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 or the equivalent frame method is permitted.

The effects of concentrated loads, slab openings, and slab voids 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.

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 20.6.

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

*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:***h**(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.

For

*exceeding 80,000 psi, the calculated deflection limits in 8.3.2 shall be satisfied.***f**_{y}**Table 8.3.1.1—Minimum thickness of nonprestressed two-way slabs without interior beams (in.)**

^{[1]}f, psi_{y}^{[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/33_{n} |
ℓ/36_{n} |
ℓ/36_{n} |
ℓ/36_{n} |
ℓ/40_{n} |
ℓ/40_{n} |

60,000 | ℓ/30_{n} |
ℓ/33_{n} |
ℓ/33_{n} |
ℓ/33_{n} |
ℓ/36_{n} |
ℓ/36_{n} |

80,000 | ℓ/27_{n} |
ℓ/30_{n} |
ℓ/30_{n} |
ℓ/30_{n} |
ℓ/33_{n} |
ℓ/33_{n} |

^{[1]}

*ℓ*is the clear span in the long direction, measured face-to-face of supports (in.).

_{n}^{[2]}For

*f*between the values given in the table, minimum thickness shall be calculated by linear interpolation.

_{y}For nonprestressed slabs with beams spanning between supports on all sides, overall slab thickness

*shall satisfy the limits in Table 8.3.1.2, unless the calculated deflection limits of 8.3.2 are satisfied.***h****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. | ||
---|---|---|---|

α_{fm ≤ 0.2} | 8.3.1.1 applies | (a) | |

0.2 < α ≤ 2.0_{fm} | Greater of: | (b)^{[1],[2]} | |

5.0 | (c) | ||

α_{fm > 0.2} | Greater of: | (d) | |

3.5 | (e) |

^{[3]}β is the ratio of clear spans in long to short directions of slab.

If single- or multiple-leg stirrups are used as shear reinforcement, the slab thickness shall be sufficient to satisfy the requirements for

*in 22.6.7.1.***d**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.

Nonprestressed slabs shall be tension-controlled in accordance with Table 21.2.2.

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.

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}**, and***c*_{2}*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.***ℓ**_{n}A middle strip is a design strip bounded by two column strips.

For slabs built integrally with supports,

*at the support shall be permitted to be calculated at the face of support.***M**_{u}The fraction of factored slab moment resisted by the column, γ

**, shall be assumed to be transferred by flexure, where γ**_{f}M_{sc}*shall be calculated by:*_{f}(8.4.2.2.2) |

The effective slab width

*b*for resisting γ_{slab}*shall be the width of column or capital plus a distance on each side in accordance with Table 8.4.2.2.3.*_{f}M_{sc}**Table 8.4.2.2.3—Dimensional limits for effective slab width**

Distance on each side of column or capital | ||
---|---|---|

Without drop panel or shear cap | Lesser | 1.5h of slab |

Distance to edge of slab | ||

With drop panel or shear cap | Lesser | 1.5h of drop or cap |

Distance to edge of the drop or cap plus 1.5h of slab |

For nonprestressed slabs, where the limitations on

*and***ν**_{uv}**ε**in Table 8.4.2.2.4 are satisfied,_{t}**γ**shall be permitted to be increased to the maximum modified values provided in Table 8.4.2.2.4, where_{f}*is calculated in accordance with 22.6.5.***ν**_{c}**Table 8.4.2.2.4—Maximum modified values of γ**

*for nonprestressed two-way slabs*_{f}Column location | Span direction | ν_{uv} | ε (within _{t}b)_{slab} | Maximum modified γ_{f} |
---|---|---|---|---|

Corner column | Either direction | ≤0.5ϕν_{c} | ≥ε + 0.003_{ty} | 1.0 |

Edge column | Perpendicular to the edge | ≤0.75ϕν_{c} | ≥ε + 0.003_{ty} | 1.0 |

Parallel to the edge | ≤0.4ϕν_{c} | ≥ε + 0.008_{ty} | ||

Interior column | Either direction | ≤0.4ϕν_{c} | ≥ε + 0.008_{ty} |

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 8.4.2.2.2 and 8.4.2.2.3.

The fraction of

*not calculated to be resisted by flexure shall be assumed to be resisted by eccentricity of shear in accordance with 8.4.4.2.***M**_{sc}For slabs built integrally with supports,

*at the support shall be permitted to be calculated at the face of support.***V**_{u}Sections between the face of support and a critical section located

*from the face of support for nonprestressed slabs and***d****from the face of support for prestressed slabs shall be permitted to be designed for***h*/2*at that critical section if (a) through (c) are satisfied:***V**_{u}(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 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.

For two-way shear with factored slab moment resisted by the column, factored shear stress

*shall be calculated at critical sections in accordance with 8.4.4.1. Factored shear stress***v**_{u}*corresponds to a combination of***v**_{u}*and the shear stress produced by***v**_{uv}**γ**, where_{v}M_{sc}**γ**is given in 8.4.4.2.2 and_{v}*is given in 8.4.2.2.1.***M**_{sc}The fraction of

*transferred by eccentricity of shear,***M**_{sc}**γ**, shall be applied at the centroid of the critical section in accordance with 8.4.4.1, where:_{v}M_{sc}γ = 1 — γ_{v}_{f} | (8.4.4.2.2) |

The factored shear stress resulting from

**γ**shall be assumed to vary linearly about the centroid of the critical section in accordance with 8.4.4.1._{v}M_{sc}For each applicable factored load combination, design strength shall satisfy ϕ

**, including (a) through (d). Interaction between load effects shall be considered.***S*≥_{n}*U*(a) ϕ

**at all sections along the span in each direction***M*≥_{n}*M*_{u}(c) ϕ

**at all sections along the span in each direction for one-way shear***V*≥_{n}*V*_{u}(d) ϕ

**at the critical sections defined in 8.4.4.1 for two-way shear***v*≥_{n}*v*_{u}ϕ shall be in accordance with 21.2.

*M*shall be calculated in accordance with 22.3.

