Analysis and Design of Waffle Slabs

1Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar

Lecture-11Analysis and Design of Two-way Slab Systems

(Two-way Slab with Beams & Two Way joist Slabs)

B P f D Q i Ali

Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures 1

By: Prof Dr. Qaisar Ali

Civil Engineering Department

NWFP UET [email protected]

Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar

Topics Addressedy Moment Coefficient Method for Two way slab with

bbeams

y Introduction

y Cases

y Moment Coefficient Tables

R i f t R i t

Prof. Dr. Qaisar Ali

y Reinforcement Requirements

y Steps

y Example

2


Topics Addressedy Two-way Joist Slaby Introduction

y Behavior

y Characteristics

y Basic Steps for Structural Design


y Example

3


y Moment Coefficient Method (Introduction)

Two Way Slabs

z The Moment Coefficient Method included for the first time in1963 ACI Code is applicable to two-way slabs supported onfour sides of each slab panel by walls, steel beams relativelydeep, stiff, edge beams (h = 3hf).

z Although, not included in 1977 and later versions of ACI code,


its continued use is permissible under the ACI 318-08 codeprovision (13.5.1). Visit ACI 13.5.1.

4


y Moment Coefficient Method laMa,neg

Ma,pos

Two Way Slabs

y Moments:Ma, neg = Ca, negwula2

Mb, neg = Cb, negwulb2

Ma, pos, (dl + ll) = M a, pos, dl + M a, pos, ll = Ca, pos, dl wu, dl la2 + Ca, pos, ll wu, ll la2

Mb, pos, (dl + ll) = Mb, pos, dl + Mb, pos, ll = Cb, pos, dl wu, dl lb2 + Cb, pos, ll wu, ll lb2

y Where C C = Tabulated moment coefficients

Ma,neglb

Mb,neg Mb,negMb,pos


y Where Ca, Cb = Tabulated moment coefficientswu = Ultimate uniform load, psf

la, lb = length of clear spans in short and long directions

respectively.

5


y Moment Coefficient Method: Cases

Two Way Slabs

y Moment Coefficient Method: Casesy Depending on the support conditions, several cases are possible:

Prof. Dr. Qaisar Ali 6



Two Way Slabs





Two Way Slabs





Two Way Slabs




Two Way Slabs

y Moment Coefficient Tables:y Moment Coefficient Tables:



Two Way Slabs




Two Way Slabs




Two Way Slabs




Two Way Slabs

y Load Coefficient Table:y Load Coefficient Table:



y Maximum spacing and minimum reinforcement

Two Way Slabs

requirement:

z Maximum spacing (ACI 13.3.2):

smax = 2 hf in each direction.

z Minimum Reinforcement (ACI 7.12.2.1):

Asmin = 0.0018 b hf for grade 60.


Asmin 0.0018 b hf for grade 60.

Asmin = 0.002 b hf for grade 40 and 50.


y Special Reinforcement at exterior corner of Slabz The reinforcement at exterior ends of the slab shall be provided as per ACI

Two Way Slabs

z The reinforcement at exterior ends of the slab shall be provided as per ACI13.3.6 in top and bottom layers as shown.

z The positive and negative reinforcement in any case, should be of a size andspacing equivalent to that required for the maximum positive moment (per footof width) in the panel.


10


y Moment Coefficient Method

Two Way Slabs

y Stepsy Find hmin = perimeter/ 180 = 2(la + lb)/180

y Calculate loads on slab (force / area)

y Calculate m = la/ lby Decide about case of slab,


Decide about case of slab,

y Use table to pick moment coefficients,

y Calculate moments and then design.

y Apply reinforcement requirements (smax = 2hf, ACI 13.3.2)

19


y Moment Coefficient Method: Example

Two Way Slabs

o e t Coe c e t et od a p e

y A 100 60, 3-storey commercial building is to be designed.The grids of column plan are fixed by the architect.


