Lap splices shall not be used in locations (a) through (c):
(a) Within the joints
(c) Within a distance of twice the beam depth from critical sections where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior
Unless used in a special moment frame as permitted by 18.9.2.3, prestressing shall satisfy (a) through (d):
(a) The average prestress f_{pc} calculated for an area equal to the least cross-sectional dimension of the beam multiplied by the perpendicular cross-sectional dimension shall not exceed the lesser of 500 psi and f_{c}'/10.
(b) Prestressed reinforcement shall be unbonded in potential plastic hinge regions, and the calculated strains in prestressed reinforcement under the design displacement shall be less than 0.01.
(c) Prestressed reinforcement shall not contribute more than one-fourth of the positive or negative flexural strength at the critical section in a plastic hinge region and shall be anchored at or beyond the exterior face of the joint.
(d) Anchorages of post-tensioning tendons resisting earthquake-induced forces shall be capable of allowing tendons to withstand 50 cycles of loading, with prestressed reinforcement forces bounded by 40 and 85 percent of the specified tensile strength of the prestressing reinforcement.
Hoops shall be provided in the following regions of a beam:
(a) Over a length equal to twice the beam depth measured from the face of the supporting column toward midspan, at both ends of the beam
(b) Over lengths equal to twice the beam depth on both sides of a section where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior.
Where hoops are required, primary longitudinal reinforcing bars closest to the tension and compression faces shall have lateral support in accordance with 25.7.2.3 and 25.7.2.4. The spacing of transversely supported flexural reinforcing bars shall not exceed 14 in. Skin reinforcement required by 9.7.2.3 need not be laterally supported.
Hoops in beams shall be permitted to be made up of two pieces of reinforcement: a stirrup having seismic hooks at both ends and closed by a crosstie. Consecutive crossties engaging the same longitudinal bar shall have their 90-degree hooks at opposite sides of the flexural member. If the longitudinal reinforcing bars secured by the crossties are confined by a slab on only one side of the beam, the 90-degree hooks of the crossties shall be placed on that side.
The first hoop shall be located not more than 2 in. from the face of a supporting column. Spacing of the hoops shall not exceed the least of (a) through (d):
(a) d/4
(b) 6 in.
(c) For Grade 60, 6d_{b} of the smallest primary flexural reinforcing bar excluding longitudinal skin reinforcement required by 9.7.2.3
(d) For Grade 80, 5d_{b} of the smallest primary flexural reinforcing bar excluding longitudinal skin reinforcement required by 9.7.2.3
Where hoops are not required, stirrups with seismic hooks at both ends shall be spaced at a distance not more than d/2 throughout the length of the beam.
In beams having factored axial compressive force exceeding A_{g}f_{c}'/10, hoops satisfying 18.7.5.2 through 18.7.5.4 shall be provided along lengths given in 18.6.4.1. Along the remaining length, hoops satisfying 18.7.5.2 shall have spacing s not exceeding the least of 6 in., 6d_{b} of the smallest Grade 60 enclosed longitudinal beam bar, and 5d_{b} of the smallest Grade 80 enclosed longitudinal beam bar. Where concrete cover over transverse reinforcement exceeds 4 in., additional transverse reinforcement having cover not exceeding 4 in. and spacing not exceeding 12 in. shall be provided.
The design shear force V_{e} shall be calculated from consideration of the forces on the portion of the beam between faces of the joints. It shall be assumed that moments of opposite sign corresponding to probable flexural strength, M_{pr}, act at the joint faces and that the beam is loaded with the factored gravity and vertical earthquake loads along its span.
Transverse reinforcement over the lengths identified in 18.6.4.1 shall be designed to resist shear assuming V_{c} = 0 when both (a) and (b) occur:
(a) The earthquake-induced shear force calculated in accordance with 18.6.5.1 represents at least one-half of the maximum required shear strength within those lengths.
(b) The factored axial compressive force P_{u} including earthquake effects is less than A_{g}f_{c}'/20.
This section shall apply to columns of special moment frames that form part of the seismic-force-resisting system and are proportioned primarily to resist flexure, shear, and axial forces.
Columns shall satisfy (a) and (b):
(a) The shortest cross-sectional dimension, measured on a straight line passing through the geometric centroid, shall be at least 12 in.
(b) The ratio of the shortest cross-sectional dimension to the perpendicular dimension shall be at least 0.4.
Columns shall satisfy 18.7.3.2 or 18.7.3.3, except at connections where the column is discontinuous above the connection and the column factored axial compressive force P_{u} under load combinations including earthquake effect, E, are less than A_{g}f_{c}'/10.
The flexural strengths of the columns shall satisfy
ΣM_{nc} ≥ (6/5)ΣM_{nb} | (18.7.3.2) |
where
ΣM_{nc} is sum of nominal flexural strengths of columns framing into the joint, evaluated at the faces of the joint. Column flexural strength shall be calculated for the factored axial force, consistent with the direction of the lateral forces considered, resulting in the lowest flexural strength.
ΣM_{nb} is sum of nominal flexural strengths of the beams framing into the joint, evaluated at the faces of the joint. In T-beam construction, where the slab is in tension under moments at the face of the joint, slab reinforcement within an effective slab width defined in accordance with 6.3.2 shall be assumed to contribute to M_{nb} if the slab reinforcement is developed at the critical section for flexure.
Area of longitudinal reinforcement, A_{st}, shall be at least 0.01A_{g} and shall not exceed 0.06A_{g}.
Over column clear height, longitudinal reinforcement shall be selected such that 1.25ℓ_{d} ≤ ℓ_{u}/2.
Mechanical splices shall conform to 18.2.7 and welded splices shall conform to 18.2.8. Lap splices shall be permitted only within the center half of the member length, shall be designed as tension lap splices, and shall be enclosed within transverse reinforcement in accordance with 18.7.5.2 and 18.7.5.3.
Transverse reinforcement required in 18.7.5.2 through 18.7.5.4 shall be provided over a length ℓ_{o} from each joint face and on both sides of any section where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior. Length ℓ_{o} shall be at least the greatest of (a) through (c):
(a) The depth of the column at the joint face or at the section where flexural yielding is likely to occur
(b) One-sixth of the clear span of the column
(c) 18 in.
Transverse reinforcement shall be in accordance with (a) through (f):
(a) Transverse reinforcement shall comprise either single or overlapping spirals, circular hoops, or single or overlapping rectilinear hoops with or without crossties.
(c) Crossties of the same or smaller bar size as the hoops shall be permitted, subject to the limitation of 25.7.2.2. Consecutive crossties shall be alternated end for end along the longitudinal reinforcement and around the perimeter of the cross section.
(d) Where rectilinear hoops or crossties are used, they shall provide lateral support to longitudinal reinforcement in accordance with 25.7.2.2 and 25.7.2.3.
(e) Reinforcement shall be arranged such that the spacing h_{x} of longitudinal bars laterally supported by the corner of a crosstie or hoop leg shall not exceed 14 in. around the perimeter of the column.
(f) Where P_{u} > 0.3A_{g}f_{c}' or f_{c}' > 10,000 psi in columns with rectilinear hoops, every longitudinal bar or bundle of bars around the perimeter of the column core shall have lateral support provided by the corner of a hoop or by a seismic hook, and the value of h_{x} shall not exceed 8 in. P_{u} shall be the largest value in compression consistent with factored load combinations including E.
