-
Lectures on Reinforced Concrete Design: Lecture 1
INTRODUCTION
BYBYDr.A.W.HAGO
-
Reinforced ConcreteReinforcedConcrete
Reinforcedconcreteisastrongdurablebuildingmaterialthatcanbeformedinto
many varied shapes and sizes (flexible in
shaping)manyvariedshapesandsizes(flexibleinshaping).
Itsutilityandversatilityareachievedbycombiningthebestfeaturesofconcrete
andsteel.C i th diff i ti f th t t i l
Comparingthedifferingpropertiesofthesetwomaterials:
Property Concrete Steel
strength in tension poor goodstrengthintension poor good
strengthincompression good good,butslenderbarswillbuckle
strengthinshear fair goodg g
Durability good corrodesifunprotected
fireresistance good poor
suffersrapidlossofstrengthathightemperatures
It can be seen from this list that the materials are
complementary. when they are combined, the steel is able to provide
the tensile strength and y gprobably some of the shear strength,
while the concrete, strong in compression, protects the steel to
give durability and fire resistance.
-
CompositeAction1. The tensile strength of concrete is about 10
%of its compressive strength.2. For this reason, reinforced
concrete structures are designed assuming
concrete does not resist any tensile forces.3. Reinforcing steel
bars are designed to carry tensile forces, which are
transferred by bond between the two materials (composite
action).4. Inadequate bond causes reinforcing bars to slip (no
composite action).5. Bond improves by compacting concrete around
the the reinforcement, and
some bars are ribbed or twisted so that there is an extra
mechanical grip.6. with perfect bond, the strain in the
reinforcement is identical to the strain in the
dj t tadjacent concrete.7. when tension occurs, cracking of
concrete will take place. Reinforcement will
restrain the cracking of concrete8 When compressive or shearing
forces exceed the strength of the8. When compressive or shearing
forces exceed the strength of the
concrete, steel reinforcement must also be provided to
supplement the load-carrying capacity concrete.
-
Stress Strain RelationsStressStrainRelations
Stress
f67.0
Stress
cuf67.0
Steel
002.0 Strain
ConcreteConcrete
-
IdealizedStressstrainCurveforConcrete
Fordesignpurposes,thetypicalstressstraincurveforconcreteisgiven
below
5.1mod'
factorsafetyMaterialulussYoungE
strengtheCompressivf
m
cu
ff ym
EcEco=
-
Stress strain relations for SteelStressstrainrelationsforSteelS
l h l i i i d i Steelhasequalpropertiesintensionandcompression
YoungsmodulusEs=200kN/mm2
Becauseofitsgoodductility,itisassumedfordesignpurposestohavenolimitingstrain.
Gradesofsteelare:460N/mm2 and250N/mm2
Es
051mod'
f tf tM t i lulussYoungE
strengthYieldf y
05.1 factorsafetyMaterialm
-
MaterialsSpecificationforDesign:Concrete
Theselectionofthetypeofconcreteisgovernedbythestrengthrequired.
Theconcretestrengthisassessedbymeasuringthecrushingstrengthofcubesor
cylinders of concrete made from the mix These are usually cured
and
testedcylindersofconcretemadefromthemix.Theseareusuallycured,andtestedaftertwentyeightdaysaccordingtostandardprocedures.
Concreteofagivenstrengthisidentifiedbyits'grade'.AgradeC25
concretehasa characteristic cube crushing strength of 25
N/mm2acharacteristiccubecrushingstrengthof25N/mm2
TheTablebelowshowsalistofcommonlyusedgradesandalsothelowestgradeappropriateforvarioustypesofconstruction.
Exposureconditionsanddurabilitycanalsoaffectthechoiceofthemixdesignandthegradeofconcrete,e.gastructuresubjecttocorrosiveconditionsinachemicalplantwouldrequireadenserandhighergradeofconcretethantheinterior
b f h l ffi bl kmembersofaschoolorofficeblock.Grade
Lowestgradeforuseasspecified
C7.5,C10 Plainconcrete
C15,C20 Reinforced concretewithlightweightaggregate
C25,C30 Reinforced concretewithdenseaggregate
C35 Concretewithposttensionedtendons
C40,C50,C60 Concretewithpretensionedtendons
-
MaterialsSpecificationforDesign:Steel1.
