Punching Shear Strength of Asymmetrically Reinforced Concrete Slabs
Paper Reinforced Concrete Slabs
Transcript of Paper Reinforced Concrete Slabs
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PAPERREINFORCED CONCRETE SLABS
Randi Mirah
14202109003
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PREFACE
Thank to Almighty God who has given His bless to the writer for finishing the paperassignment entitled Reinforced Concrete Slabs The writer also wish to e!press his deepand sincere gratit"de for those who have g"ided in completing this paper
This paper contains some e!ample of #esign Reinforced Concrete Slabs that can help theviewer to improve knowledge Hopef"lly$ this paper can help the readers to e!pand theirknowledge abo"t Reinforced Concrete Slabs
%anado$ #ecember &'th$ ()&*
A"thor
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INTRODUCTION
Reinforced concrete slabs are "sed in floors$ roofs and walls of b"ildings and as the decks
of bridges The floor system of a str"ct"re can take many forms s"ch as in sit" solid slab$ribbed slab or pre+cast "nits Slabs may span in one direction or in two directions and theymay be s"pported on monolithic concrete beam$ steel beams$ walls or directly by thestr"ct"re,s col"mns
Contin"o"s slab sho"ld in principle be designed to withstand the most "nfavorablearrangements of loads$ in the same manner as beams -eca"se there are greateropport"nities for redistrib"tion of loads in slabs$ analysis may however often besimplified by the "se of a single load case -ending moment coefficient based on thissimplified method are provided for slabs which span in one direction with appro!imatelye."al spans$ and also for flat slabs
The moments in slabs spanning in two directions can also be determined "singcoefficients tab"lated in the code of practice$ -S /&&) Slab which are not rectang"lar in
plan or which s"pport an irreg"lar loading arrangement may be analy0ed by techni."ess"ch as the yield line method or the Helliborg strip method
Concrete slab behave primarily as fle!"ral members and the design is similar to that forbeams$ altho"gh in general it is somewhat simpler beca"se1
& the breadth of the slab is already fi!ed and a "nit breadth of &m is "sed in thecalc"lations$
( the shear stress are "s"ally low in a slab e!cept when there are heavy concentratedloads$ and
2 compression reinforcement is seldom re."ired
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LITERATURE REVIEW
TYPES OF SLABS
Type of slab "sed in constr"ction sectors are3
Solid slab 4lat slab Ribbed slab 5affle slab Hollow block floor6slab
7a8 Solid slab
7b8 4lat slab
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7c8 Ribbed slab
7d8 5affle slab
4ig"re &3 Types of slab
4lat slab floor is a reinforced concrete slab s"pported directly by concrete col"mnswitho"t the "se of intermediary beams The slab may be of constant thicknessthro"gho"t or in the area of the col"mn it may be thickened as a drop panel Thecol"mn may also be of constant section or it may be flared to form a col"mn head
or capital These vario"s form of constr"ction are ill"strated in 4ig"re 2(
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4ig"re (3 #rop panels and col"mn head
The drop panels are effective in red"cing the shearing stresses where the col"mnis liable to p"nch thro"gh the slab$ and they also provide an increased moment ofresistance where the negative moments are greatest
The flat slab floor has many advantages over the beam and slab floor Thesimplified formwork and the red"ced storey heights make it more economical5indows can e!tend "p to the "nderside of the slab$ and there are no beams toobstr"ct the light and he circ"lation of air The absence of sharp corner givesgreater fire resistance as there is less danger of the concrete spalling an e!posingthe reinforcement #eflection re."irements will generally govern slab thicknesswhich sho"ld not be less than &(* mm
Typical ribbed and waffle slab are shown in 4ig"re 2&97c8$ 7d8: Ribbed slabs$which are two+way spanning and are constr"cted with ribs in both direction ofspan Ribbed slab floors are formed "sing temporary or permanent sh"tteringsystem while the hollow block floor is generally constr"cted with block made ofclay tile or with concrete containing a light+weight aggregate ;f the block ares"itably man"fact"red and have an ade."ate strength they can be considered tocontrib"te to the strength of the slab in the design calc"lations$ b"t in manydesigns no s"ch allowance is made
