This chapter shall apply to the design of nonprestressed and prestressed slabs reinforced for flexure in two directions, with or without
beams between supports, including (a) through (d):
(a) Solid slabs
(b) Slabs cast on stayinplace, noncomposite steel deck
(c) Composite slabs of concrete elements constructed in separate placements but connected so that all elements resist loads as a unit
(d) Twoway joist systems in accordance with 8.8
A slab system shall be permitted to be designed by any procedure satisfying equilibrium and geometric compatibility, provided that
design strength at every section is at least equal to
required strength, and all serviceability requirements are satisfied. The direct design method of 8.10 or the equivalent frame method of 8.11 is permitted for design where applicable.
The effects of concentrated
loads and openings shall be considered in design.
Slabs prestressed with an average effective compressive stress less than 125 psi shall be designed as nonprestressed slabs.
A
drop panel in a nonprestressed slab, where used to reduce the minimum required thickness in accordance with
8.3.1.1 or the quantity of deformed negative moment
reinforcement at a support in accordance with
8.5.2.2, shall satisfy (a) and (b):
(a) The drop panel shall project below the slab at least onefourth of the adjacent slab thickness.
(b) The drop panel shall extend in each direction from the centerline of support a distance not less than onesixth the span length measured from centertocenter of supports in that direction.
A
shear cap, where used to increase the critical section for shear at a slab
column joint, shall project below the slab soffit and extend horizontally from the face of the
column a distance at least equal to the thickness of the projection below the slab soffit.
For nonprestressed slabs without interior
beams spanning between supports on all sides, having a maximum ratio of longtoshort span of 2, overall slab thickness
h shall not be less than the limits in Table 8.3.1.1, and shall be at least the value in (a) or (b), unless the calculated deflection limits of
8.3.2 are satisfied:
(a) Slabs without drop panels as given in 8.2.4... 5 in.
(b) Slabs with drop panels as given in 8.2.4........ 4 in.
Table 8.3.1.1—Minimum thickness of nonprestressed twoway slabs without interior beams (in.)^{[1]}
f_{y}, psi^{[2]}  Without drop panels^{[3]}  With drop panels^{[3]} 
Exterior panels  Interior panels  Exterior panels  Interior panels 
Without edge beams  With edge beams^{[4]}   Without edge beams  With edge beams^{[4]}  
40,000  ℓ_{n}/33  ℓ_{n}/36  ℓ_{n}/36  ℓ_{n}/36  ℓ_{n}/40  ℓ_{n}/40 
60,000  ℓ_{n}/30  ℓ_{n}/33  ℓ_{n}/33  ℓ_{n}/33  ℓ_{n}/36  ℓ_{n}/36 
75,000  ℓ_{n}/28  ℓ_{n}/31  ℓ_{n}/31  ℓ_{n}/31  ℓ_{n}/34  ℓ_{n}/34 
^{[1]}ℓ_{n} is the clear span in the long direction, measured facetoface of supports (in.).
^{[2]}For f_{y} between the values given in the table, minimum thickness shall be calculated by linear interpolation.
^{[3]}Drop panels as given in 8.2.4.
^{[4]}Slabs with beams between columns along exterior edges. Exterior panels shall be considered to be without edge beams if α_{f} is less than 0.8. The value of α_{f} for the edge beam shall be calculated in accordance with 8.10.2.7.
For nonprestressed slabs with
beams spanning between supports on all sides, overall slab thickness
h shall satisfy the limits in Table 8.3.1.2, unless the calculated deflection limits of
8.3.2 are satisfied.
Table 8.3.1.2—Minimum thickness of nonprestressed twoway slabs with beams spanning between supports on all sides
α_{fm}^{[1]} 
Minimum h, in. 

α_{fm} ≤ 0.2 
8.3.1.1 applies

(a) 
0.2 < α_{fm} ≤ 2.0 
Greater of: 

(b)^{[2],[3]} 
5.0 
(c) 
α_{fm} > 2.0 
Greater of: 

(d)^{[2],[3]} 
3.5 
(e) 
^{[1]}α_{fm} is the average value of α_{f} for all beams on edges of a panel and α_{f} shall be calculated in accordance with 8.10.2.7.
^{[2]}ℓ_{n} is the clear span in the long direction, measured facetoface of beams (in.).
^{[3]}β is the ratio of clear spans in long to short directions of slab.
