1. INTR INTROD ODUC UCTI TION ON
A reinforced concrete flat slab, also called as beamless slab, is a slab supported directly by columns without beams. A part of the slab bounded on each of the four sides by centre line of column is called panel. The flat slab is often thickened closed to supporting columns to provide adequate strength in shear and to reduce the amount of negative reinforcement in the support regions. The thickened portion meets the floor slab or a drop panel, is enlarged so as to increase primarily the perimeter of the critical cr itical section, for shear and hence, increasing the capacity of the slab for resisting two-way shear and to reduce negative bending moment at the support. Such enlarged or flared portion of and a capital. Slabs of constant thickness which do not have drop panels or column capitals are referred r eferred to as flat plates. The strength of the flat plate structure is often limited due to punching shear action around columns, and consequently they are used for light loads and relatively small spans. The flat slab system of construction is one in which the beam is used in the conventional methods of construction done away with the directly rests on column and the load from the slabs is directly transferred to the columns and then to the foundation. Drops or columns are generally provided with column heads or capitals. rid floor systems consisting of beams spaced at regular intervals in perpendicular directions, monolithic with slab A flat slab consists of a reinforced concrete slab that is directly supported by concrete columns without the use of intermediate beams. !.A.". Turner constructed flat slabs in #.S.A. in $%&' $%&' main mainly ly usin usingg intu intuit itiv ivee and conce concept ptual ual ideas ideas,, which which was was start start of this this type type of construction. (any slabs were load-tested between $%$&- )& in #.S.A. *t was only in $%$+ that icholas proposed a method of analysis of flat slabs based on simple statics. This method is used even today for the design of flat slabs and flat plates and is known as the direct design method. Structural engineers commonly use the equivalent frame method with equivalent beams such as the one proposed by acob S. rossman in practical practical engineering engineering for the analysis of flat plate structures. loor systems s ystems consisting of flat f lat slabs are very v ery popular in countries where castc astin place construction is predominant form of construction because of many advantages in terms of architectural fle/ibility, use of space, easier formwork, and shorter construction time. lat 1
slabs are being used mainly in office buildings due to reduced formwork cost, fast e/cavation, and easy installation.
1.1. 1.1.
DETA DETAILED ILED SPECIF SPECIFICA ICAT TION OF OF BUIL BUILDIN DING: G:
1) EARTHWORK EXCAVATION FOR FOUNDAT FOUNDATION: ION:
oundation trenches shall be dug out to the e/act width of foundation and sides shall be vertically e/ecuted earth shall not be placed within the meter of the trench. 2) CEME CEMENT NT CON CONCR CRET ETE: E:
Aggregate shall be of insert materials and should be lean hard sound durable, no observant and capable of developing good bond with moisture 3) AGG AGGREGA REGAT TE:
The coarse aggregate shall be +&mm si0e of stone ballast. 4) REINFO REINFORCE RCED D CEMEN CEMENT T CONC CONCRET RETE: E:
Steel reinforced bars shall be deformed steel. *t should be free from corrosion loose and scales, oil grease paints etc. During laying and compacting of concrete. The steel bars should not be disturbed. !entering and sheltering shall be made with timber or steel palte close and light of percentage leakage mortar i.e.1 shall be 2$3)3+4 proportion by volume of slabs, beams and lintels. The rate of reinforced cement concrete shall be for the complete work e/cluding steel bars, including all tools and plants. 5) BASEMEN MENT:
illing the basement with e/cavation earth including all leads and lifts. 2
) SE SECO COND ND CLAS CLASS S BRI BRICK CKS: S:
All All brick brickss shal shalll be stan standa dard rd appl applic icat atio ionn made made of good good brick brickss thoro thoroug ughly hly burne burnedd shall be of deep cherry red copper color having bursting strength of 567. !ement mortar shall be used as $38 to $3' bricks work shall be measured in centimeters. 1.2. 1.2. ST STRU RUCT CTUR URAL AL PLA PLANN NNIN ING: G:
After getting an architectural plan of the building, the structural planning of the building framing is done Struct Structural ural plannin planningg is first stage in any structur structural al design. design. *t involves involves the determi determinat nation ion of appropriate form of structure, material to be used, and the structural system, the layout of its components components and the method of analysis. As the success of an engineering pro9ect pro9ect is measured in terms of safety safety and economy economy,, the emphas emphasis is today being more on economy economy.. Struct Structural ural planning is the first step towards successful structural structur al design. This involves determination of following. a4 b4 c4 d4 e4 f4
"ositi "ositionin oningg and orie orienta ntatio tionn of colum column. n. "osting of beams. Span Spanni ning ng of slab slabs. s. :ayo :ayout ut of of stai stairs rs.. Select Selectio ionn of of foo footi ting ng.. "osi "ositi tion on of of shea shearr wall wall..
1.2.1. POSITIONING POSITIONING AND ORIENTA ORIENTATION TION OF COLUMNS COLUMNS A. COLUMNS COLUMNS SHOULD SHOULD PREFER PREFERABL ABL! ! BE LOCAT LOCATED ED AT "OR) "OR) NEAR NEAR TH THE E CORNER CORNER OF A BUILDING AND AT THE INTERSECTION OF BEAMS#WALLS.
i. ii. ii.
The ba base of co column umn is is to to su suppor port sl slabs or or be beams. Thee comm Th commerc ercia iall bui build ldin ingg have have norm normal ally ly recta rectangu ngula larr patt pattern ern of grid grid syst system. em.
B. AVOID LARGER LARGER SPANS SPANS "OR) C#C DISTAN DISTANCE CE BETWEEN BETWEEN COLUMNS
i.
:arg :arger er spaci spacing ng of colum columns ns not not only only incr increa eases ses the the span span and and the the cost cost of the the beam beam but but itit increases the load on the column at each floor posing problem of stocky columns in lower story;s of a multi-storied building. 3
C. COLUMNS ON PROPERT! LINE
i.
The columns on property line need special treatment. Since column required certain
ii. iii.
area beyond the column This encountered certain difficulties mainly in providing footing for such columns. *n such cases the column is shifted in side along the side wall to make room for accommodating the footing within the property line.
D. ORIENTATION OF COLUMN
i.
$. A%&'( *&+,-'&/ &0 -&/ &'(, , 6$:
"ro9ection of columns outside the wall in the room should be avoided as they not only give bad appearance but also obstruct the use of the floor space and create problems in placing furniture.
7. O*',/ , -&/ & $ , (, &0 -&/ ' -&/$'/,( '/ , $+&* $/, &0 7,/('/8 "&*) ' ,*,/('-$* & , $+&* ' &0 7'('/8
i.
The above principle of governing orientation of columns given below can easily understand 2
ii.
addition to the a/ial loads. *n such cases the column should be so oriented that the depth of the column is perpendicular to the ma9or a/is of bending. So as to gets larger moment of inertial and greater moment resisting
iii.
capacity. Since the bending moment will be very large in the plane of the frame 2eg3 => plane4 the depth of the column has been provided has been provided in the plane of bending to the moment resistance capacity the column and reduced :eff?D ratio and increase the stiffness of the column.
4
FIGURE: SHOWING COLUMN PLAN DESIGN OF COLUMNS DESIGN OF COLUMN 1: S,-'0'-$'&/:
#sing ()&grade concrete and e +$6 grade steel :ength of column @ 8&6&mm Assume b@ )8&mm, d @ +&&mm LOADS:
Self wt of column @ density volume 5
@)68.&6&.)8&.+ @5.&)7
actored load @ $.6%6.)% @ $+).%%7 Total load on the ground floor column @factored load o. of floors @$+).%+6 Total load
@5$+.57
or a/ially loaded short column "u @ &.+ ck AcC&.'5 f y Asc Asc @ &.&&BAc 5$+.5$&$&$&@ &.+)&AcC&.'5+$6&.&&BAc Ac @ '%%.$mm) 6
So provide a si0e of column @ )8&+&& Asc @ &.&&BAc @ &.&&B'%%&$ @ 6%%.) @'&& 2appro/.4 o of ars @Asc?&.5B6d) @ '&&?&.5B6$)$) @6.8$ @'no;s "rovide 'no;s of $)mm dia. bars T*$/%,*, *,'/0&*-,,/:
Diameter should not be less than a Dia of bars of no. + @ $)?+ @8mm b 'mm Eence adopt 'mm diameter bars Spacing of ties should be least of a :east lateral dimension for column @ )8&mm b $'times the dia. of longitudinal bars @$'$) @$%)mm c 8&&mm
"rovide 'mm lateral ties at )&&mm c?c spacing.
DESIGN OF COLUMN 2: S,-'0'-$'&/:
#sing ()&grade concrete and e +$6 grade steel :ength of column @ 8&6&mm 7
Assume b@ )8&mm
d @ '&&mm
LOADS:
Self wt of column @ density volume @)68.&6&.)8&.' @ $&.67
@$8.587 Total wall load@ B).%7 T&$ &$( 9 1;3.4KN
actored load @ $.6$58.+ @)'&.$7 Total load on the ground floor column @factored loadno of floors @)'&.$6 Total load
@$8&&.$7
or a/ially loaded short column "u @ &.+f ck AcC&.'5f yAsc
2*S3 +6'-)&&& - page+B4
$8&&.$$&3@ &.+)&AcC&.'5+$6&.&&BAc Ac @ $)5$%'mm) So provide a si0e of column @ )8&'&& Asc @ &.&&BAc @ &.&&B$)5$%' @$&$5.'mm) "rovide +no;s $'mm dia. bars and )no $) mm bars T*$/%,*, *,'/0&*-,,/ 3
Diameter should not be less than $4 Dia. of bar of no. + @ $'?+ @ +mm )4'mm Eence adopt 'mm diameter bars Spacing of ties should be least of $4 :east lateral dimension for column @ )8&mm 9
)4$'times the dia. of longitudinal bars @$'$' @)6'mm 848&&mm "rovide 'mm lateral ties at )&&mm c?c spacing
1.2.2.
