(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 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 also 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.*

*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*:

(a) Ordinary moment frames shall satisfy 18.3.

(b) Ordinary reinforced concrete structural walls *and ordinary precast structural walls* need not satisfy any provisions in Chapter 18.

(c) Intermediate moment frames shall satisfy 18.4.

(d) Intermediate precast *structural* walls shall satisfy 18.5.

(e) Special moment frames shall satisfy 18.6 through 18.9.

(f) Special structural walls shall satisfy 18.10.

(g) Special structural walls constructed using precast concrete shall satisfy 18.11.

All special moment frames and special structural walls shall also satisfy 18.2.4 through 18.2.8.

*Welded splices in special moment frames and special structural walls*

**in tension at the face of support.**

*f*_{y}**shall have**

*ℓ*≤ 5_{u}*c*_{1}**ϕ**at least the lesser of (a) and (b):

*V*_{n}(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**substituted for

_{o}E**.**

*E***in tension at the face of support.**

*f*_{y}*V*shall be at least the lesser of (a) and (b):

_{n}(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 loads

(b) The maximum shear obtained from design load combinations that include ** E**, with

**taken as twice that prescribed by the general building code**

*E***2**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):

*h*(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.

*V*shall be at least the lesser of (a) and (b):

_{n}(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**substituted for

_{o}E

*E***over a length**

*s*_{o}**measured from the joint face. Spacing**

*ℓ*_{o}**shall not exceed the smallest of (a) through (d):**

*s*_{o}(a) 8 times the diameter of the smallest longitudinal bar enclosed

(b) 24 times the diameter of the hoop bar

(c) One-half of the smallest cross-sectional dimension of the column

(d) 12 in.

Length ** ℓ_{o}** shall not be less than the greatest of (e), (f), and (g):

(e) One-sixth of the clear span of the column

(f) Maximum cross-sectional dimension of the column

(g) 18 in.

**, spacing of transverse reinforcement shall be in accordance with 10.7.6.5.2.**

*ℓ*_{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**

*s*_{o}**. 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*/10_{g}f'_{c}**shall be increased to**

*A*/10_{g}f'_{c}**. Transverse reinforcement shall extend above and below the column in accordance with 18.7.5.6(b).**

*A*/4_{g}f'_{c}**γ**. Effective slab width for exterior and corner connections shall not extend beyond the column face a distance greater than

_{f}M_{sc}**measured perpendicular to the slab span.**

*c*_{t}**at the face of support as defined in 8.10.3.2.1.**

*f*_{y}*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.*

*S*of the yielding portion of the connection.

_{y}**ρ**shall not exceed 0.025.

**and 4 in. Lap splices shall not be used in locations (a) through (c):**

*d*/4(a) Within the joints

(b) Within a distance of twice the beam depth from the face of the joint

(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

(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*'/10_{c}(b) Prestressing steel shall be unbonded in potential plastic hinge regions, and the calculated strains in prestressing steel under the design displacement shall be less than 0.01.

(c) Prestressing steel 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 steel.

(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.

(a) *d*/4

(b) Six times the diameter of the smallest primary flexural reinforcing bars excluding longitudinal skin reinforcement required by 9.7.2.3

(c) 6 in.

**throughout the length of the beam.**

*d*/2**, 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**

*A*/10_{g}f'_{c}**not exceeding the lesser of six times the diameter of the smallest longitudinal beam bars and 6 in. 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.**

*s***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,**

*V*_{e}**, act at the joint faces and that the beam is loaded with the factored tributary gravity load along its span.**

*M*_{pr}**when both (a) and (b) occur:**

*V*= 0_{c}(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*/20_{g}f'_{c}(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.

∑ M≥ (6/5)∑_{nc}M_{nb} | (18.7.3.2) |

where

**∑ M_{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.

**∑ M_{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

**if the slab reinforcement is developed at the critical section for flexure.**

*M*_{nb}Flexural strengths shall be summed such that the column moments oppose the beam moments. Equation (18.7.3.2) shall be satisfied for beam moments acting in both directions in the vertical plane of the frame considered.

