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4 — Openings in slab systems

4 — Openings in slab systems

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solutions based on discrete elements, or yield-line analyses,

including, in all cases, evaluation of the stress conditions

around the supports in relation to shear and torsion as well

as flexure. The design of a slab system involves more than

its analysis, and any deviations in physical dimensions of

the slab from common practice should be justified on the

basis of knowledge of the expected loads and the reliability

of the calculated stresses and deformations of the structure. — Design of a slab system for gravity loads,

including the slab and beams (if any) between

supports and supporting columns or walls forming

orthogonal frames, by either the Direct Design Method

of 13.6 or the Equivalent Frame Method of 13.7, shall

be permitted.

R13.5.1.1 — For gravity load analysis of two-way slab

systems, two analysis methods are given in 13.6 and 13.7.

The specific provisions of both design methods are limited

in application to orthogonal frames subject to gravity loads

only. Both methods apply to two-way slabs with beams as

well as to flat slabs and flat plates. In both methods, the

distribution of moments to the critical sections of the slab

reflects the effects of reduced stiffness of elements due to

cracking and support geometry. — For lateral loads, analysis of frames shall

take into account effects of cracking and reinforcement

on stiffness of frame members.

R13.5.1.2 — During the life of a structure, construction

loads, ordinary occupancy loads, anticipated overloads, and

volume changes will cause cracking of slabs. Cracking reduces

stiffness of slab members, and increases lateral flexibility when

lateral loads act on the structure. Cracking of slabs should be

considered in stiffness assumptions so that drift caused by

wind or earthquake is not grossly underestimated.

The structure may be modeled for lateral load analysis using

any approach that is shown to satisfy equilibrium and

geometric compatibility and to be in reasonable agreement

with test data.13.10,13.11 The selected approach should

recognize effects of cracking as well as parameters such as

l2/l1, c1/l1, and c2/c1. Some of the available approaches are

summarized in Reference 13.12, which includes a discussion

on the effects of cracking. Acceptable approaches include

plate-bending finite-element models, the effective beam

width model, and the equivalent frame model. In all cases,

framing member stiffnesses should be reduced to account

for cracking.

For nonprestressed slabs, it is normally appropriate to

reduce slab bending stiffness to between one-half and onequarter of the uncracked stiffness. For prestressed construction,

stiffnesses greater than those of cracked, nonprestressed

slabs may be appropriate. When the analysis is used to

determine design drifts or moment magnification, lowerbound slab stiffnesses should be assumed. When the analysis is

used to study interactions of the slab with other framing

elements, such as structural walls, it may be appropriate to

consider a range of slab stiffnesses so that the relative

importance of the slab on those interactions can be assessed. — Combining the results of the gravity load

analysis with the results of the lateral load analysis

shall be permitted.

ACI 318 Building Code and Commentary






13.5.2 — The slab and beams (if any) between

supports shall be proportioned for factored moments

prevailing at every section.

13.5.3 — When gravity load, wind, earthquake, or

other lateral forces cause transfer of moment between

slab and column, a fraction of the unbalanced moment

shall be transferred by flexure in accordance with through — The fraction of unbalanced moment not

transferred by flexure shall be transferred by eccentricity of shear in accordance with 11.11.7. — A fraction of the unbalanced moment

given by γf Mu shall be considered to be transferred by

flexure within an effective slab width between lines that

are one and one-half slab or drop panel thickness

(1.5h) outside opposite faces of the column or capital,

where Mu is the factored moment to be transferred and



γ f = ----------------------------------------------1 + ( 2 ⁄ 3 ) b1 ⁄ b2

R13.5.3 — This section is concerned primarily with slab

systems without beams. Tests and experience have shown

that, unless measures are taken to resist the torsional and

shear stresses, all reinforcement resisting that part of the

moment to be transferred to the column by flexure should be

placed between lines that are one and one-half the slab or

drop panel thickness, 1.5h, on each side of the column. The

calculated shear stresses in the slab around the column are

required to conform to the requirements of 11.11.2. See

R11.11.1.2 and R11.11.2.1 for more details on application

of this section.

(13-1) — For nonprestressed slabs with unbalanced

moments transferred between the slab and columns, it

shall be permitted to increase the value of γf given by

Eq. (13-1) in accordance with the following:

(a) For edge columns with unbalanced moments

about an axis parallel to the edge, γf = 1.0 provided

that Vu at an edge support does not exceed

0.75φVc , or at a corner support does not exceed


(b) For unbalanced moments at interior supports,

and for edge columns with unbalanced moments

about an axis perpendicular to the edge, increase γf

to as much as 1.25 times the value from Eq. (13-1),

but not more than γf = 1.0, provided that Vu at the

support does not exceed 0.4φVc. The net tensile

strain εt calculated for the effective slab width

defined in shall not be less than 0.010.

The value of Vc in items (a) and (b) shall be calculated

in accordance with

R13.5.3.3 — The 1989 Code procedures remain unchanged,

except that under certain conditions it is permitted to adjust the

level of moment transferred by shear without revising member

sizes. Tests indicate that some flexibility in distribution of

unbalanced moments transferred by shear and flexure at both

exterior and interior supports is possible. Interior, exterior, and

corner supports refer to slab-column connections for which the

critical perimeter for rectangular columns has four, three, or

two sides, respectively. Changes in the 1995 Code recognized,

to some extent, design practices before the 1971 Code.13.13

At exterior supports, for unbalanced moments about an axis

parallel to the edge, the portion of moment transferred by

eccentricity of shear γv Mu may be reduced provided that the

factored shear at the support (excluding the shear produced

by moment transfer) does not exceed 75 percent of the shear

strength φVc as defined in for edge columns or

50 percent for corner columns. Tests13.14,13.15 indicate that

there is no significant interaction between shear and

unbalanced moment at the exterior support in such cases.

