Evaluation of Design Provisions for One-Way Solid Slabs in SBC-304
Hassan M. Alamri1 , Tariq M. Nahhas2 , Hamdy Elgohary31Engineer, Dept. of Civil Engineering, College of Engineering, Umm Al Qura University, Makkah, Saudi Arabia
2 Professor, Dept. of Civil Engineering, College of Engineering, Umm Al Qura University, Makkah, Saudi Arabia
3 Professor, Dept. of Civil Engineering, College of Engineering, Umm Al Qura University, Makkah, Saudi Arabia
Abstract - Buildingcode's minimumthicknessprovisionsfor concrete members, are generally used in engineeringpractice to comply with the serviceability requirements without prediction of the expected deflection under service circumstances. However, concerns have beenraised aboutthe effect that the 50 year old provisions in ACI 318 (American Concrete Institute) [1] and SBC 304 (Saudi Building Code) [2] have in controlling slab deflections within the allowable values, predicting the deflection serviceability of reinforced concrete members is fraught with uncertainties.
This study aims to evaluate the effect of the parameters that affected on thedesign of one waysolidslabandnotconsidered in the span to depth ratio provided in the SBC Code. These parameters are, live load, concrete modulus of elasticity (which is a function of concrete compressive strength) and reinforcing steel yield strength. A parametric study has been carried out to study the effect of the above mentioned parameters on the effect of the span to depth ratio and the predicted deflection. On the bases of this parametric study a new modified span to depth ratio relation is recommended, in which all affecting parameters have been included. The proposed formula has been verified for a practical range of one way slab design. Results of this verification show that the recommended formula gives more economic and safe design for both ultimate strength and serviceability limit states.
slab.Limitsondeformationweresetmanydecadesago.To justifytheneedtomodifytheCodeprovisions,andenable moresustainableandeconomicdesigns,knowledgeofthe backgroundtocurrentlimitsandofcurrentperformanceis needed.Partofthatistoreviewtheresentstudiescarried outinthelastyears.
1. INTRODUCTION
This Most current codes provide two approaches for deflectioncontrol.Firstapproachrecommendsamaximum limitforspantodepthratiodependingonelementtypeand boundary conditions. While in the other approach, the designermaychooseadifferentdepthvalueandthencheck fordeflection.
TheSBC 304Codeprovidesminimumthicknessvaluesfor one waysolidslabs(similartoACI 318),underprescribed conditions,asafunctionofspanlength,boundaryconditions, and steel yield strength as a basis for deflection control. Deflectionofone waysolidslabsisaprincipalcriterionin design, it governs thickness, which in turn has a large economicimpact.Deflectionisusuallycontrolledbylimiting thespantodepthratio.Thisresearchevaluatesthehistory ofthespan to depthmethodofdesignintheone waysolid
Youngetal.(2010),[3]pointedoutthattheseprovisions have remained essentially unchanged since 1971 and are appealingduetotheirsimplicity.Severalauthorshaveraised questions and criticism about the validity of the current provisions in ACI 318 and SBC 304 under certain design conditions (Grossman 1981[4]; Rangan 1982[5]; Gilbert 1985[6]; Hwang and Chang 1996[7]; Scanlon and Choi 1999[8];Scanlonetal.2001[9];Bondy2005[10]).Younget al.(2010)showedtheeffectsofdesignparameterssuchas spanlength,supportconditionandvalueofappliedloadare evaluated. The results indicated that ACI 318 (SBC 304) provisionsneedtoberevisedtoconsidertherangeofdesign parametersthatare prevalentin these days practicesand the parametric study found that while these minimum thickness values are easy to apply, limitations need to be placedontheapplicabilityofthecurrentCodes.Theresults presentedinAndrewetal.(1999),[11]studyindicatethat theminimumthicknessvaluesgiveninACI318(SBC 304) are conservative for slabs not supporting nonstructural elementslikelytobedamagedbylargedeflectionsforspan lengthsusuallyfoundinbuildingstructures.Authorshave arrivedatthisconclusioneitherbyanalyzingafewamounts of field data (Rangan and McMullen 1978),[12] or after conductingfullparametricstudies(ScanlonandThompson 1990[13]; Lee and Scanlon 2010[14]). Moreover, some of them have proposed other provisions that include an allowancefortheactualloadlevels,concreteproperties,and deflectionlimits,reportingintheendthattheygivebetter resultsthancodeprovisionsforthatsamedata.Elgoharyet al.(2021),[15],carriedoutacomparisonbetweenACI 318 (SCB 304)andEgyptianCodeECP 203.Theyconcludedthat thespantodepthratioinACI 318ismoreconservativeand always gives overdesigned slab thickness. Using a larger valueofthespantodepthratioasinECP 203[16]leadsto more efficient design with 10% saving in the overall self weightofthebuilding.