Reinforcingsteelissuppliedinformofbars.Thesecanbeclassified
accordingtotheirmanufacturingprocessinto:) Mild l b (H ll d) i h
i ld h f 250 N/ 2a) Mildsteelbars(Hotrolled)withyieldstrengthfy
=250N/mm2
b) Highyieldbars(Hotrolled&coldworked)withyieldstrengthfy
=460N/mm2/
2.
Thenominalsizeofabaristhediameterofanequivalentcirculararea.3.
Hotrolledmildsteelbarsusuallyhaveasmoothsurface.4.
Highyieldbarsaremanufacturedeitherwitharibbedsurface(Type2)or
intheformofatwistedsquare(Type1).Squaretwistedbarshaveinferiorbondcharacteristicsandaremoreorlessobsolete.
5.
Floorslabs,walls,shellsandroadsmaybereinforcedwithaweldedfabricofreinforcement,suppliedinrollsandhavingasquareorrectangular
meshrectangularmesh.
6.
Thebartypesarecommonlyidentifiedindesignsbythefollowingcodes:R=mildsteel;Y=highyielddeformedsteel,typeI;
T=highyielddeformedsteel,type2;
-
Objectives oftheDesignofReinforcedConcreteStructures
Everystructurehasitsform,functionandaesthetics.y f ,
fNormallythearchitects willtakecareofthemandthestructuralengineers
willbesolelyresponsibleforthestrengthandsafetyofthestructure.However,therolesofarchitectsandstructuralengineersareverymuchinteractiveto
produce a good designtoproduceagooddesign.
The objectives of the design are as
follows:Theobjectivesofthedesignareasfollows:
-
Objectives of the Design of R.C. Structures
1 The structures so designed should have an acceptable
probability of1.
Thestructuressodesignedshouldhaveanacceptableprobabilityofperformingsatisfactorilyduringtheirintendedlife.
2.
Thedesignedstructureshouldsustainallloadsanddeformwithinlimitsforconstructionanduse.Adequatestrengthsandlimiteddeformationsarethetworequirementsofthedesignedstructure.Thestructuresshouldgivesufficientwarningtotheoccupantsandmustnotfailsuddenly.
3.
Thedesignedstructuresshouldbedurable.Thematerialsofreinforcedconcretestructuresgetaffectedbytheenvironmentalconditions.Thedesigned
structures therefore must be checked for
durabilitydesignedstructures,therefore,mustbecheckedfordurability.
4.
Thedesignedstructuresshouldadequatelyresisttotheeffectsofmisuseandfire.Properlydesignedstructuresshouldallowsufficienttimeandsaferouteforthepersonsinsidetovacatethestructuresbeforetheyactuallycollapse.
-
Methods of DesignMethodsofDesign
Designobjectivescanbefulfilledbyunderstandingthestrengthanddeformation
characteristics of the materials used in the design as also
their
deteriorationcharacteristicsofthematerialsusedinthedesignasalsotheirdeteriorationunderhostileexposure.
Thenecessaryinformationregardingpropertiesandstrengthofthesematerialsare
available in the standard codes of practices It is necessary to
follow
theseareavailableinthestandardcodesofpractices.Itisnecessarytofollowtheseclearlydefinedstandardsformaterials,production,workmanshipandmaintenance,andtheperformanceofstructuresinservice.Thecodeofpracticeused
in this course is BS8110 The structural use of
concreteusedinthiscourseisBS8110Thestructuraluseofconcrete.
Theknownmethodsofdesignofreinforcedconcretestructuresare:1.
Thepermissiblestressmethodinwhichultimatestrengthsofthematerials
are divided by a factor of safety to provide design stresses
which are usuallyaredividedbyafactorofsafety
toprovidedesignstresseswhichareusuallywithintheelasticrange.
2.
Theloadfactormethodinwhichtheworkingloadsaremultipliedbyafactorf f
tofsafety.
3.
Thelimitstatemethodwhichmultipliestheworkingloadsbypartialfactorsofsafetyandalsodividesthematerials'ultimatestrengthsbyfurtherpartialf
f ffactorsofsafety
BS8110isbasedontheLimitstatemethod.
-
Design
StepsDesignStepsInanymethodofdesign,thefollowingarethecommonstepsto
b f ll dbefollowed:1.
