Upcodes Diagrams
This chapter shall apply to the design of nonprestressed and prestressed slabs reinforced for flexure in one direction, including:
(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) Precast, prestressed hollow-core slabs
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.
For solid nonprestressed slabs not supporting or attached to partitions or other construction likely to be damaged by large deflections, overall slab thickness h shall not be less than the limits in Table 7.3.1.1, unless the calculated deflection limits of 7.3.2 are satisfied.
Table 7.3.1.1—Minimum thickness of solid nonprestressed one-way slabs
| Support condition | Minimum h[1] |
|---|---|
| Simply supported | ℓ/20 |
| One end continuous | ℓ/24 |
| Both ends continuous | ℓ/28 |
| Cantilever | ℓ/10 |
[1]Expression applicable for normalweight concrete and fy = 60,000 psi. For other cases, minimum h shall be modified in accordance with 7.3.1.1.1 through 7.3.1.1.3, as appropriate.
For fy other than 60,000 psi, the expressions in Table 7.3.1.1 shall be multiplied by (0.4 + fy/100,000).
For nonprestressed slabs made of lightweight concrete having wc in the range of 90 to 115 lb/ft3, the expressions in Table 7.3.1.1 shall be multiplied by the greater of (a) and (b):
(a) 1.65 — 0.005wc
(b) 1.09
For nonprestressed composite slabs made of a combination of lightweight and normalweight concrete, shored during construction, and where the lightweight concrete is in compression, the modifier of 7.3.1.1.2 shall apply.
For nonprestressed slabs, εt shall be at least 0.004.
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 in Chapter 6.
For slabs built integrally with supports, Mu at the support shall be permitted to be calculated at the face of support.
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 or 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 region 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
For each applicable factored load combination, design strength at all sections shall satisfy ϕSn ≥ U including (a) and (b). Interaction between load effects shall be considered.
(a) ϕMn ≥ Mu
(b) ϕVn ≥ Vu
For prestressed slabs, external tendons shall be considered as unbonded tendons in calculating flexural strength, unless the external tendons are effectively bonded to the concrete section along the entire length.
If primary flexural reinforcement in a slab that is considered to be a T-beam flange is parallel to the longitudinal axis of the beam, reinforcement perpendicular to the longitudinal axis of the beam shall be provided in the top of the slab in accordance with (a) and (b). This provision does not apply to joist construction.
(a) Slab reinforcement perpendicular to the beam shall be designed to resist the factored load on the overhanging slab width assumed to act as a cantilever.
(b) Only the effective overhanging slab width in accordance with 6.3.2 need be considered.
A minimum area of flexural reinforcement, As,min, shall be provided in accordance with Table 7.6.1.1.
Table 7.6.1.1—As,min for nonprestressed one-way slabs
| Reinforcement type | fy, psi | As,min | |
|---|---|---|---|
| Deformed bars | < 60,000 | 0.0020Ag | |
| Deformed bars or welded wire reinforcement | ≥ 60,000 | Greater of: |  |
| 0.0014Ag | |||
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 as given in 19.2.3.
For slabs with both flexural and shear design strength at least twice the required strength, 7.6.2.1 need not be satisfied.
For slabs with unbonded tendons, the minimum area of bonded deformed longitudinal reinforcement, As,min, shall be:
| As,min ≥ 0.004Act | (7.6.2.3) |
where Act is the area of that part of the cross section between the flexural tension face and the centroid of the gross section.
A minimum area of shear reinforcement, Av,min, shall be provided in all regions where Vu > ϕVc. For precast prestressed hollow-core slabs with untopped h > 12.5 in., Av,min shall be provided in all regions where Vu > 0.5ϕVcw.
If shown by testing that the required Mn and Vn can be developed, 7.6.3.1 need not be satisfied. Such tests shall simulate effects of differential settlement, creep, shrinkage, and temperature change, based on a realistic assessment of these effects occurring in service.
If shear reinforcement is required, Av,min shall be in accordance with 9.6.3.3.
Reinforcement shall be provided to resist shrinkage and temperature stresses in accordance with 24.4.
If prestressed shrinkage and temperature reinforcement in accordance with 24.4.4 is used, 7.6.4.2.1 through 7.6.4.2.3 shall apply.
