Comparison of working stress method and limit state method
Working
1.The method based on the
elastic theory which assumes that concret and steel are elastic and the strees
strain curve is linear for both .
2. In this method the factor of safety
are applied to the yield stresses to get permissible stresses.
3.No factor of safety is used for loads.
4.Exact margin of safety is not known.
5.This method gives thicker ,section ,so less economical.
6.This method assumes that the actual loads ,permissible stresses and
factor of safety rae known . so it is called as deterministic method.
Limit state method
1.This method is based on the actual stress-strain curves of stell and
concret for concrete, the stress strain curve is non-linear.
2.In this method,partial safety factors are applied to get design values of
stresses.
3.Design loads are obtained by multiplying partial safety factors of
load to the working loads.
4.Exact margin of safety is known.
5.This method is more economical as it gives thinner sections.
6.This method is based upon the probabilistic approach which depends
upon the actual data or experience, hence it is called as non-deterministic method.
Cement: as we known that cement is a binding materials produced
by buring together in a define proportion a mixture of silicon argillaceous and
calcareous materals in partial fussion at a temperat1400to1450oc.
Chemical composition of cement:
Oxide composition
limitsof ordinary Portland cement.
|
oxide |
Content(%) |
|
cao |
59-64 |
|
sio |
19-24 |
|
Al2o3 |
3-6 |
|
Fe2o3 |
1-4 |
|
So3 |
1-3 |
|
mgo |
0.5-4 |
|
alkalis |
0.2-1.3 |
When water is mixed
with cement the chemical process of hydrolyisis and hydration occur
simultaneously during the reaction of cement and water hydration is the process
of combination of cement with water ,as
s result of hydration setting and hardeninig of cement take place.
Types of cements:
1.ordinary
portland cement
2.Rapid
hardening portand
3.Extra
rapid “
4.Low
heat “
5.sulphate
resisting “
6.supersulphated
cement
7.High
alumina cement
8.portland
blast furnace “
9.pozzolanic “
10.white
Portland “
11.Air
entraning “
12.Hydrophopic
“
Phyical requiredments of cement:
1.Chemical
composition
•
Loss on ignition
•
Insoluble residues
•
Lime and alumina
content
•
Magnesia content
•
Sulphur content
2.Fineness
3.normal consist
4.setting time
5.soundness
6.heat of hydration
7.strengt of cement
1.chemical
comp:required for chemical comp. of cement have been recommended by IS 269-1967 for controlling te quality of
cement .
•
Loss on ignition :
it occurs due to evaporation pf the moisture and carboudioxide in the cement
.moisture and atmosphere which causes pre-hydration og cemet.
•
i nsoluble
residues: these are inactive materials .these are mesure of adulteration in
cement maninly due to impurities in gypsum.
•
lime and alumina content
Express of free
lime cause unsoundness .hence the % age of lime to silica alumina and iron
axide express
Magnesia content
Excess of
magnesia causes unsoundness. Hence the quantity of free magnwsia must conform
to the requirement.
Sulphur content
The sulphur in
cement combine with lime and alumina and
forms crystalline calcium sulphoaluminate .this cause expansion and conseguently
unsoundness.
2.Fineness
of the cement
The number of particles of cement power in unit weight reflects the
fineness of the cement .the rate of hydration of cement depends thits fineness
. the more rapid is the developmentof strength.
3.Normal consistency:
For tests of somephysical properties of cement such as initial and
final setting time,tenile and compressive strength and sounness a cement paste
of normal consistency is used.
4.Initial and final setting time
When water is mixed with cement compound of cement react with water .
5.soundness
The change in the volume of hardness concret due to delayed or slow
hydration of free lime magnesia and calcium sulphate present in cement is known
as unsoundness.
6.Heat of hydration
It is the quantity of heat expreesed as cal/g .evolved on given
temperature .
7.Strength of cement
The mechanical
strength of cement is most important for its structural use .the strength of
cement is determind from the compressive and tensile tests on the hardened cement and atandard Leighton buzzard annove
sand in 1:3 proportion and water of (0.25pn+3.5)percent of combined weigth of
cement and sand.
