dalle beton armé.pptx

Author
soukainacherradi 
Category
Documents

view
20 
download
1
Embed Size (px)
Transcript of dalle beton armé.pptx

5/19/2018 dalle beton arm.pptx
1/30
Reinforced Concrete Slabs TYPES OF SLABS In reinforced concrete construction, slabs are used to
provide flat, useful surfaces. A reinforced concrete slab is abroad, flat plate, usually horizontal, with top and bottomsurfaces parallel or nearly so. It may be supported by
reinforced concrete beams (and is usually cast monolithicallywith such beams), by masonry or reinforced concrete walls, bystructural steel members, directly by columns, or continuouslyby the ground.
Slabs may be supported on two opposite sides only, as shownin Fig. 1 a, in which case the structural action of the slab isessentially oneway, the loads being carried by the slab in thedirection perpendicular to the supporting beams.
There may be beams on all four sides, as shown in Fig. 1 b, sothat twoway slab action is obtained. Concrete slabs in somecases may be carried directly by columns, as shown in Fig. 1 d,without the use of beams or girders. Such slabs are describedas flat plates and are commonly used where spans are notlarge and loads not particularly heavy. Flat slab construction,shown in Fig. 1 e, is also beamless but incorporates a thickenedslab region in the vicinity of the column and often employs
flared column tops. Both are devices to reduce stresses due toshear and negative bending around the columns. They arereferred to as drop panels and column capitals, respectively.Closely related to the flat plate slab is the twoway joist, alsoknown as a grid or waffle slab, shown in Fig. 1 f . To reduce thedead load of solidslab construction, voids ar formed in arectilinear pattern through use of metal or fiberglass forminserts. A two way ribbed construction results. Usually inserts
are omitted near the columns, so a solid slab is formed to resistmoments and shears better in these areas
FIGURE 1
Types of structural slabs

5/19/2018 dalle beton arm.pptx
2/30
DESIGN OF ONEWAY
SLABS The structural action of a oneway slab may be visualized in terms of
the deformed shape of the loaded surface. Figure 2 shows a
rectangular slab, simply supported along its two opposite long edges
and free of any support along the two opposite short edges. If a
uniformly distributed load is applied to the surface, the deflected
shape will be as shown by the solid lines. Curvatures, andconsequently bending moments, are the same in all strips s spanning
in the short direction between supported edges, whereas there is no
curvature, hence no bending moment, in the long strips I parallel to
the supported edges. The surface approximately cylindrical.
For purposes of analysis and design, a unit strip of such a slab cut out
at right angles to the supporting beams, as shown in Fig. 2, may be
considered as a rectangular beam of unit width, with a depth h equalto the thickness of the slab and a span la equal to the distance
between supported edges. This strip can then be analyzed by the
methods that were used for rectangular beams, the bending moment
being computed for the strip of unit width. The load per unit area on
the slab becomes the load per unit length on the slab strip. The loads
recommended by ASCE for different usage of slabs are shown in
table 1. Since all of the load on the slab must be transmitted to the
two supporting beams, it follows that all of the reinforcement should
be placed at right angles to these beams, with the exception of any
bars that may be placed in the other direction to control shrinkage
and temperature cracking. A oneway slab, thus, consists of a set of
rectangular beams side by side.
This simplified analysis, which assumes Poisson's ratio to be zero, is
slightly conservative. Actually, flexural compression in the concreteFig. 2