Spacing of transverse reinforcement shall not exceed the least of (a) through (d):
(a) One-fourth of the minimum column dimension
(b) For Grade 60, 6d_{b} of the smallest longitudinal bar
(c) For Grade 80, 5d_{b} of the smallest longitudinal bar
(d) s_{o}, as calculated by:
(18.7.5.3) |
The value of s_{o} from Eq. (18.7.5.3) shall not exceed 6 in. and need not be taken less than 4 in.
Amount of transverse reinforcement shall be in accordance with Table 18.7.5.4.
The concrete strength factor k_{f} and confinement effectiveness factor k_{n} are calculated according to Eq. (18.7.5.4a) and (18.7.5.4b).
(a) | (18.7.5.4a) |
(b) | (18.7.5.4b) |
where n_{l} is the number of longitudinal bars or bar bundles around the perimeter of a column core with rectilinear hoops that are laterally supported by the corner of hoops or by seismic hooks.
Transverse reinforcement | Conditions | Applicable expressions | |
---|---|---|---|
A_{sh}/sb_{c} for rectilinear hoop | P_{u} ≤ 0.3A_{g}f_{c}' and f_{c}' ≤ 10,000 psi | Greater of (a) and (b) | |
P_{u} > 0.3A_{g}f_{c}' or f_{c}' > 10,000 psi | Greatest of (a), (b), and (c) | ||
ρ_{s} for spiral or circular hoop | P_{u} ≤ 0.3A_{g}f_{c}' and f_{c}' ≤ 10,000 psi | Greater of (d) and (e) | |
P_{u} > 0.3A_{g}f_{c}' or f_{c}' > 10,000 psi | Greatest of (d), (e), and (f) |
Beyond the length ℓ_{o} given in 18.7.5.1, the column shall contain spiral reinforcement satisfying 25.7.3 or hoop and crosstie reinforcement satisfying 25.7.2 and 25.7.4 with spacing s not exceeding the least of 6 in., 6d_{b} of the smallest Grade 60 longitudinal column bar, and 5d_{b} of the smallest Grade 80 longitudinal column bar, unless a greater amount of transverse reinforcement is required by 18.7.4.4 or 18.7.6.
Columns supporting reactions from discontinued stiff members, such as walls, shall satisfy (a) and (b):
- Transverse reinforcement required by 18.7.5.2 through 18.7.5.4 shall be provided over the full height at all levels beneath the discontinuity if the factored axial compressive force in these columns, related to earthquake effect, exceeds A_{g}f_{c}'/10. Where design forces have been magnified to account for the overstrength of the vertical elements of the seismic-force-resisting system, the limit of A_{g}f_{c}'/10 shall be increased to A_{g}f_{c}'/4.
- Transverse reinforcement shall extend into the discontinued member at least ℓ_{d} of the largest longitudinal column bar, where ℓ_{d} is in accordance with 18.8.5. Where the lower end of the column terminates on a wall, the required transverse reinforcement shall extend into the wall at least ℓ_{d} of the largest longitudinal column bar at the point of termination. Where the column terminates on a footing or mat, the required transverse reinforcement shall extend at least 12 in. into the footing or mat.
If the concrete cover outside the confining transverse reinforcement required by 18.7.5.1, 18.7.5.5, and 18.7.5.6 exceeds 4 in., additional transverse reinforcement having cover not exceeding 4 in. and spacing not exceeding 12 in. shall be provided.
The design shear force V_{e} shall be calculated from considering the maximum forces that can be generated at the faces of the joints at each end of the column. These joint forces shall be calculated using the maximum probable flexural strengths, M_{pr}, at each end of the column associated with the range of factored axial forces, P_{u}, acting on the column. The column shears need not exceed those calculated from joint strengths based on M_{pr} of the beams framing into the joint. In no case shall V_{e} be less than the factored shear calculated by analysis of the structure.
Transverse reinforcement over the lengths ℓ_{o}, given in 18.7.5.1, shall be designed to resist shear assuming V_{c} = 0 when both (a) and (b) occur:
(a) The earthquake-induced shear force, calculated in accordance with 18.7.6.1, is at least one-half of the maximum required shear strength within ℓ_{o}.
(b) The factored axial compressive force P_{u} including earthquake effects is less than A_{g}f_{c}'/20.
This section shall apply to beam-column joints of special moment frames forming part of the seismic-force-resisting system.
Forces in longitudinal beam reinforcement at the joint face shall be calculated assuming that the stress in the flexural tensile reinforcement is 1.25f_{y}.
Longitudinal reinforcement terminated in a joint shall extend to the far face of the joint core and shall be developed in tension in accordance with 18.8.5 and in compression in accordance with 25.4.9.
Where longitudinal beam reinforcement extends through a beam-column joint, the depth h of the joint parallel to the beam longitudinal reinforcement shall be at least the greatest of (a) through (c):
(a) of the largest Grade 60 longitudinal bar, where λ = 0.75 for lightweight concrete and 1.0 for all other cases
(b) 26d_{b} of the largest Grade 80 longitudinal bar
(c) h/2 of any beam framing into the joint and generating joint shear as part of the seismic-force-resisting system in the direction under consideration
Where beams frame into all four sides of the joint and where each beam width is at least three-fourths the column width, the amount of reinforcement required by 18.7.5.4 shall be permitted to be reduced by one-half, and the spacing required by 18.7.5.3 shall be permitted to be increased to 6 in. within the overall depth h of the shallowest framing beam.
Longitudinal beam reinforcement outside the column core shall be confined by transverse reinforcement passing through the column that satisfies spacing requirements of 18.6.4.4, and requirements of 18.6.4.2, and 18.6.4.3, if such confinement is not provided by a beam framing into the joint.
ϕ shall be in accordance with 21.2.4.4.
V_{n} of the joint shall be in accordance with Table 18.8.4.3.
Table 18.8.4.3—Nominal joint shear strength V_{n}
Column | Beam in direction of V_{u} | Confinement by transverse beams according to 15.2.8 | V_{n}, lb^{[1]} |
---|---|---|---|
Continuous or meets 15.2.6 | Continuous or meets 15.2.7 | Confined | |
Not confined | |||
Other | Confined | ||
Not confined | |||
Other | Continuous or meets 15.2.7 | Confined | |
Not confined | |||
Other | Confined | ||
Not confined |
^{[1]}λ shall be 0.75 for lightweight concrete and 1.0 for normalweight concrete. A_{j} shall be calculated in accordance with 15.4.2.4.
For bar sizes No. 3 through No. 11 terminating in a standard hook, ℓ_{dh} shall be calculated by Eq. (18.8.5.1), but ℓ_{dh} shall be at least the greater of 8d_{b} and 6 in. for normalweight concrete and at least the greater of 10d_{b} and 7-1/2 in. for lightweight concrete.
(18.8.5.1) |
The value of λ shall be 0.75 for concrete containing lightweight aggregate and 1.0 otherwise.
The hook shall be located within the confined core of a column or of a boundary element, with the hook bent into the joint.
For headed deformed bars satisfying 20.2.1.6, development in tension shall be in accordance with 25.4.4, by substituting a bar stress of 1.25f_{y} for f_{y}.
For bar sizes No. 3 through No. 11, ℓ_{d}, the development length in tension for a straight bar, shall be at least the greater of (a) and (b):
Straight bars terminated at a joint shall pass through the confined core of a column or a boundary element. Any portion of ℓ_{d} not within the confined core shall be increased by a factor of 1.6.
If epoxy-coated reinforcement is used, the development lengths in 18.8.5.1, 18.8.5.3, and 18.8.5.4 shall be multiplied by applicable factors in 25.4.2.5 or 25.4.3.2.
