Download [David a. Fanella] Reinforced Concrete Structures.(Book4You) PDF

Title[David a. Fanella] Reinforced Concrete Structures.(Book4You)
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Document Text Contents
Page 2

Reinforced
Concrete

Structures

Page 326

313T w o - W a y S l a b s

3. Successive span lengths, centerline-to-centerline of supports, in each direction
must not differ by more than one-third of the longer span.

4. Columns must not be offset more than 10% of the span in the direction of offset
from either axis between the centerlines of successive columns.

5. Loads applied to the slab must be uniformly distributed gravity loads where
the ratio of the unfactored live load to the unfactored dead load is equal to or
less than 2.

6. For panels with column-line beams on all sides, ACI Eq. (13-2) must be satisfied.

7. Redistribution of bending moments in accordance with ACI 8.4 is not permitted.

It is important to note that the Direct Design Method is based on tests where only
uniformly distributed gravity loads were considered.5 A frame analysis is required
where lateral forces, such as wind or seismic forces, act on a structure. Combining the
results from the Direct Design Method with those from the frame analysis is permitted
(ACI 13.5.1.3). The rationale behind other limitations of this method can be found in
ACI R13.6.1.

ACI 13.6.1.8 permits the use of the Direct Design Method even when the limitations
are not satisfied, provided it can be shown by analysis that a particular limitation does
not apply to the structure.

Analysis Procedure In cases where all of the applicable limitations outlined in ACI 13.6.1
are satisfied, the Direct Design Method may be used to determine the bending moments
in the slab. The three-step analysis procedure is summarized next.

Step 1: Determine the total factored static moment Mo in each span. The total
factored static moment Mo is determined by ACI Eq. (13-4), which is similar to Eq. (7.7)
derived earlier:

Mo =
qu�2�2n

8
(7.8)

In this equation, qu is the total factored gravity loads acting on the slab; �n is the clear
span in the direction of analysis; and �2 is the centerline-to-centerline span length per-
pendicular to �n. Where the transverse spans of panels on either side of the centerline of
supports are not the same (see Fig. 7.18), �2 is set equal to the average of these transverse
span lengths (i.e., �2 = [(�2)A + (�2)B]/2). Also, where the span adjacent and parallel to
an edge is considered, the value of �2 that is to be used in Eq. (7.8) is equal to the distance
from the edge of the slab to the panel centerline. Thus, for the edge design strip de-
picted in Fig. 7.18, �2 is equal to (�2)B/2 plus one-half of the column dimension parallel
to (�2)B .

Requirements on how to determine the clear span length �n are given in ACI 13.6.2.5
and are illustrated in Fig. 7.20. In general, �n is to extend face-to-face of columns, capitals,
brackets, or walls. In cases where the supporting member does not have a rectangular
cross-section or if the sides of the rectangle are not parallel to the spans, such members
are to be treated as a square support that has the same area as that of the actual support.
ACI 13.6.2.5 also requires that �n be equal to or greater than 65% of the span length �1.

Page 327

314 C h a p t e r S e v e n

FIGURE 7.20 Definition of clear span.

Step 2: Distribute Mo into negative and positive bending moments in each span.
Once Mo has been calculated, it is divided into negative and positive moments within
each span in accordance with the distribution factors given in ACI 13.6.3. The resulting
bending moments are the total bending moments in the design strip in the direction of
analysis. The negative factored bending moments are located at the face of a support
(ACI 13.6.3).

According to ACI 13.6.3.2, the total negative factored bending moment at the face
of a support in an interior span is equal to 65% of Mo . The positive factored bending
moment is equal to 35% of Mo .

A summary of the bending moment coefficients of ACI 13.6.3.3 for an end span
is given in Table 7.2. These coefficients are based on the equivalent column stiffness
expressions derived in Refs. 6 through 8. An unrestrained edge would correspond to

Page 651

638 I n d e x

Two-way slab systems (contd.)
minimum thickness requirements,

295
control of deflections, 296–300
fire resistance requirements,

301–302
shear strength requirements,

300–301
requirements, 352t
shear, design for, 362

one-way shear, 363–364, 363f
two-way shear, 364–391

two-way joist construction, 294–295
Two-way/punching shear, 291,

364–391
at corner piles, 590
critical shear section, 364f, 365f, 366f,

367f
effect of openings, 368
general requirements, 364–366
slab edges, effect of, 366–368

at interior pile, 589
with overlapping critical

perimeters, 589–590
requirements, 300
shear strength

provided by concrete, 368
provided by shear reinforcement,

369–374
slab–column connections, transfer of

moment at, 374
factored shear stress, 375–377
strength design, requirements for,

377–378
unbalanced moment transferred

by eccentricity of shear,
374–375

U
Ultimate limit, 103
Ultimate strength design method,

103
Unbalanced loads, 80
Unfactored loads, 528
Unified Design Method, 126
Uniform Building Code, 106, 504

Unreinforced concrete beam, 1, 2
U-stirrups, 237, 239f
Unsupported length, of compression

member, 437, 438f, 439f

V
Variable loads, 67, 106
Vertical forming systems

conventional column/wall system,
16

ganged systems, 16
jump forms, 16
self-raising forms, 16
slipforms, 16

Vertical reinforcements, 519
Volume changes

in concrete members, 46–49
in high-strength concrete, 51

Volumetric spiral reinforcement ratio,
469

W
Waffle slab system. See Two-way joist

system
Wall footing, 521–522, 522f, 536
Walls, 10

axial loads and flexure, design
methods for

compression members, walls
designed as, 490–501

empirical design method, 501–503
overview, 490
slender walls, alternative design

of, 504–512
definition of, 489
design procedure, 519
minimum reinforcement

requirements for, 491t
overview, 489–490
shear, design for

design shear strength, 513
overview, 513
shear strength, for concrete,

513–514
shear strength provided by shear

reinforcement, 514–518

Page 652

639I n d e x

Water, for making concrete, 23
Wave loads, 82
Web-shear cracks, 232
Welded splices, 227–228, 479
Welded wire reinforcement (WWR),

236, 604t
general, 62
mechanical properties, 63
style designations, 62–63

Welding, of reinforcing bars, 55–56
Wide-module joist system, 7, 7f

reinforcement details for, 247f
Wind loads, 82–85
Windward snow drift, 80, 80f
Wire reinforcement institute (WRI)

standard wire reinforcement, 604t
Working stress design method, 4, 10,

103

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