Design of One-Way Slab

DESIGN OF REINFORCED

CONCRETE STRUCTURE

ONE WAY SLAB

Presented by -

MD. Mohotasimur Rahman (Anik)

24th batch, AUST

INTROCDUCTION

Slab in which the deflected surface is predominantly

cylindrical termed as one-way slabs spanning in the

direction of curvature. Curvatures, and consequently

bending moments, of this slab shall be assumed same for all

strips spanning in the shorted direction or in the direction of

predominant curvature, the slab being designed to resist

flexural stress in that direction only.1

2

If a slab is supported on two opposite sides only, it will bent or deflect in a direction perpendicular to the

supported edge. The structure is one way, and the loads are carried by the slab in the deflected short

direction (fig-2a).2 If the slab is supported on four sides and the ration of the long side to the short side is

equal to or greater than 2, most of the load (about 95% or more) is carried in the short direction, and one-

way action is considered for all practical purposes (fig-2b).2

Figure 1. Deflection of One-Way Slab

3

Figure 2. One-way slab

DESIGN OF ONE-WAY SOLID SLABS

One-way slab may be treated as a beam. A unit strip of slab, usually 1 ft. (or 1 m) at right angles to the

supporting girders, is considered a rectangular beam.3

One-way slabs shall be designed to have adequate stiffness to limit deflections or any deformations that

affect strength or serviceability of a structure adversely.4

Minimum thickness stipulated in the table 1, shall apply for one-way slabs not supporting or attached to

partitions or other construction likely to be damaged by large deflection, unless computation of deflection

indicates that a lesser thickness can be used without adverse effects.4

The total slab thickness (𝑕) is usually rounded to the next higher 1 4 inch (5mm). For slab up to thickness

6 inch. Thickness and next higher 0.5 inch. (or 10 mm) for thicker slabs.5

Concrete cover in slabs shall not be less than 3 4 inch.6 (20 mm) at surface surfaces not exposed to weather

or ground. In this case, 𝑑 = 𝑕 − 34 − (𝑕𝑎𝑙𝑓 𝑏𝑎𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟).Where, 𝑑 is defined as distance from

extreme compression fiber to centriod of tension reinforcement.7

Factored moment and shears in one way slab can be found either by elastic analysis or through the use of

the same coefficients stated ACI 8.3.3. printed in table 2.8

4

Table 1: Minimum Thickness of Non-Prestressed One-Way Slab

(Normal weight concrete and Grade 60 (Grade 420) Reinforcement)𝟗

Member Minimum thickness, h

Simply supported One end continuous Both end continuous cantilever

Solid one-way slab 𝑙

20

𝑙

24

𝑙

28

𝑙

10

Ribbed one-way slabs 𝑙

16

𝑙

18.5

𝑙

21

𝑙

8

No

te:

(1) For 𝑓𝑦 other than 60,000 𝑝𝑠𝑖 () multiplied tabulated value by 0.4 + (𝑓𝑦 100,000) [for 𝑓𝑦 other than

420 𝑁 𝑚𝑚2 multiplied tabulated value by 0.4 + (𝑓𝑦 700) ]

(2) For structural light weight concrete, multiply tabulated values by (1.65 − 0.005𝑤𝑐) but not less than

1.09. where 𝑤𝑐 is range in 90 𝑡𝑜 115 𝑙𝑏 𝑓𝑡3 .[For structural light weight concrete, multiply

tabulated values by ( 1.65 − 0.003𝑤𝑐 ) but not less than 1.09 . where 𝑤𝑐 is range in

1440 𝑡𝑜 1840 𝑘𝑔 𝑚3 .]


5

6


Table:2 Approximate Moments and Shears in Continuous Beams.𝟏𝟎

Positive moment

End span

Discontinuous end unrestrained 𝑤𝑢𝑙𝑛2 11

Discontinuous end integral with support 𝑤𝑢𝑙𝑛2 14

Interior span 𝑤𝑢𝑙𝑛2 16

Negative moments at exterior face of first interior support

Two spans 𝑤𝑢𝑙𝑛2 9

More than two spans 𝑤𝑢𝑙𝑛2 10

Negative moment at other faces of interior supports 𝑤𝑢𝑙𝑛2 11

Negative moment at face of all supports for (1) Slabs with spans not exceeding 10 ft. and

(2) beams where ratio of sum of column stiffness to beam stiffness exceeds eight at each

end of the span.