This section shall apply to special moment frames constructed using precast concrete forming part of the seismic-force-resisting system.
Special moment frames with ductile connections constructed using precast concrete shall satisfy (a) through (c):
(a) Requirements of 18.6 through 18.8 for special moment frames constructed with cast-in-place concrete
(b) V_{n} for connections calculated according to 22.9 shall be at least 2V_{e}, where V_{e} is in accordance with 18.6.5.1 or 18.7.6.1
(c) Mechanical splices of beam reinforcement shall be located not closer than h/2 from the joint face and shall satisfy 18.2.7
Special moment frames with strong connections constructed using precast concrete shall satisfy (a) through (e):
(a) Requirements of 18.6 through 18.8 for special moment frames constructed with cast-in-place concrete
(b) Provision 18.6.2.1(a) shall apply to segments between locations where flexural yielding is intended to occur due to design displacements
(c) Design strength of the strong connection, ϕS_{n}, shall be at least S_{e}
(d) Primary longitudinal reinforcement shall be made continuous across connections and shall be developed outside both the strong connection and the plastic hinge region
(e) For column-to-column connections, ϕS_{n} shall be at least 1.4S_{e}, ϕM_{n} shall be at least 0.4M_{pr} for the column within the story height, and ϕV_{n} shall be at least V_{e} in accordance with 18.7.6.1
Special moment frames constructed using precast concrete and not satisfying 18.9.2.1 or 18.9.2.2 shall satisfy (a) through (c):
(a) ACI 374.1
(b) Details and materials used in the test specimens shall be representative of those used in the structure
(c) The design procedure used to proportion the test specimens shall define the mechanism by which the frame resists gravity and earthquake effects, and shall establish acceptance values for sustaining that mechanism. Portions of the mechanism that deviate from Code requirements shall be contained in the test specimens and shall be tested to determine upper bounds for acceptance values.
This section shall apply to special structural walls, including ductile coupled walls, and all components of special structural walls including coupling beams and wall piers forming part of the seismic-force-resisting system.
Special structural walls constructed using precast concrete shall be in accordance with 18.11 in addition to 18.10.
The distributed web reinforcement ratios, ρ_{ℓ} and ρ_{t}, for structural walls shall be at least 0.0025, except that if V_{u} does not exceed shall be permitted to be reduced to the values in 11.6. Reinforcement spacing each way in structural walls shall not exceed 18 in. Reinforcement contributing to V_{n} shall be continuous and shall be distributed across the shear plane.
At least two curtains of reinforcement shall be used in a wall if or h_{w}/ℓ_{w} ≥ 2.0, in which h_{w} and ℓ_{w} refer to height and length of entire wall, respectively.
Reinforcement in structural walls shall be developed or spliced for f_{y} in tension in accordance with 25.4, 25.5, and (a) through (d):
(a) Except at the top of a wall, longitudinal reinforcement shall extend at least 12 ft above the point at which it is no longer required to resist flexure but need not extend more than ℓ_{d} above the next floor level.
(b) At locations where yielding of longitudinal reinforcement is likely to occur as a result of lateral displacements, development lengths of longitudinal reinforcement shall be 1.25 times the values calculated for f_{y} in tension.
(c) Lap splices of longitudinal reinforcement within boundary regions shall not be permitted over a height equal to h_{sx} above, and ℓ_{d} below, critical sections where yielding of longitudinal reinforcement is likely to occur as a result of lateral displacements. The value of h_{sx} need not exceed 20 ft. Boundary regions include those within lengths specified in 18.10.6.4(a) and within a length equal to the wall thickness measured beyond the intersecting region(s) of connected walls.
(d) Mechanical splices of reinforcement shall conform to 18.2.7 and welded splices of reinforcement shall conform to 18.2.8.
Walls or wall piers with h_{w}/ℓ_{w} ≥ 2.0 that are effectively continuous from the base of structure to top of wall and are designed to have a single critical section for flexure and axial loads shall have longitudinal reinforcement at the ends of a vertical wall segment that satisfies (a) through (c).
(a) Longitudinal reinforcement ratio within 0.15ℓ_{w} from the end of a vertical wall segment, and over a width equal to the wall thickness, shall be at least .
(b) The longitudinal reinforcement required by 18.10.2.4(a) shall extend vertically above and below the critical section at least the greater of ℓ_{w} and M_{u}/3V_{u}.
(c) No more than 50 percent of the reinforcement required by 18.10.2.4(a) shall be terminated at any one section.
Reinforcement in coupling beams shall be developed for f_{y} in tension in accordance with 25.4, 25.5, and (a) and (b):
- If coupling beams are reinforced according to 18.6.3.1, the development length of longitudinal reinforcement shall be 1.25 times the values calculated for f_{y} in tension.
- If coupling beams are reinforced according to 18.10.7.4, the development length of diagonal reinforcement shall be 1.25 times the values calculated for f_{y} in tension.
The design shear force V_{e} shall be calculated by:
V_{e} = Ω_{v}ω_{v}V_{u} ≤ 3V_{u} | (18.10.3.1) |
where V_{u}, Ω_{v}, and ω_{v} are defined in 18.10.3.1.1, 18.10.3.1.2, and 18.10.3.1.3, respectively.
V_{u} is the shear force obtained from code lateral load analysis with factored load combinations.
Ω_{v} shall be in accordance with Table 18.10.3.1.2.
Table 18.10.3.1.2—Overstrength factor Ω_{v} at critical section
Condition | Ω_{v} | |
---|---|---|
h_{wcs}/ℓ_{w} > 1.5 | Greater of | M_{pr}/M_{u}^{[1]} |
1.5^{[2]} | ||
h_{wcs}/ℓ_{w} ≤ 1.5 | 1.0 |
^{[1]} For the load combination producing the largest value of Ω_{v.}
^{[2]} Unless a more detailed analysis demonstrated a smaller value, but not less than 1.0.
For walls with h_{wc}_{s}/ℓ_{w} < 2.0, ω_{v} shall be taken as 1.0. Otherwise, ω_{v} shall be calculated as:
(18.10.3.1.3) |
where n_{s} shall not be taken less than the quantity 0.007h_{wcs}.
V_{n} shall be calculated by:
(18.10.4.1) |
where:
α_{c} = 3 for h_{w}/ℓ_{w} ≤ 1.5
α_{c} = 2 for h_{w}/ℓ_{w} ≥ 2.0
It shall be permitted to linearly interpolate the value of α_{c} between 3 and 2 for 1.5 < h_{w}/ℓ_{w} < 2.0.
In 18.10.4.1, the value of ratio h_{w}/ℓ_{w} used to calculate V_{n} for segments of a wall shall be the greater of the ratios for the entire wall and the segment of wall considered.
Walls shall have distributed shear reinforcement in two orthogonal directions in the plane of the wall. If h_{w}/ℓ_{w} does not exceed 2.0, reinforcement ratio ρ_{ℓ} shall be at least the reinforcement ratio ρ_{t}.
For all vertical wall segments sharing a common lateral force, V_{n} shall not be taken greater than . For any one of the individual vertical wall segments, V_{n} shall not be taken greater than , where A_{cw} is the area of concrete section of the individual vertical wall segment considered.
For horizontal wall segments and coupling beams, V_{n} shall not be taken greater than , where A_{cw} is the area of concrete section of a horizontal wall segment or coupling beam.
The requirements of 21.2.4.1 shall not apply to walls or wall piers designed according to 18.10.6.2.