Aggregate
A mixture of only cement and water is costely
and possesses low strength and shrinks unacceptably on drying .it should be
free from organic matter which reduces the hydraulic activity of cement and
affects its normal setting and hardening .it should also be free from
constituents which decompose or exposure to atmosphere or react adversely with the hardned cement paste.
Classifiction of aggregates:
Aggregates or classified as coagate and fine of regate based upon their sizes coarse aggregate is
materials whish passes through 80m sieve and retained on a 4.75mm seive .it may be uncrushed gravel
if it results from the natural distitergration of rock or crushed stone or
crushed gravel.
1.normal density aggregates:
It includes aggregates having a
specific gravity b/w 2.5 and 3.0 and a bulk density in the range of 14.5 to 17.5kn/m3.it includes most
widely used of all aggregates ,namely gravels ,crushed rocks and blast furnace
slag.
2.light weight aggregates:
These are porous solids,both natural and man made. The higher the
porosity of the aggregate the lower the thermal
conductivity density and strength of the light weight concrete made with
it.
3.High density aggregate:
They are obtained from barytes (barium sulphate rocks )ferrous metal
granules such as shot and punching and ferrous are such as magnetite hematite
and limonite and are used to make high density concret for such application as
screening radioactive sources.
4.Fibrous aggregates:
It is nous rocks
used in the naturally accurring fibrous rocks used in the production of as
bestos cements goods such as roofing sheets
etc.
5.Gaseous aggregates:
These are gases that act as individual ps such as articles of
aggregate.they are small bubble of gases
such as air which are formed in
fresh cement paste by using appropriate foaming agents and mixing equipment.
Physical properties of aggregates:
1.size ofaggregate .
2.shape of paticles
3.surface texture
4.strength of coarse aggregates
5.specific gravity
6.bulk density
7.water absoption and surface moisture
8.bulking of sand
9.deterioussubstance
10.soundness
11.durability
1.size of aggregate:
It is the aggregate is designeded by the maximum size of the
individual aggregate present in
substaintial amount .the aggregate is said
be of 20mm size if it passes through a 20mm sieve and retainded on a
16mm sieve .
.coarse aggregate :
It passes through an 80mm sieve and retaind on a 4-75mm sieve .
.Fine aggregate:
It passes through a 4-75mm sieve and reaind on a 75micron sieve
particles b/w 0.06mm and 0.002mm sieve .
Aggregate are also
classified based on the distribution of particle size as follows:
Single –size
aggregate : it has a majority of particles of the same size .
Grade aggregate:it
has particles of all size .
All in aggregate :it is a
combination of coarse and fine
aggregate.
2.Shape of the particles:
1.Rounded
2.irregular or party rounded
3.angular
4.flanky
5.elongated
6.flanky and elongated
Admixtures:
Admixtures are materials used in concretes to modify its properties .they may be classified according
to the purpose for which they are used in concrete some of the important
admixtures are disscuss below :
1.Accelerating admixyure
2.ReTARDING Admix.
3.Water reducing admix.
4.Air-entraining admix.
1.Accelerating admix.:
These are used to accelerate the rate of development of strength at an
early age .calcis chlorixide flurosilicates and tri-ethanonly mine are the most
commonly used acetated.
2.Retarding admix.:
These are
used to retard setting and there by reduce evolution of heat.
3.water reducing admix.
These are used to reduce the
water content while main training the working of concrete.
4.Air-entering admix.
These are used to entrain air in the form of of very small
disconnected air bubbles in concreted usually to increase workability and
resistance to freezing and thawing.the commonly used air entraining agents are:
1 animal and vegetable oils and fats .
2 naturals wood resin and their sodium salf such as visnol resin.
Reinforcement :
The commonly used types of steel reinforcement
are mild steel,medium ,tensile steel and high yield strength deformed round
bars.
The reinforcing
bars should be free from craks,surface flows laminations rough . In
length :
Length not
spcied -25mm
+75mm
Minimum
lengh “ =75mm.
Maximum
lengh “ -50m
In weight :
Diameter≤8mm ± 4%
Diameter
>8mm ±2.5%
In diameter:
Diameter ≤25mm ±0.5%
The requirements of important
mechanical properties of mild steel high strength steel and “sail ma
steel”.
