Heads up: There are no amended sections in this chapter.
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 stay-in-place, 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) Two-way 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 one-fourth of the adjacent slab thickness.

(b) The drop panel shall extend in each direction from the centerline of support a distance not less than one-sixth the span length measured from center-to-center 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.
Design properties for concrete shall be selected to be in accordance with Chapter 19.
Design properties for steel reinforcement shall be selected to be in accordance with Chapter 20.
Materials, design, and detailing requirements for embedments in concrete shall be in accordance with 20.7.
Beam-column and slab-column joints shall satisfy Chapter 15.
For nonprestressed slabs without interior beams spanning between supports on all sides, having a maximum ratio of long-to-short 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 two-way slabs without interior beams (in.)[1]

fy, 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 n/33 n/36 n/36 n/36 n/40 n/40
60,000 n/30 n/33 n/33 n/33 n/36 n/36
75,000 n/28 n/31 n/31 n/31 n/34 n/34

[1]n is the clear span in the long direction, measured face-to-face of supports (in.).

[2]For fy 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 αf is less than 0.8. The value of αf 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 two-way slabs with beams spanning between supports on all sides

αfm[1] Minimum h, in.  
αfm ≤ 0.2

8.3.1.1 applies

(a)
0.2 < αfm ≤ 2.0 Greater of: (b)[2],[3]
5.0 (c)
αfm > 2.0 Greater of: (d)[2],[3]
3.5 (e)

[1]αfm is the average value of αf for all beams on edges of a panel and αf shall be calculated in accordance with 8.10.2.7.

[2]n is the clear span in the long direction, measured face-to-face 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 αf ≥ 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 multiple-leg 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 time-dependent deflections shall be calculated in accordance with 24.2 and shall not exceed the limits in 24.2.2 for two-way 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 long-to-short 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, εt 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 factored load combinations in Chapter 5.
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 c1, c2, and 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 0.252 and 0.251. A column strip shall include beams within the strip, if present.
A middle strip is a design strip bounded by two column strips.
A panel is bounded by column, beam, or wall centerlines on all sides.
For monolithic or fully composite construction supporting two-way 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, Mu 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, Mu 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 Msc, 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, γfMsc, shall be assumed to be transferred by flexure, where γf shall be calculated by:
(8.4.2.3.2)
The effective slab width bslab for resisting γfMsc 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 vug and εt in Table 8.4.2.3.4 are satisfied, γf shall be permitted to be increased to the maximum modified values provided in Table 8.4.2.3.4, where vc is calculated in accordance with 22.6.5, and vug is the factored shear stress on the slab critical section for two-way action due to gravity loads without moment transfer.

Table 8.4.2.3.4—Maximum modified values of γf for nonprestressed two-way slabs

Column location Span direction vug εt (within bslab) Maximum modified γf
Corner column Either direction ≤0.5ϕvc ≥0.004 1.0
Edge column Perpendicular to the edge ≤0.75ϕvc ≥0.004 1.0
Parallel to the edge ≤0.4ϕvc ≥0.010
Interior column Either direction ≤0.4ϕvc ≥0.010
Concentration of reinforcement over the column by closer spacing or additional reinforcement shall be used to resist moment on the effective slab width defined in 8.4.2.3.2 and 8.4.2.3.3.
The fraction of Msc 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, Vu 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 Vu 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 two-way shear in the vicinity of columns, concentrated loads, and reaction areas at critical sections in accordance with 22.6.4.
Slabs reinforced with stirrups or headed shear stud reinforcement shall be evaluated for two-way shear at critical sections in accordance with 22.6.4.2.
Slabs reinforced with shearheads shall be evaluated for two-way shear at critical sections in accordance with 22.6.9.8.
For two-way shear with factored slab moment resisted by the column, factored shear stress vu shall be calculated at critical sections in accordance with 8.4.4.1. Factored shear stress vu corresponds to a combination of vug and the shear stress produced by γvMsc, where γv is given in 8.4.4.2.2 and Msc is given in 8.4.2.3.1.
The fraction of Msc transferred by eccentricity of shear, γvMsc, shall be applied at the centroid of the critical section in accordance with 8.4.4.1, where:
γv = 1 — γf (8.4.4.2.2)
The factored shear stress resulting from γvMsc 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 ϕSnU, including (a) through (d). Interaction between load effects shall be considered.