Structural walls and portions of such walls subject to combined flexure and axial loads shall be designed in accordance with 22.4. Concrete and developed longitudinal reinforcement within effective flange widths, boundary elements, and the wall web shall be considered effective. The effects of openings shall be considered.
The need for special boundary elements at the edges of structural walls shall be evaluated in accordance with 18.10.6.2 or 18.10.6.3. The requirements of 18.10.6.4 and 18.10.6.5 shall also be satisfied.
Walls or wall piers with h_{wcs}/ℓ_{w} ≥ 2.0 that are effectively continuous from the base of structure to top of wall and are designed to have a single critical section for flexure and axial loads shall satisfy (a) and (b):
(a) Compression zones shall be reinforced with special boundary elements where
(18.10.6.2a) |
and c corresponds to the largest neutral axis depth calculated for the factored axial force and nominal moment strength consistent with the direction of the design displacement δ_{u}. Ratio δ_{u}/h_{wcs} shall not be taken less than 0.005.
(b) If special boundary elements are required by (a), then (i) and either (ii) or (iii) shall be satisfied.
(i) Special boundary element transverse reinforcement shall extend vertically above and below the critical section a least the greater of ℓ_{w} and M_{u}/4V_{u}, except as permitted in 18.10.6.4(j).
(ii)
(iii) δ_{c}/h_{wcs} ≥ 1.5δ_{u}/h_{wcs}, where:
(18.10.6.2b) |
The value of δ_{c}/h_{wcs} in Eq. (18.10.6.2b) need not be taken less than 0.015.
Structural walls not designed in accordance with 18.10.6.2 shall have special boundary elements at boundaries and edges around openings of structural walls where the maximum extreme fiber compressive stress, corresponding to load combinations including earthquake effects E, exceeds 0.2f_{c}'. The special boundary element shall be permitted to be discontinued where the calculated compressive stress is less than 0.15f_{c}'. Stresses shall be calculated for the factored loads using a linearly elastic model and gross section properties. For walls with flanges, an effective flange width as given in 18.10.5.2 shall be used.
If special boundary elements are required by 18.10.6.2 or 18.10.6.3, (a) through (k) shall be satisfied:
(a) The boundary element shall extend horizontally from the extreme compression fiber a distance at least the greater of c — 0.1ℓ_{w} and c/2, where c is the largest neutral axis depth calculated for the factored axial force and nominal moment strength consistent with δ_{u}.
(b) Width of the flexural compression zone, b, over the horizontal distance calculated by 18.10.6.4(a), including flange if present, shall be at least h_{u}/16.
(c) For walls or wall piers with h_{w}/ℓ_{w} ≥ 2.0 that are effectively continuous from the base of structure to top of wall, designed to have a single critical section for flexure and axial loads, and with c/ℓ_{w} ≥ 3/8, width of the flexural compression zone b over the length calculated in 18.10.6.4(a) shall be greater than or equal to 12 in.
(d) In flanged sections, the boundary element shall include the effective flange width in compression and shall extend at least 12 in. into the web.
(e) The boundary element transverse reinforcement shall satisfy 18.7.5.2(a) through (d) and 18.7.5.3, except the transverse reinforcement spacing limit of 18.7.5.3(a) shall be one-third of the least dimension of the boundary element. The maximum vertical spacing of transverse reinforcement in the boundary element shall also not exceed that in Table 18.10.6.5(b).
(f) Transverse reinforcement shall be arranged such that the spacing h_{x} between laterally supported longitudinal bars around the perimeter of the boundary element shall not exceed the lesser of 14 in. and two-thirds of the boundary element thickness. Lateral support shall be provided by a seismic hook of a crosstie or corner of a hoop. The length of a hoop leg shall not exceed two times the boundary element thickness, and adjacent hoops shall overlap at least the lesser of 6 in. and two-thirds the boundary element thickness.
(g) The amount of transverse reinforcement shall be in accordance with Table 18.10.6.4(g).
Table 18.10.6.4(g)—Transverse reinforcement for special boundary elements
Transverse reinforcement | Applicable expressions | ||
---|---|---|---|
A_{sh}/sb_{c} for rectilinear hoop | Greater of | (a) | |
(b) | |||
ρ_{s} for spiral or circular hoop | Greater of | (c) | |
(d) |
(h) Concrete within the thickness of the floor system at the special boundary element location shall have specified compressive strength at least 0.7 times f_{c}' of the wall.
(i) For a distance above and below the critical section specified in 18.10.6.2(b), web vertical reinforcement shall have lateral support provided by the corner of a hoop or by a crosstie with seismic hooks at each end. Transverse reinforcement shall have a vertical spacing not to exceed 12 in. and diameter satisfying 25.7.2.2.
(j) Where the critical section occurs at the wall base, the boundary element transverse reinforcement at the wall base shall extend into the support at least ℓ_{d}, in accordance with 18.10.2.3, of the largest longitudinal reinforcement in the special boundary element. Where the special boundary element terminates on a footing, mat, or pile cap, special boundary element transverse reinforcement shall extend at least 12 in. into the footing, mat, or pile cap, unless a greater extension is required by 18.13.2.4.
(k) Horizontal reinforcement in the wall web shall extend to within 6 in. of the end of the wall. Reinforcement shall be anchored to develop f_{y} within the confined core of the boundary element using standard hooks or heads. Where the confined boundary element has sufficient length to develop the horizontal web reinforcement, and A_{s}f_{y}/s of the horizontal web reinforcement does not exceed A_{s}f_{yt}/s of the boundary element transverse reinforcement parallel to the horizontal web reinforcement, it shall be permitted to terminate the horizontal web reinforcement without a standard hook or head.
Where special boundary elements are not required by 18.10.6.2 or 18.10.6.3, (a) and (b) shall be satisfied:
(a) Except where V_{u} in the plane of the wall is less than , horizontal reinforcement terminating at the edges of structural walls without boundary elements shall have a standard hook engaging the edge reinforcement or the edge reinforcement shall be enclosed in U-stirrups having the same size and spacing as, and spliced to, the horizontal reinforcement.
(b) If the maximum longitudinal reinforcement ratio at the wall boundary exceeds 400/f_{y}, boundary transverse reinforcement shall satisfy 18.7.5.2(a) through (e) over the distance calculated in accordance with 18.10.6.4(a). The vertical spacing of transverse reinforcement at the wall boundary shall be in accordance with Table 18.10.6.5(b).
Table 18.10.6.5(b)—Maximum vertical spacing of transverse reinforcement at wall boundary
Grade of primary flexural reinforcing bar | Transverse reinforcement required | Maximum vertical spacing of transverse reinforcement^{[1]} | |
---|---|---|---|
60 | Within the greater of ℓ_{w} and M_{u}/4V_{u} above and below critical sections^{[2]} | Lesser of: | 6d_{b} |
6 in. | |||
Other locations | Lesser of: | 8d_{b} | |
8 in. | |||
80 | Within the greater of ℓ_{w} and M_{u}/4V_{u} above and below critical sections^{[2]} | Lesser of: | 5d_{b} |
6 in. | |||
Other locations | Lesser of: | 6d_{b} | |
6 in. | |||
100 | Within the greater of ℓ_{w} and M_{u}/4V_{u} above and below critical sections^{[2]} | Lesser of: | 4d_{b} |
6 in. | |||
Other locations | Lesser of: | 6d_{b} | |
6 in. |
^{[1]}In this table, d_{b} is the diameter of the smallest primary flexural reinforcing bar.
^{[2]}Critical sections are defined as locations where yielding of longitudinal reinforcement is likely to occur as a result of lateral displacements.
