Heads up:
There are no amended sections in this chapter.
This chapter shall apply to member design for minimum serviceability, including (a) through (d):
(a) Deflections due to service-level gravity loads (24.2)
(b) Distribution of flexural reinforcement in one-way slabs and beams to control cracking (24.3)
(c) Shrinkage and temperature reinforcement (24.4)
(d) Permissible stresses in prestressed flexural members (24.5)
Members subjected to flexure shall be designed with adequate stiffness to limit deflections or deformations that adversely affect strength or serviceability of a structure.
Deflections calculated in accordance with 24.2.3 through 24.2.5 shall not exceed the limits in Table 24.2.2.
Table 24.2.2—Maximum permissible calculated deflections
Member | Condition | Deflection to be considered | Deflection limitation | |
---|---|---|---|---|
Flat roofs | Not supporting or attached to nonstructural elements likely to be damaged by large deflections | Immediate deflection due to maximum of L_{r}, S, and R | ℓ/180^{[1]} | |
Floors | Immediate deflection due to L | ℓ/360 | ||
Roof or floors | Supporting or attached to nonstructural elements | Likely to be damaged by large deflections | That part of the total deflection occurring after attachment of nonstructural elements, which is the sum of the time-dependent deflection due to all sustained loads and the immediate deflection due to any additional live load^{[2]} | ℓ/480^{[3]} |
Not likely to be damaged by large deflections | ℓ/240^{[4]} |
^{[1]}Limit not intended to safeguard against ponding. Ponding shall be checked by calculations of deflection, including added deflections due to ponded water, and considering time-dependent effects of sustained loads, camber, construction tolerances, and reliability of provisions for drainage.
^{[2]}Time-dependent deflection shall be calculated in accordance with 24.2.4, but shall be permitted to be reduced by amount of deflection calculated to occur before attachment of nonstructural elements. This amount shall be calculated on basis of accepted engineering data relating to time-deflection characteristics of members similar to those being considered.
^{[3]}Limit shall be permitted to be exceeded if measures are taken to prevent damage to supported or attached elements.
^{[4]}Limit shall not exceed tolerance provided for nonstructural elements.
Immediate deflections shall be calculated using methods or formulas for elastic deflections, considering effects of cracking and reinforcement on member stiffness.
Effect of variation of cross-sectional properties, such as haunches, shall be considered when calculating deflections.
Deflections in two-way slab systems shall be calculated taking into account size and shape of the panel, conditions of support, and nature of restraints at the panel edges.
Modulus of elasticity, E_{c}, shall be permitted to be calculated in accordance with 19.2.2.
For nonprestressed members, unless obtained by a more comprehensive analysis, effective moment of inertia, I_{e}, shall be calculated in accordance with Table 24.2.3.5 using:
(24.2.3.5) |
Table 24.2.3.5—Effective moment of inertia, I_{e}
Service moment | Effective moment of inertia, I_{e}, in.^{4} | |
---|---|---|
M_{a} ≤ (2/3)M_{cr} | I_{g} | (a) |
M_{a} > (2/3)M_{cr} | (b) |
For continuous one-way slabs and beams, I_{e} shall be permitted to be taken as the average of values obtained from Table 24.2.3.5 for the critical positive and negative moment sections.
For prismatic one-way slabs and beams, I_{e} shall be permitted to be taken as the value obtained from Table 24.2.3.5 at midspan for simple and continuous spans, and at the support for cantilevers.
For prestressed Class T and Class C slabs and beams as defined in 24.5.2, deflection calculations shall be based on a cracked transformed section analysis. It shall be permitted to base deflection calculations on a bilinear moment-deflection relationship or I_{e} in accordance with Eq. (24.2.3.9a)
(24.2.3.9a) |
where M_{cr} is calculated as
(24.2.3.9b) |
Unless obtained from a more comprehensive analysis, additional time-dependent deflection resulting from creep and shrinkage of flexural members shall be calculated as the product of the immediate deflection caused by sustained load and the factor λ_{Δ}
(24.2.4.1.1) |
In Eq. (24.2.4.1.1), ρ' shall be calculated at midspan for simple and continuous spans, and at the support for cantilevers.
In Eq. (24.2.4.1.1), values of the time-dependent factor for sustained loads, ξ, shall be in accordance with Table 24.2.4.1.3.
Additional time-dependent deflection of prestressed concrete members shall be calculated considering stresses in concrete and reinforcement under sustained load, and the effects of creep and shrinkage of concrete and relaxation of prestressed reinforcement.
If composite concrete flexural members are shored during construction so that, after removal of temporary supports, the dead load is resisted by the full composite section, it shall be permitted to consider the composite member equivalent to a monolithically cast member for calculation of deflections.
If composite concrete flexural members are not shored during construction, the magnitude and duration of load before and after composite action becomes effective shall be considered in calculating time-dependent deflections.
Deflections resulting from differential shrinkage of precast and cast-in-place components, and of axial creep effects in prestressed members, shall be considered.
Bonded reinforcement shall be distributed to control flexural cracking in tension zones of nonprestressed and Class C prestressed slabs and beams reinforced for flexure in one direction only.