At discontinuous edges of slabs conforming to
8.3.1.2, an edge
beam with
α_{f} ≥ 0.80 shall be provided, or the minimum thickness required by (b) or (d) of
Table 8.3.1.2 shall be increased by at least 10 percent in the panel with a discontinuous edge.
The thickness of a
concrete floor finish shall be permitted to be included in
h if it is placed monolithically with the floor slab, or if the floor finish is designed to be composite with the floor slab in accordance with
16.4.
If single or multipleleg
stirrups are used as shear
reinforcement, the slab thickness shall be sufficient to satisfy the requirements for
d in
22.6.7.1.
Immediate and timedependent deflections shall be calculated in accordance with
24.2 and shall not exceed the limits in
24.2.2 for twoway slabs given in (a) through (c):
(a) Nonprestressed slabs not satisfying 8.3.1
(b) Nonprestressed slabs without interior beams spanning between the supports on all sides and having a ratio of longtoshort span exceeding 2.0
(c) Prestressed slabs
For nonprestressed composite
concrete slabs satisfying
8.3.1.1 or
8.3.1.2, deflections occurring after the member becomes composite need not be calculated. Deflections occurring before the member becomes composite shall be investigated, unless the precomposite thickness also satisfies
8.3.1.1 or
8.3.1.2.
For nonprestressed slabs, ε_{t} shall be at least 0.004.
Prestressed slabs shall be designed as Class U with
. Other stresses in prestressed slabs immediately after
transfer and at
service loads shall not exceed the permissible stresses in
24.5.3 and
24.5.4.
Required strength shall be calculated in accordance with the analysis procedures given in
Chapter 6. Alternatively, the provisions of 8.10 for the direct design method shall be permitted for the analysis of nonprestressed slabs and the provisions of 8.11 for the equivalent frame method shall be permitted for the analysis of nonprestressed and prestressed slabs, except
8.11.6.5 and
8.11.6.6 shall not apply to prestressed slabs.
For prestressed slabs, effects of reactions induced by prestressing shall be considered in accordance with
5.3.11.
For a slab system supported by
columns or
walls, dimensions
c_{1},
c_{2}, and
ℓ_{n} shall be based on an effective support area. The effective support area is the intersection of the bottom surface of the slab, or
drop panel or
shear cap if present, with the largest right circular cone, right pyramid, or tapered wedge whose surfaces are located within the
column and the capital or bracket and are oriented no greater than 45 degrees to the axis of the
column.
A
column strip is a design strip with a width on each side of a
column centerline equal to the lesser of
0.25ℓ_{2} and
0.25ℓ_{1}. A
column strip shall include
beams within the strip, if present.
A middle strip is a design strip bounded by two
column strips.
For monolithic or fully composite construction supporting twoway slabs, a
beam includes that portion of slab, on each side of the
beam extending a distance equal to the projection of the
beam above or below the slab, whichever is greater, but not greater than four times the slab thickness.
Combining the results of a gravity
load analysis with the results of a lateral
load analysis shall be permitted.
For slabs built integrally with supports,
M_{u} at the support shall be permitted to be calculated at the face of support, except if analyzed in accordance with
8.4.2.2.
For slabs analyzed using the direct design method or the equivalent frame method,
M_{u} at the support shall be located in accordance with
8.10 or 8.11, respectively.
If gravity
load, wind, earthquake, or other effects cause a
transfer of moment between the slab and
column, a fraction of
M_{sc}, the factored slab moment resisted by the
column at a
joint, shall be transferred by flexure in accordance with
8.4.2.3.2 through
8.4.2.3.5.
The fraction of factored slab moment resisted by the
column,
γ_{f}M_{sc}, shall be assumed to be transferred by flexure, where
γ_{f} shall be calculated by:
 (8.4.2.3.2) 
The effective slab width
b_{slab} for resisting
γ_{f}M_{sc} shall be the width of
column or capital plus
1.5h of slab or
drop panel on either side of
column or capital.
For nonprestressed slabs, where the limitations on
v_{ug} and
ε_{t} in Table 8.4.2.3.4 are satisfied,
γ_{f} shall be permitted to be increased to the maximum modified values provided in Table 8.4.2.3.4, where
v_{c} is calculated in accordance with
22.6.5, and
v_{ug} is the factored shear stress on the slab critical section for twoway action due to gravity
loads without moment
transfer.