5/19/2018 dalle beton arm.pptx
3/30

5/19/2018 dalle beton arm.pptx
4/30

5/19/2018 dalle beton arm.pptx
5/30
in the direction of la will result in lateral expansion in the direction of
lb unless the compressed concrete is restrained. In a oneway slab, this
lateral expansion is resisted by adjacent slab strips, which tend to
expand also. The result is a slight strengthening and stiffening in the
span direction, but this effect is small and can be disregarded.
Factored moments and shears in oneway slabs can be found either by
elastic analysis or through the use ofthe same coefficients as used for
beams . If the slab rests freely on its supports, the span length may be
taken equal to the clear span plus the depth of the slab but need not
exceed the distance between centers of supports, according to ACI
Code 8.9.1. In general, centertocenter distances should be used in
continuous slab analysis, but a reduction is allowed in negative
moments to account for support width as discussed in Chapter 12. For
slabs with clear spans not more than 10 ft that are built integrally withtheir supports, ACI Code 8.9.4 permits analysis as a continuous slab on
knife edge supports with spans equal to the clear spans and the width
of the beams otherwise neglected. If moment and shear coefficients
are used, computations should be based on clear spans.
ACI Code 9.5.2 specifies the minimum thickness in Table 2 for
nonprestressed slabs of normal weight concrete (wc = 145 pcf) using
Grade 60 reinforcement, provided that the slab is not supporting orattached to construction that is likely to be damaged by large
deflections. Lesser thicknesses may be used if calculation of
deflections indicates no adverse effects. For concretes having unit
weight wc in the range from 90 to 115 pcf, the tabulated values should
be multiplied by 1.65  0.005wc' but not less than 1.09. For
reinforcement having a yield stress other than 60,000 psi, the
tabulated values should be multiplied by 0.4 +1/100,000. Slab
deflections may be calculated, if required, by the same methods as forbeams . The total slab thickness h is usually rounded to the next higher
Table. 2
Minimum thickness h of
non prestressed oneway slabs

5/19/2018 dalle beton arm.pptx
6/30
in. for slabs up to 6 in. thickness, and to the next higher in. for
thicker slabs.
Shear will seldom control the design of oneway slabs, particularly if
low tensile reinforcement ratios are used. It will be found that the
shear capacity of the concrete Vc will, almost without exception, be
well above the required shear strength Vn at factored loads. The concrete protection below the reinforcement should follow the
requirements of ACI Code 7.7.1, calling for in. below the bottom of
the steel . In a typical slab, 1 in. below the center of the steel may be
assumed.
The lateral spacing of the bars, except those used only to control
shrinkage and temperature cracks (see Section 13.3), should not
exceed 3 times the thickness h or 18 in., whichever is less, according
to ACI Code 7.6.5. Generally, bar size should be selected so that the
actual spacing is not less than about 1.5 times the slab thickness, to
avoid excessive cost for bar fabrication and handling. Also, to reduce
cost, straight bars are usually used for slab reinforcement, cut off
where permitted are as described for beams .
Since concrete is weak in tension, these temperature and shrinkage
stresses are likely to result in cracking. Cracks of this nature are not
detrimental, provided their size is limited to what are known ashairline cracks. This can be achieved by placing reinforcement in the
slab to counteract contraction and distribute the cracks uniformly. In
oneway slabs, the reinforcement provided for resisting the bending
moments has the desired effect of reducing shrinkage and
distributing cracks. However, as contraction takes place equally in all

5/19/2018 dalle beton arm.pptx
7/30
directions, it is necessary to provide special reinforcement for
shrinkage and temperature contraction in the direction
perpendicular to the main reinforcement. This added steel is
known as temperature or shrinkage reinforcement, or
distribution steel.
Reinforcement for shrinkage and temperature stresses normal
to the principal reinforcement should be provided in a
structural slab in which the principal reinforcement extends in
one direction only. ACI Code 7.12.2 specifies the minimum
ratios of reinforcement area to gross concrete area (i.e., based
on the total depth of the slab) shown in Table 13.2, but in no
case may such reinforcing bars be placed farther apart than 5
times the slab thickness or more than 18 in. In no case is the
reinforcement ratio to be less than 0.0014. The steel required
by the ACI Code for shrinkage and temperature crack control
also represents the minimum permissible reinforcement in the
span direction of oneway slabs; the usual minimums for
flexural steel do not apply.
Table. 3
Minimum ratios of temperature and shrinkage reinforcementin slabs based on gross concrete area