POSITIONING OF BEAMS
ollowing are the some of the guidelines for positioning of beams A. B,$ $ /&*$< 7, *&%'(,( /(,* , 6$ "&*) 7,&6 $ ,$%< -&/-,/*$,( &$(
i.
Since beams are primarily to support slabs, its spacing shall be decided by the
ii.
ma/imum span of slabs. Slab requires the ma/imum volume of concrete to carry a given load. Therefore the
iii.
thickness of slab is required to be kept minimum. Since in our pro9ect the design is of flat slabs the beams are provided only on the periphery of the building slab.
N&,: T, $= *$-'-$ '->/, 0&* -&,*-'$#&00'-'$#7'- 7'('/8 ' 3?? 6', '/' ' 125 0&* 0'*, *,'$/-, -&/'(,*$'&/. B. A%&'( $*8,* $-'/8 &0 -&/ 0*& (,0,-'&/ $/( -*$->'/8 -*',*'$
i.
:arger spans of columns shall also be from the consideration of controlling the deflection and cracking. This is because it is know that the deflection varies directly with the cube of the span and inversely the cube of the depth.
1.2.3. SLABS
Slabs are plate elements forming floor and roofs of building and carrying loads primarily by fle/ure. *nclined slabs may be used as ramps for multi-storey car parks. A staircase can be considered be an inclined slab. A slab may be supported by beams or walls and may used as the flanges of a T-o :-beam. (oreover, a slab may be simply supported or continuous over one more supports and is classified according to the manner of support3 a4 b4 c4 d4
Fne way slabs spanning in one direction Two way slabs spanning in two directions !ircular slabs lat slabs resting directly on columns with no beams and 10
e4 rid floor with ribbed slabs. 1.2.4.
INTRODUCTION TO STAIRCASE
Stairs are provided in a building to afford a means of communication between the various floors, they are called staircase. Since they have to perform the very important function, the slab over which the steps rest should be designed properly to provide ma/imum comfort, easy and safety. The most important aspect in providing staircase is its location. The location of staircase should be such as to provide as easy access so that in case of causality, e.g.3 fire break, earth, wood etc. *n residential G commercial buildings, it should be placed centrally so as to3 i. ii. iii.
"rovide easy access from all rooms. (aintain privacy *n public building, the stair case should be located near the main entrance.
1.2.4.1.
RE@UIREMENT OF A GOOD STAIRCASE:
A well planned and design stair should provide an easy, quick and safe mode of communication between the various floors. The general requirements of stairs are given below3 a. b. c. d. e. f. g. h.
:ocation. Hffective span of staircase Distribution of loading on stair
DESIGN OF STAIR CASE: SPECIFICATION:
#SH ()&grade concrete and e+$6 grade steel ck @)&?mm) 11
y @+$6?mm) :et thread @8&&mm Iise @$6&mm D : of waist slab @ &.$6)6 @8567?m) !orresponding load per sq m on plan @ 8.%$7?m) Dead load on steps @ 2$6&?)mm avg.4)6 @&.56)6 @$.B567?m) Top finish
@$7?m)
:ive load
@87?m)
Total load
@%.')67?m)
Since the landing slab is two way slab, the load on it may be taken as %.5B6?) @+.B% light !3 Hffective span @ c?c dist between supports @ +.$$+m Ieaction J each support @ 22%.')6$.%B4C+.B%$.&544?) @$).$+7 (u @ 2$).$).&'4-+.B%$.&5$.684-22%.')6&.%%&.%%4?)4 @$).)B actored moment @ $.6$).)B @ $B.+) (u, lim @ ).5'bd) d @ B$.BBmm "rovide depth of $)6mm is adequate3 12
Ast @++).%$mm) Spacing @ )66.$mm "rovide $)mm dia.. bars with )&&mm c?c spacing light A3 Hffective span @ c?c dist between supports @).B'5m I b).B'5 @ 2%.')6$.B&.%4C2+.6%$.&'5)&.884 I b @%.'$7 I a @$).B6 :et the shear force be 0ero at a dist / from A
$).B6-%.')6/ @& =@$.8+m (a/ bending moment @I a/-5.')6/)?) @2$).B6$.8+4-225.')6$.8+$.8+4?)4 @$&.857?m actored moment @$.6$&.85 @ $6.6'7?m Ast @8'Bmm) "rovide $)mm dia. bars Spacing @8&5mm @)&&mm "rovide $) mm dia. bars with )&& mm c?c spacing 13
1.2.5.
SELECTION OF FOOTING
A building is generally composed of super structure above the ground and a substructure which forms the foundation below ground. The safe bearing capacity of soli must not be e/ceed otherwise e/cessive settlement may occur, resulting in damage to the building and it service facilities, such as water or gas mains. oundation failure can also be effect the overall stability of the structure so that it is liable to slide, to lift vertically or over turn. ooting or foundation is defined as the part of substructure, which transmits the loads form the super-structure to surrounding soil stratum safely. oundations are classified as two types. i. Shallow foundation ii. Deep foundation The depth of foundation is less than or equal to the width of the foundation then the foundation is said to be shallow foundation. *f the depth of the foundation is greater than width of the foundation is said to be deep foundation. The footings are classified as follows3 $. I&$,( under individual column. These may be square, rectangular or circular in plan. 7. S*' 0&&'/8 $/( 6$ 0&&'/8. -. C&7'/, 0&&'/8, supporting two or more loads these may be rectangular or trape0oidal
in plan or they may be isolated beam basis 9oin by a beam. The latter case is referred to as foot strapping.
(. R$0 &* $ 0&/($'&/ is
a large continuous foundation supporting on the column of
structure. This is normally used when soil conditions are poor or differential settlement is to be provided. ,. *n ', 0&/($'&/ , pile caps are sued to tie a group of piles together these may support isolated columns or group of several columns or group of several columns or loads leaving columns.
14
FIG.: FIGURE SHOWING PLAN OF FOOTING
15
FIG.: FIGURE SHOWING FOOTING
16
B,$*'/8 -$$-'< &0 &': T, ', &0 , 0&/($'&/ &/ ,*''7, 7,$*'/8 -$$-'< &0 &':
Total load per unit are under the foundation must be less than the permissible bearing capacity of the soil to prevent the e/cessive settlement. *t is important to have an engineering survey made of the soil under a propose structure so that variation in the strata and the soil properties can be determined. Drill holes or trail pits should be sunk in situation test such a penetration test performed and the samples of the soil taken earth bearing pressure and if necessary calculating possible settlement of a structure. *n the design of foundations, the areas of the bases in contact with the ground should be such that the safe bearing pressures will not be e/ceeded. Settlement takes place during the working life of the structure. These loads are to be properly transmitted1 footings must be designed to prevent e/cessive settlement or rotation, to minimi0e differential settlement and to provide adequate safety against sliding and overturning. C&'-, &0 0&&'/8 <,:
The type of footing depends upon the load carried by the column and the bearing capacity of type supporting soli. or framed structures under study, isolated column footing are normally referred in case of soil with very low bearing capacities. *f such soil or black cotton soil e/its for greater depth pile foundation can be an appropriate choice. *f columns are very closely spaced and bearing capacity of soil is low, raft foundation can also be an alternative solution. or a column on a boundary line, a combined footing or a strap footing may be provided. The type of footing depends upon the load carried by the column and the bearing capacity of soil.