𝑤𝑢𝑙𝑛2 12

Continued

7


Negative moment at interior face of exterior support for members built integrally with supports

Where support is spandrel beam 𝑤𝑢𝑙𝑛2 24

Where support is a column 𝑤𝑢𝑙𝑛2 16

Shear in end members at face of first interior support 1.15 𝑤𝑢𝑙𝑛 2

Shear at face of all other supports 𝑤𝑢𝑙𝑛 2

Where , 𝑤𝑢 = 𝑢𝑛𝑖𝑓𝑜𝑟𝑚𝑙𝑦 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑑 𝑙𝑜𝑎𝑑 ; 𝑙𝑛 = 𝑠𝑝𝑎𝑛 𝑙𝑒𝑛𝑔𝑡𝑕

• If the slab rests freely on its supports the span length may be taken equal to the clear span plus depth of the

slab but did not exceed the distance between centers of supports.11

• In analysis of frames or continuous construction for determination of moments, span length shall be taken

as the distance center-to-center of supports.11

• It shall be permitted to analyze solid or ribbed slabs built integrally with supports, with clear spans not

more than 10ft, as continuous slabs on knife edge supports with spans equal to the clear spans of the slab

and width of beams otherwise neglected.11

8


Figure 4: Summary of ACI Moment Coefficient: (a) beams with more than two span (b) beams with

two spans only (c) slabs with spans not exceeding 10 ft. (d) beams in which the sum of column stiffness

exceeds 8 times the sum of beam stiffness at each end of span.𝟏𝟐

9


The conditions under which the moment coefficients for continuous beam and slabs given in table 2 should

be used can be summarized as follows:10

• Spans are approximately equal, with the larger of two adjacent spans not greater than the shorter by

more than 20 percent.

• There are two or more spans.

• Loads are uniformly distributed.

• Unit live load does not exceed three times unit dead load.

• Members are prismatic.

The maximum reinforcement ratio, 𝜌𝑚𝑎𝑥 = 0.85𝛽1𝑓′𝑐𝑓𝑦

𝜖𝑢

𝜖𝑢:𝜖𝑡; where, ∈𝑡= 0.004 a minimum set tensile

strain at the nominal member subjected to axial loads less than 0.10𝑓′𝑐𝐴𝑔 where 𝐴𝑔 is the gross area of the

cross section, provides the maximum reinforcement ratio.13 and 𝜖𝑢 = Maximum usable strain at extreme

concrete compression fiber shall be assumed equal to 0.003.14

The minimum required effective depth 𝑑𝑟𝑒𝑞 =𝑀𝑢

∅𝜌𝑚𝑎𝑥𝑓𝑦𝑏(1;0.59𝜌𝑚𝑎𝑥𝑓𝑦

𝑓′𝑐);15

Check 𝑑 > 𝑑𝑟𝑒𝑞; (okay) .15

Figure 5. distance from

extreme compression fiber to

centriod of tension reinforcement

10


Reinforcement, 𝐴𝑠 =𝑀𝑢

∅𝑓𝑦 𝑑;𝑎 2 ; where, 𝑎 =

𝐴𝑠𝑓𝑦

0.85𝑓′𝑐 𝑏; at first assumed, 𝑎 = 1 to calculate 𝐴𝑠; that value

can be substituted in equation of 𝑎 to get a better estimate of 𝑎 and hence a new 𝑑 − 𝑎 2 can be

determined.16

For structural slabs of uniform thickness the minimum area of tensile reinforcement, 𝐴𝑠𝑚𝑖𝑛 in the direction

of the span shall be the same as temperature and shrinkage reinforcement area.17 In no case is the

reinforcement ration to be less than 0.0014 .18

Table 3: Minimum Ratios of Temperature and Shrinkage Reinforcement in Slab based on Gross Area.𝟏𝟖

Slabs where Grade 40 (275) or 50 (350) deformed bars are used 0.0020

Slabs where Grade 60 (420) deformed bars or welded wire fabric (plain or deformed) are used 0.0018

Slabs where reinforcement with yield stress exceeding 60,000 psi (420 MPa) measured at a

yield strain of 0.35 percent is used

0.0018 × 60,000

𝑓𝑦

In slabs, primary flexural reinforcement shall be spaced not farther apart than three times slab thickness,

nor 18 inch (450 mm).19 and Shrinkage and temperature reinforcement shall be spaced not farther apart

than five times the slab thickness, nor 18 in.18

11

Check shear requirements. Determine 𝑉𝑢 at the distance from 𝑑 and calculate ∅𝑉𝑐 = 2∅ 𝑓′𝑐𝑏𝑑. If

1

2∅𝑉𝑐 > 𝑉𝑢 the shear is adequate.20 Note that the provision of minimum area of shear reinforcement where

𝑉𝑢 exceeds 1

2∅𝑉𝑐 does not apply to slabs .21 If 𝑉𝑢 >

1

2∅𝑉𝑐 , it is a common practice to increase the depth of

slab .22 so 𝑑 can be determine, assuming 𝑉𝑢 = ∅𝑉𝑐 = 2∅ 𝑓′𝑐𝑏𝑑.23

Straight-bar systems may be used in both tops and bottom of continuous slabs. An alternative bar system of

straight and bent (trussed) bars placed alternately may also be used.7

The choice of bar diameter and detailing depends mainly on the steel areas, spacing requirements, and

development length.24


Figure 6. Reinforcement Details in Continuous One-Way Slab: (A) Straight Bars And (B) Bent Bars.𝟐𝟒

12

QUESTION:

The cross-section of a continuous one-way slab in a building is shown in figure 7. The slab are supported by

beams that span 12 ft. between simple supports. The dead load on the slab due to self-weight plus 77psf; the

live load psf. Design the continuous slab and draw a detailed section. Given 𝑓′𝑐= 3 𝑘𝑠𝑖 and 𝑓𝑦 = 40 𝑘𝑠𝑖