**, shall be at least**

*A*_{st}**0.01**and shall not exceed

*A*_{g}**0.06**.

*A*_{g}**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):**

*ℓ*_{o}(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.

(a) Transverse reinforcement shall comprise either single or overlapping spirals, circular hoops, or rectilinear hoops with or without crossties.

(b) Bends of rectilinear hoops and crossties shall engage peripheral longitudinal reinforcing bars.

(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

**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**

*f'*> 10,000 psi_{c}**shall not exceed 8 in.**

*h*_{x}**shall be the largest value in compression consistent with factored load combinations including**

*P*_{u}**.**

*E*(a) One-fourth of the minimum column dimension

(b) Six times the diameter of the smallest longitudinal bar

(c) ** 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.

The concrete strength factor ** k_{f}** and confinement effectiveness factor

**are calculated according to Eq. (18.7.5.4a) and (18.7.5.4b).**

*k*_{n}(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.

**Table 18.7.5.4—Transverse reinforcement for columns of special moment frames**

Transverse reinforcement | Conditions | Applicable expressions | |
---|---|---|---|

A/_{sh}sb for rectilinear hoop_{c} | P ≤ 0.3_{u}A' and _{g}f_{c}f' ≤ 10,000 psi_{c} | Greater of (a) and (b) | |

P > 0.3_{u}A' or _{g}f_{c}f' > 10,000 psi_{c} | Greatest of (a), (b), and (c) | ||

ρ_{s} for spiral or circular hoop | P ≤ 0.3_{u}A' and _{g}f_{c}f' ≤ 10,000 psi_{c} | Greater of (d) and (e) | |

P > 0.3_{u}A' or _{g}f_{c}f' > 10,000 psi_{c} | Greatest of (d), (e), and (f) |

**given in 18.7.5.1, the column shall contain spiral or hoop reinforcement satisfying 25.7.2 through 25.7.4 with spacing**

*ℓ*_{o}**not exceeding the lesser of six times the diameter of the smallest longitudinal column bars and 6 in., unless a greater amount of transverse reinforcement is required by 18.7.4.3 or 18.7.6.**

*s*(a) 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

**shall be increased to**

*A*'/10_{g}f_{c}**.**

*A*'/4_{g}f_{c}(b) Transverse reinforcement shall extend into the discontinued member at least ** ℓ_{d}** of the largest longitudinal column bar, where

**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.**

*ℓ*_{d}**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,**

*V*_{e}**, at each end of the column associated with the range of factored axial forces,**

*M*_{pr}**, acting on the column. The column shears need not exceed those calculated from joint strengths based on**

*P*_{u}**of the beams framing into the joint. In no case shall**

*M*_{pr}**be less than the factored shear calculated by analysis of the structure.**

*V*_{e}**, given in 18.7.5.1, shall be designed to resist shear assuming**

*ℓ*_{o}**when both (a) and (b) occur:**

*V*= 0_{c}(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*'/20_{g}f_{c}**1.25**.

*f*_{y}**of the joint shall not be less than one-half of depth**

*h***of any beam framing into the joint and generating joint shear as part of the seismic-force-resisting system.**

*h***of the shallowest framing beam.**

*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.**

*h**V*of the joint shall be in accordance with Table 18.8.4.1.

_{n}**Table 18.8.4.1—Nominal joint shear strength V_{n}**

Joint configuration | V_{n} |
---|---|

For joints confined by beams on all four faces^{[1]} | ^{[2]} |

For joints confined by beams on three faces or on two opposite faces^{[1]} | ^{[2]} |

For other cases | ^{[2]} |

^{[1]}Refer to 18.8.4.2.

^{[2]}λ shall be 0.75 for lightweight concrete and 1.0 for normalweight concrete. *A _{j}* is given in 18.8.4.3.