DESIGN OF FOOTINGS 17
D,'8/ &0 0&&'/8 1:
"u @5$+.$7 2load from slab, beam, columns4 Self wt of footing @$&K of load Total load 2"4 @ 5$+.$ C 2&.$&5$+.$4 @5B'.$57 The safe bearing capacity of soil is found to be 2S!4 86&7?m) Area 2A4 @ "?S! @5B'.$5?86& Area
@86&m)
The si0e of column is )8&+&& The ratio of length, breadth of footing shall be appro/imately same as width and depth of column :? @ +&&?)8&
@$.5+
: @$.5+b Area @ length breadth +.$@).'$bb @$.8+m
:@$.%Bm
"rovide a footing of si0e)$.86m et upward pressure intensity 2#"*4 @ "?A @ 5$+.5?)$.86 @ )'67?m) Design for fle/ure = @ 22)-&.+4?)4 =@&.Bm
F$-&*,( &,/: 18
(u @
@ B+.B7?m
T*$/%,*, &,/:
> @ 2$.86-&.)84?) > @ &.6'm (u L traverse 2Fr4 (u short @
i.e.1 steel along width of footing Ast @)%)mm) "rovide$)mm dia. bars Spacing @ 2$$8?)%)4$&&& @ 8B5mm "rovide a spacing of )&&mm c?c C,-> 0&* &/, 6$< ,$*:
!ritical section occurs at a distance d@+&&mm from the face of column Shear force 2Mu4 @$.86load in shaded area 19
@$.86&.+)'6 @$+8.$7 Shear stress Ʈv @Mu?bd @ 2$+8.$?$&$&$&4?2$86&+&&4 @&.)'6?mm) "ermissible stress in concrete "t@ 2Ast?bd4$&& @ 2'&5?$&&&+&&4$&& @ &.$6K Ʈc @ &.)B?mm) Ʈv N Ʈc
The section is safe in one way shear !heck for punching shear3 !ritical section occurs at a distance d?) from the face of the column d?) @ )&&mm :oad causing punching shear M @"u-load in shaded area @ 25$+.54-2&.B&.'8)'64 @6B$.$+7 "unching stress @ 26B$.+$&$&$&4?)2'8&CB&&4+&&
@&.6$?mm)
!lause 8$.'.8.$2*S3 +6'-)&&&4 when shear reinforcement is not provided the calculated shear stress at the critical section shall not e/ceed3 "ermissible stress @ $.)m) "unching stress O permissible stress Section is safe in punching
20
D,'8/ &0 0&&'/8 2:
"u @$8&&.6 2load from slab, beam, columns4 Self wt of footing @$&K of load Total load 2"4 @ $8&&.6 C 2&.$&$8&&.64 @$+8&.'7 The safe bearing capacity of soil 2S!4 86&7?m) Area 2A4 @ "?S! @$+8&.'?86& @ +.&%m The si0e of column is )8&'&& The ratio of length, breadth of footing shall be appro/imately same as width and depth of column :? @ '&&?)8& @).'$ : @).'$b Area @ length breadth +.&%@).'$bb @$.)6m, :@8.)5m "rovide a footing of si0e 8.8$.)6m et upward pressure intensity 2#"*4 @ "?A @ $8&&.6?8.8$.)6 @ 8$6.)57?m) Design for fle/ure = @ 228.8-&.'4?)4 =@$.86m F$-&*,( &,/:
(u @
> @ 2$.)6-&.)84?) > @ &.6$m (u L traverse 2Fr4 (u short @
i.e.1 steel along width of footing Ast @)&B.)$mm) "rovide $)mm dia. bars Spacing @ 2$$8?)&B.)$4$&&& @6+).Bmm "rovide a spacing of )&&mm c?c C,-> 0&* &/, 6$< ,$*:
!ritical section occurs at a distance d @ 86&mm from the face of column Shear force 2Mu4 @$.)6load in shaded area @ $.)6&.B8$6.)5 @ 8$6.)57 Shear stress Ʈv @Mu?bd @ 28$6.)5?$&34# "$)6&66&4 @&.+'?mm) "ermissible stress in concrete 22
"t @ 2Ast?bd4$&& @ 2$68'.'?$&&&66&4$&&@&.)BK Ʈc @ &.85?mm) Ʈv N Ʈc
The section is safe in one way shear C,-> 0&* /-'/8 ,$*:
!ritical section occurs at a distance d?) from the face of the column d?) @ )56mm :oad causing punching shear M @ "u - load in shaded area @ 2$8&&.64-2$.$6&.5B8$6.)54 @ $&$5.57 "unching stress @ 2$&$5.5$&34?)25B&C$$6&466&
@&.+B?mm)
C$, 31..3.1"IS: 452???)
1.2..
POSITION OF SHEAR WALLS: 23
A shear wall is wall which is designed to resist shear, the lateral force which causes the bulk of damage in earthquakes. (any building codes mandate the use of shear walls to make homes safer and more stable.
24
2. T!PES OF STRUCTURES: There are two types of structures they are a4 :oad bearing structure b4 ramed structure L&$( 7,$*'/8 *-*,:
*t is a structure in which all the loads coming from slabs is taken by walls and distributed to the soil through foundation. *n this neither beams nor columns provided the structure is fully based on walls. y this structure we can reduce the cost of steel and concrete due to no provision of beams and columns. ut in life of loads bearing structure is very less compared to framed structure in other way it becomes difficult on the higher levels. F*$,( *-*,:
*t is a structure in which all the loads coming from the slab is taken by beam and column distributed to the subsoil by means of I!! footing. *n this type of beams, columns and footings are provided .hence the structure the cist by decrease the thickness of walls does not takes any loads from the lab. y framed structure we can construct at higher levels also. ow-a-days the load bearing structure become absolute in the view of future construction and in cost comparison there is no much difference between load bearing and framed structure.
2.1.T!PES OF SLABS:
25
26
CHOICE OF T!PE OF SLAB FLOOR
The choice of type of slab for a particular floor depends on many factors. Hconomy of construction is obviously an important consideration, but this is a qualitative argument until specific cases are discussed, and is a geographical variable. The design loads, required spans, serviceability requirements, and strength requirements are all important. or beamless slabs, the choice between a flat slab and a flat plate is usually a matter of loading and span. lat plate strength is often governed by shear strength at the columns, and for service live loads greater than perhaps $&& lb?ft) 2+.B 7?m)4 and spans greater than about )& to )+ ft 25 to B m4 the flat slab is often the better choice. *f architectural or other requirements rule out capitals or drop panels, the shear strength can be improved by using metal shear heads or some other form of shear reinforcement, but the costs may be high. Serviceability requirements must be considered, and deflections are sometimes difficult to control in reinforced concrete beamless slabs. :arge live loads and small limits on permissible deflections may force the use of large column capitals. egative-moment cracking around columns is sometimes a problem with flat plates, and again a column capital may be useful in its control. Deflections and shear stresses may also be controlled by adding beams instead of column capitals. *f severe deflection limits are imposed, the two-way slab will be most suitable, as the introduction of even moderately stiff beams will reduce deflections more than the largest reasonable column capital is able to. eams are also easily reinforced for shear forces. The choice between two-way and beamless slabs for more normal situations is comple/. *n terms of economy of material, especially of steel, the two- way slab is often best because of the large effective depths of the beams. Eowever, in terms of labor in building the floor, the flat plate is much cheaper because of the very simple formwork and less comple/ arrangement of steel. The flat slab is somewhat more e/pensive in labor than is the flat plates, but the forms for the column capitals are often available as prefabricated units, which can help limit costs. The real cost parameter is the ratio of costs of labor relative to material. ew two-way slabs are built 27
in areas of high labor costs unless there are definite structural reasons, and many are built where steel is the most costly item. Eollow -tile slabs are still built in some places, but only where the cost of both steel and cement is very high relative to labor. :ocal customs among builders, designers, and users should not be overlooked when selecting the slab type. There is a natural human tendency to want to repeat what one has previously done successfully, and resistance to change can affect costs. Eowever, old habits should not be allowed to dominate sound engineering decisions. *f a flat plate or flat slab is otherwise suitable for a particular structure, it will be found that there is the additional benefit of minimi0ing the story height. *n areas of absolute height restrictions, this may enable one to have an additional floor for appro/imately each $& floors, as compared with a two-way slab with the same clearstory heights. The savings in height lead to other economies for a given number of floors, since mechanical features such as elevator shafts and piping are shorter. There is less outside wall area, so wind loadings may be less severe and the building weighs less, which may bring cost reductions in foundations and other structural components. There are other cost savings when the ceiling finishes can be applied directly to the lower surfaces of the slabs. eamless slabs will be at a disadvantage if they are used in structures that must resist large hori0ontal loads by frame action rather than by shear walls or other lateral bracing. The transfer of moments between columns and a slab sets up high local moments, shears, and twisting moments that may be hard to reinforce for. *n this situation, the two-way slab is the more capable structure because of the relative ease with which its beams may be reinforced for these forces. *n addition, it will provide greater lateral stiffness because of both the presence of the beams and the greater efficiency of the beam-column connections. The possible choice of a precast one-way floor system, consisting of prestressed concrete members placed side-by-side and spanning between the beams, girders, or walls and generally covered by a cast-in-place concrete topping slab, should not be overlooked.
28
2.2.
DESIGN OF ONEWA! SLABS
The structural action of a one-way slab may be visuali0ed in terms of the deformed shape of the loaded surface. igure shows a rectangular slab, simply supported along its two opposite long edges and free of any support along the two opposite short edges. *f a uniformly distributed load is applied to the surface, the deflected shape will be as shown by the solid lines. !urvatures, and consequently 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 l parallel to the supported edges. The surface is cylindrical.
or purposes of analysis and design, a unit strip of such a slab cut out at right angles to the supporting beams, as in igure, may be considered as a rectangular beam of unit width, with a depth h equal to the thickness of the slab and a span l a equal to the distance between supported edges. This strip can then be analy0ed 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. Since all the load on the slab must be transmitted to the two supporting beams, it follows that all the reinforcement should be placed at right angles to these beams, with the e/ception of any bars that may be placed in the other direction to control shrinkage and temperature cracking. A one-way slab thus consists of a set of rectangular beams side by side. This simplified analysis, which assumes "oisson;s ratio to be 0ero, is slightly conservative. Actually, fle/ural compression in the concrete in the direction of l a will result in lateral e/pansion in the direction of l b unless the compressed concrete is restrained. *n a one-way slab, this lateral e/pansion is resisted by ad9acent slab strips, which tend to e/pand also. The result is a slight strengthening and stiffening in the span direction, but this effect is small and can be disregarded. The ratio of steel in a slab can be determined by dividing the sectional area of one bar by the area of concrete between two successive bars, the latter area being the product of the depth to the center of the bars and the distance between them, center to center. The ratio of steel can also be determined by dividing the average area of steel per foot of width by the effective area of concrete in a $ ft strip. The average area of steel per foot of width is equal to the area of one bar times the average number of bars in a $ ft strip 2$) divided by the spacing in inches4, and the effective area of concrete in a $ ft 2or $) inch.4 strip is equal to $) times the effective depth d . To illustrate the latter method of obtaining the steel ratio r , assume a 6 in. slab with an effective depth of + in., with o. + bars spaced + $?) in, center to center.