The principal advantage of these floors is the red"ction in weight achieved byremoving part of the concrete below the ne"tral a!is and$ in the case of the hollowblock floor$ replacing it with a lighter form of constr"ction Ribbed and hollowblock floors are economical for b"ildings where there are long spans$ over abo"t *m$ and light or moderate live loads$ s"ch as in hospital wards or apartment
b"ildings They wo"ld not be s"itable for str"ct"res having a heavy loading$ s"chas wareho"ses and garages
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baypanel
as they are stopped off$ there is no abr"pt change in cross+section e!tendingacross the slab The slabs are "s"ally made solid "nder partitions andconcentrated loads #"ring constr"ction the hollow tiles sho"ld be well soaked inwater prior to placing the concrete$ otherwise shrinkage cracking of the topconcrete flange is liable to occ"r
SIMPLIFIED ANALYSIS
-S /&&) permit the "se of simplified load arrangement for all slabs of ma!im"m"ltimate design load thro"gho"t all spans or panels provided that the followingcondition are met1
a8 in one+way slab$ the area of each bay > 2) m(b8 ?ive load$ @k &(* #ead load$ Gkc8 ?ive load$ @k * k
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A
C D
B
lx
ly
l!
l!6(
l!
Beam AC and BD
w = n lx/ 3
E*)
C
A
D
B
E F
ly
l!
E*)
Beam AB and CD
w = n lx/ 6 {3 !l
x/ l
y)2}
LOAD DISTRIBUTION FROM SLAB
#efine the type of slab either one+way direction or two+way direction$ fordetermine the shape of load distrib"tion from slab to beam
;fIy6IxF ( consider as two+way slab Iy6Ix > ( consider as one+way slab
where Ix + length of shorter side Iy + length of longer side
a8 ne+way slab
b8 Two+way slab
-eam A- and C#w = n lx/ "
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4ig"re E3 ?oad distrib"tion of slabS#EAR IN SLAB
The shear resistance of slab may be calc"lated by the proced"res given in -S/&&)$ Cl2**( I!perimental works has indicated that$ compared wit beams$
shallow slab fail at slightly higher shear stresses and this is incorporated into theval"es of design "ltimate shear stress vc7Refer to Table 2$ -S /&&)8 The shearstress at a section in a solid slab is given by1
v = Vb.d
where Vis the shear force d"e to "ltimate load$ dis the effective depth of the slaband b is the width of section considered 7Refer to Table 2&D and Cl 2**(8Calc"lation is "s"ally based on strip of slab &m wide
The -S /&&) re."ires that for solid slab1
& vF )/ J fc"or *
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e."al to at least don either sideCheck sho"ld also be "ndertaken to ens"re that the stress vcalc"lated forthe perimeter at the face of the loaded area is less than smaller of )/ J fc"or *
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service stress of 2)D
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The ma!im"m clear spacing given in Table 22)$ and Cla"se 2&(&&$ -S /&&)$7apply to bars in beams when a ma!im"m likely crack width of )2 mm isacceptable an the cover to reinforcement does not e!ceed *) mm8$ and are similarto beams e!cept that for thin slabs$ or if the tensile steel percentage is small$
spacing may be increased from those given in Table 22)$ -S /&&) to a ma!im"mof the lesser of 2dor D*) mm
c8 Reinforcement in the flange of a T P or ?+-eam5hen the slab from the flange of a T or ? beam the area of reinforcement in theflange and at right angles to the beam sho"ld not be less than )&* percent of thelongit"dinal cross+section of the flange
d8 C"rtailment and anchorage of reinforcement
At a simply s"pported end the bars sho"ld be anchored as specified in 4ig"re 2D
4ig"re D3 Anchorage at simple s"pported for a slab
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E%AMPLES AND DISCUSSION
SLAB DESI$N
SOLID SLABS SPANNIN$ IN ONE DIRECTION
The slabs are design as if they consist of a series of beams of & m breadthThe main steel is in the direction of the span and secondary or distrib"tionsteel re."ired in the transverse direction The main steel sho"ld from theo"ter layer of reinforcement to give it the ma!im"m level arm
The calc"lations for bending reinforcement follow a similar proced"re tothat "sed in beam design The lever+arm c"rve of 4ig"re 2/ is "sed todetermine the lever arm 7!8 and the area of tension reinforcement is thengiven by1
As= "#/ 0.$% fy.!