5/19/2018 dalle beton arm.pptx
8/30
DESIGN LIMITATIONS ACCORDING TO THE ACI CODE
The following limitations are specified by the ACI Code.
1. A typical imaginary strip 1ft (or 1m) wide is assumed.
2. The minimum thickness of oneway slabs using grade 60
steel according to the ACI Code,
for solid slabs and for beams or ribbed oneway slabs
should be equal to the following:
For simply supported spans: solid slabs, h = Ll20 (ribbed
slabs, h = L/16).
For oneend continuous spans: solid slabs, h = Ll24
(ribbed slabs, h = Ll18.5).
For bothend continuous spans: solid slabs, h = Ll28
(ribbed slabs, h = Ll21).
For cantilever spans: solid slabs, h = LItO (ribbed slabs,
h = Ll8).
Forfy other than 60 ksi, these values shall be
multiplied by 0.4 + 0.01 fy, where fy is in ksi.
This minimum thickness should be used unless
computation of deflection indicates a lesser thickness
can be used without adverse effects.
3. Deflection is to be checked when the slab supports are
attached to construction likely to be damaged by large
deflections. Deflection limits are set by the ACI Code,
Table 9.5b.
4. It is preferable to choose slab depth to the nearest in.
(or to mm).
5. Shear should be checked, although it does not usually
control.
6. Concrete cover in slabs shall not be less than in. (20
mm) at surfaces not exposed to weather or ground. In
this case, d = h  (3/4 in.)  (halfbar diameter).
7. In structural slabs of uniform thickness, the minimum
amount of reinforcement in the direction of the span
shall not be less than that required for shrinkage andtemperature reinforcement (ACI Code, Section 7.12). .
8. The principal reinforcement shall be spaced not farther
apart than three times the slab thickness nor more
than 18 in. (ACI Code, Section 7.6.5).
9. Straightbar systems may be used in both tops and
bottoms of continuous slabs. An alternative bar
system of straight and bent (trussed) bars placedalternately may also be used.
10. In addition to main reinforcement, steel bars at right
angles to the main must be provided. This additional
steel is called secondary, distribution, shrinkage, or
temperature reinforcement

5/19/2018 dalle beton arm.pptx
9/30
Oneway slab design. Example.
1. A reinforced concrete slab is built integrally with its supports
and consists of two equal spans, each with a clear span of 15 ft.
The service live load is 100 psf,v and 4000 psi concrete is
specified for use with steel with a yield stress equal to 60,000
psi.Requiremaent
2. Design the slab, following the provisions of the ACI Code.
Solution
3. Thickness of Slab.
h= L/28 Table 3
h= 15x12/28 = 6.43 in Say 6.5 in
4. Factored Loads
Dead Load = 1.2x( 6.5x150/12) = 97 psf
Live Load = 1.6x 100 = 160
Total = 257
5.For this case, factored moments at critical sections may be
found using the ACI moment coefficients(see Table 12.1):
6. Max Steel ratio
Notes

5/19/2018 dalle beton arm.pptx
10/30
7. Determine As for max negative BM (6.43 lb ft)
( Assume a=1 and find As)
( Check a for As determined )
As = 0.27 sq in at mid support
As = 0.17 sq in at mid span
As = 0.1 sq in at ext support
8. Temperature and shrinkage Reinforcement
As = 0.0018 X 12 X 6.50 = 0.14 in2
9. Shear Force .
The factored shear force at a distance d from the face of the interiorsupport is
Ok
10. Check spacing of reinforcement etc
Notes

5/19/2018 dalle beton arm.pptx
11/30

5/19/2018 dalle beton arm.pptx
12/30
Two Way Slab
When the slab is supported on all four sides and the length is
less than twice the width. The slab will deflect in two
directions. and the loads on the slab arc transferred to all four
supports. This slab is referred to as a twoway slab. The
bending moments and deflections in such slabs are less than
those in oneway slabs: thus. the same slab can carry more
load when supported on four sides. The load in this case is
carried in two directions, and the bending moment in each
direction is much less than the bending moment in the slab if
the load were carried in one direction only. Typical twoway
slabs is shown in Fig. 1
To visualize its flexural performance, it is convenient to think of
it as consisting of two sets of parallel strips, in each of the two
directions, intersecting each other. Evidently, part of the load iscarried by one set and transmitted to one pair of edge
supports, and the remainder by the other. Figure 1 shows the
two center strips of a rectangular plate with short span la and
long span lb' If the uniform load is q per square foot of slab,
each of the two strips acts approximately as a simple beam,
uniformly loaded by its share of q. Because these imaginary
strips actually are part of the same monolithic slab, their
deflections at the intersection point must be the same.
Equating the center deflections of the short and long strips
gives
Fig. 1