11



Two Way Slabs

o e t Coe c e t et od a p e

y Complete analysis of the slab is done by analyzing four panels

Panel I Panel IPanel III Panel III


Panel I Panel I

Panel II Panel II

Panel III Panel III

Panel IV Panel IV



Two Way Slabs

p

y A 100 60, 3-storey commercial building: Sizes and Loads.y Sizes:

y Minimum slab thickness = perimeter/180 = 2 (20+25)/180 = 6

However, for the purpose of comparison, take hf = 7

y Columns = 14 14 (assumed)


y Beams = 14 20 (assumed)y Loads:

y S.D.L = Nil ; Self Weight = 0.15 x (7/12) = 0.0875 ksfy L.L = 144 psf ; wu = 0.336 ksf

22

12



Two Way Slabs

y Panels are analyzed using Moment Coefficient MethodCase = 4m = la/lb = 0.8

Mb,neg Mb,negMb,pos

Ma,neg

Ma,pos

Ma,neg




Two Way Slabs


Ca,neg = 0.071Cb,neg = 0.029Ca,posLL = 0.048Cb,posLL = 0.020C 0 039


Ca,posDL = 0.039Cb,posDL = 0.016

13



Two Way Slabs







Two Way Slabs





14



Two Way Slabs







Two Way Slabs





15



Two Way Slabs







Two Way Slabs

y Panels are analyzed using Moment Coefficient Method

Panel I

Case = 4m = la/lb = 0.8


Mb,neg Mb,negMb,pos

Ma,neg

Ma,pos

Ma,neg



Ma,neg = 9.5 k-ftMa,pos = 6.1 k-ftMb,neg = 6.1 k-ftMb,pos = 3.9 k-ft For slab supported on Spandrals, Mneg,ext = 1/3Mpos

16


Two Way Slabsy Moment Coefficient Method: Example

Panel II

Case = 9m = la/lb = 0.8

Ca,neg = 0.075Cb,neg = 0.017Ca,posLL = 0.042Cb,posLL = 0.017C 0 029 M MM

Ma,neg




Ma,neg = 10.1 k-ftMa,pos = 5.1 k-ftMb,neg = 3.6 k-ftMb,pos = 3.1 k-ft

Mb,neg Mb,negMb,pos

Ma,pos

Ma,neg



Panel III

Case = 8m = la/lb = 0.8


Mb,neg Mb,negMb,pos

Ma,neg

Ma,pos

Ma,neg





17



Panel IV

Case = 2m = la/lb = 0.8

Ca,neg = 0.065Cb,neg = 0.027Ca,posLL = 0.041Cb,posLL = 0.017C 0 026 M MM

Ma,neg





Mb,neg Mb,negMb,pos

Ma,pos

Ma,neg


Two Way Slabsy Moment Coefficient Method: Exampley Slab analysis summary

8.77.4

7.4

8.6 8.65.43.7

10.19.5

9.5

6.1 6.13.9

6.1


3.2

4.95.75.7

8.7

3.25.13.6

10.1

3.6

18


Two Way Slabsy Moment Coefficient Method: Exampley Slab Reinforcement Details

A

C

C

C CBA

A

C

C

B BA

A= #4 @ 12


A

BBB

C

A

BA

C

@B = #4 @ 6C = #4 @ 4

Two-Way Joist Slab

36

19

y Introduction

Two-Way Joist

z A two-way joist system, or waffle slab, comprises evenlyspaced concrete joists spanning in both directions and areinforced concrete slab cast integrally with the joists.

37

Joist

y Introduction

Two-Way Joist

z Like one-way joist system, a two way system will be qualifiedto be said as two-way joist system if clear spacing betweenribs (dome width) does not exceed 30 in.

38

20

y Introduction

Two-Way Joist

39


y Introduction

Two-Way Joist

z The joists are commonly formed by using Standard Squaredome forms and the domes are omitted around the columnsto form the solid heads.


21


y IntroductionStandard Dome Data

Two-Way Joist

z Standard Dome Data

z Generally the dome for waffle slab can be of any size. However thecommonly used standard domes are discussed as follows:

z 30-in 30-in square domes with 3-inch flanges; from which 6-inchwide joist ribs at 36-inch centers are formed: these are available instandard depths of 8, 10, 12, 14, 16 and 20 inches.

19 i h 19 i h d ith 2 i h fl f hi h


z 19-inch 19-inch square domes with 2 -inch flanges, from which5-inch wide joist ribs at 24-inch centers are formed. These areavailable in standard depths of 8, 10, 12, 14 and 16 inches.

41


y IntroductionStandard Dome Data

Two-Way Joist

z Standard Dome Data


22


y Behavior

Two-Way Joist

z The behavior of two-way joist slab is similar to a two way flatSlab system.



y Characteristics

Two-Way Joist

z Dome voids reduce dead load

z Attractive ceiling (waffle like appearance)

z Electrical fixtures can be placed in the voids

z Particularly advantageous where the use of longer spans


and/or heavier loads are desired without the use ofdeepened drop panels or supported beams.