Coupling beams with (ℓ_{n}/h) < 2 and with shall be reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan, unless it can be shown that loss of stiffness and strength of the coupling beams will not impair the vertical load-carrying ability of the structure, the egress from the structure, or the integrity of nonstructural components and their connections to the structure.
Coupling beams reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan shall satisfy (a), (b), and either (c) or (d), and the requirements of 9.9 need not be satisfied:
(a) V_{n} shall be calculated by
(18.10.7.4) |
where α is the angle between the diagonal bars and the longitudinal axis of the coupling beam.
(b) Each group of diagonal bars shall consist of a minimum of four bars provided in two or more layers.
(c) Each group of diagonal bars shall be enclosed by rectilinear transverse reinforcement having out-to-out dimensions of at least b_{w}/2 in the direction parallel to b_{w} and b_{w}/5 along the other sides, where b_{w} is the web width of the coupling beam. The transverse reinforcement shall be in accordance with 18.7.5.2(a) through (e), with A_{sh} not less than the greater of (i) and (ii):
(i)
(ii)
For the purpose of calculating A_{g}, the concrete cover in 20.5.1 shall be assumed on all four sides of each group of diagonal bars. The transverse reinforcement shall have spacing measured parallel to the diagonal bars satisfying 18.7.5.3(d) and not exceeding 6d_{b} of the smallest diagonal bars, and shall have spacing of crossties or legs of hoops measured perpendicular to the diagonal bars not exceeding 14 in. The transverse reinforcement shall continue through the intersection of the diagonal bars. At the intersection, it is permitted to modify the arrangement of the transverse reinforcement provided the spacing and volume ratio requirements are satisfied. Additional longitudinal and transverse reinforcement shall be distributed around the beam perimeter with total area in each direction of at least 0.002b_{w}s and spacing not exceeding 12 in.
(d) Transverse reinforcement shall be provided for the entire beam cross section in accordance with 18.7.5.2(a) through (e) with A_{sh} not less than the greater of (i) and (ii):
(i)
(ii)
Longitudinal spacing of transverse reinforcement shall not exceed the lesser of 6 in. and 6d_{b} of the smallest diagonal bars. Spacing of crossties or legs of hoops both vertically and horizontally in the plane of the beam cross section shall not exceed 8 in. Each crosstie and each hoop leg shall engage a longitudinal bar of equal or greater diameter. It shall be permitted to configure hoops as specified in 18.6.4.3.
Wall piers shall satisfy the special moment frame requirements for columns of 18.7.4, 18.7.5, and 18.7.6, with joint faces taken as the top and bottom of the clear height of the wall pier. Alternatively, wall piers with (ℓ_{w}/b_{w}) > 2.5 shall satisfy (a) through (f):
(a) Design shear force shall be calculated in accordance with 18.7.6.1 with joint faces taken as the top and bottom of the clear height of the wall pier. If the general building code includes provisions to account for overstrength of the seismic-force-resisting system, the design shear force need not exceed Ω_{o} times the factored shear calculated by analysis of the structure for earthquake load effects.
(b) V_{n} and distributed shear reinforcement shall satisfy 18.10.4.
(c) Transverse reinforcement shall be hoops except it shall be permitted to use single-leg horizontal reinforcement parallel to ℓ_{w} where only one curtain of distributed shear reinforcement is provided. Single-leg horizontal reinforcement shall have 180-degree bends at each end that engage wall pier boundary longitudinal reinforcement.
(d) Vertical spacing of transverse reinforcement shall not exceed 6 in.
(e) Transverse reinforcement shall extend at least 12 in. above and below the clear height of the wall pier.
(f) Special boundary elements shall be provided if required by 18.10.6.3.
For wall piers at the edge of a wall, horizontal reinforcement shall be provided in adjacent wall segments above and below the wall pier and be designed to transfer the design shear force from the wall pier into the adjacent wall segments.
Ductile coupled walls shall satisfy the requirements of this section.
Individual walls shall satisfy h_{wcs}/ℓ_{w} ≥ 2 and the applicable provisions of 18.10 for special structural walls.
Construction joints in structural walls shall be specified according to 26.5.6, and contact surfaces shall be roughened consistent with condition (b) of Table 22.9.4.2.
This section shall apply to special structural walls constructed using precast concrete forming part of the seismic-force-resisting system.
Special structural walls constructed using precast concrete shall satisfy all the requirements of 18.10 for cast-in-place special structural walls in addition to 18.5.2.
Special structural walls constructed using precast concrete and unbonded post-tensioning tendons and not satisfying the requirements of 18.11.2.1 are permitted provided they satisfy the requirements of ACI ITG-5.1.
This section shall apply to diaphragms and collectors forming part of the seismic-force-resisting system in structures assigned to SDC D, E, or F and to SDC C if 18.12.1.2 applies.
Section 18.12.11 shall apply to diaphragms constructed using precast concrete members and forming part of the seismic-force-resisting system for structures assigned to SDC C, D, E, or F.
Section 18.12.12 shall apply to structural trusses forming part of the seismic-force-resisting system in structures assigned to SDC D, E, or F.
The earthquake design forces for diaphragms shall be obtained from the general building code using the applicable provisions and load combinations.
All diaphragms and their connections shall be designed and detailed to provide for transfer of forces to collector elements and to the vertical elements of the seismic-force-resisting system.
Elements of a structural diaphragm system that are subjected primarily to axial forces and used to transfer diaphragm shear or flexural forces around openings or other discontinuities shall satisfy the requirements for collectors in 18.12.7.6 and 18.12.7.7.
A cast-in-place composite topping slab on a precast floor or roof shall be permitted as a structural diaphragm, provided the cast-in-place topping slab is reinforced and the surface of the previously hardened concrete on which the topping slab is placed is clean, free of laitance, and intentionally roughened.
A cast-in-place noncomposite topping on a precast floor or roof shall be permitted as a structural diaphragm, provided the cast-in-place topping slab acting alone is designed and detailed to resist the design earthquake forces.
Concrete slabs and composite topping slabs serving as diaphragms used to transmit earthquake forces shall be at least 2 in. thick. Topping slabs placed over precast floor or roof elements, acting as diaphragms and not relying on composite action with the precast elements to resist the design earthquake forces, shall be at least 2-1/2 in. thick.
The minimum reinforcement ratio for diaphragms shall be in conformance with 24.4. Except for post-tensioned slabs, reinforcement spacing each way in floor or roof systems shall not exceed 18 in. Where welded wire reinforcement is used as the distributed reinforcement to resist shear in topping slabs placed over precast floor and roof elements, the wires parallel to the joints between the precast elements shall be spaced not less than 10 in. on center. Reinforcement provided for shear strength shall be continuous and shall be distributed uniformly across the shear plane.
Bonded tendons used as reinforcement to resist collector forces, diaphragm shear, or flexural tension shall be designed such that the stress due to design earthquake forces does not exceed 60,000 psi. Precompression from unbonded tendons shall be permitted to resist diaphragm design forces if a seismic load path is provided.
All reinforcement used to resist collector forces, diaphragm shear, or flexural tension shall be developed or spliced for f_{y} in tension.
Type 2 splices are required where mechanical splices on Grade 60 reinforcement are used to transfer forces between the diaphragm and the vertical elements of the seismic-force-resisting system. Grade 80 and Grade 100 reinforcement shall not be mechanically spliced for this application.
Longitudinal reinforcement for collectors shall be proportioned such that the average tensile stress over length (a) or (b) does not exceed ϕf_{y} where the value of f_{y} is limited to 60,000 psi.