5/19/2018 dalle beton arm.pptx
13/30
where qais the share of the load q carried in the short direction
and qb is the share of the load q carried in the long direction.
Consequently,
One sees that the larger share of the load is carried in the short
direction, the ratio of the two portions of the total load being
inversely proportional to the fourth power of the ratio of the
spans.
This result is approximate because the actual behavior of a slab is
more complex than that of the two intersecting strips. Forinstancefor a simply supportId square slab, qa = qb = q/2 . If only
bending were present, the maximum moment in each strip would
be
The exact theory of bending of elastic plates shows that actually
the maximum moment in such a square slab is only O.048ql2, sothat in this case the twisting moments relieve the bending
moments by about 25 percent. Inelastic redistribution also
modifies these bending moments further. A complicated situation
is therefore obtained. Various design method are suggested to
resolve this situation.

5/19/2018 dalle beton arm.pptx
14/30
Choice of Concrete Slabs Various types of floor systems can be used for general
buildings. such as residential. office. And institutional buildings.
The choice of an adequate and economic floor system depends
on the type of building. architectural layout. aesthetic features.
and the span length between columns. In general. the
superimposed live load on buildings varies between 80 and 150
psf. A general guide for the economical use of Boor systems can
be summarized as follows.
Flat plates are most suitable for spans of 20 to 25 ft and live
loads between 60 and 100 psf. The advantages of adopting flat
plates include lowcost formwork, exposed fl al ceilings. and
fast construction. Flat plates have low shear capacity and
relatively low stiffness. which may cause noticeable deflection.
Flat plates are widely used in buildings either as reinforced orprestressed concrete slabs.
Flat slabs are most suitable for spans of 20 to 30 ft and for live
loads of 80 to 150 psf. They need more fonnwork than flat
plates. especially for column capitals. In most cases. only drop
panels without column capitals are used.
Waffle slabs are suitable for spans of 30 to 48 ft and live loads
of 80 to 150 psf They carry heavier loads than flat plates andhave attractive exposed ceilings. Formwork. including the use
of pans. is quite expensive.

5/19/2018 dalle beton arm.pptx
15/30
Slabs on beams are suitable for spans between 20 and 30 ft and live
loads of 60 to 120 psf . The beams increase the stiffness of the slabs.
producing relatively low deflection. Additional form wor k for the beams
is needed.
Oneway slabs on beams are most suitable for spans of 10 to 20 ft and a
live load of 60 to 100 psf. They can be used for larger spans with
relatively higher cost and higher slab deflection . Additional formworkfor the beams is needed.
A oneway joist floor system is most suitable for spans of 20 to 30 ft and
live loads of 80 to 120 psf. Because of the deep ribs. the concrete and
steel quantities are relatively low, but expensive formwork is expected.
The exposed ceiling of the slabs may look attractive.
Twoway slabs a re extremely complex and statically indeterminate.Many attempts, analytical and empirical, have been made to determine
the division of the moments an d shears between the two spans and the
distribution of these along the principal axes of the slab. Many elastic
analyses of .twoway slabs have been proposed. All have shortcomings.
They neglect Poisson's ratio, torsion, changes in stiffness, ultimate
capacity, edge restraint, variation of moments and shears along span,
and others.
The direct design method. DDM (ACI Code. Section 13.6). is an
approximate procedure for the analysis and design of twoway slabs. It is
limited to slab systems subjected to uniformly distributed loads and
supported on equally or nearly equally spaced columns. The method
uses a set of coefficients to determine the design moments at critical
sections. Twoway slab systems that do not meet the limitations of the
ACI Code. Section 13.6.1, must be analyzed by more accurate
procedures.
Design of Twoway Slabs