Spacing of bonded reinforcement closest to the tension face shall not exceed the limits in Table 24.3.2, where c_{c} is the least distance from surface of deformed or prestressed reinforcement to the tension face. Calculated stress in deformed reinforcement, f_{s}, and calculated change in stress in bonded prestressed reinforcement, Δf_{ps}, shall be in accordance with 24.3.2.1 and 24.3.2.2, respectively.
Table 24.3.2—Maximum spacing of bonded reinforcement in nonprestressed and Class C prestressed one-way slabs and beams
Reinforcement type | Maximum spacing s | |
---|---|---|
Deformed bars or wires | Lesser of: | |
Bonded prestressed reinforcement | Lesser of: | |
Combined deformed bars or wires and bonded prestressed reinforcement | Lesser of: | |
Stress f_{s} in deformed reinforcement closest to the tension face at service loads shall be calculated based on the unfactored moment, or it shall be permitted to take f_{s} as (2/3)f_{y}.
Change in stress, Δf_{ps}, in bonded prestressed reinforcement at service loads shall be equal to the calculated stress based on a cracked section analysis minus the decompression stress f_{dc}. It shall be permitted to take f_{dc} equal to the effective stress in the prestressed reinforcement f_{se}. The value of Δf_{ps} shall not exceed 36,000 psi. If Δf_{ps} does not exceed 20,000 psi, the spacing limits in Table 24.3.2 need not be satisfied.
If there is only one bonded bar, pretensioned strand, or bonded tendon nearest to the extreme tension face, the width of the extreme tension face shall not exceed s determined in accordance with Table 24.3.2.
If the flange of a T-beam is in tension, the portion of the bonded flexural tension reinforcement not located over the beam web shall be distributed within the lesser of the effective flange width, as defined in accordance with 6.3.2 and ℓ_{n}/10. If ℓ_{n}/10 controls, additional bonded longitudinal reinforcement satisfying 24.4.3.1 shall be provided in the outer portions of the flange.
The spacing of bonded flexural reinforcement in nonprestressed and Class C prestressed one-way slabs and beams subject to fatigue, designed to be watertight, or exposed to corrosive environments, shall be selected based on investigations and precautions specific to those conditions and shall not exceed the limits of 24.3.2.
Reinforcement to resist shrinkage and temperature stresses shall be provided in one-way slabs in the direction perpendicular to the flexural reinforcement in accordance with 24.4.3 or 24.4.4.
If shrinkage and temperature movements are restrained, the effects of T shall be considered in accordance with 5.3.6.
Deformed reinforcement to resist shrinkage and temperature stresses shall conform to Table 20.2.2.4(a) and shall be in accordance with 24.4.3.2 through 24.4.3.5.
The ratio of deformed shrinkage and temperature reinforcement area to gross concrete area shall be greater than or equal to 0.0018.
The spacing of deformed shrinkage and temperature reinforcement shall not exceed the lesser of 5h and 18 in.
At all sections where required, deformed reinforcement used to resist shrinkage and temperature stresses shall develop f_{y} in tension.
For one-way precast slabs and one-way precast, prestressed wall panels, shrinkage and temperature reinforcement is not required in the direction perpendicular to the flexural reinforcement if (a) through (c) are satisfied.
(a) Precast members are not wider than 12 ft
(b) Precast members are not mechanically connected to cause restraint in the transverse direction
(c) Reinforcement is not required to resist transverse flexural stresses
Prestressed reinforcement to resist shrinkage and temperature stresses shall conform to Table 20.3.2.2, and the effective prestress after losses shall provide an average compressive stress of at least 100 psi on gross concrete area.
For calculation of stresses at transfer of prestress, at service loads, and at cracking loads, elastic theory shall be used with assumptions (a) and (b):
(a) Strains vary linearly with distance from neutral axis in accordance with 22.2.1.
(b) At cracked sections, concrete resists no tension.
Prestressed flexural members shall be classified as Class U, T, or C in accordance with Table 24.5.2.1, based on the extreme fiber stress in tension f_{t} in the precompressed tension zone calculated at service loads assuming an uncracked section.
Table 24.5.2.1—Classification of prestressed flexural members based on f_{t}
Assumed behavior | Class | Limits of f_{t} |
---|---|---|
Uncracked | U^{[1]} | |
Transition between uncracked and cracked | T | |
Cracked | C |
^{[1]}Prestressed two-way slabs shall be designed as Class U with .
For Class U and T members, stresses at service loads shall be permitted to be calculated using the uncracked section.
For Class C members, stresses at service loads shall be calculated using the cracked transformed section.
Calculated extreme concrete fiber stress in tension immediately after transfer of prestress, but before time-dependent prestress losses, shall not exceed the limits in Table 24.5.3.2, unless permitted by 24.5.3.2.1.
Table 24.5.3.2—Concrete tensile stress limits immediately after transfer of prestress, without additional bonded reinforcement in tension zone
Location | Concrete tensile stress limits |
---|---|
Ends of simply-supported members | |
All other locations |
The limits in Table 24.5.3.2 shall be permitted to be exceeded where additional bonded reinforcement in the tension zone resists the total tensile force in the concrete calculated with the assumption of an uncracked section.
For Class U and T members, the calculated extreme concrete fiber stress in compression at service loads, after allowance for all prestress losses, shall not exceed the limits in Table 24.5.4.1.