**beyond the joint face are considered adequate for confining that joint face. Extensions of beams shall satisfy 18.6.2.1(b), 18.6.3.1, 18.6.4.2, 18.6.4.3, and 18.6.4.4.**

*h***, shall be calculated from joint depth times effective joint width. Joint depth shall be the overall depth of the column,**

*A*_{j}**. Effective joint width shall be the overall width of the column, except where a beam frames into a wider column, effective joint width shall not exceed the lesser of (a) and (b):**

*h*(a) Beam width plus joint depth

(b) Twice the smaller perpendicular distance from longitudinal axis of beam to column side

**shall be calculated by Eq. (18.8.5.1), but**

*ℓ*_{dh}**shall be at least the greater of**

*ℓ*_{dh}**8**and 6 in. for normalweight concrete and at least the greater of

*d*_{b}**10**and 7-

*d*_{b}^{1}/

_{2}in. for lightweight concrete.

(18.8.5.1) |

The value of **λ** shall be 0.75 for lightweight and 1.0 for normalweight concrete.

The hook shall be located within the confined core of a column or of a boundary element, with the hook bent into the joint.

**3**or greater.

*d*_{b}**, the development length in tension for a straight bar, shall be at least the greater of (a) and (b):**

*ℓ*_{d}(a) 2.5 times the length in accordance with 18.8.5.1 if the depth of the concrete cast in one lift beneath the bar does not exceed 12 in.

(b) 3.25 times the length in accordance with 18.8.5.1 if the depth of the concrete cast in one lift beneath the bar exceeds 12 in.

**not within the confined core shall be increased by a factor of 1.6.**

*ℓ*_{d}(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

**2**, where

*V*_{e}**is in accordance with 18.6.5.1 or 18.7.6.1**

*V*_{e}(c) Mechanical splices of beam reinforcement shall be located not closer than ** h/2** from the joint face and shall satisfy 18.2.7

(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, **ϕ S_{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, **ϕ S_{n}** shall be at least

**1.4**,

*S*_{e}**ϕ**shall be at least

*M*_{n}**0.4**for the column within the story height, and

*M*_{pr}**ϕ**shall be at least

*V*_{n}**in accordance with 18.7.6.1**

*V*_{e}(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.

**ρ**and

_{ℓ}**ρ**, for structural walls shall be at least 0.0025, except that if

_{t}**does not exceed ,**

*V*_{u}**ρ**and

_{ℓ}**ρ**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

_{t}**shall be continuous and shall be distributed across the shear plane.**

*V*_{n}**, in which**

*h*/_{w}*ℓ*≥ 2.0_{w}**and**

*h*_{w}**refer to height and length of entire wall, respectively.**

*ℓ*_{w}**in tension in accordance with 25.4, 25.5, and (a) through (c):**

*f*_{y}(a) Longitudinal reinforcement shall extend beyond the point at which it is no longer required to resist flexure by least **0.8 ℓ_{w}**, except at the top of a wall

(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) Mechanical splices of reinforcement shall conform to 18.2.7 and welded splices of reinforcement shall conform to 18.2.8

**shall be obtained from the lateral load analysis in accordance with the factored load combinations.**

*V*_{u}*V*of structural walls shall not exceed:

_{n}(18.10.4.1) |

where the coefficient **α _{c}** is 3.0 for

**, is 2.0 for**

*h*/_{w}*ℓ*≤ 1.5_{w}**, and varies linearly between 3.0 and 2.0 for**

*h*/_{w}*ℓ*≥ 2.0_{w}**between 1.5 and 2.0.**

*h*/_{w}*ℓ*_{w}**used to calculate**

*h*/_{w}*ℓ*_{w}**for segments of a wall shall be the greater of the ratios for the entire wall and the segment of wall considered.**

*V*_{n}**does not exceed 2.0, reinforcement ratio**

*h*/_{w}*ℓ*_{w}**ρ**shall be at least the reinforcement ratio

_{ℓ}**ρ**.

_{t}**shall not be taken greater than , where**

*V*_{n}**is the gross area of concrete bounded by web thickness and length of section. For any one of the individual vertical wall segments,**

*A*_{cv}**shall not be taken greater than , where**

*V*_{n}**is the area of concrete section of the individual vertical wall segment considered.**

*A*_{cw}**shall not be taken greater than , where**

*V*_{n}**is the area of concrete section of a horizontal wall segment or coupling beam.**

*A*_{cw}**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), or shall be designed by 18.10.6.3:**

*h*/_{w}*ℓ*≥ 2.0_{w}(a) Compression zones shall be reinforced with special boundary elements where

(18.10.6.2) |

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**. Ratio

_{u}**δ**shall not be taken less than 0.005.