Table 8.4.2.3.4—Maximum modified values of γ_{f} for nonprestressed twoway slabs
Column location  Span direction  v_{ug}  ε_{t} (within b_{slab})  Maximum modified γ_{f} 
Corner column  Either direction  ≤0.5ϕv_{c}  ≥0.004  1.0 
Edge column  Perpendicular to the edge  ≤0.75ϕv_{c}  ≥0.004  1.0 
Parallel to the edge  ≤0.4ϕv_{c}  ≥0.010  
Interior column  Either direction  ≤0.4ϕv_{c}  ≥0.010  
The fraction of
M_{sc} not calculated to be resisted by flexure shall be assumed to be resisted by eccentricity of shear in accordance with
8.4.4.2.
For slabs built integrally with supports, V_{u} at the support shall be permitted to be calculated at the face of support.
Sections between the face of support and a critical section located
d from the face of support for nonprestressed slabs and
h/2 from the face of support for prestressed slabs shall be permitted to be designed for
V_{u} at that critical section if (a) through (c) are satisfied:
(a) Support reaction, in direction of applied shear, introduces compression into the end regions of the slab.
(b) Loads are applied at or near the top surface of the slab.
(c) No concentrated load occurs between the face of support and critical section.
Slabs shall be evaluated for twoway shear in the vicinity of
columns, concentrated
loads, and reaction areas at critical sections in accordance with
22.6.4.
Slabs reinforced with shearheads shall be evaluated for twoway shear at critical sections in accordance with
22.6.9.8.
For twoway shear with factored slab moment resisted by the
column, factored shear stress
v_{u} shall be calculated at critical sections in accordance with
8.4.4.1. Factored shear stress
v_{u} corresponds to a combination of
v_{ug} and the shear stress produced by
γ_{v}M_{sc}, where
γ_{v} is given in
8.4.4.2.2 and
M_{sc} is given in
8.4.2.3.1.
The fraction of
M_{sc} transferred by eccentricity of shear,
γ_{v}M_{sc}, shall be applied at the centroid of the critical section in accordance with
8.4.4.1, where:
γ_{v} = 1 — γ_{f}  (8.4.4.2.2) 
The factored shear stress resulting from
γ_{v}M_{sc} shall be assumed to vary linearly about the centroid of the critical section in accordance with
8.4.4.1.
For each applicable
factored load combination,
design strength shall satisfy
ϕS_{n} ≥ U, including (a) through (d). Interaction between
load effects shall be considered.
(a) ϕM_{n} ≥ M_{u} at all sections along the span in each direction
(b) ϕM_{n} ≥ γ_{f}M_{sc} within b_{slab} as defined in 8.4.2.3.3
(c) ϕV_{n} ≥ V_{u} at all sections along the span in each direction for oneway shear
(d) ϕv_{n} ≥ v_{u} at the critical sections defined in 8.4.4.1 for twoway shear
ϕ shall be in accordance with
21.2.
If shearheads are provided,
22.6.9 and
8.5.1.1(a) shall be satisfied in the vicinity of the
column. Beyond each arm of the shearhead,
8.5.1.1(a) through (d) shall apply.
M_{n} shall be calculated in accordance with
22.3.
In calculating
M_{n} for prestressed slabs,
external tendons shall be considered as unbonded unless the
external tendons are effectively bonded to the slab along its entire length.
For oneway shear, where each critical section to be investigated extends in a plane across the entire slab width,
V_{n} shall be calculated in accordance with
22.5.
For twoway shear,
v_{n} shall be calculated in accordance with
22.6.
For composite
concrete slabs, horizontal shear strength
V_{nh} shall be calculated in accordance with
16.4.
Openings of any size shall be permitted in slab systems if shown by analysis that all strength and serviceability requirements, including the limits on deflections, are satisfied.
As an alternative to
8.5.4.1, openings shall be permitted in slab systems without
beams in accordance with (a) through (d).
(a) Openings of any size shall be permitted in the area common to intersecting middle strips, but the total quantity of reinforcement in the panel shall be at least that required for the panel without the opening.
(b) At two intersecting column strips, not more than oneeighth the width of column strip in either span shall be interrupted by openings. A quantity of reinforcement at least equal to that interrupted by an opening shall be added on the sides of the opening.