The spacing of bars that is necessary to furnish a given area of steel per foot of width is obtained by dividing the number of bars required to furnish this area into $). To furnish an average area of ?.4 '/2#0 with + no. of bars, requires bars must be spaced not more than
?.4 #?.2? 9 2.3 7$* ,* 0&&
12#2.3 9 5.2 '/ . center to
the
center. The determination of
slab steel areas for various combinations of bars and spacing is facilitated by the following table3
Design moments and shears in one-way slabs can be found either by elastic analysis or through the use of the same coefficients as used for beams. *f 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 e/ceed the distance between centers of supports. *n general, center-to-center distances should be used in continuous slab analysis, but a reduction is allowed in negative moments to account for support width. or slabs with clear spans not more than $& ft that are built integrally with their supports, analysis as a continuous slab on knife-edge supports with spans equal to the clear spans and the width of the beams otherwise neglected. *f moment and shear coefficients are used, computations should be based on clear spans. Fne-way slabs are normally designed with tensile steel ratios well below the ma/imum permissible value to have tension failure. Typical steel ratios range from about &.&&+ to &.&&B. This is partially for reasons of economy, because the saving in steel associated with increasing the effective depth more than compensates for the cost of the additional concrete, and partially because very thin slabs with high steel ratios would be likely to permit large deflections. Thus, fle/ural design may start with selecting a relatively low steel ratio, say about &.)& ρb, setting M u @ φM n and solving for the required effective depth d , given that b @ $) in. for the unit strip.
T$7, : M'/' '->/, &0 /&/ *,*,,( &/,6$< $7
Simply supported
l?)&
Fne end continuous
l?)+
oth end continuous
l?)B
!antilever
l?$&
Shear will seldom control the design of one-way slabs, particularly if low tensile steel ratios are used. *t will be found that the shear capacity of the concrete, φV c will almost without e/ception be well above the required shear strength V u at factored loads. P*$-'-$ C&/'(,*$'&/
The total slab thickness h is usually rounded to the ne/t higher $?+ in. for slabs up to ' in. thickness, and to the ne/t higher $?) in. for thicker slabs. The concrete protection below the reinforcement should call for ) inch. elow the bottom of the steel. *n a typical slab, $ in. below the center of the steel may be assumed. The lateral spacing of the bars, e/cept those used only to control shrinkage and temperature cracks should not e/ceed 8 times the thickness h or $B in., whichever is less. enerally, bar si0e should be selected so that the actual spacing is not less than about $.6 times the slab thickness, to avoid e/cessive cost for bar fabrication and handling. Also, to reduce cost, straight bars are usually used for slab reinforcement. TEMPERATURE AND SHRINKAGE REINFORCEMENT
!oncrete shrinks as the cement paste hardens. *t is advisable to minimi0e such shrinkage by using concretes with the smallest possible amounts of water and cement compatible with other requirements, such as strength and workability, and by thorough moist-curing of sufficient duration. Eowever, no matter what precautions are taken, a certain amount of shrinkage is usually unavoidable. *f a slab of moderate dimensions rests freely on its supports, it can contract to accommodate the shortening of its length produced by shrinkage. #sually, however, slabs and other members are 9oined rigidly to other parts of the structure and cannot contract freely. This results in tension stresses known as shrinkage stresses. A
decrease in temperature relative to that, at which the slab was poured, particularly in outdoor structures such as bridges, may have an effect similar to shrinkage. That is, the slab tends to contract and if restrained from doing so becomes sub9ect to tensile stresses. Since concrete is weak in tension, these temperature and shrinkage stresses are likely to result in cracking. !racks of this nature are not detrimental, provided their si0e is limited to what are known as hairline cracks. This can be achieved by placing reinforcement in the slab to counteract contraction and distribute the cracks uniformly. As the concrete tends to shrink, such reinforcement resists the contraction and consequently becomes sub9ect to compression. The total shrinkage in a slab so reinforced is less than that in one without reinforcement1 in addition, whatever cracks do occur will be of smaller width and more evenly distributed by virtue of the reinforcement. *n one-way slabs the reinforcement provided for resisting the bending moments has the desired effect of reducing shrinkage and distributing cracks. Eowever, as contraction takes place equally in all directions, it is necessary to provide special reinforcement for shrinkage and temperature. !ontraction in the direction perpendicular to the main reinforcement. This added steel is known as temperature or shrinkage reinforcement, or distribution steel. Ieinforcement for shrinkage and temperature stresses normal to the principal reinforcement should be provided in a structural slab in which the principal reinforcement e/tends in one direction only. The minimum ratios of reinforcement area to gross concrete area but in no case shall such reinforcing bars be placed farther apart than 6 times the slab thickness or more than $B in. *n no case is the steel ratio to be less than &.&&$+. The steel required by the *S !ode for shrinkage and temperature crack control also represents the minimum permissible reinforcement in the span direction of one-way slabs1 the usual minimums for fle/ural steel do not apply.
2.3.
D,'8/ &0 T6&6$< S$7:
This section covers the following topics. • • • •
*ntroduction Analysis and Design eatures in (odeling and Analysis Distribution of (oments to Strips
2.3.1. I/*&(-'&/
The slabs are presented in two groups3
&/,6$< $7
and 6&6$< $7. The one-
way slabs are presented in Section %.).
slabs do not have beams between the columns, drop panels or column
capitals. #sually, there are spandrel beams at the edges. F$ $7: These slabs do not have beams but have drop panels or column capitals. T6&6$< $7 6' 7,$: There are beams between the columns. *f the beams are wide and shallow, they are termed as band beams. or long span construction, there are ribs in both the spanning directions of the slab. This type of slabs is called waffle slabs. The slabs can be cast-in-situ 2cast-in-place4. Hlse, the slabs can be precast at ground level and lifted to the final height. The later type of slabs is called lift slabs. A slab in a framed building can be a two-way slab depending upon its length-to-breadth 2 L / B 4 ratio. Two-way slabs are also present as mat 2raft4 foundation.
The following sketches show the plan of various cases of two-way slabs. The spanning directions in each case are shown by the double headed arrows.
FIG.: PLAN OF TWO WA! SLABS
The absence of beams in flat plates and flat slabs lead to the following advantages. $4 ormwork is simpler )4 Ieduced obstruction to service conduits 84 (ore fle/ibility in interior layout and future refurbishment. Two-way slabs can be post-tensioned. The main advantage of prestressing a slab is the increased span-to-depth ratio. The following photographs show post-tensioned flat plate and flat slab.
FIG.: FLAT PLATE
FIG.: FLAT SLABS
2.4.
ANAL!SIS AND DESIGN
A/$<'
The analysis of two-way slabs is given in
S,-'&/ 31 IS: 45 2??? , under
Plat SlabsQ.
The analysis is applicable to flat plates, flat slabs and two-way slabs with deflecting beams. or two-way slabs with beams, if the beams are sufficiently stiff, then the method 2based on moment coefficients4 given in A//,= D IS: 45 2??? , is applicable. The direct design method of analy0ing a two-way slab is not recommended for prestressed slabs. The equivalent frame method is recommended by S7,-'&/ 31.5 IS: 45 2??? .
plates and flat slabs.
ACI 31?2.
*t is given in
This method is briefly covered in this section for flat
The slab system is represented by a series of two dimensional equivalent frames for each spanning direction. An equivalent frame along a column line is a slice of the building bound by the centre-lines of the bays ad9acent to the column line. The width of the equivalent frame is divided into a column strip and two middle strips. The column strip 2!S4 is the central half of the equivalent frame. Hach middle strip 2(S4 consists of the remaining portions of two ad9acent equivalent frames. The following figure shows the division in to strips along one direction. The direction under investigation is shown by the double headed arrow.
F'8*,: E'%$,/ 0*$, $&/8 C&/ L'/, 2
*n the above figure, $ @ span of the equivalent frame in a bay
l
) @ width of the equivalent frame. This is the tributary width for calculating the loads.
l
The following figure shows a typical elevation of an equivalent frame.
F'8*,: E,%$'&/ &0 $/ ,'%$,/ 0*$,
The analysis is done for each typical equivalent frame. An equivalent frame is modeled by slab-beam members and equivalent columns. The equivalent frame is analy0ed for gravity load and lateral load 2if required4, the negative and positive moments at the critical sections of the slab-beam members are distributed along the transverse direction. This provides the design moments per unit width of a slab.
*f the analysis is restricted to gravity loads, each floor of the equivalent frame can be analy0ed separately with the columns assumed to be fi/ed at their remote ends, as shown in the following figure. The pattern loading is applied to calculate the moments for the critical load cases. This is discussed later.