4or solid slabs spanning one way the simplified r"les for c"rtailing bars asshown in 4ig"re 2 may be "sed provided the loads are s"bstantially"niformly distrib"ted 5ith a contin"o"s slab it is also necessary that thespans are appro!imately e."al the simplified single load case analysis has
been "sed
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The Q val"es on the a!is mark the limitfor singly reinforced sections with momentredistrib"tion applied
4ig"re /3 ?ever+arm
4ig"re 3 Simplified r"les for c"rtailment of bars in slab spanning in onedirection
S&m'() S*''+,-ed S+(&d S(a.
The effective span of the slab is taken as the lesser of3
a8 The centre+to+centre distance of the bearings$ or
b8 The clear distance between s"pports pl"s the effective depth of the slab
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The basic span+effective depth ratio for this type of slab is ()3& 7Refer toTable 2&) and Cl 2E'2 in -S /&&)8
Eam'(e 0
The slab is to be design to carry a live load 2) k
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4rom Table 2&& -S /&&)$ forfsN 2)D v ? v > :+ n+ :@ea, ,e&n+,emen- &:
,e;*&,ed
*
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anchorage length K 2) mm or end bearing 7s"pport width862
end bearing N (2) mm
Therefore1
an@+,ae (en-@ = "39 / 3 = mm 39 mm
beyond the centre line of the s"pport
4ig"re &)3 Ind Anchorage
6* srb#o, / >ra,sverse eel
4rom Table 2(D -S /&&)$fyN E') -+' (a)e,
?* @rac, chec
The bar spacing does not e!ceed D*) mm or 2 d and theminim"m reinforcement is less than )2Q 7Refer Cl2&(&&(D and Table 22)$ -S /&&)8
Allowable clear spacing of bars N 2dN 27&/)8 N *E) mm
A-*a( (ea, :'a&n = "19 89 = "49 mm ? 3d +7
C+n-&n*+*: S+(&d S(a.
4or a contin"o"s slab$ bottom reinforcement is re."ired within the span
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and top reinforcement over the s"pports The effective span is the distancebetween the centre lines of s"pports The basic span+effective depth ratio is('3& 7Refer to Table 2&) and Cl 2E'28
;f the simplified load arrangement for all slabs of ma!im"m "ltimate
design load thro"gho"t all spans or panels provided that the followingcondition are met for the single load case analysis$ bending moment anshear forces coefficients as shown in Table 2&2$ -S /&&) may be "sed
Eam'(e 0
The fo"r+span slab shown in 4ig"re 2&& s"pport a live load )f 2)k
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4or & meter width of slab1
Vltimate loadB C = (1. + 1.?q* .6
N 7&E ! */ L &' ! 2)87E*8
F= 184 7N 'e, me-,e w&d-@
1* e,d, (Defer o @E 3.6.2.3B $110*
ince the bay si0e K 2)m($ the spans are e."al and .kF &(* gk themoment coefficients shown in Table 2&2 -s /&&) may be "sedTh"s$ ass"ming that the end s"pport is simply s"pported$ from Table
2&2 for the first span3" = 0.0$?CE N 7))/' ! */&E 87E*8 N ((* k
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Similar calc"lation for the s"pport and the interior span give thesteel areas shown in 4ig"re 2&(
3* srb#o, / >ra,sverse eel
4rom Table 2(D -S /&&)$fy N E') able 3.13 $110*
Shear$ V = 0.? C N )' 7*/&E8 N 2E k