(c) At the intersection of one column strip and one middle strip, not more than onefourth of the reinforcement in either strip shall be interrupted by openings. A quantity of reinforcement at least equal to that interrupted by an opening shall be added on the sides of the opening.
(d) If an opening is located within a column strip or closer than 10h from a concentrated load or reaction area, 22.6.4.3 for slabs without shearheads or 22.6.9.9 for slabs with shearheads shall be satisfied.
A minimum area of flexural
reinforcement,
A_{s,min}, shall be provided near the tension face in the direction of the span under consideration in accordance with Table 8.6.1.1.
Table 8.6.1.1—A_{s,min} for nonprestressed twoway slabs
For prestressed slabs, the
effective prestress force
A_{ps}f_{se} shall provide a minimum average compressive stress of 125 psi on the slab section tributary to the
tendon or
tendon group. For slabs with varying cross section along the slab span, either parallel or perpendicular to the
tendon or
tendon group, the minimum average
effective prestress of 125 psi is required at every cross section tributary to the
tendon or
tendon group along the span.
For prestressed slabs, a minimum area of bonded deformed longitudinal
reinforcement,
A_{s,min}, shall be provided in the
precompressed tension zone in the direction of the span under consideration in accordance with Table 8.6.2.3.
Table 8.6.2.3—Minimum bonded deformed longitudinal reinforcement A_{s,min} in twoway slabs with bonded or unbonded tendons
Region  Calculated f_{t} after all losses, psi  A_{s,min}, in.^{2}  
Positive moment   Not required  (a) 
  (b)^{[1],[2],[4]} 
Negative moment at columns   0.00075A_{cf}  (c)^{[3],[4]} 
^{[1]}The value of f_{y} shall not exceed 60,000 psi.
^{[2]}N_{c} is the resultant tensile force acting on the portion of the concrete cross section that is subjected to tensile stresses due to the combined effects of service loads and effective prestress.
^{[3]}A_{cf} is the greater gross crosssectional area of the slabbeam strips of the two orthogonal equivalent frames intersecting at a column of a twoway slab.
^{[4]}For slabs with bonded tendons, it shall be permitted to reduce A_{s},_{min} by the area of the bonded prestressed reinforcement located within the area used to determine N_{c} for positive moment, or within the width of slab defined in 8.7.5.3(a) for negative moment.
Bundled bars shall be detailed in accordance with
25.6.
For nonprestressed solid slabs, maximum
spacing s of deformed longitudinal
reinforcement shall be the lesser of
2h and 18 in. at critical sections, and the lesser of
3h and 18 in. at other sections.
For prestressed slabs with uniformly distributed
loads, maximum
spacing s of
tendons or groups of
tendons in at least one direction shall be the lesser of
8h and 5 ft.
At exterior corners of slabs supported by edge
walls or where one or more edge
beams have a value of
α_{f} greater than 1.0,
reinforcement at top and bottom of slab shall be designed to resist
M_{u} per unit width due to corner effects equal to the maximum positive
M_{u} per unit width in the slab panel.
Factored moment due to corner effects, M_{u}, shall be assumed to be about an axis perpendicular to the diagonal from the corner in the top of the slab and about an axis parallel to the diagonal from the corner in the bottom of the slab.
Reinforcement shall be provided for a distance in each direction from the corner equal to onefifth the longer span.
Reinforcement shall be placed parallel to the diagonal in the top of the slab and perpendicular to the diagonal in the bottom of the slab. Alternatively,
reinforcement shall be placed in two layers parallel to the sides of the slab in both the top and bottom of the slab.
Where a slab is supported on spandrel
beams,
columns, or
walls, anchorage of
reinforcement perpendicular to a discontinuous edge shall satisfy (a) and (b):
(a) Positive moment reinforcement shall extend to the edge of slab and have embedment, straight or hooked, at least 6 in. into spandrel beams, columns, or walls
(b) Negative moment reinforcement shall be bent, hooked, or otherwise anchored into spandrel beams, columns, or walls, and shall be developed at the face of support
Where a slab is not supported by a spandrel
beam or
wall at a discontinuous edge, or where a slab cantilevers beyond the support, anchorage of
reinforcement shall be permitted within the slab.
For slabs without
beams,
reinforcement extensions shall be in accordance with (a) through (c):
(a) Reinforcement lengths shall be at least in accordance with Fig. 8.7.4.1.3a, and if slabs act as primary members resisting lateral loads, reinforcement lengths shall be at least those required by analysis.