23


y Basic Steps for Structural Designz Step No 01 (Sizes): Sizes of all structural and non

Two-Way Joist

z Step No. 01 (Sizes): Sizes of all structural and nonstructural elements are decided.

z Step No. 02 (Loads): Loads on structure are determinedbased on occupational characteristics and functionality (referAppendix C of class notes).

z Step No 03 (Analysis): Effect of loads are calculated on all


z Step No. 03 (Analysis): Effect of loads are calculated on allstructural elements.

z Step No. 04 (Design): Structural elements are designed for

the respective load effects following code provisions.

45


y Sizesz Minimum Joist Depth

Two-Way Joist

z Minimum Joist Depth

z For Joist depth determination, waffle slabs are considered as flat slab(ACI 13.1.3, 13.1.4 & 9.5.3).

z The thickness of equivalent flat slab is taken from table 9.5 (c).

z The thickness of slab and depth of rib of waffle slab can be thencomputed by equalizing the moment of inertia of equivalent flat slab tothat of waffle slab


that of waffle slab.

z However since this practice is time consuming, tables have beendeveloped to determine the size of waffle slab from equivalent flat slabthickness.

46

24


y Sizesz Minimum Joist Depth

Two-Way Joist

z Minimum Joist Depth

z Equivalent Flat Slab Thickness

z ACI 318-05 Sect. 9.5.3

z Minimum thickness = ln/33


y Sizesy Minimum Joist Depth

Two-Way Joist

y Minimum Joist Depthy Slab and rib depth from equivalent flat slab thickness

Table 01: Waffle flat slabs (19" 19" voids at 2'-0")-Equivalent thicknessRib + Slab Depths (in.) Equivalent Thickness te (in.)

8 + 3 8.898 + 4 10.1110 + 3 10.51

48

10 + 4 11.7512 + 3 12.12

12 + 4 13.3814 + 3 13.72

14 + 4 15.0216 + 3 15.31

16 + 4 16.64Reference: Table 11-2 of CRSI Design Handbook 2002.

Note: Only first two columns of the table are reproduced here.

25

y Sizesy Minimum Joist Depth

Two-Way Joist

y Minimum Joist Depthy Slab and rib depth from equivalent flat slab thickness

Table 02: Waffle flat slabs (30" 30" voids at 3'-0")-Equivalent thicknessRib + Slab Depths (in.) Equivalent Thickness te (in.)

8 + 3 8.618 + 4 9.7910 + 3 10.18

10 + 4 11.37

49

12 + 3 11.7412 + 4 12.9514 + 3 13.3

14 + 4 14.5416 + 3 14.85

16 + 4 16.1220 + 3 17.92



y Sizesy Minimum Width of Rib

Two-Way Joist

y Minimum Width of Riby ACI 8.11.2 states that ribs shall be not less than 4 inch in width.

y Maximum Depth of Riby A rib shall have a depth of not more than 3 times the minimum

width of rib.

y Minimum Slab Thickness

50

y Minimum Slab Thicknessy ACI 8.11.6.1 states that slab thickness shall be not less than one-

twelfth the clear distance between ribs, nor less than 2 in.

26

y Loadsy Floor dead load for two-way joist with certain dome size, dome depth can

Two-Way Joist

y j , pbe calculated from the table shown for two options of slab thicknesses (3inches and 4 inches).

Table 03: Standard Dome Dimensions and other Data

Dome Size Dome Depth (in.) Volume of Void (ft3)

Floor Dead Load (psf) per slab thickness

3 inches 4 inches

8 3.98 71 9010 4 92 80 99

51

30-in

10 4.92 80 9912 5.84 90 10914 6.74 100 11916 7.61 111 12920 9.3 132 151

19-in

8 1.56 79 9810 1.91 91 11012 2.25 103 12214 2.58 116 13416 2.9 129 148

Reference: Table 11-1, CRSI Design Handbook 2002

y Loadsy Floor dead load (w ) for two way joist can also be

Two-Way Joist

y Floor dead load (wdj) for two-way joist can also becalculated as follows:

36

8

3

30

Volume of solid:Vsolid = (36 36 11)/1728 = 8.24 ft3Volume of void:Vvoid = (30 30 8)/1728 = 4.166 ft3Total Load of joists per dome:

52

Total Load of joists per dome:wdj = (Vsolid Vvoid) conc

= ( 8.24 4.166) 0.15 = 0.61 kipTotal Load of joists per sq. ft:wdj/ (dome area) = 0.61/ (3 3) = 0.0679 ksf

= 68 psf 71 psf (from table 03)The difference is because sloped ribs are not considered.