(a) Length between the end of a collector and location at which transfer of load to a vertical element begins
(b) Length between two vertical elements
Collector elements with compressive stresses exceeding 0.2f_{c}' at any section shall have transverse reinforcement satisfying 18.7.5.2(a) through (e) and 18.7.5.3, except the spacing limit of 18.7.5.3(a) shall be one-third of the least dimension of the collector. The amount of transverse reinforcement shall be in accordance with Table 18.12.7.6. The specified transverse reinforcement is permitted to be discontinued at a section where the calculated compressive stress is less than 0.15f_{c}'.
If design forces have been amplified to account for the overstrength of the vertical elements of the seismic-force-resisting system, the limit of 0.2f_{c}' shall be increased to 0.5f_{c}', and the limit of 0.15f_{c}' shall be increased to 0.4f_{c}'.
Table 18.12.7.6—Transverse reinforcement for collector elements
Transverse reinforcement | Applicable expressions | ||
---|---|---|---|
A_{sh}/sb_{c} for rectilinear hoop | (a) | ||
ρ_{s} for spiral or circular hoop | Greater of: | (b) | |
(c) |
Longitudinal reinforcement detailing for collector elements at splices and anchorage zones shall satisfy (a) or (b):
(a) Center-to-center spacing of at least three longitudinal bar diameters, but not less than 1-1/2 in., and concrete clear cover of at least two and one-half longitudinal bar diameters, but not less than 2 in.
(b) Area of transverse reinforcement, providing A_{v} at least the greater of and 50b_{w}s/f_{yt}, except as required in 18.12.7.6
Diaphragms and portions of diaphragms shall be designed for flexure in accordance with Chapter 12. The effects of openings shall be considered.
V_{n} of diaphragms shall not exceed:
(18.12.9.1) |
For cast-in-place topping slab diaphragms on precast floor or roof members, A_{cv} shall be calculated using only the thickness of topping slab for noncomposite topping slab diaphragms and the combined thickness of cast-in-place and precast elements for composite topping slab diaphragms. For composite topping slab diaphragms, the value of f_{c}' used to calculate V_{n} shall not exceed the lesser of f_{c}' for the precast members and f_{c}' for the topping slab.
V_{n} of diaphragms shall not exceed .
Above joints between precast elements in noncomposite and composite cast-in-place topping slab diaphragms, V_{n} shall not exceed:
V_{n} = A_{vf}f_{y}µ | (18.12.9.3) |
where A_{vf} is the total area of shear friction reinforcement within the topping slab, including both distributed and boundary reinforcement, that is oriented perpendicular to joints in the precast system and coefficient of friction, µ, is 1.0λ, where λ is given in 19.2.4. At least one-half of A_{vf} shall be uniformly distributed along the length of the potential shear plane. The area of distributed reinforcement in the topping slab shall satisfy 24.4.3.2 in each direction.
Diaphragms and collectors constructed using precast concrete members with composite topping slab and not satisfying 18.12.4, and untopped precast concrete diaphragms, are permitted provided they satisfy the requirements of ACI 550.5. Cast-in-place noncomposite topping slab diaphragms shall satisfy 18.12.5 and 18.12.6.
Connections and reinforcement at joints used in the construction of precast concrete diaphragms satisfying 18.12.11.1 shall have been tested in accordance with ACI 550.4.
Extrapolation of data on connections and reinforcement at joints to project details that result in larger construction tolerances than those used to qualify connections in accordance with ACI 550.4 shall not be permitted.
Structural truss elements with compressive stresses exceeding 0.2f_{c}' at any section shall have transverse reinforcement, in accordance with 18.7.5.2, 18.7.5.3, 18.7.5.7, and Table 18.12.12.1, over the length of the element.
Table 18.12.12.1—Transverse reinforcement for structural trusses
Transverse reinforcement | Applicable expressions | ||
---|---|---|---|
A_{sh}/sb_{c} for rectilinear hoop | Greater of: | (a) | |
(b) | |||
ρ_{s} for spiral or circular hoop | Greater of: | (c) | |
(d) |
All continuous reinforcement in structural truss elements shall be developed or spliced for f_{y} in tension.
Foundations resisting earthquake-induced forces or transferring earthquake-induced forces between a structure and ground shall comply with the requirements of 18.13 and other applicable provisions of ACI 318 unless modified by Chapter 18 of the International Building Code.
The provisions of this section shall apply to structures assigned to SDC D, E, or F.
Longitudinal reinforcement of columns and structural walls resisting forces induced by earthquake effects shall extend into the footing, mat, or pile cap, and shall be fully developed for tension at the interface.
Columns designed assuming fixed-end conditions at the foundation shall comply with 18.13.2.2 and, if hooks are required, longitudinal reinforcement resisting flexure shall have 90-degree hooks near the bottom of the foundation with the free end of the bars oriented toward the center of the column.
Columns or boundary elements of special structural walls that have an edge within one-half the footing depth from an edge of the footing shall have transverse reinforcement in accordance with 18.7.5.2 through 18.7.5.4 provided below the top of the footing. This reinforcement shall extend into the footing, mat, or pile cap a length equal to the development length, calculated for f_{y} in tension, of the column or boundary element longitudinal reinforcement.
Where earthquake effects create uplift forces in boundary elements of special structural walls or columns, flexural reinforcement shall be provided in the top of the footing, mat, or pile cap to resist actions resulting from the factored load combinations, and shall be at least that required by 7.6.1 or 9.6.1.
Pile caps incorporating batter piles shall be designed to resist the full compressive strength of the batter piles acting as short columns. The slenderness effects of batter piles shall be considered for the portion of the piles in soil that is not capable of providing lateral support, or in air or water.
For structures assigned to SDC D, E, or F, grade beams and beams that are part of a mat foundation subjected to flexure from columns that are part of the seismic-force-resisting system shall be in accordance with 18.6.
For structures assigned to SDC C, D, E, or F, slabs-on-ground that resist in-plane earthquake forces from walls or columns that are part of the seismic-force-resisting system shall be designed as diaphragms in accordance with 18.12. The construction documents shall clearly indicate that the slab-on-ground is a structural diaphragm and part of the seismic-force-resisting system.
For structures assigned to SDC C, D, E, or F, individual pile caps, piers, or caissons shall be interconnected by foundation seismic ties in orthogonal directions, unless it can be demonstrated that equivalent restraint is provided by other means.
For structures assigned to SDC D, E, or F, individual spread footings founded on soil defined in ASCE/SEI 7 as Site Class E or F shall be interconnected by foundation seismic ties.
Where required, foundation seismic ties shall have a design strength in tension and compression at least equal to 0.1S_{DS} times the greater of the pile cap or column factored dead load plus factored live load unless it is demonstrated that equivalent restraint will be provided by (a), (b), (c), or (d):
(a) Reinforced concrete beams within the slab-on-ground
(b) Reinforced concrete slabs-on-ground
(c) Confinement by competent rock, hard cohesive soils, or very dense granular soils
(d) Other means approved by the building official
For structures assigned to SDC D, E, or F, grade beams designed to act as horizontal foundation seismic ties between pile caps or footings shall have continuous longitudinal reinforcement that shall be developed within or beyond the supported column or anchored within the pile cap or footing at all discontinuities and shall satisfy (a) and (b):
(a) The smallest cross-sectional dimension of the grade beam shall be at least equal to the clear spacing between connected columns divided by 20, but need not exceed 18 in.
(b) Closed tie transverse reinforcement shall be provided at a spacing not to exceed the lesser of 0.5 times the smallest orthogonal cross-sectional dimension and 12 in.
