The document discusses the working stress method for designing reinforced concrete structures. It defines key terms like neutral axis, lever arm, and moment of resistance. It describes the assumptions of the working stress method, including perfect bond between steel and concrete and linear elastic behavior. It discusses balanced, under-reinforced, and over-reinforced beam sections. The document also notes some limitations of the working stress method and introduces the concept of the limit state method.

1. RCCDESIGNBYWO
RKING
STRESSMETHOD
NAME-PRADIP BARUA
ROLL NO-25501321010
DEPT-CIVIL

3. Introduction
• The design of a structure may be regarded as
theprocess of selecting proper materials
andproportionedelementsofthestructure,accordingt
otheart,engineeringscienceandtechnology.Inorderto
fulfill its purpose, the structure must meet
itsconditions of safety, serviceability, economy
andfunctionality.

4. TermsofRCCdesign
• NeutralAxis(n)
• Neutral axis lies at the centre of gravity of the section. It is defined as
thataxis at which the stresses are zero. It divides the section into tension
andcompression zone. The position of the neutral axis depends upon
theshape(dimensions)ofthe sectionand the amountof steel provided.

5. Leverarm-
• Leverarmisthedistancebetweentheresultantcompressiveforceandthere
sultanttensileforce.
MomentofResistance(Mr)
Moment of resistance is the resistance offered by the beam against external loads. As
thereisnoresultantforceactingonthebeamandthesectionisinequilibrium,thetotal
compressive force is equal to the total tensile force. These two forces (equaland
opposite separated by a distance) will form a couple (and the moment of
thiscouple isequal to theresistingmomentor momentofresistanceofthesection.

6. WORKINGSTRESSMETHOD
• Working Stress Method is the traditionalmethod ofdesign not only for Reinforced Concrete
butalso for structuralsteeland timber design. The conceptualbasis ofthe WSM assumes that
thestructuralmaterialbehaves in a linear elastic manner and that appropriate safetycan be
ensuredbysuitably limiting the stresses in the material due to the presumed working loads
(serviceloads)onthestructure.
• WSMalsoassumesthatboththesteelreinforcementandconcreteacttogetherandareperfectlyelastic
at all stages, and hence the modular ratio can be used to determine the stresses in
steelandconcrete.
• Thestressesundertheworkingloadsareobtainedbyapplyingthemethodsof‘strengthof
materials’likethesimplebendingtheory.Thelimitationsduetonon-linearityandbucklingareneglected.
• The stresses caused by the ‘characteristic’ or service loads are checked against the
permissible(allowable) stress, which is a fraction of the ultimate or yield stress. The
permissible stress maybe defined in terms of a factor of safety, which takes care of the
overload or other unknownfactors.

8. Assumptions of elastic theory
• PlaneSectionbeforebending will remainplaneafterbending
• Bondbetweensteel andconcreteisperfectwithin elasticlimitofsteel
• The steel and concrete behaves
aslinear elasticmaterial
• All tensile stresses are taken
byreinforcement and none
byconcrete
• The stressesin steel
and concrete are related by
afactorknownas“modularratio
• The Stress-strainrelationshipof steel
andconcreteisaStraightlineunderworkingload

9. • StepstodesignbeamsectionbyWSM
• Step1-calculationofdesignconstants.
• Step 2-calculationofbendingmoment.
• Step3-design ofsection.
• Step4- reinforcement
• Step5-checkforshearanddesignof shearreinforcement.
• Step6- detailsofreinforcement.

10. BalancedBeamSection
• Reinforced concrete beam sections in which the tension steel also
reachesyield strain simultaneously as the concrete reaches the failure
strain inbendingarecalled balancedsections.

11. Under-Reinforced Beam Section
• Reinforcedconcretebeamsectionsinwhichthesteelreachesyieldstrainatloads
lower than the load at which the concrete reaches failure strain
arecalledunder-reinforcedsections.
• Everysinglyreinforcedbeamshouldbedesignedasunder-
reinforcedsectionsbecausethissectiongivesenoughwarningbeforefailu
re.
• Yieldingofsteelinunder-reinforcedbeamsectiondoesnotmeanthe
structure has failed, as when
steelyields, excessive deflection
andcracking in beam will occur
beforefailure which gives enough
time tooccupants to escape before the
sectionfails.
• The failure in under-reinforced
beamsectionisduetotheconcretereachingi
ts ultimate failure strain of 0.0035
beforethe steel reaches its failure strain
whichIsmuchhigher0.20to0.25.

12. Over-ReinforcedBeamSection
• Reinforced concrete beam sections in which the failure strain in
concreteis reached earlier than the yield strain of steel is reached, are
called over-reinforcedbeamsections.
• If over-reinforced beam is designed and loaded to full capacity then
thesteel in tension zone will not yield much before the concrete reaches
itsultimate strain of 0.0035. This due to little yielding of steel the
deflectionand cracking of beam does not occur and does not give
enough warningpriortofailure.
• Failures in over-reinforced sections are all of a sudden. This type
ofdesignisnotrecommendedin practice ofbeam design.

13. CONCEPT OF TRANSFORMED
OREQUIVALENTSECTION
(i)
The bond between steel and concrete is assumed to be perfect so the strains in steel and the
surroundingconcrete willbeequal
(ii)
Itmeansthatstressinsteel ismtimesthestress inconcreteorloadcarriedbysteelismtimestheloadcarriedby
concrete ofequalarea.UsingEqns.(i)and(ii)

14. Limitationsof workingstressmethod
• The assumptions of linear elastic behaviour and control of
stresseswithin specially defined permissible stresses are unrealistic due
toseveral reasons viz., creep, shrinkage and other long term effects,
stressconcentrationand othersecondaryeffects
• Different types of load acting simultaneously have different degrees
ofuncertainties. This cannot be taken into account in the working
stressmethod
• The actual factor of safety is not known in this method of design.
Thepartial safety factors in the limit state method is more realistic
than theconcept of permissible stresses in the working stress method
to havefactorofsafetyin the design.

15. Creep
Shrinkage

16. LimitStateMethod
• The stresses are obtained from
designloads and compared with
designstrength.
• In this method, it follows linear
strainrelationship but not
linearstressrelationship (one of the
majordifference between the
twomethodsofdesign).
• The ultimatestresses ofmaterialsitself
areusedasallowablestresses.
• The material capabilities are not
underestimated as much as theyare
inworking stress method. Partial
safetyfactorsareused in
limitstatemethod.

17. • Accordingly, the working stress method is gradually replaced by the limit state method.
TheIndian code IS 456 has given working stress method in Annex B to give greater emphasis
tolimit state design. Moreover, cl. 18.2.1 of IS 456 specifically mentions of using limit
statemethod normally for structures and structural elements. However, cl.18.2.2 recommends
theuse of working stress method where the limit state method cannot be conveniently
adopted.Due to its simplicity in the concept and applications, better structural performance in
servicestate and conservative design, working stress method is still being used for the design
ofreinforcedconcretebridges,
watertanksandchimneys.Infact,designoftensionstructuresandliquid retaining structures are not
included in IS 456 for the design guidelines in the limit statemethodofdesign
• Calculationalonedonotproducesafe,serviceableanddurablestructures.Suitablematerial
qualitycontroladequatedetailingand goodsupervisionareequallyimportant.