(b) If adjacent spans are unequal, extensions of negative moment reinforcement beyond the face of support in accordance with Fig. 8.7.4.1.3a shall be based on the longer span.
(c) Bent bars shall be permitted only where the depthtospan ratio permits use of bends of 45 degrees or less.
Fig. 8.7.4.1.3a—Minimum extensions for deformed reinforcement in twoway slabs without beams.
All bottom deformed bars or deformed wires within the
column strip, in each direction, shall be continuous or spliced with full mechanical, full welded, or Class B tension splices. Splices shall be located in accordance with
Fig. 8.7.4.1.3a.
At least two of the
column strip bottom bars or wires in each direction shall pass within the region bounded by the longitudinal
reinforcement of the
column and shall be anchored at exterior supports.
In slabs with shearheads where it is not practical to pass the bottom bars through the
column in accordance with
8.7.4.2.2, at least two bottom bars or wires in each direction shall pass through the shearhead as close to the
column as practicable and be continuous or spliced with full mechanical, full welded, or Class B tension splices. At exterior
columns, the bars or wires shall be anchored at the shearhead.
External tendons shall be attached to the slab in a manner that maintains the specified eccentricity between the
tendons and the
concrete centroid through the full range of anticipated member deflections.
If bonded deformed longitudinal
reinforcement is required to satisfy flexural strength or for tensile stress conditions in accordance with Eq. (
8.6.2.3(b)), the detailing requirements of
7.7.3 shall be satisfied.
Bonded longitudinal
reinforcement required by Eq. (
8.6.2.3(c)) shall be placed in the top of the slab, and shall be in accordance with (a) through (c):
(a) Reinforcement shall be distributed between lines that are 1.5h outside opposite faces of the column support.
(b) At least four deformed bars, deformed wires, or bonded strands shall be provided in each direction.
(c) Maximum spacing s between bonded longitudinal reinforcement shall not exceed 12 in.
Posttensioning anchorages and couplers shall be designed and detailed in accordance with
25.8.
Length of
deformed reinforcement required by
8.6.2.3 shall be in accordance with (a) and (b):
(a) In positive moment areas, length of reinforcement shall be at least ℓ_{n}/3 and be centered in those areas
(b) In negative moment areas, reinforcement shall extend at least ℓ_{n}/6 on each side of the face of support
Except as permitted in
8.7.5.6.3, at least two
tendons with
^{1}/
_{2} in. diameter or larger strand shall be placed in each direction at
columns in accordance with (a) or (b):
(a) Tendons shall pass through the region bounded by the longitudinal reinforcement of the column.
(b) Tendons shall be anchored within the region bounded by the longitudinal reinforcement of the column, and the anchorage shall be located beyond the column centroid and away from the anchored span.
Minimum bottom
deformed reinforcement A_{s} in each direction shall be the greater of (a) and (b):
(a)  (8.7.5.6.3.1a) 
(b)  (8.7.5.6.3.1b) 
where b_{w} is the width of the column face through which the reinforcement passes.
Stirrup anchorage and geometry shall be in accordance with
25.7.1.
The overall height of the shear stud assembly shall be at least the thickness of the slab minus the sum of (a) through (c):
(a) Concrete cover on the top flexural reinforcement
(b) Concrete cover on the base rail
(c) Onehalf the bar diameter of the flexural tension reinforcement
Headed shear stud reinforcement location and
spacing shall be in accordance with Table 8.7.7.1.2.
Table 8.7.7.1.2—Shear stud location and spacing limits
Direction of measurement  Description of measurement  Condition  Maximum distance or spacing, in. 
Perpendicular to column face  Distance from column face to first peripheral line of shear studs  All  d/2 
Constant spacing between peripheral lines of shear studs  Nonprestressed slab with   3d/4 
Nonprestressed slab with   d/2 
Prestressed slabs conforming to 22.6.5.4  3d/4 
Parallel to column face  Spacing between adjacent shear studs on peripheral line nearest to column face  All  2d 
Nonprestressed twoway joist construction consists of a monolithic combination of regularly spaced ribs and a top slab designed to span in two orthogonal directions.
Width of ribs shall be at least 4 in. at any location along the depth.