27

y Loadsy At locations where solid head is present the floor dead load

Two-Way Joist

y At locations where solid head is present, the floor dead loadcan be calculated as follows:

y If, wdj = dead load in joist area

y Wsh = dead load in solid head area

= hsolid concy Wdj+sh = {wshb + wdj(l2-b)}/l2

wdjWdj+sh

ln

a a

Wdj+sh

53

dj+sh { sh dj( 2 )} 2

bl2a a

y Loadsy Factored loads can be calculated as:

Two-Way Joist

y Factored loads can be calculated as:

y If wL = live load (load/area), theny Load out of solid head region

wosh = 1.2 wdj + 1.6wL

y Load in solid head region

1 2 1 6

wish wish

woshWish

ln

a a

Wish

54

wish = 1.2wdj+sh+1.6wL bl2a a

wosh

28


y AnalysisACI code allows use of DDM for analysis of waffle slabs (ACI

Two-Way Joist

z ACI code allows use of DDM for analysis of waffle slabs (ACIR13.1). In such a case, waffle slabs are considered as flatslabs, with the solid head acting as drop panels (ACI 13.1.3).



y AnalysisStatic moment calculation for DDM analysis:

Two-Way Joist

z Static moment calculation for DDM analysis:

wosh

ln

woshWish

lna a

Wish

Mosh Mish

ln


Mosh = woshl2ln2/8 Mish = (wish-wosh)ba2/2

Mish

Mo = Mosh + Mish

b

l2a a

29


y DesignDesign of slab for punching shear

Two-Way Joist

z Design of slab for punching shear

z The solid head shall be checked against punching shear.

z The critical section for punching shear is taken at a section d/2 from faceof the column, where d is the effective depth at solid head.



y DesignDesign of slab for

Two-Way Joist

z Design of slab forpunching shear

z Load on tributary area willcause punch out shear.

z Within tributary area, twotypes of loads are acting:

l1


z Solid head load

z Joist load

z Both types shall beconsidered while calculatingpunching shear demand

58

l2 d/2

30


y DesignDesign of slab for punching

Two-Way Joist

z Design of slab for punchingshear

z Total area = l1 l2z Solid area = Asolid

z Joist part area (Aj) = (l1l2) -Asolidz Critical perimeter area = Acp

l1


z Critical perimeter area Acp

z Vu =Ajwosh+ (Asolid Acp) wishz Where,

wosh = joist part load

wish = load inside solid head

59

l2 d/2


y Designz Shear Strength of Slab in punching shear:

Two-Way Joist

Shear Strength of Slab in punching shear:

z Vn = Vc + Vs

z Vc is least of:

z 4 (fc)bod

z (2 + 4/c) (fc)bod

z {(sd/bo +2} (fc)bod


c = longer side of column/shorter side of column

s = 40 for interior column, 30 for edge column, 20 for corner columns

31


y Designz Design of Joist for Beam Shear:

Two-Way Joist

Design of Joist for Beam Shear:

z Beam shear Demand

z Beam shear is not usually a problem in slabs including waffle slabs.However for completion of design beam shear may also bechecked. Beam shear can cause problem in case where largerspans and heavier loads with relatively shallow waffle slabs areused.


z The critical section for beam shear is taken at a section d from faceof the column, where d is the effective depth at solid head.


y Designz Design of Joist for Beam Shear:

Two-Way Joist

g

z Beam shear capacity of concrete joist

z Vn = Vc + Vs

z Vc is least of:

z 2 (fc)bribd

z Vs = Avfy/bribs

Stirrup


z If required, one or two single legged stirrups are provided in the rib to increase the shear capacity of waffle slab.