Key Words: one waysolidslabs,deflection,spantodepth ratio,SaudiBuildingCodeInternational 2395-0056 09 Issue: 04
2. ONE WAY SLAB PROVISIONS IN SBC 304
InSBC 304theminimumthicknessvaluesareindependentof appliedloadsand/orconcretemodulesofelasticity(concrete compressivestrength).Modificationfactorsareprovidedfor steelyieldstrengthfyandlightweightconcrete.Spantodepth ratio provided in the Code enables designers to initial estimatetheslabthicknessthatwillcontroldeflectiontobe within the code limits. To show to which level these provisions are very conservative an initial study is performed. In this study, one way simply supported solid slabswithpracticalrangeofspan(from2.0to5.2m)andlive load (from 2.0 to 5.0 KN/m2) according to Nadim, H., Al Manaseer, A., (2015),[17] will be considered. Additional imposed dead load (weight of finishing floor materials) is taken 2.0 KN/m2. The concrete compressive strength is chosen21and30MPa,andsteelyieldstrengthequals420 MPa.Foralltheseslabstheinstantaneousdeflectiondueto live load and long term deflection have been determined. Figures 1 and 2 represent the relationship between short spanoftheslabandinstantaneousdeflectionduetoliveload, forthetwocasesofconcretestrength,respectively.Thecode limit(L/360)isalsoshowninthesefigures. It'sclearthatthe predicteddeflectionistoosmallcomparedtothecodelimit. Forconcretestrengthfc'=21Mpaandspan=5.2m,thecode limitis3.3timesthepredicteddeflectionforthecaseoflive load=5kN/m2,whileitis23.9forthecaseofliveload=2 kN/m2.Forconcretestrengthfc'=30Mpaandspan=5.2m, the code limit is 8.2 times the predicted deflection for the caseofliveload=5kN/m2,whileitis28.6forthecaseoflive load=2kN/m2.
Charts3and4representthesamerelationshipforthecaseof concretestrengthfc'=21and30MPa.Thecodelimit(L/240) isalsoshowninthesecharts.
Chart -1: SlabSpan-InstantaneousDeflectionrelationship forfc'=21Mpa
Chart 3: SlabSpan Long termDeflectionrelationshipfor fc'=21Mpa
Chart 2: SlabSpan InstantaneousDeflectionrelationship forfc'=30Mpa
Chart 4: SlabSpan Long termDeflectionrelationshipfor fc'=30Mpa
Forconcretestrengthfc'=21Mpaandspan=5.2m,thecode limitis2.3timesthepredicteddeflectionforthecaseoflive load = 5kN/m2, while it is 6.5 for the case of live load=2 kN/m2.Forconcretestrengthfc'=30Mpaandspan=5.2m, the code limit is 3.6 times the predicted deflection for the caseofliveload=5kN/m2,whileitis7.8forthecaseoflive load=2kN/m2.
Thethicknessofone wayslabspredictedusingspantodepth ratioprovisionsofSBC 304leadtoaverysafedeflection.The largeslabthicknessobtainedusingcoderelationsleadstoa significantincreaseindeadloadsofslabandconsequentlyon theloadsofsupportingelements.Itisessentialtoestablisha modified span to depth ratio for one way slab design and deflection control considering all affecting parameters for moreefficientdesign.