_{u}/*h*_{w}(b) Where special boundary elements are required by (a), the special boundary element transverse reinforcement shall extend vertically above and below the critical section at least the greater of ** ℓ_{w}** and

**, except as permitted in 18.10.6.4(g).**

*M*/4_{u}*V*_{u}**, exceeds**

*E***0.2**. The special boundary element shall be permitted to be discontinued where the calculated compressive stress is less than

*f*'_{c}**0.15**. 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.

*f*'_{c}(a) The boundary element shall extend horizontally from the extreme compression fiber a distance at least the greater of ** c — 0.1ℓ_{w}** and

**, where**

*c*/2**is the largest neutral axis depth calculated for the factored axial force and nominal moment strength consistent with**

*c***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*/16._{u}(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

**, width of the flexural compression zone**

*c*/*ℓ*≥ 3/8_{w}**over the length calculated in 18.10.6.4(a) shall be greater than or equal to 12 in.**

*b*(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 (e) and 18.7.5.3, except the value ** h_{x}** in 18.7.5.2 shall not exceed the lesser of 14 in. and two-thirds of the boundary element thickness, and the transverse reinforcement spacing limit of 18.7.5.3(a) shall be one-third of the least dimension of the boundary element.

(f) The amount of transverse reinforcement shall be in accordance with Table 18.10.6.4(f).

**Table 18.10.6.4(f)—Transverse reinforcement for special boundary elements**

Transverse reinforcement | Applicable expressions | ||
---|---|---|---|

A/_{sh}sb for rectilinear hoop_{c} | Greater of | (a) | |

(b) | |||

ρ_{s} for spiral or circular hoop | Greater of | (c) | |

(d) |

(g) 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 18.13.2.3.

(h) 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

**of the horizontal web reinforcement does not exceed**

*A*/_{s}f_{y}*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.**

*A*/_{s}f_{yt}*s*(a) If the 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 longitudinal spacing of transverse reinforcement at the wall boundary shall not exceed the lesser of 8 in. and

**8**of the smallest primary flexural reinforcing bars, except the spacing shall not exceed the lesser of 6 in. and

*d*_{b}**6**within a distance equal to the greater of

*d*_{b}**and**

*ℓ*_{w}**above and below critical sections where yielding of longitudinal reinforcement is likely to occur as a result of inelastic lateral displacements.**

*M*/4_{u}*V*_{u}(b) 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.

**(**and with

*ℓ*/_{n}*h*) < 2

**V**_{u}≥**4λ √f'****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.**

_{c}A_{cw}(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. The diagonal bars shall be embedded into the wall at least 1.25 times the development length for ** f_{y}** in tension.

(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

**and**

*b*_{w}**along the other sides, where**

*b*/5_{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**

*b*_{w}**not less than the greater of (i) and (ii):**

*A*_{sh}(i)

(ii)

For the purpose of calculating ** A_{g}**, the concrete cover in 20.6.1 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(c) and not exceeding

**6**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

*d*_{b}**0.002**and spacing not exceeding 12 in.

*b*_{w}s(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 **6 d_{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.

**)**

*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 cast-in-place special structural walls*in addition to 18.5.2.

^{1}/

_{2}in. thick.

**in tension.**

*f*_{y}**0.2**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 18.12.7.5. The specified transverse reinforcement is permitted to be discontinued at a section where the calculated compressive stress is less than

*f*'_{c}**0.15**.

*f*'_{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 **0.2 f_{c}'** shall be increased to

**0.5**, and the limit of

*f*'_{c}**0.15**shall be increased to

*f*'_{c}**0.4**.