32


y DesignDesign for Flexure

Two-Way Joist

z Design for Flexure

z The design of waffle slab is done by usual procedures.

z However, certain reinforcement requirements apply discussed next.



y ACI recommendations on reinforcement requirement of waffle slab:

Two-Way Joist

requirement of waffle slab:

z ACI 10.6.7 states that if the effective depth d of a beam orjoist exceeds 36 in., longitudinal skin reinforcement shall beprovided as per ACI section 10.6.7.

z According to ACI 13.3.2, for cellular or ribbed constructionreinforcement shall not be less than the requirements of ACI


reinforcement shall not be less than the requirements of ACI7.12.

z As per ACI 7.12, Spacing of top bars cannot exceed 5h or18 inches.

64

33


y ACI recommendations on reinforcement requirement of waffle slab:

Two-Way Joist

requirement of waffle slab:



y Other important points:The amount of reinforcement and if necessary the top slab

Two-Way Joist

z The amount of reinforcement and, if necessary, the top slabthickness can be changed to vary the load capacities fordifferent spans, areas, or floors of a structure.

z Each joist rib contains two bottom bars. Straight bars aresupplied over the column centerlines for negative factoredmoment.


Bottom bar

34


y Other important points:For layouts that do not meet the standard 2 feet and 3 feet

Two-Way Joist

z For layouts that do not meet the standard 2-feet and 3-feetmodules, it is preferable that the required additional width beobtained by increasing the width of the ribs framing into thesolid column head.

z The designer should sketch out the spacing for a typical paneland correlate with the column spacing as a part of the early


p g p yplanning.

67


y Example: Design the slab system of hall shown in figure as waffleslab, according to ACI 318. Use Direct Design Method for slab

Two-Way Joist

analysis.z fc = 4 ksi

z fy = 60 ksi

z Live load = 100 psf


35


y Solution:z A 108 144 building divided into twelve (12) panels supported at

Two-Way Joist

z A 108 144 building, divided into twelve (12) panels, supported attheir ends on columns. Each panel is 36 36.

z The given slab system satisfies all the necessary limitations for DirectDesign Method to be applicable.



y Step No 01: SizesColumns

Two-Way Joist

z Columns

z Let all columns be 18 18.

z Slab

z Adopt 30 30 standard dome.

z Minimum equivalent flat slab thickness (hf) can be found using ACI Table9 5 (c):


9.5 (c):

z Exterior panel governs. Therefore,

hf = ln/33

= [{36 (2 18/2)/12}/33] 12 = 12.45

70

36


y Step No 01: SizesSlab

Two-Way Joist

z Slab

z The closest depth of doom that will fulfill the requirement of equivalentthickness of flat slab equal to 12.45 is 12 in. with a slab thickness of 4 in. for a dome size of 30-in.

Table: Waffle flat slabs (30" 30" voids at 3'-0")-Equivalent thickness

Rib + Slab Depths (in.) Equivalent Thickness te (in.)

8 + 3 8.618 + 4 9.79


10 + 3 10.1810 + 4 11.3712 + 3 11.74

12 + 4 12.9514 + 3 13.3

14 + 4 14.5416 + 3 14.85

16 + 4 16.1220 + 3 17.92




y Step No 01: SizesPlanning of Joist layout

Two-Way Joistl = 36-0 = 432Standard module = 36 36

z Planning of Joist layout No. of modules in 36-0:n = 432/36 = 12

Planning:First module is placed on interiorcolumn centerline and providedtowards exterior ends of panel.In this way, width of exterior joistcomes out to be 15.


37


y Step No 01: SizesSolid Head

Two-Way Joist

z Solid Head

z Solid head dimension from column centerline = l/6 = 36/6 = 6

z Total length of solid head= 2 6 = 12z As 3 3 module is selected, therefore 4 voids will make an interior solid

head of 12.5 12.5.z Depth of the solid head = Depth of standard module = 12 + 4.5 = 16.5



y Step No 02: Loadsz Floor (joist) dead load (wdj) = 109 psf = 0 109 ksf

Two-Way Joist

z Floor (joist) dead load (wdj) 109 psf 0.109 ksf

Table: Standard Dome Dimensions and other Data

Dome Size Dome Depth (in.) Volume of Void (ft3)