This section shall apply to the following types of deep foundations
(c) Concrete filled pipe piles
For structures assigned to SDC C, D, E, or F, piles, piers, or caissons resisting tension loads shall have continuous longitudinal reinforcement over their length to resist design tension forces.
For structures assigned to SDC C, D, E, or F, the minimum longitudinal and transverse reinforcement required by 18.13.5.7 through 18.13.5.10 shall be extended over the entire unsupported length for the portion of deep foundation member in air or water, or in soil that is not capable of providing adequate lateral restraint to prevent buckling throughout this length.
For structures assigned to SDC C, D, E, or F, hoops, spirals, and ties in deep foundation members shall be terminated with seismic hooks.
For structures assigned to SDC D, E, or F or located in Site Class E or F, concrete deep foundation members shall have transverse reinforcement in accordance with 18.7.5.2, 18.7.5.3, and Table 18.7.5.4 Item (e) within seven member diameters above and below the interfaces between strata that are hard or stiff and strata that are liquefiable or soft.
For structures assigned to SDC C, D, E, or F, reinforcement shall be provided in uncased cast-in-place drilled or augered concrete piles where required by analysis and in accordance with the requirements in Table 18.13.5.7.1.
Table 18.13.5.7.1—Minimum reinforcement for uncased cast-in-place or augered concrete piles or piers
Minimum reinforcement | SDC C — All Site Classes | SDC D, E, and F — Site Class A, B, C, and D | SDC D, E, and F — Site Class E and F | |
---|---|---|---|---|
Minimum longitudinal reinforcement ratio (minimum number of bars) | 0.0025 (minimum number of bars in accordance with 10.7.3.1) | 0.005 (minimum number of bars in accordance with 10.7.3.1) | 0.005 (minimum number of bars in accordance with 10.7.3.1) | |
Minimum reinforced pile length | Longest of (a) through (d): (a) 1/3 pile length (b) 10 ft (c) 3 times the pile diameter (d) Flexural length of pile - distance from bottom of pile cap to where 0.4M_{cr} exceeds M_{u} | Longest of (a) through (d): (a) 1/2 pile length (b) 10 ft (c) 3 times the pile diameter (d) Flexural length of pile - distance from bottom of pile cap to where 0.4M_{cr} exceeds M_{u} | Full length of pile except in accordance with [1] or [2]. | |
Transverse confinement reinforcement zone | Length of reinforcement zone | 3 times the pile diameter from the bottom of the pile cap | 3 times the pile diameter from the bottom of the pile cap | 7 times the pile diameter from the bottom of the pile cap |
Type of transverse reinforcement | Closed ties or spirals with a minimum 3/8 in. diameter | Minimum of No. 3 closed tie or 3/8 in. diameter spiral for piles ≤ 20 in. diameter Minimum No. 4 closed tie or 1/2 in. diameter spiral for piles > 20 in. diameter | ||
In accordance with 18.7.5.2 | ||||
Spacing and amount of transverse reinforcement | Spacing shall not exceed lesser of 6 in. or 8 longitudinal bar diameters | In accordance with 18.7.5.3 and not less than one-half the requirement of Table 18.7.5.4 Item (e) | In accordance with 18.7.5.3 and not less than the requirement of Table 18.7.5.4 Item (e). | |
Transverse reinforcement in remainder of reinforced pile length | Type of transverse reinforcement | Closed ties or spirals with minimum 3/8 in. diameter | Minimum of No. 3 closed tie or 3/8 in. diameter spiral for piles ≤ 20 in. diameter Minimum of No. 4 closed tie or 1/2 in. diameter spiral for piles > 20 in. diameter | |
In accordance with 18.7.5.2 | ||||
Spacing and amount of transverse reinforcement | Maximum spacing of 16 longitudinal bar diameters | Spacing shall not exceed the least of (a) through (c): (a) 12 longitudinal bar diameters (b) 1/2 the pile diameter (c) 12 in. |
[1] For piles sufficiently embedded in firm soil or rock, reinforcement shall be permitted to be terminated a length above the tip equal to the lesser of 5 percent of the pile length and 33 percent of the length of the pile within rock or firm soil.
[2] In lieu of providing full length minimum flexural reinforcement, the deep foundation element shall be designed to withstand maximum imposed curvatures from the earthquake ground motions and structural response. Curvatures shall include free-field soil strains modified for soil-foundation-structure interaction coupled with foundation element deformations associated with earthquake loads imparted to the foundation by the structure. Minimum reinforced length shall not be less than the requirement for SDC D, E, or F; Site Class D.
Minimum longitudinal and transverse reinforcement shall be provided along minimum reinforced lengths measured from the top of the pile in accordance with Table 18.13.5.7.1.
Longitudinal reinforcement shall extend at least the development length in tension beyond the flexural length of the pile, which is defined in Table 18.13.5.7.1 as the distance from the bottom of the pile cap to where 0.4M_{cr} > M_{u}.
For structures assigned to SDC C, D, E, or F, longitudinal reinforcement requirements and minimum reinforced lengths for metal-cased concrete piles shall be the same as for uncased concrete piles in 18.13.5.7.
Metal-cased concrete piles shall have a spiral-welded metal casing of a thickness not less than 0.0747 in. (No. 14 gauge) that is adequately protected from possible deleterious action due to soil constituents, changing water levels, or other factors indicated by boring records of site conditions.
For structures assigned to SDC C, D, E or F, concrete-filled pipe piles shall have longitudinal reinforcement in the top of the pile with a total area of at least 0.01A_{g} and with a minimum length within the pile equal to two times the required embedment length into the pile cap, but not less than the development length in tension of the reinforcement.
For precast concrete driven piles, the length of transverse reinforcement provided shall be sufficient to account for potential variations in the elevation of pile tips.
Precast nonprestressed concrete piles for structures assigned to SDC C shall satisfy (a) through (d):
(a) Minimum longitudinal steel reinforcement ratio shall be 0.01.
(b) Longitudinal reinforcement shall be enclosed within a minimum of No. 3 closed ties or 3/8 in. diameter spirals, for up to 20 in. diameter piles, and No. 4 closed ties or 1/2 in. diameter spirals, for larger diameter piles.
(c) Spacing of transverse reinforcement within a distance of 3 times the least cross-sectional dimension of the pile from the bottom of the pile cap shall not exceed the lesser of 8 times the diameter of the smallest longitudinal bar and 6 in.
(d) Transverse reinforcement shall be provided throughout the length of the pile at a spacing not exceeding 6 in.
For structures assigned to SDC D, E, or F, precast nonprestressed concrete piles shall satisfy the requirements of 18.13.5.10.2 and the requirements for uncased cast-in-place or augered concrete piles in SDC D, E, or F in Table 18.13.5.7.1.
For structures assigned to SDC C, precast-prestressed concrete piles shall satisfy (a) and (b):
(a) If the transverse reinforcement consists of spirals or circular hoops, the volumetric ratio of transverse reinforcement, ρ_{s}, in the upper 20 ft shall not be less than that calculated by Eq. (18.13.5.10.4a) or calculated from a more detailed analysis by Eq. (18.13.5.10.4b):
(18.13.5.10.4a) |
(18.13.5.10.4b) |
and f_{yt} shall not be taken greater than 100,000 psi.
(b) A minimum of one-half of the volumetric ratio of spiral reinforcement required by Eq. (18.13.5.10.4a) or Eq. (18.13.5.10.4b) shall be provided for the remaining length of the pile.