F'8*,: S''0',( &(, &0 $/ ,'%$,/ 0*$,
The steps of analysis of a two-way slab are as follows. $4 Determine the factored negative 2 M u L 4 and positive moment 2 M uC4 demands at the critical sections in a slab-beam member from the analysis of an equivalent frame. The values of M u L are calculated at the faces of the columns. The values of M uCare calculated at the spans. The following sketch shows a typical moment diagram in level of an equivalent frame due to gravity loads
F'8*,: T<'-$ &,/ ('$8*$ (, & 8*$%'< &$(
)4 Distribute M u – to the !S and the (S. These components are represented as M u, – CS and – M , u, MS
respectively. Distribute M u+ to the !S and the (S. These components are
represented as M u,+CS and M u,+ MS, respectively.
F'8*,: D'*'7'&/ &0 &,/ & -&/ *' $/( '((, *'
84 *f there is a beam in the column line in the spanning direction, distribute each of M u, – CS and M u, +CS between the beam and rest of the !S.
F'8*,: D'*'7'&/ &0 &,/ & 7,$ -&/ *' $/( '((, *'
+4 Add the moments M u, – MS and M u, + MS for the two portions of the (S 2from ad9acent equivalent frames4. 64 !alculate the design moments per unit width of the !S and (S. D,'8/
Fnce the design moments per unit width of the !S and (S are known, the steps of design for prestressing steel are same as that for one-way slab. The profile of the tendons is selected similar to that for continuous beams. The fle/ural capacity of prestressed slab is controlled by total amount of prestressing steel and pre-stress rather than by tendon distribution. ut the tendon distribution affects the load balancing. Some e/amples of tendon distribution are shown.
FIG.: T<'-$ ,/(&/ $<&
(a/imum spacing of tendons or groups of tendons should be limited to B h or $.6 m, whichever is less. Eere, h is the thickness of the slab. A minimum of two tendons shall be provided in each direction through the critical section for /-'/8 ,$* around a column. The critical section for punching shear is described in Section %.+, Two-way Slabs 2"art **4. rouping of tendons is permitted in band beams. A minimum amount of non pre-stressed reinforcement is provided in each direction based on temperature and shrinkage requirement. As per
IS: 45 2??? , C$, 2.5.2.1,
the
minimum amount of reinforcement 2 A st, min in mm)4 for unit width of slab is given as follows. A st, min
@ &.$6K $&&& h for e )6& grade of steel @ &.$)K $&&& h for e +$6 grade of steel.
The ducts for placing the individual strands are oval shaped to maintain the eccentricity, reduce frictional losses and convenient placement of crossing ducts. The ducts are not commonly grouted as the use of unbounded tendon is not detrimental in buildings. The following photo shows the ducts for the prestressing tendons and the non-prestressed reinforcement in a two-way slab. The transverse beam need not be a visible beam, but a part of the slab in the transverse direction, bounded by the edges of the column or column capital. *n presence of beam or column capital or in absence of beam, the cross-section of the modeled transverse beam is taken as shown in the following sketches.
F'8*,: C*&,-'&/ &0 &(,,( *$/%,*, 7,$
The following figure shows the variation of the moment of inertia of the slab beam member.
F'8*,: $) E,%$'&/ &0 ,'%$,/ 0*$, 7) V$*'$'&/ &0 , &,/ &0 '/,*'$ &0 , $77,$ ,7,*
A**$/8,,/ &0 '%, &$(
Since the factored live load 2wu, LL4 may not occur uniformly in all the spans in a floor, a distribution is considered to generate the ma/imum values of the negative 2 M u – 4 and
positive moments 2 M u+4 at the critical sections. *f the distribution of wu, LL is known, then the load is applied accordingly. *f the distribution is not known, then a
$,*/ &$('/8
is
considered based on the value of wu, LL with respect to that of the factored dead load 2 wu, DL
4. Ff course, the load case with wu, LL on all the spans should be also analy0ed.
$4 or wu, LL R wu, DL The possible variation in Wu, LL in the different spans is neglected. Wu, LL is applied uniformly on all the spans.
F'8*,:
D'*'7'&/ &0 '%, &$( 0&* w
u, LL
w
u, DL
)4 or wu LL N wu,DL or ma/imum value of M u+ in a span, wu,LL is applied on the span and the alternate spans. or e/ample, if the ma/imum value of M u+ in Span ! of the frame below is to be determined, then wu,LL is placed in Spans ! and DH. This distribution will also give the ma/imum value of M u+ in Span DH. or ma/imum value of M u – near the support, wu – is applied on the ad9acent spans only. or e/ample, if the ma/imum value of M near LL u
Support is to be determined, then wu,LL is placed in Spans A and !.
D'*'7'&/ &0 '%, &$( 0&* $=' M
+
u
'/ S$/ BC $/( DE
-
D'*'7'&/ &0 '%, &$( 0&* $=' M /,$* S&* B u
F'8*,:
D'*'7'&/ &0 '%, &$( 0&* w
u LL
Jw
u,DL
C*''-$ ,-'&/ /,$* $ &*
The critical section is determined as follows. $4 At interior support at the face of support 2column or column capital, if any4, but not further than &.$56l $ from the center line of the column. )4 At e/terior support at a distance from the face of column not greater than half the pro9ection of the column capital 2if any4.
3. T!PES OF FLAT SLABS:
!ommon practice of design and construction is to support the slabs by beams and support the beams by columns. This may be called as beam-slab construction. The beams reduce the available net clear ceiling height. Eence in warehouses, offices and public halls sometimes beams are avoided and slabs are directly supported by columns. These types of construction are aesthetically appealing also. These slabs which are directly supported by columns are called F$ S$7.
The column head is sometimes widened so as to reduce the punching shear in the slab. The widened portions are called -&/ ,$(. The column heads may be provided with any angle from the consideration of architecture but for the design, concrete in the portion at +6 on either side of vertical only is considered as effective for the design.
(oments in the slabs are more near the column. Eence the slab is thickened near the columns by providing the drops as shown in ig. Sometimes the drops are called as capital of the column. Thus we have the following types of flat slabs3
2i4 Slabs without drop and column head. 2ii4 Slabs without drop and column with column head. 2iii4 Slabs with drop and column without column head. 2iv4Slabs with drop and column head.
The portion of flat slab that is bound on each of its four sides by centre lines of ad9acent columns is called a panel. The panel shown in ig. has si0e : $ U :). A panel may be divided into column strips and middle strips. !olumn Strip means a desig designn strip havin havingg a width of &.)6:$ or &.)6: ), whichever is less. The remaining middle portion which is bound by the column strips is called middle strip. ig. shows the division of flat slab panel into column and middle strips in the direction .
3.1.
PROPORTIONING OF FLAT SLABS
IS 452??? C$, 31.2 gives the following guidelines for
proportioning.
3.1.1. D*&
The drops when provided shall be rectangular in plan, and have a length in each direction not less than one third of the panel in that direction. or e/terior panels, the width of drops at right angles to the non continuous edge and measured from the centre-line of the columns shall be equal to one half of the width of drop for interior panels. 3.1. 3. 1.2. 2. C& C& / / H,$ H,$( (
3.1.3. 3.1 .3. T' T'->/ ->/, , &0 F$ F$ S$7 S$7
rom the consideration of deflection control *S +6'-)&&& specifies minimum thickness in terms of span to effective depth ratio. or this purpose larger span is to be considered. *f drop as specified is provided, then the ma/imum value of ratio of larger span to thickness shall be @ +&, if mild steel is used @ 8), if e +$6 or e 6&& steel is used *f drops are not provided or si0e of drops do not satisfy the specification, then the ratio shall not e/ceed &.% times the value specified above i.!., @ +& U &.% @ 8', if mild steel is used. @ 8) U &.% @ )B.B, if E>SD bars are used *t is also specified that in no case, the thickness of flat slab shall be less than $)6 mm. 3.2 .2..
DETE DE TERM RMIINA NAT TION OF BEND NDIING MOMEN ENT T AND SH SHEA EAR R FOR ORCE CE::
or this *S +6'-)&&& permits use of any one of the following f ollowing two methods3 2a4 The Direct Design (ethod 2b4 The Hquivalent Hquivalent rame rame (ethod
3.2.1. 3.2 .1. THE DIR DIRECT ECT DES DESIGN IGN ME METHO THOD D
This method has the limitation that it can be used only if the following conditions are fulfilled3
2a4 There shall be minimum of three continuous spans in each direction. 2b4 The panels shall be rectangular and the ratio of the longer span to the shorter span within a panel shall not be greater than ). 2c4 The successive span length in each direction shall not differ by more than one-third of longer span. 2d 4 The design live load shall not e/ceed three times the design dead load. 2!4 The end span must be shorter but not greater than the interior span. 2 " 4 *t shall be permissible to offset columns a ma/imum of $& percent of the span in the direction of the offset notwithstanding the provision in 2 b4. Total Design (oment The absolute sum of the positive and negative moment in each direction is given by
!ircular supports shall be treated as square supports having the same area i.!., squares of si0e &.BB'D.
#b$
Ac is the ratio of fle/ural stiffness at the e/terior columns to the fle/ural stiffness of the slab at a 9oint taken in the direction moments are being determined and is given by Ac @V7 c ? V7 s
(!r c!nt '" )'tal )'tal S% &'%
Distribut!d M'm!nt
M'm!nt
A
egative ( at the e/terior support
$&&
B
egative ( at the interior support
56
C
"ositive bending moment
'&
M&,/ '/ C&/
*n this type of constructions column moments are to be modified as suggested in
IS 452???