Floor Dead Load (psf) per slab thickness

3 inches 4 inches

30-in

8 3.98 71 9010 4.92 80 9912 5.84 90 10914 6.74 100 11916 61 111 129


16 7.61 111 12920 9.3 132 151

19-in

8 1.56 79 9810 1.91 91 11012 2.25 103 12214 2.58 116 13416 2.9 129 148

Reference: Table 11-1, CRSI Design Handbook 2002

38

y Step No 02: Loadsy Floor (joist) dead load (wdj) = 109 psf = 0 109 ksf

Two-Way Joist

y Floor (joist) dead load (wdj) 109 psf 0.109 ksf

y Solid Head dead load (wsh) = {(12 + 4.5)/12} 0.15 = 0.206 ksf

y Wdj+sh = {wshb + wdj(l2-b)}/l2= {0.20612.5 + 0.109 (36 12.5)}/36= 0.143 ksf

wdjWdj+sh

l

a a

Wdj+sh

75

ln

b = 12.5l2a = 5.25 a

y Step No 02: Loadsy w = 100 psf = 0 100 ksf

Two-Way Joist

y wL = 100 psf = 0.100 ksf

y Load out of solid head region

wosh = 1.2 wdj + 1.6wL

= 1.20.109 + 1.60.100= 0.291 ksf

wish wish

76

y Load in solid head region

wish = 1.2wdj+sh+1.6wL

= 1.2 0.143 + 1.6 0.100 = 0.33 ksf

bl2a a

wosh


Two Way Joisty Step No 03: Frame Analysis (E-W Interior Frame)

Two-Way Joist

z Step 1: Marking E-W Interior Frame:

l 36 0

l2 = 36-0

l1 = 36-0ln = 34-6




Two-Way Joist

z Step 01: Marking E-W Interior Frame

z Design Span of frame (c/c) = l1 = 36

Design Length of frame = ln = 36 (2 18/2)/12 = 34.5

Width of frame = l2 = 36

Half column strip width = (Shorter span)/ 4 = 36/4 = 9




Two-Way Joist

z Step 2: Marking Column and Middle Strips

MS/2 = 9-0

a = 5-3 CS/2 = 9-0

CS/2 = 9-0

a 5 -3

b= 12-6

CS/2 = Least of l1/4 or l2/4

l /4 = 36/4 = 9

MS/2 = 9-0


l2/4 = 36/4 = 9



Two-Way Joist

z Step 03: Static Moment Calculation

z Mosh (outside head) = woshl2ln2/8

= 0.291 36 34.52/8 = 1557.56 ft-k

Mish (solid head) = (wish wosh) ba2/2

= (0.330.291)12.55.252/2 = 6.70 ft-k

Mo (total static moment) = Mosh + Mish = 1557.56 + 6.70 = 1564.26 ft-k

Note: Since normally, Mish is much smaller than Mosh the former can be conveniently ignored in design calculations




Two-Way Joist

z Step 04: Longitudinal distribution of Total static moment (Mo).




Two-Way Joist

z Step 05: Lateral Distribution of Longitudinal moment (L.M).

INT36 =0 {no interior beams}

l2/l1 = 36/36 = 1

INT36l2/l1 = 0



Two Way Joisty Step No 03: Frame Analysis (E-W Exterior Frame)

Two-Way Joist

z Step 01: Marking E-W exterior Frame

l 36 0l1 = 36-0ln = 34-6

l2 = 18-0 + (9/12) = 18.75


2 ( )



Two-Way Joist

z Step 01: Marking E-W exterior Frame

z Design Span of frame (c/c) = l1 = 36

Design Length of frame = ln = 36 (2 18/2)/12 = 34.5

Width of frame = l2 = 9 + 9 + (9/12) = 18.75

Half column strip width = (Shorter span)/ 4 = 36/4 = 9




Two-Way Joist

z Step 02: Marking Column and Middle Strips

l 36 0l1 = 36-0ln = 34-6

CS/2 = Least of l1/4 or l2/4

l /4 = 36/4 = 9

MS/2 = 9-0a = 5 3


CS/2 = 9-0l2/4 = 36/4 = 9 a = 5 -3

b= 7-0



Two-Way Joist

z Step 03: Static Moment Calculation

z Mosh (outside head) = woshl2ln2/8

= 0.291 18.75 34.52/8 = 811.78 ft-k

Mish (solid head) = (wish wosh) ba2/2

= (0.330.291)75.252/2 = 3.76 ft-k

Mo (total static moment) = Mosh + Mish = 811.78 + 3.76 = 815.54 ft-k

Note: Since normally, Mish is much smaller than Mosh the former can be conveniently ignored in design calculations



Two Way Joisty Step No 03: Analysis

Two-Way Joist

z Step 04: Longitudinal distribution of Total static moment (Mo).