Overall depth of ribs shall not exceed 3.5 times the minimum width.
V_{c} shall be permitted to be taken as 1.1 times the values calculated in 22.5.
For
structural integrity, at least one bottom bar in each joist shall be continuous and shall be anchored to develop
f_{y} at the face of supports.
Reinforcement area perpendicular to the ribs shall satisfy slab moment strength requirements, considering
load concentrations, and shall be at least the shrinkage and temperature
reinforcement area in accordance with
24.4.
Twoway joist construction not satisfying the limitations of
8.8.1.1 through
8.8.1.4 shall be designed as slabs and
beams.
If permanent burned clay or
concrete tile fillers of material having a unit compressive strength at least equal to
f'_{c} in the joists are used,
8.8.2.1.1 and
8.8.2.1.2 shall apply.
Slab thickness over fillers shall be at least the greater of onetwelfth the clear distance between ribs and 1.5 in.
For calculation of shear and negative moment strength, it shall be permitted to include the vertical shells of fillers in contact with the ribs. Other portions of fillers shall not be included in strength calculations.
If fillers not complying with
8.8.2.1 or removable forms are used, slab thickness shall be at least the greater of onetwelfth the clear distance between ribs and 2 in.
In slabs constructed with liftslab methods where it is impractical to pass the
tendons required by
8.7.5.6.1 or the bottom bars required by
8.7.4.2 or
8.7.5.6.3 through the
column, at least two posttensioned
tendons or two bonded bottom bars or wires in each direction shall pass through the lifting collar as close to the
column as practicable, and be continuous or spliced with full mechanical, full welded, or Class B tension splices. At exterior
columns, the
reinforcement shall be anchored at the lifting collar.
Twoway slabs satisfying the limits in
8.10.2 shall be permitted to be designed in accordance with this section.
Variations from the limitations in
8.10.2 shall be permitted if demonstrated by analysis that equilibrium and geometric compatibility are satisfied, the
design strength at every section is at least equal to the
required strength, and serviceability conditions, including limits on deflection, are met.
Circular or regular polygonshaped supports shall be treated as square supports with the same area.
There shall be at least three continuous spans in each direction.
Successive
span lengths measured centertocenter of supports in each direction shall not differ by more than onethird the longer span.
Panels shall be rectangular, with the ratio of longer to shorter panel dimensions, measured centertocenter of supports, not to exceed 2.
Column offset shall not exceed 10 percent of the span in direction of offset from either axis between centerlines of successive
columns.
All
loads shall be due to gravity only and uniformly distributed over an entire panel.
For a panel with
beams between supports on all sides, Eq. (8.10.2.7a) shall be satisfied for
beams in the two perpendicular directions.
 (8.10.2.7a) 
where α_{f1} and α_{f2} are calculated by:
 (8.10.2.7b) 
Total factored static moment M_{o} for a span shall be calculated for a strip bounded laterally by the panel centerline on each side of the centerline of supports.
The absolute sum of positive and average negative
M_{u} in each direction shall be at least:
 (8.10.3.2) 
In Eq. (
8.10.3.2),
ℓ_{n} is the clear
span length in the direction that moments are considered, shall extend from face to face of
columns, capitals, brackets, or
walls, and shall be at least
0.65ℓ_{1}.
In Eq. (
8.10.3.2), if the transverse span of panels on either side of the centerline of supports varies,
ℓ_{2} shall be taken as the average of adjacent transverse spans.
In Eq. (
8.10.3.2), if the span adjacent and parallel to a slab edge is being considered, the distance from edge to panel centerline shall be substituted for
ℓ_{2}.
In an interior span, M_{o} shall be distributed as follows: 0.65M_{o} to negative moment and 0.35M_{o} to positive moment.
In an end span,
M_{o} shall be distributed in accordance with Table 8.10.4.2.
Table 8.10.4.2—Distribution coefficients for end spans
 Exterior edge unrestrained  Slab with beams between all supports  Slab without beams between interior supports  Exterior edge fully restrained 
Without edge beam  With edge beam 
Interior negative  0.75  0.70  0.70  0.70  0.65 
Positive  0.63  0.57  0.52  0.50  0.35 
Exterior negative  0  0.16  0.26  0.30  0.65 
Modification of negative and positive factored moments by up to 10 percent shall be permitted if the total factored static moment for a panel,
M_{o}, in the direction considered is at least that calculated by Eq. (
8.10.3.2). Moment redistribution in accordance with
6.6.5 is not permitted.