Note that as γv Mu is decreased, γf Mu is increased.

Evaluation of tests of interior supports indicate that some

flexibility in distributing unbalanced moments transferred

by shear and flexure is possible, but with more severe

limitations than for exterior supports. For interior supports,

the unbalanced moment transferred by flexure is permitted

to be increased up to 25 percent provided that the factored

shear (excluding the shear caused by the moment transfer)

at the interior supports does not exceed 40 percent of the

shear strength φVc as defined in

ACI 318 Building Code and Commentary





When the factored shear for a slab-column connection is

large, the slab-column joint cannot always develop all of the

reinforcement provided in the effective width. The modifications for interior slab-column connections in are

permitted only when the reinforcement (within the effective

width) required to develop the unbalanced moment γf Mu

has a net tensile strain εt not less than 0.010. The use of

Eq. (13-1) without the modification permitted in

will generally indicate overstress conditions on the joint.

The provisions of are intended to improve ductile

behavior of the slab-column joint. When a reversal of

moments occurs at opposite faces of an interior support,

both top and bottom reinforcement should be concentrated within the effective width. A ratio of top to bottom

reinforcement of approximately 2 has been observed to

be appropriate.

For the 2008 Code, two changes were introduced to (1) the limitation for the amount of reinforcement

in the effective slab width to 37.5 percent of the balanced

steel ratio was updated to refer to a minimum net tensile

strain of 0.010 to be consistent with the unified design

approach adopted in the 2002 Code, and (2) the requirement

for the minimum net tensile strain was eliminated for

moment transfer about the slab edge for edge and corner

connections based on the original recommendations from

Joint ACI-ASCE Committee 352.13.15 — 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

13.5.4 — Design for transfer of load from slabs to

supporting columns or walls through shear and torsion

shall be in accordance with Chapter 11.

13.6 — Direct design method

R13.6 — Direct design method

The direct design method consists of a set of rules for

distributing moments to slab and beam sections to satisfy

safety requirements and most serviceability requirements

simultaneously. Three fundamental steps are involved as


(1) Determination of the total factored static moment (see


(2) Distribution of the total factored static moment to

negative and positive sections (see 13.6.3);

(3) Distribution of the negative and positive factored

moments to the column and middle strips and to the

beams, if any (see 13.6.4 through 13.6.6). The distribution

of moments to column and middle strips is also used in

the equivalent frame method (see 13.7).

ACI 318 Building Code and Commentary







13.6.1 — Limitations

R13.6.1 — Limitations

Design of slab systems within the limitations of through by the direct design method

shall be permitted.

The direct design method was developed from considerations

of theoretical procedures for the determination of moments

in slabs with and without beams, requirements for simple

design and construction procedures, and precedents

supplied by performance of slab systems. Consequently, the

slab systems to be designed using the direct design method

should conform to the limitations in this section. — There shall be a minimum of three

continuous spans in each direction.

R13.6.1.1 — The primary reason for the limitation in this

section is the magnitude of the negative moments at the

interior support in a structure with only two continuous

spans. The rules given for the direct design method assume

that the slab system at the first interior negative moment

section is neither fixed against rotation nor discontinuous. — Panels shall be rectangular, with a ratio

of longer to shorter span center-to-center of supports

within a panel not greater than 2.

R13.6.1.2 — If the ratio of the two spans (long span/short

span) of a panel exceeds 2, the slab resists the moment in

the shorter span essentially as a one-way slab. — Successive span lengths center-tocenter of supports in each direction shall not differ by

more than one-third the longer span.

R13.6.1.3 — The limitation in this section is related to the

possibility of developing negative moments beyond the

point where negative moment reinforcement is terminated,

as prescribed in Fig. 13.3.8. — Offset of columns by a maximum of 10

percent of the span (in direction of offset) from either

axis between centerlines of successive columns shall

be permitted.

R13.6.1.4 — Columns can be offset within specified

limits from a regular rectangular array. A cumulative total

offset of 20 percent of the span is established as the upper

limit. — All loads shall be due to gravity only and

uniformly distributed over an entire panel. The

unfactored live load shall not exceed two times the

unfactored dead load.

R13.6.1.5 — The direct design method is based on

tests13.16 for uniform gravity loads and resulting column

reactions determined by statics. Lateral loads such as wind

or seismic require a frame analysis. Inverted foundation

mats designed as two-way slabs (see 15.10) involve application

of known column loads. Therefore, even where the soil

reaction is assumed to be uniform, a frame analysis should

be performed.

In the 1995 Code, the limit of applicability of the direct

design method for ratios of live load to dead load was

reduced from 3 to 2. In most slab systems, the live to dead

load ratio will be less than 2 and it will not be necessary to

check the effects of pattern loading. — For a panel with beams between

supports on all sides, Eq. (13-2) shall be satisfied for

beams in the two perpendicular directions

R13.6.1.6 — The elastic distribution of moments will

deviate significantly from those assumed in the direct design

method unless the requirements for stiffness are satisfied.


α f 1l2

0.2 ≤ -------------≤ 5.0


α f 2l1


where αf1 and αf 2 are calculated in accordance with

Eq. (13-3).

ACI 318 Building Code and Commentary

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