5/19/2018 dalle beton arm.pptx
16/30
The equivalent frame method. EFM (ACI Code. Section 13.7). isone in which a three dimensional building is divided into a seriesof twodimensional equivalent frames by cutting the buildingalong lines midway between columns. The resulting frames areconsidered separately in the longitudinal and transverse directionsof the building and treated 1100r by floor. as shown in Fig.
In elastic analysis, a concrete slab may be treated as an elastic
plate. The flexure, shear, and deflection may be calculated by thefourth differential equation relating load to deflection for thinplates with small displacements, as presented by Timoshenko .Finite difference as well as finite element solutions have beenproposed to analyze In the finite element method, the slab isdivided into a mesh of triangles or quadrilaterals. Thedisplacement functions of the nodes (intersecting mesh points)are usually established, and the stiffness matrices are developedfor computer analysis slabs and plates.
For plastic analysis, three methods are available. The yield linemethod was developed by Johansen to determine the limit state ofthe slab by considering the yield lines that occur in the slab as acollapse mechanism. The strip method was developed byHillerborg . The slab is divided into strips, and the load on the slabis distributed in two orthogonal directions. The strips are analyzedas simple beams. The third method is optimal analysis. There hasbeen considerable research into optimal solutions. Rozvany andothers presented methods for minimizing reinforcement based onplastic analysis. Optimal solutions are complex in analysis andproduce complex patterns of reinforcement.
Nonlinear analysis simulates the true load deformationcharacteristics of a reinforced concrete slab when the finiteelement method takes into consideration the nonlinearity of thestress strainrelationship of the individual elements [11,12]. In this
case, the solution becomes complex unless simplified empiricalrelationships are assumed.

5/19/2018 dalle beton arm.pptx
17/30
Coefficient Method This method has been used extensively since 1963 for slabs
supported at the edges by walls, steel beams, or monolithic
concrete beams having a total depth not less than about 3 times
the slab thickness. While it was not a part of the 1977 or later ACI
Codes, its continued use is permissible under the ACI 31808 code
provision (13.5.1) that a slab system may be designed by any
procedure satisfying conditions of equilibrium and geometric
compatibility, if it is shown that the design strength at every
section is at least equal to the requires strength, and that
serviceability requirements are met.
The method makes use of tables of moment coefficients for a
variety of conditions. These coefficients are based on elastic
analysis but also account for inelastic redistribution. In
consequence, the design moment in either direction is smaller byan appropriate amount than the elastic maximum moment in that
direction.
Table 14 gives coefficients for different conditions for bending
moments and shear force. These also specify formula to
determine design parameters. The method since falls with in
framework of ACI 31808; all other specification of code do govern
relevant design parameters. Span length of members not built integrally with supports shall be
considered as the clear span plus the depth of the member, but
need not exceed distance between centers of supports. ACI 8.9.1
Deflection of twoway slab should not exceed the limits specified
in table 9.5(b)

5/19/2018 dalle beton arm.pptx
18/30
TABLE 9.5(b)MAXIMUM
PERMISSIBLE COMPUTED
DEFLECTIONS
For slabs with beams spanning between the supports on all sides,the minimum thickness, h, shall be as follows:
For fm greater than 0.2 but not
greater than 2.0, h shall not
be less than but not less than 5 in.
For fm greater than 2.0,
h shall not be less than but
not less than 3.5 in.
. Max spacing of reinforcement should not exceed twice thickness
of slab or that given by temperature and shrinkage .
. The twisting moments are of consequence only at exterior corners
of a twoway slab system, where they tend to crack the slab at thebottom along the panel diagonal, and at the top perpendicular to
the panel diagonal. Special reinforcement should be provided at
exterior corners in both the bottom and top of the slab, for a
distance in each direction from the corner equal to onefifth the
longer span of the corner panel. The spacing and size should be
same as for positive bending moment.