Critical section for negative M_{u} shall be at the face of rectangular supports.
Negative M_{u} shall be the greater of the two interior negative M_{u} calculated for spans framing into a common support unless an analysis is made to distribute the unbalanced moment in accordance with stiffnesses of adjoining elements.
Edge
beams or edges of slabs shall be designed to resist in torsion their share of exterior negative
M_{u}.
The
column strip shall resist the portion of interior negative
M_{u} in accordance with Table 8.10.5.1.
Table 8.10.5.1—Portion of interior negative M_{u} in column strip
α_{f1}ℓ_{2}/ℓ_{1}  ℓ_{2}/ℓ_{1} 
0.5  1.0  2.0 
0  0.75  0.75  0.75 
≥1.0  0.90  0.75  0.45 
Note: Linear interpolations shall be made between values shown.
The
column strip shall resist the portion of exterior negative
M_{u} in accordance with Table 8.10.5.2.
Table 8.10.5.2—Portion of exterior negative M_{u} in column strip
α_{f1}ℓ_{2}/ℓ_{1}  β_{t}  ℓ_{2}/ℓ_{1} 
0.5  1.0  2.0 
0  0  1.0  1.0  1.0 
≥2.5  0.75  0.75  0.75 
≥1.0  0  1.0  1.0  1.0 
≥2.5  0.90  0.75  0.45 
Note: Linear interpolations shall be made between values shown. β_{t} is calculated using Eq. (8.10.5.2a), where C is calculated using Eq. (8.10.5.2b).
 (8.10.5.2a) 
 (8.10.5.2b) 
For T or Lsections, it shall be permitted to calculate the constant
C in Eq. (
8.10.5.2b) by dividing the section, as given in
8.4.1.8, into separate rectangular parts and summing the values of
C for each part.
If the width of the
column or
wall is at least
(3/4)ℓ_{2}, negative
M_{u} shall be uniformly distributed across
ℓ_{2}.
The
column strip shall resist the portion of positive
M_{u} in accordance with Table 8.10.5.5.
Table 8.10.5.5—Portion of positive M_{u} in column strip
α_{f1}ℓ_{2}/ℓ_{1}  ℓ_{2}/ℓ_{1} 
0.5  1.0  2.0 
0  0.60  0.60  0.60 
≥1.0  0.90  0.75  0.45 
Note: Linear interpolations shall be made between values shown.
For slabs with
beams between supports, the slab portion of
column strips shall resist
column strip moments not resisted by
beams.
Beams between supports shall resist the portion of
column strip
M_{u} in accordance with Table 8.10.5.7.1.
Table 8.10.5.7.1—Portion of column strip M_{u} in beams
α_{f1}ℓ_{2}/ℓ_{1}  Distribution coefficient 
0  0 
≥1.0  0.85 
Note: Linear interpolation shall be made between values shown.
In addition to moments calculated according to
8.10.5.7.1,
beams shall resist moments caused by
factored loads applied directly to the
beams, including the weight of the
beam stem above and below the slab.
That portion of negative and positive factored moments not resisted by
column strips shall be proportionately assigned to corresponding half middle strips.
Each middle strip shall resist the sum of the moments assigned to its two half middle strips.
A middle strip adjacent and parallel to a wallsupported edge shall resist twice the moment assigned to the half middle strip corresponding to the first row of interior supports.
At an interior support,
columns or
walls above and below the slab shall resist the factored moment calculated by Eq. (8.10.7.2) in direct proportion to their stiffnesses unless a general analysis is made.
M_{sc} = 0.07[(q_{Du}+ 0.5q_{Lu})ℓ_{2}ℓ_{n}^{2} — q_{Du}'ℓ_{2}'(ℓ_{n}')^{2}]  (8.10.7.2) 
where q_{Du}', ℓ_{2}', and ℓ_{n}' refer to the shorter span.
The gravity
load moment to be transferred between slab and edge
column in accordance with
8.4.2.3 shall not be less than
0.3M_{o}.
Beams between supports shall resist the portion of shear in accordance with Table 8.10.8.1 caused by
factored loads on tributary areas in accordance with Fig. 8.10.8.1.