Two-Way Joist

z Step 05: Lateral Distribution of Longitudinal moment (L.M)[Refer to ACI 13.6.4 to ACI 13.6.6].

z EXT36 =0 {no exterior beams}

z l2/l1 = 36/36 = 1

z EXT36l2/l1 = 0




Two-Way Joist

z Analysis of N-S Interior and Exterior Frame will be same as E-W respectiveframes due to square panels.

N-S Exterior Frame

N-S Interior Framel2 = 36-0

l2 = 18-9



Two Way Joisty Step No 04: Design

Two-Way Joist

z For E-W Interior slab strip:

z davg = 12 + 4.5 1 (concrete cover) 0.75 (avg. bar dia) = 14.75g

z Asmin = 0.0018bte (Where te = equivalent flat slab thickness)

Asmin = 0.0018 12 12.95 = 0.279 in2

z Now, Equation used to calculate () in table below is as follows:

Mu = fybdavg2{1 0.59fy/fc} = 0.9601214.752{1 0.5960/4}

z After solving the above equation for , we get:

= [140980.5 {(140980.5)2 (4 1247677 Mu 12)}]/2(1247677).(A)




Two-Way Joist

z For E-W Interior slab strip:




Two-Way Joist

z For E-W exterior slab strip:

z davg = 12 + 4.5 1 0.75 = 14.75 g

z Asmin = 0.0018bte (Where te = equivalent flat slab thickness)

Asmin = 0.0018 12 12.95 = 0.279 in2

z Now, Equation used to calculate () in table below is as follows:

Mu = fybdavg2{1 0.59fy/fc} = 0.9601214.752{1 0.5960/4}

z After solving the above equation for , we get:

= [140980.5 {(140980.5)2 (4 1247677 Mu 12)}]/2(1247677).(A)




Two-Way Joist

z For E-W exterior slab strip:




Two-Way Joist

z Design of N-S Interior and Exterior Frame will be same as E-W respective frames due to square panels and also for thereason that davg is used in design.




Two-Way Joist

z Note: For the completion of design problem, the waffle slabshould also be checked for beam shear and punching shear.



Two Way Joisty Step No 05: Detailing (E-W Frames)

Two-Way Joist

#6 @ 12 #6 @ 6 #6 @ 6 #6 @ 12

Prof. Dr. Qaisar Ali 96#6 @ 12 #6 @ 6 #6 @ 6 #6 @ 12

#6 @ 18 #6 @ 18 #6 @ 18 #6 @ 18


Two Way Joisty Step No 05: Detailing (N-S Frames)

Two-Way Joist

#6 @ 12#6 @ 18#6 @ 12

#6 @ 6#6 @ 18#6 @ 6

#6 @ 6#6 @ 18#6 @ 6



Two Way Joisty Step No 05: Detailing (E-W Interior Frame)

Two-Way Joist

#6 @ 6 c/c

18-0

Column Strip (Interior Frame); section taken over support

#6 @ 12 c/c2 #7 Bars

#6 @ 12 c/c

Prof. Dr. Qaisar Ali 98Column Strip (Exterior Frame); section taken over support2 #7 Bars


Two Way Joisty Step No 05: Detailing (E-W Interior Frame)

Two-Way Joist

#6 @ 18 c/c

18-0

Middle Strip (Interior Frame); Section taken over column line

#6 @ 18 c/c2 #7 Bars

#6 @ 18 c/c

Prof. Dr. Qaisar Ali 99Middle Strip (Exterior Frame); Section taken over column line2 #7 Bars


Two Way Joisty Step No 05: Detailing (E-W Exterior Frame)

Two-Way Joist

#6 @ 6 c/c

9-0

Column Strip (Interior Frame); section over support2 #7 Bars

#6 @ 12 c/c


Column Strip (Exterior Frame); section over support2 #7 Bars


Two Way Joisty Step No 05: Detailing (E-W Exterior Frame)

Two-Way Joist

#6 @ 18 c/c

9-0

Middle Strip (Interior Frame) ; section over support2 #7 Bars

#6 @ 18 c/c


Middle Strip (Exterior Frame); section over support2 #7 Bars


The End


Analysis and Design of Waffle Slabs

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