3. PARAMETRIC STUDY
Theobjectivesoftheparametricstudyaretoinvestigatethe effect of all parameters affecting the deflection calculation andtodeterminemodifiedspantodepthratiorelationthat will give more efficient design. The deflection of concrete elementsdependsontheappliedliveload,span,modulusof elasticity(concretecompressivestrength)andtheyielding strengthofreinforcingsteel.Fortheparametricstudyandto
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coverthepracticalrangethefollowingparametershavebeen consideredasfollows:
Liveloadischosenequals(L.L.)2.0;2.5;3.0;3.5;4.0;4.5;5.0 KN/m2
Slabshortspanistaken(L)2.0;2.8;3.6;4.4;and5.2m
Concretecompressivestrengthischosen(fc')21;23;25;28; 30;35MPa
Reinforcingsteelyieldstrength(fy)istakenas280and420 MPa
Spantodepthratioisselectedas20;22;24;26;28;and30
Forthese2520slabmodel,theinstantaneousdeflectiondue toliveloadandlong termdeflectionhavebeendetermined andcomparedwiththecodelimitof(L/360)and(L/240), respectively. Selected results of the parametric study are showningraphspresentedinCharts5to18
3.1 Effect of Live Load
The effect of live load on the predicted deflection, for the boundary cases of the parametric study, is presented in Charts 5 to 12. The relationships between instantaneous deflection due to live load and the value of live load for differentspantodepthratiosarepresentedinFigures5to8, whileforlong termdeflectioninCharts9to12.Ingeneral deflectionisnonlinearlydirectlyproportionalwiththevalue of live load. For most cases the predicted deflections are withinthecodelimits,exceptforthecasesofhighvaluesof spantodepthratio,liveload,andspan.
Chart 6: ImmediateDeflection LiveLoadRelationship forConcreteCompressiveStrength=30Mpaandspan=2m
Chart 7: ImmediateDeflection LiveLoadRelationshipfor ConcreteCompressiveStrength=21Mpaandspan=5.2m
Chart 5: ImmediateDeflection LiveLoadRelationship forConcreteCompressiveStrength=21Mpaandspan=2m
Chart 8: ImmediateDeflection LiveLoadRelationshipfor ConcreteCompressiveStrength=30Mpaandspan=5.2m
Chart 9: Long TermDeflection LiveLoadRelationshipfor ConcreteCompressiveStrength=21Mpaandspan=2m
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Chart 10: Long TermDeflection LiveLoadRelationship forConcreteCompressiveStrength=30Mpaandspan=2m
Chart 13: ImmediateDeflection SlabShortSpan RelationshipforConcreteCompressiveStrength=30Mpa andspan=3.5m
Chart 11: Long TermDeflection LiveLoadRelationship forConcreteCompressiveStrength=21Mpaandspan= 5.2m
Chart 14: Long TermDeflection SlabShortSpan RelationshipforConcreteCompressiveStrength=30Mpa andspan=3.5m
3.3 Effect of Concrete Compressive Strength
Chart 12: Long TermDeflection LiveLoadRelationship forConcreteCompressiveStrength=30Mpaandspan= 5.2m
3.2 Effect of Slab Short Span
Theeffectofslabshortspanonthepredicteddeflectionis presented in Charts 13 and 14. It is encountered that deflectionisnonlinearlydirectlyproportionaltoslabshort span.Similarly,formostcasesthepredicteddeflectionsare withinthecodelimits,exceptforthecasesofhighvaluesof spantodepthratio,liveload,andspan.
Theeffectofconcretecompressivestrengthonthepredicted deflectionispresentedinCharts15and16.Itisclearthat, deflectionisnonlinearlyinverselyproportionaltoslabshort span.Formostcasesthepredicteddeflectionsarewithinthe code limits, except for the cases of high values of span to depthratio,liveload,andspan.