For structures assigned to SDC D, E, or F, precast-prestressed concrete piles shall satisfy (a) through (e) and the ductile pile region shall be defined as the length of pile measured from the bottom of the pile cap to the point of zero curvature plus 3 times the least pile dimension, but not less than 35 ft. If the total pile length in the soil is 35 ft or less, the ductile pile region shall be taken as the entire length of the pile:
(a) In the ductile pile region, the center-to-center spacing of spirals or hoop reinforcement shall not exceed the least of 0.2 times the least pile dimension, 6 times the diameter of the longitudinal strand, and 6 in.
(b) Spiral reinforcement shall be spliced by lapping one full turn, by welding, or by the use of a mechanical splice. If spiral reinforcement is lap spliced, the ends of the spiral shall terminate in a seismic hook. Mechanical and welded splices of deformed bars shall comply with 25.5.7.
(c) If the transverse reinforcement consists of spirals, or circular hoops, the volumetric ratio of transverse reinforcement, ρ_{s}, in the ductile pile region shall not be less than that calculated by Eq. (18.13.5.10.5a) or calculated from a more detailed analysis by Eq. (18.13.5.10.5b), and the required volumetric ratio shall be permitted to be obtained by providing an inner and outer spiral.
(18.13.5.10.5a) |
(18.13.5.10.5b) |
and f_{yt} shall not be taken as greater than 100,000 psi.
(d) Outside of the ductile pile region, spiral or hoop reinforcement shall be provided with a volumetric ratio not less than one-half of that required within the ductile pile region, and the maximum spacing shall be in accordance with Table 13.4.5.6(b).
(e) If transverse reinforcement consists of rectangular hoops and crossties, the total cross-sectional area of lateral transverse reinforcement in the ductile region shall be the greater of Eq. (18.13.5.10.5c) and Eq. (18.13.5.10.5d). The hoops and crossties shall be equivalent to deformed bars not less than No. 3 in size, and rectangular hoop ends shall terminate at a corner with seismic hooks.
(18.13.5.10.5c) |
(18.13.5.10.5d) |
and f_{yt} shall not be taken as greater than 100,000 psi.
For structures assigned to SDC C, D, E, or F, the maximum factored axial load for precast prestressed piles subjected to a combination of earthquake lateral force and axial load shall not exceed the following values:
(a) 0.2f_{c}'A_{g} for square piles
(b) 0.4f_{c}'A_{g} for circular or octagonal piles
For structures assigned to SDC C, D, E, or F, the longitudinal reinforcement in piles, piers, or caissons resisting tension loads shall be detailed to transfer tension forces within the pile cap to supported structural members.
For structures assigned to SDC C, D, E, or F, concrete piles and concrete filled pipe piles shall be connected to the pile cap by embedding the pile reinforcement in the pile cap a distance equal to the development length or by the use of field-placed dowels anchored in the concrete pile. For deformed bars, the compression development length is used if the pile is in compression. In the case of uplift, the tension development length is used without reduction in length for excess reinforcement.
For structures assigned to SDC D, E, or F, if tension forces induced by earthquake effects are transferred between pile cap or mat foundation and precast pile by reinforcing bars grouted or post-installed in the top of the pile, the grouting system shall have been demonstrated by testing to develop at least 1.25f_{y} of the bar.
This section shall apply to members not designated as part of the seismic-force-resisting system in structures assigned to SDC D, E, and F.
Members not designated as part of the seismic-force-resisting system shall be evaluated for gravity load combinations of 5.3 including the effect of vertical ground motion acting simultaneously with the design displacement δ_{u}.
Cast-in-place beams, columns, and joints shall be detailed in accordance with 18.14.3.2 or 18.14.3.3 depending on the magnitude of moments and shears induced in those members when subjected to the design displacement δ_{u}. If effects of δ_{u} are not explicitly checked, the provisions of 18.14.3.3 shall be satisfied.
Where the induced moments and shears do not exceed the design moment and shear strength of the frame member, (a) through (d) shall be satisfied:
(a) Beams shall satisfy 18.6.3.1. Transverse reinforcement shall be provided throughout the length of the beam at spacing not to exceed d/2. Where factored axial force exceeds A_{g}f_{c}'/10, transverse reinforcement shall be hoops satisfying 18.7.5.2 at a spacing not to exceed the lesser of 6d_{b} of the smallest enclosed longitudinal bar and 6 in.
(b) Columns shall satisfy 18.7.4.1 and 18.7.6. Spiral reinforcement satisfying 25.7.3 or hoop reinforcement satisfying 25.7.4 shall be provided over the full length of the column with spacing not to exceed the lesser of 6d_{b} of the smallest enclosed longitudinal bar and 6 in. Transverse reinforcement satisfying 18.7.5.2(a) through (e) shall be provided over a length ℓ_{o}, as defined in 18.7.5.1, from each joint face.
(c) Columns with factored gravity axial forces exceeding 0.35P_{o} shall satisfy 18.14.3.2(b) and 18.7.5.7. The minimum amount of transverse reinforcement provided shall be, for rectilinear hoops, one-half the greater of Table 18.7.5.4 parts (a) and (b) and, for spiral or circular hoops, one-half the greater of Table 18.7.5.4 parts (d) and (e). This transverse reinforcement shall be provided over a length ℓ_{o}, as defined in 18.7.5.1, from each joint face.
(d) Joints shall satisfy Chapter 15.
Where the induced moments or shears exceed ϕM_{n} or ϕV_{n} of the frame member, or if induced moments or shears are not calculated, (a) through (d) shall be satisfied:
(a) Materials, mechanical splices, and welded splices shall satisfy the requirements for special moment frames in 18.2.5 through 18.2.8.
Precast concrete frame members assumed not to contribute to lateral resistance, including their connections, shall satisfy (a) through (d):
(a) Requirements of 18.14.3
For slab-column connections of two-way slabs without beams, slab shear reinforcement satisfying the requirements of 18.14.5.3 and either 8.7.6 or 8.7.7 shall be provided at any slab critical section defined in 22.6.4.1 for the following conditions:
(a) Nonprestressed slabs where Δ_{x}/h_{sx} ≥ 0.035 — (1/20) (v_{uv}/ϕv_{c})
(b) Unbonded post-tensioned slabs with f_{pc} in each direction meeting the requirements of 8.6.2.1, where Δ_{x}/h_{sx} ≥ 0.040 — (1/20)(v_{uv}/ϕv_{c})
The load combinations to be evaluated for v_{uv} shall only include those with E. The value of (Δ_{x}/h_{sx}) shall be taken as the greater of the values of the adjacent stories above and below the slab-column connection, v_{c} shall be calculated in accordance with 22.6.5; and, for unbonded post-tensioned slabs, the value of V_{p} shall be taken as zero when calculating v_{c}.
The shear reinforcement requirements of 18.14.5.1 need not be satisfied if (a) or (b) is met:
(a) Δ_{x}/h_{sx} ≤ 0.005 for nonprestressed slabs
(b) Δ_{x}/h_{sx} ≤ 0.01 for unbonded post-tensioned slabs with f_{pc} in each direction meeting the requirements of 8.6.2.1
Required slab shear reinforcement shall provide at the slab critical section and shall extend at least four times the slab thickness from the face of the support adjacent to the slab critical section.
Wall piers not designated as part of the seismic-force-resisting system shall satisfy the requirements of 18.10.8. Where the general building code includes provisions to account for overstrength of the seismic-force-resisting system, it shall be permitted to calculate the design shear force as Ω_{o} times the shear induced under design displacements, δ_{u}.