*f*'_{c}**Table 18.12.7.5 —Transverse reinforcement for collector elements**

Transverse reinforcement | Applicable expressions | ||
---|---|---|---|

A/_{sh}sb for rectilinear hoop_{c} | (a) | ||

ρ_{s} for spiral or circular hoop | Greater of: | (b) | |

(c) |

(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

**50**, except as required in 18.12.7.5

*b*/_{w}s*f*_{yt}*V*of diaphragms shall not exceed:

_{n}(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

**used to calculate**

*f*'_{c}**shall not exceed the lesser of**

*V*_{n}**for the precast members and**

*f*'_{c}**for the topping slab.**

*f*'_{c}*V*of diaphragms shall not exceed .

_{n}**shall not exceed:**

*V*_{n}V = _{n}Aµ_{vf} f_{y} | (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

**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.**

*A*_{vf}**0.2**at any section shall have transverse reinforcement, in accordance with 18.7.5.2, 18.7.5.3, 18.7.5.7, and Table 18.12.11.1, over the length of the element.

*f*'_{c}**Table 18.12.11.1—Transverse reinforcement for structural trusses**

Transverse reinforcement | Applicable expressions | ||
---|---|---|---|

A/_{sh}sb for rectilinear hoop_{c} | Greater of: | (a) | |

(b) | |||

ρ_{s} for spiral or circular hoop | Greater of: | (c) | |

(d) |

**in tension.**

*f*_{y}*unless modified by Chapter 18 of the International Building Code*.

**in tension, of the column or boundary element longitudinal reinforcement.**

*f*_{y}**1.25**of the bar.

*f*_{y}(a) At the top of the member for at least five times the member cross-sectional dimension, and at least 6 ft below the bottom of the pile cap

(b) For the portion of piles in soil that is not capable of providing lateral support, or in air and water, along the entire unsupported length plus the length required in (a).

**(1.2**or

*D*+ 1.0*L*+ 0.2*S*)**0.9**, whichever is critical, acting simultaneously with the design displacement

*D***δ**. The load factor on the live load,

_{u}**, shall be permitted to be reduced to 0.5 except for garages, areas occupied as places of public assembly, and all areas where**

*L***is greater than 100 lb/ft**

*L*^{2}.

**δ**. If effects of

_{u}**δ**are not explicitly checked, the provisions of 18.14.3.3 shall be satisfied.

_{u}(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

**, transverse reinforcement shall be hoops satisfying 18.7.5.2 at spacing**

*A*'/10_{g}f_{c}**, according to 18.14.3.2(b).**

*s*_{o}(b) Columns shall satisfy 18.7.4.1, 18.7.5.2, and 18.7.6. The maximum longitudinal spacing of hoops shall be ** s_{o}** for the full column length. Spacing

**shall not exceed the lesser of six diameters of the smallest longitudinal bar enclosed and 6 in.**

*s*_{o}(c) Columns with factored gravity axial forces exceeding **0.35 P_{o}** shall satisfy 18.14.3.2(b) and 18.7.5.7. The amount of transverse reinforcement provided shall be one-half of that required by 18.7.5.4 and spacing shall not exceed

**for the full column length.**

*s*_{o}**ϕ**or

*M*_{n}**ϕ**of the frame member, or if induced moments or shears are not calculated, (a) through (d) shall be satisfied:

*V*_{n}(a) Materials, mechanical splices, and welded splices shall satisfy the requirements for special moment frames in 18.2.5 through 18.2.8.

(b) Beams shall satisfy 18.14.3.2(a) and 18.6.5.

(a) Requirements of 18.14.3

(b) Ties specified in 18.14.3.2(b) over the entire column height, including the depth of the beams

(c) Structural integrity reinforcement, in accordance with 4.10

(d) Bearing length at the support of a beam shall be at least 2 in. longer than determined from 16.2.6

**Δ**. Required slab shear reinforcement shall provide

_{x}/*h*≥ 0.035 - (1/20) (_{sx}*v*/ϕ_{ug}*v*)_{c}**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. The shear reinforcement requirements of this provision shall not apply if**

*v*≥_{s}**Δ**.

_{x}/*h*≤ 0.005_{sx}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.

**shall be calculated in accordance with 22.6.5.**

*v*_{c}**is the factored shear stress on the slab critical section for two-way action due to gravity loads without moment transfer.**

*v*_{ug}**Ω**times the shear induced under design displacements,

_{o}**δ**.

_{u}