Strength:
It is the most important
properties of concrete and gives as over all idea of its quality. The
strength of concrete in direct
compression ,tension ,bond abrasion are commonly used properties for its
structural use. These are dscribed below:
1.compressive strength :
2.tensile strength:
3.bond “
4.Resistance and
abrasion
1.compressive
strength:
•
types of fineness of cement
•
strength ,size ,shape, surface, texture and grading of aggregate.
•
water to cement ratio
•
aggregate to cement ratio
•
age of concrete
2.Tensile strength:
Fcr =K
Where, fcr= flexural tensile
strength of conc.
Fck= compressive strength of conc.
K,n= coefficenent equal to 0.7 and 0.5 as specified by IS CODE
Fcr=0.7
The flexural strength is on an average 50% great than strength of
conc. In direct tension .
3.Bond strength:
4.Resistance and abrasion.
Durability:
Durability of
concrete is the resistance deterioration and environmental effects to wchich it
is exposed
Creep of concrete:
Concrete under
stress undergoes a gradual icrease in strain with time such as continuous
diormation under sustained load with time is known as creep of concrete.the
creep strain depends upon the stress in conc. Age of loading,duration of
loading,type of content of aggregate,water to cement ratio and ambient a
relative humadity.
Shrinkage of concrerte:
Shrinkage of conc.
Occurs when it loses moisture by evaporation.it increases with time at a
decreasing rate as drying of conc. Continuous with time at a decreasing
rate.shrinkage increasing with increasing in cement and water content.it can be
reduced by maintaining adeguate humadity in the atmoshpheric surrounding,the
conc.and opting refine aggregate of coarse grading.
Designed concrete mix.
In desined concrete mixes properties of ingradients of conc. Are
determined to obtain conc. Of specified properties with overall economy.the
principles factors governing and the method of mix design are discussed as
follow:
1.principles of conc. Mix
design .
2.factor governing
conc. Mix. Design
3.method of conc.
Mix desion
1.principles
of conc.mix design:
•
Compressive strength
at a specified age.
•
Working of the
fresh conc. And
•
Durability
Strength of conc.
|
Fm=fc+ks |
Where,
fm=meanstrength
Fc=characteristic
strength
k=constant
s=standard
deviation of normal distribution curve of strength of conc.
The contant
k decreases with increase in percent defectives ,as given below:
|
The
standared sesderivation increses with increases with in charactersistic
strength of conc. As given below :
Conc.
Grades
valueN/mm2
M10
3.5
M15
3.5
M20
4
M25
4
M30
5
M35
5
M40 5
•
Workability of conc.:
the
workability of conc.should be a deguate for placing conditions and proper composition
with means available .it is manily governed by its water contant for a given
aggregate characteristic.
•
Durability of conc.:
The durability of conc. Depends on its resistance to deteroration in
the environment in which its is placed.one environment one the main characteristic influence the
durability of conc.is its permeability.
2.factors
governing conc.mix. design:
•
Grade of conc.
•
Types of cement
•
Cement content
•
Size,shape,and
grading of aggregate
3.method of conc. Mix design :
•
Determine the mean strength from the characteristic strength.
•
Determine the water to cement ratio from strength requirement and
check for the requirement of durability.
•
Determine water content from the
requirement of workability.
•
Determine the relative proportion of coarse and fine aggregate from
their characterstic .
•
Determine the cement content and check for the requirement of
durability.
ONE WAY SLAB...
limit state codition/; depth of nutral axis = Xu max: O,36FCK XU MAX B =O.87FYaSTLIM./;
LEVER ARM = D-0.42xumax........: xu max /(d) =
0.oo35/(.0055+o.87(fy/f))
limitimg moment of resisstance(Mulim:
mulim = 0.36 fck xumax b{d-0.42xumax.)): mulim.= o.87fy
Ast.lim(d-o.42xumax}
for fe 250, Mu lim = o.149 fck bd2 ............for fe 415 ,Mu lim =
0.138 fck bd2.......for fe 5oo, mulim=.133fckdb2.... pt
lim..= 41.4(fck/fy)x(xumax/d}...for m 20 fe 145 ptlim = 0.9585......FOR M20 FE
500 P T LIM = 0.762%....FOR M20 FR 25O PTLIM = 1.755%.
STEP TO BE FOLLOWED BY ONY WAT SLAD....