For monolithic, cast-in-place, post-tensioned beam-and-slab construction, gross concrete area shall consist of the total beam area including the slab thickness and the slab area within half the clear distance to adjacent beam webs. It shall be permitted to include the effective force in beam tendons in the calculation of total prestress force acting on gross concrete area.
For nonprestressed and Class C prestressed slabs, spacing of bonded longitudinal reinforcement closest to the tension face shall not exceed s given in 24.3.
For nonprestressed slabs, maximum spacing s of deformed reinforcement shall be the lesser of 3h and 18 in.
Calculated tensile or compressive force in reinforcement at each section of the slab shall be developed on each side of that section.
Critical locations for development of reinforcement are points of maximum stress and points along the span where bent or terminated tension reinforcement is no longer required to resist flexure.
Reinforcement shall extend beyond the point at which it is no longer required to resist flexure for a distance at least the greater of d and 12db, except at supports of simply-supported spans and at free ends of cantilevers.
Continuing flexural tension reinforcement shall have an embedment length at least ℓd beyond the point where bent or terminated tension reinforcement is no longer required to resist flexure.
Flexural tension reinforcement shall not be terminated in a tension zone unless (a), (b), or (c) is satisfied:
(a) Vu ≤ (2/3)ϕVn at the cutoff point.
(b) For No. 11 bars and smaller, continuing reinforcement provides double the area required for flexure at the cutoff point and Vu ≤ (3/4)ϕVn.
Adequate anchorage shall be provided for tension reinforcement where reinforcement stress is not directly proportional to moment, such as in sloped, stepped, or tapered slabs, or where tension reinforcement is not parallel to the compression face.
In slabs with spans not exceeding 10 ft, welded wire reinforcement, with wire size not exceeding W5 or D5, shall be permitted to be curved from a point near the top of slab over the support to a point near the bottom of slab at midspan, provided such reinforcement is continuous over, or developed at, the support.
At simple supports, at least one-third of the maximum positive moment reinforcement shall extend along the slab bottom into the support, except for precast slabs where such reinforcement shall extend at least to the center of the bearing length.
At other supports, at least one-fourth of the maximum positive moment reinforcement shall extend along the slab bottom into the support at least 6 in.
At simple supports and points of inflection, db for positive moment tension reinforcement shall be limited such that ℓd for that reinforcement satisfies (a) or (b). If reinforcement terminates beyond the centerline of supports by a standard hook or a mechanical anchorage at least equivalent to a standard hook, (a) or (b) need not be satisfied.
(a) ℓd ≤ (1.3Mn/Vu + ℓa) if end of reinforcement is confined by a compressive reaction
(b) ℓd ≤ (Mn/Vu + ℓa) if end of reinforcement is not confined by a compressive reaction
Mn is calculated assuming all reinforcement at the section is stressed to fy and Vu is calculated at the section. At a support, ℓa is the embedment length beyond the center of the support. At a point of inflection, ℓa is the embedment length beyond the point of inflection, limited to the greater of d and 12db.
At least one-third of the negative moment reinforcement at a support shall have an embedment length beyond the point of inflection at least the greatest of d, 12db, and ℓn/16.
External tendons shall be attached to the member in a manner that maintains the specified eccentricity between the tendons and the concrete centroid through the full range of anticipated member deflections.
If nonprestressed reinforcement is required to satisfy flexural strength, the detailing requirements of 7.7.3 shall be satisfied.
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 7.6.2.3 shall be in accordance with (a) and (b):
(a) At least ℓn/3 in positive moment areas and be centered in those areas
(b) At least ℓn/6 on each side of the face of support
If shear reinforcement is required, transverse reinforcement shall be detailed according to 9.7.6.2.
Shrinkage and temperature reinforcement in accordance with 7.6.4 shall be placed perpendicular to flexural reinforcement.
Spacing of deformed shrinkage and temperature reinforcement shall not exceed the lesser of 5h and 18 in.
If spacing of slab tendons exceeds 4.5 ft, additional deformed shrinkage and temperature reinforcement conforming to 24.4.3 shall be provided parallel to the tendons, except 24.4.3.4 need not be satisfied. In calculating the area of additional reinforcement, it shall be permitted to take the gross concrete area in Table 24.4.3.2 as the slab area between faces of beams. This shrinkage and temperature reinforcement shall extend from the slab edge for a distance not less than the slab tendon spacing.