C$, N&. 31.4.5.
S,$* F&*-,
The critical section for shear shall be at a distance d from the periphery of the column?capital drop ) panel. Eence if drops are provided there are two critical sections near columns. These critical sections are shown in igs. The shape of the critical section in plan is similar to the support immediately below the slab as shown in ig.
or columns sections with re-entrant angles, the critical section shall be taken as indicated in ig
*n case of columns near the free edge of a slab, the critical section shall be taken as shown in ig.
3.2. 3. 2.2. 2.
E@UI E@ UIV VALE LENT NT FR FRAM AME E MET METHO HOD D
*S +6'L)&&& +6'L)&&& recommends recommends the analy analysis sis of flat slab and column structure structure as a rigid frame to get design moment and shear forces with the following assumptions3 2a4 eam portion of frame is taken as equivalent to the moment of inertia of flat slab bounded laterally by centre line of the panel on each side of the centre line of the column. *n frames ad9acent and parallel to an edge beam portion shall be equal to flat slab bounded by the edge and the centre line of the ad9acent panel. 2b4 (oment of inertia of the member memberss of the frame may be taken as that of the gross section of
the concrete alone. 2c4 Mariation of moment of inertia along the a/is of the slab on account of provision of drops shall be taken into account. *n the case of recessed or coffered slab which is made solid in the region of the columns, the stiffening effect may be ignored provided the solid part of the slab does not e/tend more than &.$6 l !"" into the span measured from the centre line of the columns. The stiffening effect of flared columns heads may be ignored. 2d 4 Analysis of frame may be carried out with substitute frame method or any other accepted method like moment distribution or matri/ method. L&$('/8 P$,*/
To get ma/imum moment near mid span L th of live load on the panel and full live load on alternate panel
ii.
To get ma/imum moment in the slab near the support L th of live load is on the ad9acent panel only
*t is to be carefully noted that in no case design moment shall be taken to be less than those occurring with full design live load on all panels. The moments determined in the beam of frame 2flat slab4 may be reduced in such proportion that the numerical sum of positive and average negative moments is not less than the value of total design (oment
(& @ <:n ?B
The distribution of slab moments into column strips and middle strips is to made in the same
manner as specified in direct design method. 3.3. SLAB REINFORCEMENT
S$-'/8
The spacing of bars in a flat slab shall not e/ceed ) times the slab thickness. A*,$ &0 R,'/0&*-,,/
SD bars used and &.$6 percent, if mild steel is used. M'/' L,/8 &0 R,'/0&*-,,/
At least 6& percent of bottom bars should be from support to support. The rest may be bent up. The minimum length of different reinforcement in flat slabs should be as shown in ig. 2ig. $' in *S +6'L )&&&4. *f ad9acent spans are not equal, the e/tension of the Lve reinforcement beyond each face shall be based on the longer span. All slab reinforcement should be anchored property at discontinuous edges.
4. DESIGN PHILOSOPH!
W&*>'/8 S*, M,&(
The Stresses in an element is obtained from the working loads and compared with permissible stresses. The method follows linear stress-strain behavior of both the materials. (odular ratio can be used to determine allowable stresses. (aterial capabilities are under estimated to large e/tent. actor of safety are used in working stress method. The member is considered as working stress. #ltimate load carrying capacity cannot be predicted accurately. The main drawback of this method is that it results in an uneconomical section.
L'' S$, M,&(
The stresses are obtained from design loads and compared with design strength. *n this method, it follows linear strain relationship but not linear stress relationship 2one of the ma9or difference between the two methods of design4. The ultimate stresses of materials itself are used as allowable stresses. The material capabilities are not under estimated as much as they are in working stress method. "artial safety factors are used in limit state method.
ULTIMATE STRESS METHOD
*n ultimate load method, the working loads are increased by suitable factors to obtain ultimate loads. These factors are called load factors. The structure is then designed to resist the desired ultimate loads. This structure is then designed to resist the desired ultimate loads. This method takes into account the non-linear stress-strain behavior of concrete. The term safety factor has been used in the working stress method to denote the ratio between the yield stress and the permissible stress. *t had little meaning as far as the ratio between collapse loads and working load was concerned. The team load factor has been
traditionally used to denote the ratio between the collapse or ultimate load to the working load. The knowledge of load factor is more important than the knowledge of factor of safety.
4.1. DESIGN OF THE FLAT SLAB STRUCTURES
Despite the rapid growth of flat plate?slab construction, literature and tools available for designers to design and engineer flat plate?slabs in *ndia, has been limited in terms of both *ndian standards and *ndian research papers. *ndian engineers often have to resort to other standards to design flat plate?slab. The following is a discussion of the process of designing flat plate?slabs to meet *ndian codes. :imitations in the *ndian codes
IS 45:2???
are
overcome by utili0ing ACI 31. (aintaining the *ntegrity of the Specifications Structural engineers commonly use the equivalent frame method with equivalent beams such as the one proposed by acob S. rossman in practical engineering for the analysis of flat plate structures. Architectural demands for better illumination, lesser fire resistance of sharp corners present in the form of beams G increase in the formwork cost, optimum use of space leads to the new concept in the field of structural engineering as Ieinforced concrete flat slabs.
FIG.: P$/ &6'/8 $88,*,( '/,*'&* -&/.
The design of flat slab structures involves three steps * $4 raming system )4 Hngineering analysis 84 Ieinforcement design and detailing F*$'/8 S<,:
*nitial framing system formulation provides a detailed geometric description of the column spacing and overhang. Hven though the architect provides this part of the design, the engineer should emphasi0e on the following3 $4
Three continuous spans in each direction or have an overhang at least one-forth times ad9acent span length in case of only two continuous spans.
)4
Typical panel must be rectangular
84
The spans must be similar in length i.e. ad9acent span in each direction must not differ in length by one-third Hngineering Analysis3 lat plate?slab may be analy0ed and designed by any method as long as they satisfy the strength, stiffness and stability requirements of the *S +6'3)&&&. A typical flat plate?slab can be analy0ed by direct design method or equivalent frame method as prescribed by the code. Eowever, if the flat plate?slab is a typical with unusual geometry, with irregular column spacing, or with big opening then the designer may have to use finite element method model analysis using computers. The design of flat plate?slabs irrespective of the methodology used must first assume a minimum slab and drop thickness and a minimum column dimension to ensure adequate stiffness of the system to control deflection. The *S +6'3)&&& code is not clear on these minimums. Fnce the slab thickness and column dimensions with boundary conditions are selected, the structure is loaded for different load cases and combinations prescribed by the code. The computed forces and moments in the members should be used for reinforcement design. !ritical reactions for the load combinations are used for the design of the supporting columns and foundations. Ieinforcement Design and Detailing Ieinforcement design is one of the critical parts of flat plate?slab design1 ma/imum forces from the analysis shall be used in the design of the reinforcement. Ieinforcement required for fle/ure by using minimum slab thickness per table $ typically will not require compression reinforcement. The tension steel area required and detailing for appropriate strips can be "er *S +6'3)&&&, both being similar. Eowever design for punching shears force 2including additional shear due to unbalanced moment4.
Hvery code suggests any of the two methods as Direct Design (ethod and Hquivalent rame (ethod for analysis of flat slab. Design of lat slab by Direct Design (ethod has some restrictions that3 2a4 *t should have minimum three spans in each direction. 2b4 *t should not have staggered column orientation. Eence Hquivalent rame (ethod is adopted. #sing those calculated moments calculate negative moments at both left G right support i.e. 2(-u4 G the ma/imum positive moments in the middle of span i.e. 2( C u4. All the egative G "ositive moments are distributed in the column strips G (iddle strips respectively using equivalent codes. Still moments in the slab remains unbalanced. These unbalanced slab moments at supports are transmitted to respective columns. These moments are transferred by punching shear G fle/ure in the column. The punching shear produces cracks at the critical section close to the column faces as shown below,
*n such slabs large bending moments and shears develop near the 9unctions with columns. Therefore there is a need to spread the column at its top end or thicken the slab over column.
F'8 4 : F$ $7 6' (*& $/( -&/ 6'& -&/ ,$(
The shear stress is calculated as given in *S code G A!*. *f it is more than permissible the shear reinforcement is provided.
ehavior of flat slab and flat plates are identical to those of two way slab. ands of slab in both directions along column lines are considered to act as beams. Such bands of slabs are referred as column strips which pass through the columns and middle strips, occur in the middle of two ad9acent columns. The deflections are minimum at supports and ma/imum at mid spans. The deflected flat slab at the center of panel shall have saucer shape. direction and l / and ly is the span length in = and > direction.
4.2.1. O7+,-'%,
A Ieinforced !oncrete flat slab floor is a significant advancement in the building technology. *t has been observed that possible failure mode of the Ieinforced concrete lat slabs is punching that occurs in the vicinity of a column. The main ob9ective of the study is to study method of analysis and design of flat slab with staggered column by *S +6'-)&&& The code has specified the fi/ed coefficients for lateral and transverse distribution of moments as per direct design method and equivalent frame method. The pro9ect is aimed to determine the effect of staggered column spacing and its combination of shapes such as circular, rectangular and square columns. "ro9ect is also aimed to prepare the H/cel worksheet for analysis and design of the flat slab with staggered column by equivalent frame method. S-&, &0 W&*>
The pro9ect works is concerned with the Analysis and Design of lat slab with and without staggered column and to prepare the worksheet for analysis and design of flat slabs. The scope of work will be as below.