_{n}In calculating

*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.***M**_{n}In calculating

*for prestressed slabs, external tendons shall be considered as unbonded unless the external tendons are effectively bonded to the slab along its entire length.***M**_{n}For one-way shear, where each critical section to be investigated extends in a plane across the entire slab width,

*shall be calculated in accordance with 22.5.***V**_{n}For two-way shear,

*shall be calculated in accordance with 22.6.***v**_{n}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.

A minimum area of flexural reinforcement,

*of***A**_{s,min}**0.0018**, or as defined in 8.6.1.2, shall be provided near the tension face of the slab in the direction of the span under consideration.*A*_{g}If on the critical section for two-way shear surrounding a column, concentrated load, or reaction area,

*, provided over the width***A**_{s,min}*, shall satisfy Eq. (8.6.1.2)***b**_{slab}(8.6.1.2) |

where

*is the width specified in 8.4.2.2.3, α***b**_{slab}*is given in 22.6.5.3, ϕ is the value for shear, and*_{s}**λ**is given in 22.5.5.1.3._{s}For prestressed slabs, the effective prestress force

*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.***A**_{ps}f_{se}For slabs with bonded prestressed reinforcement, total quantity of

*and***A**_{s}*shall be adequate to develop a factored load at least 1.2 times the cracking load calculated on the basis of***A**_{ps}*defined in 19.2.3.***f**_{r}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,

*, shall be provided in the precompressed tension zone in the direction of the span under consideration in accordance with Table 8.6.2.3.***A**_{s,min}**Table 8.6.2.3—Minimum bonded deformed longitudinal reinforcement**

*A*in two-way slabs with bonded or unbonded tendons_{s,min}Region | Calculated f after all losses, psi_{t} | A, in._{s,min}^{2} | |
---|---|---|---|

Positive moment | Not required | (a) | |

(b)^{[1],[2]} | |||

Negative moment at columns | 0.00075A_{cf} | (c)^{[2]} |

^{[1]}The value of

*f*shall not exceed 60,000 psi.

_{y}^{[2]}For slabs with bonded tendons, it shall be permitted to reduce

*A*by the area of the bonded prestressed reinforcement located within the area used to determine

_{s},_{min}*N*for positive moment, or within the width of slab defined in 8.7.5.3(a) for negative moment.

_{c}Splice lengths of deformed reinforcement shall be in accordance with 25.5.

Bundled bars shall be detailed in accordance with 25.6.

Minimum spacing

*shall be in accordance with 25.2.***s**For nonprestressed solid slabs, maximum spacing

*of deformed longitudinal reinforcement shall be the lesser of***s****2**and 18 in. at critical sections, and the lesser of*h***3**and 18 in. at other sections.*h*At exterior corners of slabs supported by edge walls or where one or more edge beams have a value of

**α**greater than 1.0, reinforcement at top and bottom of slab shall be designed to resist_{f}*per unit width due to corner effects equal to the maximum positive***M**_{u}*per unit width in the slab panel.***M**_{u}Factored moment due to corner effects,

*, 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.***M**_{u}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. 8.7.4.1.3, 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. 8.7.4.1.3 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. 8.7.4.1.3**—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 using mechanical or welded splices in accordance with 25.5.7 or Class B tension lap splices in accordance with 25.5.2. Splices shall be located in accordance with Fig. 8.7.4.1.3.

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.

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

**1.5**outside opposite faces of the column support.*h*(b) At least four deformed bars, deformed wires, or bonded strands shall be provided in each direction.

(c) Maximum spacing

*between bonded longitudinal reinforcement shall not exceed 12 in.***s**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

**and be centered in those areas***ℓ*/3_{n}(b) In negative moment areas, reinforcement shall extend at least

**on each side of the face of support***ℓ*/6_{n}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):

(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.

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

**in each direction shall be the larger of (a) and (b). The value of***A*_{s}*f*shall be limited to a maximum of 80,000 psi:_{y}(a) | (8.7.5.6.3.1a) |

(b) | (8.7.5.6.3.1b) |

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

*beyond the column or shear cap face.***f**_{y}Single-leg, simple-U, multiple-U, and closed stirrups shall be permitted as shear reinforcement.

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 |

*Shear reinforcement — headed studs*

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/2 | ||

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.

*V*shall be permitted to be taken as 1.1 times the values calculated in 22.5.

_{c}For structural integrity, at least one bottom bar in each joist shall be continuous and shall be anchored to develop

*at the face of supports.***f**_{y}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.

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 using mechanical or welded splices in accordance with 25.5.7 or Class B tension lap splices in accordance with 25.5.2. At exterior columns, the reinforcement shall be anchored at the lifting collar.