Toassessthedeadloadsandotherexternalloadsand
f lik l t b li d th t tforceslikelytobeappliedonthestructure,2.
Todeterminethedesignloadsfromdifferent
combinations of loads Initial member sizing is
neededcombinationsofloads.Initialmembersizingisneededforthisstep,
3 To estimate structural responses (bending moment shear3.
Toestimatestructuralresponses(bendingmoment,shearforce,axialthrustetc.)duetothedesignloads(Analysis),
4.
Todeterminethecrosssectionalareasofconcretesectionsandamountsofreinforcementneeded.
5. Preparationofdrawings
showingthedetailsofthedesignedstructure
-
LOADSANDFORCESThe following are the different types of loads and
forces acting on the structure. Their values
can be assessed based on earlier data and experiences (provided
by Codes of Practice):1 Dead loads: These are the self weight of
the structure to be designed The1. Dead loads: These are the self
weight of the structure to be designed. The
dimensions of the cross section are to be assumed initially
which enable to estimate the dead loads from the known unit weights
of the materials of the structure. The values of unit weights of
the materials are provided by the Code of Practicevalues of unit
weights of the materials are provided by the Code of Practice.
2. Imposed loads: They are also known as live loads and consist
of all loads other than the dead loads of the structure. The values
of the imposed loads depend on the functional requirement of the
structure Residential buildings will have comparativelyfunctional
requirement of the structure. Residential buildings will have
comparatively lower values of the imposed loads than those of
school or office buildings.
3. Wind loads: These loads depend on the velocity of the wind at
the location of the structure permeability of the structure height
of the structure etcstructure, permeability of the structure,
height of the structure etc.
4. Snow loads: These are important loads for structures located
in areas having snow fall, which gets accumulated in different
parts of the structure depending on projections height slope etc of
the structureprojections, height, slope etc. of the structure.
5. Earthquake forces: Earthquake generates waves which move from
the origin of its location (epicenter) with velocities depending on
the intensity and magnitude of the
th k Th i t f th k t t d d th tiff f thearthquake. The impact of
earthquake on structures depends on the stiffness of the structure,
stiffness of the soil media, height and location of the structure
etc.
-
Analysis of StructuresAnalysisofStructures
Structureswhensubjectedtoexternalloads(actions)haveinternalreactionsintheformofbendingmoment,shearforce
axial thrust and torsion in individual
membersforce,axialthrustandtorsion inindividualmembers.
Thestructuredevelopsinternalstressesandundergodeformations.deformations.
Essentially,weanalysethestructureelastically
replacingeachmemberbyaline(withElvalues)andthendesignthesectiony (
) gusingconceptsoflimitstateofcollapse.
Theexternalloadstobeappliedonthestructuresarethedesignloadsandtheanalysesofstructuresarebasedonlinearelastictheory.
-
LimitStateMethodofDesign
What are limit states?Limit states are the acceptable limits for
the safety andserviceability requirements of the structure before
failureoccurs.The design of structures by this method will thus
ensurethat they will not reach limit states and will not
becomeunfit for the use for which they are intendedunfit for the
use for which they are intended.
It is worth mentioning that structures will not just fail orIt
is worth mentioning that structures will not just fail orcollapse
by violating (exceeding) the limit states. Failure,therefore,
implies that clearly defined limit states ofstructural usefulness
has been exceededstructural usefulness has been exceeded.
-
There are two main limit
states:Therearetwomainlimitstates:(i)limitstateofcollapse
(Ultimatelimitstate)and(ii)limitstateofserviceability.( ) y
-
MainLimitStates
1. Limit state of collapse deals with the strength andstability
of structures subjected to the maximum designloads out of the
possible combinations of several types ofloads. Therefore, this
limit state ensures that neither any, ypart nor the whole structure
should collapse or becomeunstable under any combination of expected
overloads.
2. Limit state of serviceability deals with deflection
andcracking of structures under service loads, durabilityg yunder
working environment during their anticipatedexposure conditions
during service and stability of thestructure as a whole.structure
as a whole.
-
Other Limit StatesOtherLimitStates1.
Excessivevibrationswhichmaycausediscomfortoralarmor
ddamage2. Fatigue: mustbeconsideredifcyclicloadingislikely3.