5/19/2018 dalle beton arm.pptx
19/30
Example
1. Design the roof slab, beam and column of house given in figure 1.Concrete compressive strength (fc) = 3 ksi.
Steel yield strength (fy) = 40 ksi.
Load on slab:
4 thick mud. 2 thick brick tile. Live Load = 40 psf.
Requirement
2. Design of slab for room and veranda.Solution
Veranda Slab
3 Ratio of spans
lb/la = 24.75/8 = 3.09 > 2 one way slab
4 Assume slab thickness of slab = 5 in
Clear span = 8 + 5/12 = 8.42 ft ACI 8.9.1
or c/c of support = 8 + 13/24 + .5 = 9.0625 ftTake l = 8.42 ft
Min slab thickness = l/20 x (0.4+fy/100000)x12 ACI 9.5.2.1
= 4.04 in 5 in is ok
5 d = 5 0.75 3/16 = 4 in
6 Factored loads
dead load Slab = 0.15x5/12 = 0.0625 ksf
Mud = 0.12x4/12 = 0.04 ksf
Choka = 0.12x2/12= 0.02 ksf
total =0.1225 ksf
Live load = 0.04 ksf
Wu = 1.2x 0.1225 + 1.6x 0.04
= 0.211 ksf
Mu= (0.211x8.42x8.42/8)x12 = 22.44 in kip/ft

5/19/2018 dalle beton arm.pptx
20/30
7 Asmin = 0.002bhf (for fy 40 ksi, ACI 10.5.4)
= 0.002 12 5 = 0.12 in2
a = Asminfy/ (0.85fcb)
= 0.12 40/ (0.85 3 12) = 0.156 in
Mn(min) = Asminfy (da/2)
= 0.9 0.12 40 (40.156/2)
= 16.94 ink < Mu
8 Determine As for applied Mu = 22.44 inkip
Mu/0.9 = As x fy x dsq(Asxfy)/(1.7xfcxb)
As = 0.16 sq in
using #4 bars Ab= 0.2 sq in
Spacing S= 0.2 x 12 /0.16 = 15 in c/cusing #3 bar S=0.11x12/0.16 = 7.5 in or 6 in c/c is ok.
use #3 @ 6 in c/c
9 Temperature and Shrinkage Steel
Ast = 0.002 x b x hf
= 0.002 x 12 x 5 = 0.12 sq in
S =0.11 x 12 /0.12 = 11 in c/c10 Maximum spacing for main steel in one way slab according to
ACI is minimum of:
3hf =3 5 =15 in or 18 in
Therefore 6 spacing is O.K.

5/19/2018 dalle beton arm.pptx
21/30
11 Maximum spacing for shrinkage steel in one way slab
according to ACI 7.12.2 is minimum of:
5hf =5 5 =25in or 18in
Therefore 9 in spacing is O.K.
Design of Room Slab
12 Span ratio = 16/12 = 1.33 < 2 twoway slab
Min h = Perimeter/180
= 2 x ( 16 + 12 ) x 12 /180
= 3.73 in not less than 5 in Aci
hf = 5 in is ok.
13 Wu= 0.211 ksf
14 Tables to be consulted for designm = short span/long span
= 12/16 = 0.75
Since slab is continuous on long edge only; case 6 would apply
Coefficient for this slab
Ca,neg = 0.088 Cb,neg = 0
Ca,dl = 0.o48 Cb,dl = 0.012Ca,ll = 0.055 Cb,ll = 0.016
15 Calculate Bending moment

5/19/2018 dalle beton arm.pptx
22/30
16 Total design Moments
Max negative BM in Short direction(12 ft) = 32.04 in k
long (16 ft) = 0 in kmax positve BM in short Direction (12 ft ) =18.36 ink
long (16 ft ) = 8.544 ink
17 Design of Slab
As min= 0.002x12x5 =0.12 sq in
Mu(min) = 0.9x0.12x40{(40.12x40/(1.7x3x12)}
= 19.94 ink
Neg ative BM in Short span = # 3 @ 4.5 in c/c
Positive BM in short span = # 3 @ 9.0 in c/c
Negative BM in long span = nil
Positve BM in long span = # 3 @ 11 in c/c not to begreater than 2xhf = 2x5=10 in as per ACI 13.3.2 may reduce to 9in spacing for simplicity.
18 Min Reinforcement is also provided at discont edges againstpartial fixations