1) ASSUME
SUITABLE BEARING. NOT LESS THAN 100 M FIND THE SPAN B/W THE CENTER OF BEARING. 2////////)
ESTIMATE THE THICKNESS TO THE SLAB . THE THICKESS OF THE SLAB IS GOVERNED BY
DEFLECTION CONSIDRATION RATHER THAN FLEXURAL CONSIDREATION.....THICKNESS OF
SLAB = (SPAN B/W CENTER OF BEARING)/()20 X M.F;)THE MODIFICATION DEPENDES ON
THE PERCENTAGE OF TENSILE STEEL WHICH MAY BE INITIALLY ASSUMED 0.3 TO 0.4....
FOR 0.3 STEEL MODIFICATION FACTOR = 1.43 FOR FE 415 ....USING 8 MM DIA BAR IF
FE 415 IS USED.AND 10MMMDIA IF FE 250 IS GIVEN.....FIND THE EFFECTIVE COVERTO
THE REINFORCEMENT WHICH IS EQUAL TO HALF BAR DIA +15 MM....THUS
FIND THE TOTAL THICKNESS OF THE SLAB WHICH MAY BE ROUNDED OFF TO A CONVENIENT
VALUE....NOW FIND THE ACTUAL EFFECTIVE SPAN OF THE SLAB WHICH IS LESSER THAN OF
FLOWING...(1)DISTANCE B/W CENTER OF BEARING (2) CLEAR SPAN =EFF.DEPYH........
ESTIMATE THE TOTAL LOAD ON SPAN, PER SQUARE METER. IF THE THICKNESS OF THE SLAB
IS d MM. d.l. load of the
slab per square m = Dx1x25000/1ooo = 25Dn/m2for example the dl of a 120mm thick
slab = 25 x 120 = 3000n/m2..... if a floor finish is provided the dead load of
the floor finish should be estimated. unless specifically mensionad of any
special type of finishing we may assume the waight of a floor equial to that of
plain conc. weighing 24000n/m.3.........ifthe thickness of the foor finish is
D' DL OF FLOOR FINISH PER SQM = D'/1000 X 1 X 24000= 24D'n/m2... total load on
yhe span = w = Dl of the slab and floor finish + LL ON THE SLAB... THE L L MAY
BE TAKEN FRON 2000N/M2 TO 3OOON/M2....FACTORED LOAD = WU =W X PARTIALLY SAFETY
FACTOR.... NOW DETERMIND THE FACTORED MOMENT (Mu) = Wul2/8....whr l = eff.
length.
now equate the limiting moment of resistance to the factored moment
and find the effective depth required from flexural strength
considration....whem fe 415 is used Mulim = 0.138 fck bd2....ehen fe 250 steel
used mulim = o.149fckbd2.....effective depth required = d =whole underroot of (M in Mmmm)/.138x 20
x1oo....whem fe 415 ....an d d = whole undrroot Mu in Nmm/(.149x 20 x100 when
fe 2s20 is used.find the area of steel required per meter with of the sklab ...
% of steeel required . ...pt=50{((1)-/1`- 4.60xmu/bd2/fy/fck/````````````
area of steel provided per meter width = Ast =
pt/1oo(1000xd)alternatevely: ast = 0.50 fck/fy(1-4.6xMu/fckxbd2)}b x d.
the % of steel required should be greater than o.12 when fe 415 steel
is provided andgreater than 0.15% when fe 250 steel is pro vided. ...provide 8
mm dai bar of fe 415 or 10 mm dia bar for fe 250.
spacing of bar area of 1 bar x 1ooo /(Ast)...bent alternate bar at one
tength of the span between the center of bearing area of baar genraaly used in slab are given
blow....dia.of baar 8 10
10
area of bar 50 79
113..... maxmum spacing should mat exceed 1. 3 time the effective depth
of slab. 2. 300mmm. minimum spacing of bar ... 75 mm.
check for shear : sf at the edge of support = Vu = Wux clear span/(2)
normal shear stress tv = Vu/bd% of steel available
=32/2=.16%....corrosponding to .16% tc = 0.30n/m2tv =ktc ==0.39n/mm2
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