Table 8.10.8.1—Portion of shear resisted by beam
α_{f1}ℓ_{2}/ℓ_{1}  Distribution coefficient 
0  0 
≥1.0  1.0 
Note: Linear interpolation shall be made between values shown.
Fig. 8.10.8.1—Tributary area for shear on an interior beam.
In addition to shears calculated according to
8.10.8.1,
beams shall resist shears caused by
factored loads applied directly to the
beams, including the weight of the
beam stem above and below the slab.
Calculation of required slab shear strength based on the assumption that
load is distributed to supporting
beams in accordance with
8.10.8.1 shall be permitted. Shear resistance to total
V_{u} occurring on a panel shall be provided.
All sections of slabs and supporting members in twoway slab systems designed by the equivalent frame method shall resist moments and shears obtained from an analysis in accordance with
8.11.2 through
8.11.6.
It shall be permitted to account for the contribution of metal
column capitals to stiffness, resistance to moment, and resistance to shear.
It shall be permitted to neglect the change in length of
columns and slabs due to direct stress, and deflections due to shear.
The structure shall be modeled by equivalent frames on
column lines taken longitudinally and transversely through the building.
Each equivalent frame shall consist of a row of
columns or supports and slab
beam strips bounded laterally by the panel centerline on each side of the centerline of
columns or supports.
Frames adjacent and parallel to an edge shall be bounded by that edge and the centerline of the adjacent panel.
Columns or supports shall be assumed to be attached to slab
beam strips by torsional members transverse to the direction of the span for which moments are being calculated and extending to the panel centerlines on each side of a
column.
Analysis of each equivalent frame in its entirety shall be permitted. Alternatively, for gravity loading, a separate analysis of each floor or roof with the far ends of
columns considered fixed is permitted.
If slab
beams are analyzed separately, it shall be permitted to calculate the moment at a given support by assuming that the slab
beam is fixed at supports two or more panels away, provided the slab continues beyond the assumed fixed supports.
The moment of inertia of slab
beams from the center of the
column to the face of the
column, bracket, or capital shall be assumed equal to the moment of inertia of the slab
beam at the face of the
column, bracket, or capital divided by the quantity (
1 — c_{2}/ℓ_{2})
^{2}, where
c_{2} and
ℓ_{2} are measured transverse to the direction of the span for which moments are being determined.
Variation in moment of inertia along the axis of slab
beams shall be taken into account.
It shall be permitted to use the gross crosssectional area of
concrete to determine the moment of inertia of slab
beams at any cross section outside of
joints or
column capitals.
The moment of inertia of
columns from top to bottom of the slab
beam at a
joint shall be assumed to be infinite.
Variation in moment of inertia along the axis of
columns shall be taken into account.
Torsional members shall be assumed to have a constant cross section throughout their length consisting of the greatest of (a) through (c):
(a) A portion of slab having a width equal to that of the column, bracket, or capital in the direction of the span for which moments are being determined.
(b) For monolithic or fully composite construction, the portion of slab specified in (a) plus that part of the transverse beam above and below the slab.
(c) The transverse beam in accordance with 8.4.1.8.
Where
beams frame into
columns in the direction of the span for which moments are being calculated, the torsional stiffness shall be multiplied by the ratio of the moment of inertia of the slab with such a
beam to the moment of inertia of the slab without such a
beam.
At interior supports, the critical section for negative
M_{u} in both
column and middle strips shall be taken at the face of rectilinear supports, but not farther away than
0.175ℓ_{1} from the center of a
column.
At exterior supports without brackets or capitals, the critical section for negative M_{u} in the span perpendicular to an edge shall be taken at the face of the supporting element.
At exterior supports with brackets or capitals, the critical section for negative M_{u} in the span perpendicular to an edge shall be taken at a distance from the face of the supporting element not exceeding onehalf the projection of the bracket or capital beyond the face of the supporting element.
Circular or regular polygonshaped supports shall be assumed to be square supports with the same area for location of critical section for negative design moment.
Where slab systems within limitations of
8.10.2 are analyzed by the equivalent frame method, it shall be permitted to reduce the calculated moments in such proportion that the absolute sum of the positive and average negative design moments need not exceed the value obtained from Eq. (
8.10.3.2).
It shall be permitted to distribute moments at critical sections to
column strips,
beams, and middle strips in accordance with the direct design method in 8.10, provided that Eq. (
8.10.2.7a) is satisfied.