$4 Analysis and design of flat slabs is to be carried out for staggered columns using Hquivalent
rame (ethod with *S +6'-)&&&. )4 "reparation of e/cel worksheet analysis and design of flat slab with staggered column as per
*S +6'-)&&&.
4.3. DESIGN OF FLAT SLABS B! IS: 45
The term flat slab means a reinforced concrete slab with or without drops, supported generally without beams, by columns with or without flared column heads 2see ig. $)4. A flat slab may be solid slab or may have recesses formed on the soffit so that the soffit comprises a series of ribs in two directions. The recesses may be formed by removable or permanent filler blocks. :onger span
Shorter span
L$ @'.' m , L) @6.' m
L$ @6.' m , L) @'.' m
2 i 4 column strip @ &.)6 L) @ $.+ m ut not greater than &.)6 L$ @ $.'6 m
2 i 4 column strip @ &.)6 L) @ $.'6 m ut not greater than &.)6 L$ @ $.+ m
2ii4 (iddle strip @ 6.' L 2$.+C$.+4 @ ).B m
$.+ m !.S
2ii4 (iddle strip @ '.' L 2$.+C$.+4 @ 8.B m
$.+ m !.S
8.B m (.S
).B m (.S
$.+ m
$.+ m
!.S
!.S
6.' m
'.' m
The drops when provided shall be rectangular in plan, and have a length in each direction not less than one- third of the panel length in that direction. or e/terior panels, the width of drops at right angles to the non- continuous edge and measured from the centre -line of
the columns shall be equal to one -half the width of drop for interior panels. Since the span is large it is desirable to provide drop. Drop dimensions along3 :onger span
Shorter span
L$ @'.' m , L) @6.' m
L$ @6.' m , L) @'.' m
ot less than L$ ?8 @ ).) m
ot less than L$ ?8 @ $.B'' m
Eence provide a drop of si0e ).) / ).) m i.e. in column strip width.
!olumn head dimension along3 :onger span
Shorter span
L$ @'.' m , L) @6.' m ot greater than L$ ?+ @ $.'6
L$ @6.' m , L) @'.' m
m
ot greater than L$ ?+ @ $.+ m
Adopting the diameter of column head @ $.8& m @$8&& mm f4 Depth of flat slab3 The thickness of the flat slab up to spans of $& m shall be generally controlled by considerations of span 2 L 4 to effective depth 2 d 4 ratios given as below3 !antilever ;1 simply supported 2?1 !ontinuous 2. or slabs with drops, span to effective depth ratios given above shall be applied directly1 otherwise the span to effective depth ratios in accordance with above shall be multiplied by &.%. or this purpose, the longer span of the panel shall be considered. The minimum thickness of slab shall be $)6 mm Depth of flat slab3 Depth considering along3 :onger span
Shorter span
L$ @'.' m , L) @6.' m @ )6'.'
L$ @6.' m , L) @'.' m @)$6.'
Say )'& mm
Say ))& mm
The unbalanced slab moments at various supports are transmitted to respective columns. This unbalanced slab moment is shared by the column above G below in proportion to their relative stiffness. These moments are transferred by punching shear G fle/ure in the column. The punching shear produces cracks at the critical section close to the column faces as shown below,
F'8: C*''-$ ,-'&/ 0&* ,$*
ANAL!SIS AND DESIGN OF FLAT SLAB: DESIGN OF INTERIOR PANEL: STEP 1:
Thickness of slab3 d@$?)' @6.5+$& 8?)' @))&mm 2ma/imum length is been selected4 "rovide $)mm dia. bars with a clear cover of )&mm Fverall depth D@))&C$)?)C)&@)+' STEP 2:
:oads3 :ive load
@ +kn?m)
.
@ $.6kn?m )
:ength of panel @ $$.)m
@ 12.43>/#2
Si0e of drop not less than :?8:?8 @ $$.)?8$6.%?8 Adopt si0e of drop as 8.B+6.8'@ )&.'m )
C&/ ,$(:
De should be less than &.):$ @ &.)$$.) @ ).)+ not greater than @ &.)6 $6.% @ 8.%5m Adopt dia. of column head De @ ).)+C8.%5?) @ 8.$&m, r @ $.66m Area of column head A @ 8.$+$.666) @ 5.6+m) Malue of :n along length and width :n @ $$.) L ).56 @ B.+6m :n @ $6.% L ).56 @ $8.$6m
STEP 3: B,/('/8 &,/ -$-$'&/:
The absolute sum of the Cve and avg. Lve .( in each direction shall be taken as3 (o @ <:n?B < @ < :):n @ $).+8 $$.)) $8.$6 @ $B88.%67 (o @ <:n?B @ $B88.%6 $8.$6?B @ 8&$+.66-mm
STEP 4: D'*'7'&/ &0 &,/:
The negative design moment shall be located at the face of rectangular supports ,circular supports being treated as square supports having the same area . Total negative moment @ &.'6 ( o@ $%6%.+6 -mm Total positive moment @ &.86 ( o @$&66.&% -mm
STEP 5: B,/('/8 &,/ &0 -&/ *': C&/ *': egative moment at an interior support
At an interior support, the column strip shall be designed to resist 56K of the total negative moment in the panel at the support. egative design moment @ 56K of negative moment @ $+'%.6B -mm C&/ *': "ositive
moment for each span, the column strip shall be designed to resist
'&K of the total positive moment in the panel. "ositive design moment @ '&K of positive moment @ '88.&6-mm
STEP : B,/('/8 &,/ &0 '((, *':
egative design moment @)6K of negative moment @ +B%.B' -mm "ositive design moment @ +&K of positive moment @ +)).&8 -mm M'((, *':
egative moment @ $%6%.+6 L $+'%.6B @ +B%.B5 -mm "ositive moment @ $&66.&% L '88.&6 @ +)).&+ -mm
STEP ;: C,-> &0 (, &0 $7
inding depth in slab d@X'88.&6?$.6856&@$%'.+6 Eowever provide a depth of )&&mm
STEP : D, &0 (*&:
Drop depth in field should be $.56 times or ) times the depth of slab thus
"rovide a depth of @ $.56depth of slab d @ 86&mm "roviding $)mm dia. main bar overall thickness of slab Eence, depth of slab @ )&& mm depth of drop @ 86& mm
S$7 *,'/0&*-,,/ $-'/8: S$-'/8:
The spacing if bars in flat slab shall not e/ceed two times the slab thickness, e/cept
where the slab is of cellular or ribbed construction.
STEP : R,'/0&*-,,/ '/ (*&:
"t @ 6& 2$-X$-2+.'$%6%.+%$& '? ).6856&86&86&4 ? 26&&?)64 "tt @ $.)&K Ast @ $.)& 856&86&?$&& @ $656&mm ) Ast per meter length @ +)&& mm )
Spacing3 8.$+$'$'? +)&& $&&& @ $+Bmm !?! "rovide $'mm dia. bars !?! spacing of $6&mm only.
STEP 1?: R,'/0&*-,,/ '/ -&/ *':
"t @ 6& $-X$-2+.'$%6%.+%$& '? ).6856&86&86&4 ? 26&&?)64 "t @ &.B&K Ast @ &.B&856&)&&?$&& @ '&&&mm ) Ast per meter length $'&&mm ) Spacing @ 8.$+$++? $'&&$&&& @ $'6mm "rovide $)mm dia. bars with !?! spacing of $6&mm.
STEP 11: R,'/0&*-,,/ '/ '((, *':
"t @ 6& $-X$-2+.'$%6%.+%$& '? ).6856&86&86&4 ? 26&&?)64 "t @ &.%)K Ast @ &.%)856&)&&?$&& @ '%&&mm ) Ast per meter length @ $B+& mm ) Spacing @ 8.$+?+ $++? $B+& $&&& @ $%'.8mm "rovide $)mm dia. bars with !?! spacing of )&&mm
RESULT:
CODE
IS45
Shape of test specimen for concrete strength 2mm4
!ube $6&/$6&/$6&
rade of concrete2?mmY4
)&
rade of steel 2?mmY4
+$6
egative moment27-m4
$BB.6
"ositive moments27 -m4
%&
Area of reinforcement2mmY4
+)&%
Thickness of slab for
$5&
Serviceability criteria2mm4 "unching shear
Safe
5. POSTTENSIONED FLAT PLATE#SLAB
"ost-tensioned flat plat?slabs are a common variation of the conventional plate structure where most of the reinforcement is replaced by post-tensioned strands of very high strength steel. The structural advantage of post tensioning over conventional I!! is that the slab is nearly crack- free at full service load. This leads to a smaller deflection compared to conventional I!! because of the higher rigidity of the un-cracked section. Eence reduction in thickness of the slab compared to conventional I!! is the rationale for using posttensioning system for spans over $&m and above. urther the lack of cracking leads to a watertight structure. lat plat?slab design and build contractors in *ndia claim a )&K cost reduction compared to conventional I!!. Eowever, our observation of post-tensioned flat plat?slab constructions used in two construction pro9ects in *ndia built by post tensioned concrete contractors utili0ing "T system has been that there is no reduction in thickness of the slab compared to conventional I!! and the slabs are not crack free at service loads. Eence, the actual deflection in these structures is similar to that of theoretically computed I!! deflection. *n addition, water tightness was not achieved in one of the pro9ects. And with respect to costs involved, there is an escalation in cost by $6-)&K rather than reduction as claimed by "T design G build contractor. And another disadvantage in using post tensioned system in commercial buildings in *ndia is its lack of fle/ibility to create openings or drill into slabs to anchor services system when the slab is completed with post tensioning. *nvariable the owner in *ndia is not sure of the occupant when he starts the building and may have to change or create opening in slabs after construction to satisfied occupants requirement, which is not possible with a "T system.