Fireresistance thismaybeconsideredintermsof
resistancetocollapse,flamepenetrationandheattransfer4 S i l i t
lik th k i t4. Specialcircumstanceslikeearthquakeresistance
The usual procedure is to decide which is the crucial limit
state and base the design on it, then check to ensure that other
limit states are satisfied.
-
Characteristic Material StrengthCharacteristicMaterialStrength
Thestrengthsofmaterialsuponwhichdesignisbasedarecalled
characteristicstrengths. Acharacteristicstrengthisonebelowwhichl
l k l f llresultsareunlikelytofall.
Assumingnormaldistribution,thecharacteristicstrengthforconcreteistakenasthatvaluebelowwhichitisunlikelythatmorethan5
oftheyresultswillfall,andthatisgivenby:
sff 641 sff mk 64.1where :fk = the characteristic strength,fm =
the mean strength and s = the standard deviation.
-
CharacteristicLoadsWhatismeantbycharacteristicload?Characteristicloadisthatloadwhichhasa95%probabilityofnotbeingexceeded
during the life of the
structure.Theloadsarepredictedbasedonstatisticalapproach,whereitisassumedthatthevariationoftheloadsactingonstructuresfollowsthe
l di ib i Ch i i l d h ld b h h
exceededduringthelifeofthestructure.
normaldistributionCharacteristicloadshouldbemorethantheaverage/meanload
Characteristicload=Averageload+1.64(standarddeviationforload)The
characteristic dead, imposed and wind loads have the notation Gk,
Qk, Wkrespectively.
-
Design Strengths of MaterialsDesignStrengthsofMaterials We
obtain the design strengths of the materials by dividing the
characteristic strengths by the partial safety factor , i.e. mg
y p y ,
takes account of possible differences between the material in
the actualstructure and the strength derived from test specimens In
concrete this
mkfstrengthdesign /m
mstructure and the strength derived from test specimens. In
concrete, thiswould cover such items as insufficient compaction,
differences in curing,etc. For reinforcement it would cover such
items as the difference betweenassumed and actual cross-sectional
areas caused by rolling tolerances,assumed and actual cross
sectional areas caused by rolling tolerances,corrosion, etc.
The values of for each material will be different for the
different limit states by virtue of the different probabilities
that can be accepted
mstates by virtue of the different probabilities that can be
accepted.
The recommended values for are as follows :-
Limit state m for m for Steel
m
Limit state m for Concrete
m for Steel
Ultimate: Flexure 1.5 1.05Shear 1 25 1 15Shear 1.25 1.15Bond
1.4
Serviceability 1.0 1.0
-
DesignLoadsg We obtain the design load by:
Design loads characteristic load x partial safety factor f is
introduced to take account of:
1. possible unusual increases in the load2. inaccurate
assessment of effects of loading
ff
2. inaccurate assessment of effects of loading 3. variations in
dimensional accuracy in construction 4. the importance of the limit
state being considered.
i f diff t li it t t d l f diff t bi ti f varies for different
limit states and also for different combinations of loading. Values
of for ultimate limit state are given the following Table:
Load Combination
Ultimate Serviceability
ff
Combination Deadg
Imposedq
Waterw
Earth, Wind Water
ALL(g,q,w)
Dead Imposed (Earth Water)
1.4 (or 1.0) 1.6 (or 0.0) 1.4 - 1.0
Dead Imposed 1 4 (or 1 0) 1 4 1 4 1 0Dead Imposed Wind
1.4 (or 1.0) - 1.4 1.4 1.0
Dead Imposed Wind (Earth Water)
1.2 1.2 1.2 1.2 1.0
The arrangement of loads should be such as to cause the most
severe effects, i.e. the most severe stresses.
-
BASIC REQUIREMENT OF DESIGNED STRUCTURES
1. The structure must fulfil its intended function 1. The
structure must fulfil its intended function throughout its
intended(design) life and it shall do so without abnormal
maintenance costs.
2. The structure must be safe. The consequences of collapse can
be extremely serious and the possibility of
ll t b li ibl Th t t t bcollapse must be negligible. The
structure must be designed so that if loads very much greater than
the normal design loads are applied then adequtenormal design loads
are applied then adequte warning of the danger of collapse shall be
given(e.g. visible signs of cracks and large deflections) to permit
g g )appropriate action to be taken.
3. The structure must be of least cost (economical).