(a) ϕMnMu at all sections along the span in each direction

(b) ϕMn ≥ γfMsc within bslab as defined in 8.4.2.3.3

(c) ϕVnVu at all sections along the span in each direction for one-way shear

(d) ϕvnvu at the critical sections defined in 8.4.4.1 for two-way 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.
Mn shall be calculated in accordance with 22.3.
In calculating Mn for nonprestressed slabs with a drop panel, the thickness of the drop panel below the slab shall not be assumed to be greater than one-fourth the distance from the edge of drop panel to the face of column or column capital.
In calculating Mn for prestressed slabs, external tendons shall be considered as unbonded unless the external tendons are effectively bonded to the slab along its entire length.
Design shear strength of slabs in the vicinity of columns, concentrated loads, or reaction areas shall be the more severe of 8.5.3.1.1 and 8.5.3.1.2.
For one-way shear, where each critical section to be investigated extends in a plane across the entire slab width, Vn shall be calculated in accordance with 22.5.
For two-way shear, vn shall be calculated in accordance with 22.6.
For composite concrete slabs, horizontal shear strength Vnh 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 one-eighth 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 one-fourth 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, As,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—As,min for nonprestressed two-way slabs

Reinforcement type fy, psi As,min, in.2
Deformed bars < 60,000 0.0020Ag
Deformed bars or welded wire reinforcement ≥ 60,000 Greater of:
0.0014Ag
For prestressed slabs, the effective prestress force Apsfse 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 slabs with bonded prestressed reinforcement, total quantity of As and Aps shall be adequate to develop a factored load at least 1.2 times the cracking load calculated on the basis of fr defined in 19.2.3.
For slabs with both flexural and shear design strength at least twice the required strength, 8.6.2.2 need not be satisfied.
For prestressed slabs, a minimum area of bonded deformed longitudinal reinforcement, As,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 As,min in two-way slabs with bonded or unbonded tendons

Region Calculated ft after all losses, psi As,min, in.2
Positive moment Not required (a)
(b)[1],[2],[4]
Negative moment at columns 0.00075Acf (c)[3],[4]

[1]The value of fy shall not exceed 60,000 psi.

[2]Nc 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]Acf is the greater gross cross-sectional area of the slab-beam strips of the two orthogonal equivalent frames intersecting at a column of a two-way slab.

[4]For slabs with bonded tendons, it shall be permitted to reduce As,min by the area of the bonded prestressed reinforcement located within the area used to determine Nc for positive moment, or within the width of slab defined in 8.7.5.3(a) for negative moment.

Concrete cover for reinforcement shall be in accordance with 20.6.1.
Development lengths of deformed and prestressed reinforcement shall be in accordance with 25.4.
Splice lengths of deformed reinforcement shall be in accordance with 25.5.
Bundled bars shall be detailed in accordance with 25.6.
Minimum spacing s shall be in accordance with 25.2.
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.
Concentrated loads and openings shall be considered in determining tendon spacing.
At exterior corners of slabs supported by edge walls or where one or more edge beams have a value of αf greater than 1.0, reinforcement at top and bottom of slab shall be designed to resist Mu per unit width due to corner effects equal to the maximum positive Mu per unit width in the slab panel.
Factored moment due to corner effects, Mu, 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 one-fifth 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 depth-to-span ratio permits use of bends of 45 degrees or less.

Fig. 8.7.4.1.3a—Minimum extensions for deformed reinforcement in two-way 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.

Post-tensioned anchorage zones shall be designed and detailed in accordance with 25.9.
Post-tensioning 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 n/3 and be centered in those areas

(b) In negative moment areas, reinforcement shall extend at least 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.