5/19/2018 dalle beton arm.pptx
23/30
Reinforcement Plan

5/19/2018 dalle beton arm.pptx
24/30
Example
1 The floor system shown in Fig. consists of solid slabs and beams intwo directions supported on 20in. square columns. Design a typicalinterior slab pannel to carry a live load of 100 psf appart from selfweight. Use f`c= 3 ksi and fy = 60 ksi.
2 Solution
Since slab is supported on beams, we determine its thickness. To apply
the equation of ACI we need to find out Ib and Is etc. Effective XSecof T beam is Shown in fig.
The moment of inertia of the slab in the long direction assuming slabthickness of 7 in
The moment of inertia of the slab in the short direction

5/19/2018 dalle beton arm.pptx
25/30
Also, hmin = 3.5 in. Therefore, h = 6.27 in. controls. A slab
thickness of 6.5 in. or 7.0 in. may be adopted. Note that in
most practical cases, Eq. 17.2 controls.
Eq. 9.12

Eq. 9.13


5/19/2018 dalle beton arm.pptx
26/30
3. Span ratio = 20/24 = 0.83 twoway slab
thickness of slab = 7 in
4. Factored Load
Wu = 1.2x(7/12x.15) + 1.6x0.1
= 0.265 k/sq ft
5. Coefficient from Tables ( Case 2 )
Ca neg = 0.062 Cb neg =0.029
Ca dl = 0.053 Cb dl = 0.012
Ca ll = 0.039 Cb ll =0.018
6. Bending Moments
Ma neg = 0.062x0.265x20x20x12 = 78.86 ink
Ma pos = (0.053x0.105+0.039x0.16)x20x20x12 = 56.66 inkMb neg =0.029x0.265x24x24x12 = 53.12 ink
Mb pos =(0.012x0.105+0.018x0.16)x24x24 = 28.62 ink
7. Design of s lab
in short dir for neg moment As= 0.228 sq in #4 @ 10 in c/c
pos As= 0.161 #4 @ 14
In long dir for neg moment As= 0.166 #4 @ 14 pos As= 0.088 #4 @ 14
Max spacing = 2xhf = 14 in or temp & shrinkage rft
Temp= 0.0018xbxhf =0.151 sq in #4 @ 15 in c/c
Max spacing of 14 in c/c governs

5/19/2018 dalle beton arm.pptx
27/30
TABLE. 1
COEFFICIENTS FOR NEGATIVE
MOMENTS IN SLABS
*A crosshatched edge indicates thatthe slab continues across or is fixed at
the support; an unmarked edge
indicates a support at which torsional
resistance is negligible ie simple
support
*
* where w = total uniform Factored
dead plus live load

5/19/2018 dalle beton arm.pptx
28/30
TABLE.2
COEFFICIENTS FOR DEAD
LOAD POSITIVE MOMENTS IN
SLABS
*A crosshatched edge indicates thatthe slab continues across or is fixed at
the support; an unmarked edge
indicates a support at which torsional
resistance is negligible ie simple
support.
*
* where w = total uniform Factored
dead plus live load

5/19/2018 dalle beton arm.pptx
29/30
TABLE.3
COEFFICIENTS FOR LIVE LOAD
POSITIVE MOMENTS IN
SLABS
*A crosshatched edge indicates thatthe slab continues across or is fixed at
the support; an unmarked edge
indicates a support at which torsional
resistance is negligible ie simple
support.
*
* where w = total uniform Factored
dead plus live load

5/19/2018 dalle beton arm.pptx
30/30
TABLE.4
RATIO OF LOAD lV INA AND B
DIRECTIONS FOR SHEAR IN SLAB
AND LOAD ON SUPPORTS
*A crosshatched edge indicates thatthe slab continues across or is fixed at
the support; an unmarked edge
indicates a support at which torsional
resistance is negligible ie simple
support.