. T!PES OF LOADS:
A structure should be strong enough to support the loads acting on it. Eence estimation of the loads which sufficient accuracy is very essential in structural design. A structure may be acted upon many types of loads. Dead loads are estimated based on unit weight of materials. The live loads on floors and the wind loads are obtained. The effect of earthquake load is also considered and the loads are calculated according to the standards of building codes. a.
D,$( &$(:
b.
L'%, &$(:
They are permanent or stationery loads They are either moving or movable loads without any acceleration or impact. The
floor slabs are designed to carry either #D: or concentrated load c.
I$- &$(: *mpact load is caused by vibration or impact
d.
W'/( &$(:
load is primarily hori0ontally load caused by movement of air relative to
earth. The details of wind load is given by IS: ;5 "$* 3) e.
S,''- &$(: The
seismic load is caused due to seismic waves caused by the moment of
earth surface or vibration of earth surface. The details of seismic load is given in "2??2).
IS: 13
.1 APPLICATIONS OF FLATSLAB R#C STRUCTURES IN SEISMIC REGIONS
INTRODUCTION:
Advantages of flat-slab reinforced concrete structures are widely known but there are also known the disadvantages concerning their earthquake resistance. *t is remarkable that both R,'/0&*-,( C&/-*,, C&(, $/( S,''- C&(, do
IS
not forbid the use of such structural
systems however both !odes provide specific compliance criteria in order such structures to be acceptable. The advantages of these systems are3 $. ). 8. +. 6. '.
The ease of the construction of formwork. The ease of placement of fle/ural reinforcement. The ease of casting concrete. The free space for water, air pipes, etc between slab and a possible furred ceiling. The free placing of walls in ground plan. The use of cost effective prestressing methods for long spans in order to reduce
slab thickness and deflections as also the time needed to remove the formwork. 5. The reduction of building height in multi-storey structures by saving one storey height in every si/ storey;s thanks to the elimination of the beam height. These structural systems seem to attract global interest due to their advantages mainly in countries in which the seismicity is low. The application of flat-slab structures is restrained due to the belief that such structures are susceptible to seismic actions, .2. PARAMETRICAL STUD!
SPECIFICATIONS OF 3D STRUCTURAL S!STEMS
our different cases of 8D structural systems were e/amined. The categories include the following structural systems3 a4 flat-slab supported only by columns b4 flat-slab with parametric beams supported by columns c4 flat-slab supported by columns and shear walls d4 flat-slab with parametric only beams supported by columns and shear walls. The aforementioned systems were studied for all possible storey heights which can be implemented namely one to nine storey buildings with or without basement, 2underground storey4. The plan view of the four analy0ed structural systems is given a side view of the nine storey building with its basement is illustrated. The cross section of the columns is decreased, in both dimensions, by 6cm from one storey to a sequentially higher storey. Two load combinations were used3 a4 The first which imposes ultimate limit states vertical loading i.e. $.86gC$8.6&q, b4 The second one which imposes seismic loading provided by the reek Harthquake. .3. MODELLING
Mertical elements L columns and shear walls L were modeled in all cases with linear beam elements. The difference between the models is located on one hand in the use or not of diaphragm action of slabs and on the other hand in the use of shell or linear elements for the modeling of the slab. At the shell element the mass was considered to be concentrated on slab and in the first case it was modeled using a thin mesh at openings without considering a diaphragm action for the slab. *n the second case the slab was modeled using a thin mesh at openings considering the diaphragm action of the slab. or the linear model the equivalent frame method was applied according to Z%.$.5 of the reek !oncrete !ode. The effective width of the slab was calculated based on the equation3 l/ @ bo C )[hs of the reek !oncrete !ode and the mass was considered concentrated at the nodes of the elements. *t has to be noted the fact that the results of analyses using linear elements were more favorable than those using shell elements to model the slabs. *n the present study, only the least favorable results were taken into
account.
Analyses of structural systems have shown that fundamental period is not affected significantly neither by the density of the slab mesh nor by the use of diaphragm action, since the differentiation between the results is no more than &.$K. So the type of thin mesh was adopted along with the use of diaphragm action which provides satisfying results.
.4. RESULTS
The Analy0ed flat-slab structures were assessed by checking the compliance criteria of both *S G I! !odes mentioned above. The checks lead to the acceptance or re9ection of the analy0ed flat-slab structures for the design seismic action. *n the variation of coefficient \ as well as the total seismic actions -a/ial and shear loading for each case- are given correspondingly.
S,-&/( &*(,* ,00,-
!ritical criterion for the acceptance or not of a structural system was found to be the criterion of second order effects. Malues of inter storey drift sensitivity coefficient \, according to analyses of all types of structural systems in question, are shown in ig. D,'8/
After a great number of analyses, serious problems were spotted concerning, specifically, flat slab structures. The crucial ones are3 a4 Due to the slight reduction of behavior factor which is utili0ed, q @ 8 instead of
q @ 8.6, but most importantly due to the absence of strong beams, the stresses of the vertical structural elements and mainly those of the shear walls 2which have a minimal difference compared to vertical cantilevers4 are found to be unusual high. This fact is reflected to the foundation requirements and moreover it brings out the necessity of a greater number 2than usual4 of shear walls to be utili0ed in the framework of the structure in order to achieve a rational resistance of seismic actions.
b4 The necessity for ductile systems to be led e/clusively to a bending type of failure suggests creates the need, in the specific case, that the punching shear resistance, wherever it applies, must be at least over +&K of the corresponding fle/ural resistance in the same position. This over strength can be assured by assuming a behavior factor q @ 8.&?$.+ @ ).$+, which only concerns design of slabs against punching shear. Design of slabs, as well as design of vertical elements, against bending must be done using q@8. c4 *n most cases for punching shear design critical loading is the combination of non L seismic loads only. The seismic load combination is critical where vertical elements are close to each other as well as in the case of slabs which are supported at the edge of shear wall sections or at the corners !-shaped walls 2e.g. walls used for staircases4. *t is notable that the last two cases concern 2are crucial4 more the upper storey;s than the bottom storey.
d4
inally, one indirect confrontation of punching shear related problems in slabs can be achieved by the use of more shear walls in the structural system. Shear walls reduce the earthquake displacements resulting in a reduced punching shear stress on slabs.
;
CONCLUSION
$. lat plate?slab construction is a developing technology in *ndia. lat plate?slab can be designed and built either by conventional I!! or post-tensioning. Eowever, due to issues mentioned above with pt construction in *ndia and its higher cost, conventional rcc should be the preferred choice for spans up to $& meters. ). Design of conventional I!! flat plate?slab in *ndia, utili0ing *ndian codes, has many shortcomings, which have to be addressed and revised soon. #ntil then *ndian engineers will continue to use *ndian codes in combination with other standards to design and analy0e flat slabs?plates. 8. The positive mid-span moment is increasing and negative moment is decreasing when we analy0e the slab with Hquivalent rame (ethod. The negative moment;s section shall be designed to resist the larger of the two interior negative design moments for the span framing into common supports. +. egative G "ositive moments at e/terior support is increases for *S +6'-)&&& for Hquivalent rame (ethod. 6. *n the H/terior support, the total design moments 2( o4 are distributed as $&&K in column strip and &K in middle strip in both the case *S +6'-)&&& G the total design moments 2( o4 are distributed as 56K in column strip and )6K in middle strip. '. *n flat slab 2with G without staggered column4 in both cases the punching shear criteria is satisfy e/cept *nterior columns as per *S +6'
. REFERENCES: $. ".!. Marghese PAdvanced Ieinforced !oncrete DesignQ, prentice hall of *ndia limited, ew Delhi, HHH 2)&&)4. ). ureau of *ndian Standards, ew Delhi, P*S +6'3)&&&, "lain and Ieinforced !oncrete !ode of "racticeQ, ourth Ievision, uly 2)&&&4. 8. (.Anitha, .].Iahman and .Mi9ay, PAnalysis and Design of lat Slabs #sing Marious !odesQ, *nternational *nstitute of *nformation Technology, Eyderabad, April 2)&&54. +.
*ndian Standard *S +6'3)&&&, "lain and Ieinforced !oncrete !ode of "ractice.
6. "urushothaman "., Ieinforced !oncrete Structural Hlements, Tata (craw-Eill "ublication !ompany :td. ew Delhi. $%B+ '. owda harath1 owda S. . Iavishankar1 A.M !handrasekhar, Ieview and Design of lat "late?Slabs !onstruction in *ndia. 5. Structural Design uide to the A!* uilding code, Third edition, Man ostrand Ieinhold !ompany. ew >ork. $%B6.