Outside of the column and shear cap faces, the two structural integrity tendons required by 8.7.5.6.1 shall pass under any orthogonal tendons in adjacent spans.
Slabs with tendons not satisfying 8.7.5.6.1 shall be permitted if bonded bottom deformed reinforcement is provided in each direction in accordance with 8.7.5.6.3.1 through 8.7.5.6.3.3.
Minimum bottom deformed reinforcement As 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 bw is the width of the column face through which the reinforcement passes.

Bottom deformed reinforcement calculated in 8.7.5.6.3.1 shall pass within the region bounded by the longitudinal reinforcement of the column and shall be anchored at exterior supports.
Bottom deformed reinforcement shall be anchored to develop fy beyond the column or shear cap face.
Single-leg, simple-U, multiple-U, and closed stirrups shall be permitted as shear reinforcement.
Stirrup anchorage and geometry shall be in accordance with 25.7.1.
If stirrups are provided, location and spacing shall be in accordance with Table 8.7.6.3.

Table 8.7.6.3—First stirrup location and spacing limits

Direction of measurement Description of measurement Maximum distance or spacing, in.
Perpendicular to column face Distance from column face to first stirrup d/2
Spacing between stirrups d/2
Parallel to column face Spacing between vertical legs of stirrups 2d
Headed shear stud reinforcement shall be permitted if placed perpendicular to the plane of the slab.
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) One-half 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 two-way 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.
Clear spacing between ribs shall not exceed 30 in.
Vc 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 fy 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.
Two-way 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 one-twelfth 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 one-twelfth the clear distance between ribs and 2 in.
In slabs constructed with lift-slab 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 post-tensioned 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.
Two-way 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 polygon-shaped 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 center-to-center of supports in each direction shall not differ by more than one-third the longer span.
Panels shall be rectangular, with the ratio of longer to shorter panel dimensions, measured center-to-center 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.
Unfactored live load shall not exceed two times the unfactored dead load.
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 αf1 and αf2 are calculated by:

(8.10.2.7b)
Total factored static moment Mo 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 Mu in each direction shall be at least:
(8.10.3.2)
In Eq. (8.10.3.2), 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 0.651.
In Eq. (8.10.3.2), if the transverse span of panels on either side of the centerline of supports varies, 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 2.
In an interior span, Mo shall be distributed as follows: 0.65Mo to negative moment and 0.35Mo to positive moment.
In an end span, Mo 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, Mo, 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 Mu shall be at the face of rectangular supports.
Negative Mu shall be the greater of the two interior negative Mu 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 Mu.
The column strip shall resist the portion of interior negative Mu in accordance with Table 8.10.5.1.

Table 8.10.5.1—Portion of interior negative Mu in column strip

αf12/1 2/1
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 Mu in accordance with Table 8.10.5.2.

Table 8.10.5.2—Portion of exterior negative Mu in column strip

αf12/1 βt 2/1
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. βt 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 L-sections, 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)2, negative Mu shall be uniformly distributed across 2.
The column strip shall resist the portion of positive Mu in accordance with Table 8.10.5.5.

Table 8.10.5.5—Portion of positive Mu in column strip

αf12/1 2/1
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 Mu in accordance with Table 8.10.5.7.1.

Table 8.10.5.7.1—Portion of column strip Mu in beams

αf12/1 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.
Columns and walls built integrally with a slab system shall resist moments caused by factored loads on the slab system.
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.
Msc = 0.07[(qDu+ 0.5qLu)2n2 — qDu'2'(n')2] (8.10.7.2)

where qDu', 2', and 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 0.3Mo.
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

αf12/1 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 Vu occurring on a panel shall be provided.
All sections of slabs and supporting members in two-way 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.
Live load shall be arranged in accordance with 6.4.3.
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 — c2/2)2, where c2 and 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.
It shall be permitted to use the gross crosssectional area of concrete to determine the moment of inertia of columns at any cross section outside of joints or column capitals.
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 Mu in both column and middle strips shall be taken at the face of rectilinear supports, but not farther away than 0.1751 from the center of a column.
At exterior supports without brackets or capitals, the critical section for negative Mu 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 Mu in the span perpendicular to an edge shall be taken at a distance from the face of the supporting element not exceeding one-half the projection of the bracket or capital beyond the face of the supporting element.
Circular or regular polygon-shaped 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.
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