Figure 7. Continuous One-Way Slab

SOLUTION:

Minimum depth,

𝑕𝑚𝑖𝑛 = max𝐿

30=

15×12

30= 6" ,

𝐿

10=

5×12

10= 6" = 6"

Dead load =6

12× 0.15 + 0.077 𝑘𝑠𝑓 = 0.152 𝑘𝑠𝑓

Live load = 0.13 𝑘𝑠𝑓

Load, 𝑤 = 1.4 𝐷𝐿 + 1.7 𝐿𝐿 = 0.434 𝑘𝑠𝑓

Moment −𝑀𝑢= max −𝑤𝑙2

12, −

𝑤𝑙2

12, (−

𝑤𝑙2

2) = max −8.13 , −8.13, −5.42 = −8.13 𝑘′/𝑓𝑡

Moment +𝑀𝑢= max +𝑤𝑙2

14= max +6.975 = +6.975 𝑘′/𝑓𝑡

EXAMPLE OF ONE-WAY SOLID SLABS

13


SFD

BMD

14


To maintain ∅ = 0.9, reinforcement ratio corresponding to 𝜀𝑡 = 0.004 will be selected.

𝜌𝑚𝑎𝑥 = 0.85𝛽1𝑓′

𝑐

𝑓𝑦

𝜖𝑢𝜖𝑢 + 𝜖𝑡

= 0.85 × 0.85 ×3

60×

0.003

0.003 + 0.004= 0.0155

𝑑𝑟𝑒𝑞 =𝑀𝑢

∅𝜌𝑚𝑎𝑥𝑓𝑦𝑏(1;0.59𝜌𝑚𝑎𝑥𝑓𝑦

𝑓′𝑐)=

8.13 ×12

0.9×0.0155×60×12(1;0.59×0.0155×60

3) = 3.45" < 𝑑𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 = 6 − 1 " = 5" (okay)

−𝐴𝑠=𝑀𝑢

∅𝑓𝑦 𝑑;𝑎 2 =

8.13 ×12

0.9×60× 5;0.75 2 = 0.39 𝑖𝑛2 𝑓𝑡 (𝑎𝑠𝑠𝑢𝑚𝑖𝑛𝑔 𝑎 = 1) ; 𝑎 =

𝐴𝑠𝑓𝑦

0.85𝑓′𝑐 𝑏=

0.39×60

0.85×3×12= 0. 76𝑖𝑛

+𝐴𝑠=𝑀𝑢

∅𝑓𝑦 𝑑;𝑎 2 =

6.975 ×12

0.9×60× 5;0.64 2 = 0.33 𝑖𝑛2 𝑓𝑡 ; 𝑎 =

𝐴𝑠𝑓𝑦

0.85𝑓′𝑐 𝑏=

0.38×60

0.85×3×12= 0.65 𝑖𝑛

Minimum Reinforcement 𝐴𝑠𝑚𝑖𝑛= 0.0018 × 12 × 5 = 0.11 𝑖𝑛2 𝑓𝑡 ; 𝐴𝑠 =

−0.39 𝑖𝑛2 𝑓𝑡 (controls)

+0.33 𝑖𝑛2 𝑓𝑡 (controls))

Check 𝜌 =𝐴𝑠

𝑏𝑑=

0.39

12×5= 0.0065 > 𝜌𝑚𝑎𝑥; so ∅ = 0.9 (okay);

At 𝑑 distance 𝑉𝑢 =𝑤𝑙

2−𝑤𝑑 =

0.434×15

2− 0.434 × 5 = 1.085 𝑘𝑖𝑝

1

2∅𝑉𝑐 =

1

2× 2∅ 𝑓′

𝑐𝑏𝑑 = 0.85 × 3000 × 12 ×

5

1000= 2.79 𝑘𝑖𝑝 > 𝑉𝑢 ( so the provided depth is okay).

Use ∅12 𝑚𝑚 @ 5"𝑐/𝑐 at two supports, ∅12 𝑚𝑚 @ 6"𝑐/𝑐 at mid span and ∅10 𝑚𝑚 @ 12"𝑐/𝑐 for temperature

and shrinkage reinforcement.

1. BNBC-1993; pg. 6-146.

2. STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 300


4. BNBC-1993; pg. 6-155.

5. DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 416

6. ACI 318-95; SECTION 7.7.1;pg. 318\R318-68



9. NOTE ON ACI 318-08 BUILDING CODE REQUIREMENTS FOR STRUCTURAL CONCRETE 10th ed.; pg. 10-2

10. BNBC 1993; pg. 6-147

11. ACI 318-95; SECTION 8.7.4; pg.318/318R-82~83



14. ACI 318-11; SECTION 10.3.5.; pg. 138


16. BNBC-1993; pg. 6-148.

17. BNBC-2011; pg. 6-26.








REFERENCE

15

Design of One-Way Slab

Engineering

deflection of oneway

slab rests

ribbed oneway slabs

total slab thickness

continuous slabs

spans equal

design of oneway solid

end of span