Chart 15: ImmediateDeflection ConcreteCompressive StrengthRelationshipforLiveLoad=4kN/m2 andspan= 5.2m ISO
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Chart 16: Long TermDeflection ConcreteCompressive StrengthRelationshipforLiveLoad=4kN/m2 andspan= 5.2m
3.4 Effect of The Reinforcing Steel Yielding Strength
The effect of yield strength of reinforcing steel on the predictedinstantaneousandlong termdeflectionisshownin Charts17and18,respectively.Theserelationsshowthatthe yieldstrengthhasinsignificanteffectonthedeflection.
Chart -19: RelationbetweenexactL/handLiveLoad, kN/m2
Chart 20: RelationbetweenexactL/handShortSpan,m
Chart 17: ImmediateDeflection SteelYieldStrength RelationshipforLiveLoad=2kN/m2 andspan=2m
Chart -18: Long TermDeflection SteelYieldStrength RelationshipforLiveLoad=2kN/m2 andspan=2m
4. MODIFIED SPAN TO DEPTH RATIO
Inthissectionanalysishasbeenconductedtotheresultsof 2780modelstofigureoutenhancedspantodepthformulae formoreeconomicandefficientdesignfortheone waysolid slabs. Obtaining the intersection between code limits and results of the values of parameter studied gives the exact spantodepthratio.
RelationsbetweentheexactspantodepthratioL/handthe parameterstudied(LiveLoadLL,spanLengthLandconcrete compressivestrengthfc')arepresentedinCharts19to21.
Chart 21: RelationbetweenexactL/handconcrete compressivestrength, fc',Mpa
Asshownfromthepreviouschartstherelationis:
RelationbetweenL/handLLisinversenonlinearly proportion.
RelationbetweenL/handLisinversenonlinearly proportion.
Relation between L/h and fc' is direct nonlinearly proportion. 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal
International Engineering Technology e-ISSN: 2395-0056 09 Issue: 04 2022 2395-0072
From the previous relations of span to depth ratio and differentparameterstheequationformatshouldbe: where,
L/h Spantodepthratio
C1,C2,C3andC4 Constantvalues
fc' Concretecompressivestrength,Mpa
L Spanlength.m
LL Liveload,kN/m2
Applyingnonlinearregressionanalysis(IBMSPSSStatistics 26, (2019),[18] on the obtained results relating the exact values of the span to depth ratio, to the parameters the followingequationforyieldstrengthof420Mpawillhasthe form:
Chart 22: Effectoffyonlowerandhighervaluesofthe practicalrang
5. VERIFICATION OF THE RESULTS
Toverifytheresultoftheproposedequation,fiveslabmodels have been designed using the proposed equation and the SBC 304equation.ResultsareshowninTable 1forthecase of steel yield strength 420 MPa. For all models, predicted deflections are within the code limit. The slab thickness reduces by 38.9 % for models 1 and 2; and by 25% for models3and4.Thesameresultsobtainedandpresentedin Table 2 for the case ofsteel yieldstrength 280MPa, using equation(2)(equationforfy=420MPa).
Forthecaseofsteelyieldstrength280MPa,willhavethe form:
Table 1: Comparisonbetweenproposedequationandthe code'sequationoffy=420Mpa
Fordifferentvaluesofyieldstrengthfyamodifiedequation shouldbecreated.Forthispurpose,theeffectoffyhastobe understood using the previous equations. The following equationistheratioofequation(3)toequation(2):
Table 2:Comparisonbetweenproposedequationandthe code'sequationoffy=280Mpa
Applying the ratio equation (4) for lower bounds of the practical (span L=2 m, live load LL=2 kN/m2) and for the upperbound(spanL=5mandliveloadLL=5kN/m2)gives thegraphshowninChart22.Theratioforbothboundaries, isaroundtheunity.Thesteelyieldstrengthhasinsignificant effectonthespantodepthratioforone waysolidslabs.The modifierforsteelyieldstrengthprovidedinSBC 3.4,needs toberevised.Equation(2)isapplicablefordifferentvalues ofyieldstrength.
6. CONCLUSIONS
Spantodepthratioprovisionsforone waysolidslabdesign, presented in SBC 304 (ACI 318) always give very conservativevaluesofslabthickness.
UsingSBC 304 provisionstodetermine the slabthickness leadstolargervaluesofthicknessandconsequentlyincrease the own weight of the slab and loads on all supporting elements.
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Amodifiedproposedequationforthespantodepthratiois recommended for more efficient design of one way solid slab.
Theresultsofthedesignusingtheproposedequationshow moreeconomicaldesignwithsafedeflection.
Thecurrentstudyprovesthatthereinforcingsteelyielding hasinsignificanteffectonthespantodepthratioinone way solidslabdesignandcanbeneglected.
REFERENCES
[1] ACICommittee318,2019,“BuildingCodeRequirements for Structural Concrete (ACI 318) and Commentary,” AmericanConcreteInstitute,FarmingtonHills.
[2] SBC 2018 Saudi building code for construction (SBC 301 306)
[3] YoungHakLeeandAndrewScanlon,2010Comparison of One and Two Way Slab Minimum Thickness Provisions in Building Codes and Standards, ACI StructuralJournal,April
[4] Grossman, J. S., 1981, “Simplified Computations for EffectiveMomentofInertia,IeandMinimumThickness toAvoidDeflectionCalculations,”ACIStructuralJournal, V.78,No.6,Nov. Dec.,pp.423 439.
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[7] Hwang,S. J.,andChang,K. Y.,1996,“DeflectionControl of Two Way Reinforced Concrete Slabs,” Journal of StructuralEngineering,ASCE,V.122,No.2,pp.160 168.
[8] Scanlon,A.,andChoi,B. S.,1999,“EvaluationofACI318 MinimumThicknessRequirementsforOne WaySlabs,” ACIStructuralJournal,V.96,No.4,July Aug.,pp.616 621.
[9] Scanlon, A.; Cagley Orsak, D. R.; and Buettner, D. R., 2001, “ACI 318 Code Requirements for Deflection Control: A Critical Review,” Code Provisions for DeflectionControlinConcreteStructures,SP 203,E.G. NawyandA.Scanlon,eds.,AmericanConcreteInstitute, FarmingtonHills,MI,pp.1 13.
[10] Bondy, K. B., 2005, “ACI Code Deflection Requirements Time for a Change?” Serviceability of Concrete:ASymposiumHonoringDr.EdwardG.Nawy, SP 255, F. Barth, ed., American Concrete Institute, FarmingtonHills,MI,pp.133 146.
[11] AndrewScanlonandBong SeobChoi,EvaulationofACI 318 Minimum Thickness Requirements for One Way Slabs,ACIStructuralJournal,Aug1999
[12] Rangan, B. V., and McMullen, A. E., 1978, “A Rational Approach to Control of Slab Deflections,” ACI Journal Proceedings,V.75,No.6.
[13] Thompson, D. P., and Scanlon, A., 1988. “Minimum ThicknessRequirementsfor Control ofTwo WaySlab
Deflections,ACIJOURNAL,Proceedings,V.85,No.1,Jan. Feb.,pp.12 22
[14] Scanlon,A.,andLee,Y.H.,2006,“UnifiedSpan to Depth RatioEquationforNonprestressedConcreteBeamsand Slabs,”ACIStructuralJournal,V.103,No.1,Jan. Feb.,pp. 142 148
[15] Hamdy Elgohary., Abdulghafour Osama., and AbdulghafourAbdulrazak 2021“OptimumDesignand Efficiency of One Way Slab According to ACI“ International Research Journal of Engineering and Technology(IRJET)Vlume:08Issue:04 Apr2021
[16] Egyptian Code for Reinforesment Concrete Structures (ECP 203)2018,HousingandBuildingResearchCenter, Cairo,Egypt.
[17] Nadim,H.,Al Manaseer,A.,2015,Structural Concrete: TheoryandDesign6thEdition,JohnWiley&Sons,Inc., Hoboken,NewJersey.
[18] IBMSPSSStatistics 26,2019.,Chicago,IL
Authors
Hassan Mohammed Alamri1 h.m.alamri1994@gmail.com
Tariq M. Nahhas2 tnahhas@hotmail.com Hamdy Elgohary3 Gohary_h@yahoo.com
