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11.1Introduction 185

11.1.3 Analysisvs Design

11 In R/Cwe always consideroneof thefollowingproblems:

Analysis: Givena certaindesign, determinewhatis themaximummoment which canbe

applied.

Design: Given anexternalmoment to be resisted,determinecrosssectionaldimensions(band

h) as well as reinforcement (As). Notethatin many casestheexternaldimensionsof the

beam(bandh) are xedby thearchitect.

12 We oftenconsiderthemaximummoment alonga member,anddesignaccordingly.

11.1.4 BasicRelationsandAssumptions

13 In developinga design/analysismethod forreinforcedconcrete,thefollowingbasicrelations

willbe used,Fig.??:

C

T

d

e

y

T=C

M_ext=Cd

Compatibility Equilibrium

Figure11.2:InternalEquilibriumin a R/CBeam

1. Equilibrium: of forcesandmoment at thecrosssection. 1) Fx= 0 or Tensionin the

reinforcement = Compressionin concrete;and2) M= 0 or externalmoment (thatis the

oneobtainedfromthemoment envelope) equalandoppositeto theinternalone(tension

in steelandcompressionof theconcrete).

2. MaterialStressStrain:We recallthatallnormalstrengthconcretehave a failurestrain

u=: 003 in compressionirrespective off

0

c.

14 Basicassumptionsused:

Compatibility of Displacements: Perfectbondbetweensteelandconcrete(noslip).Note

thatthosetwo materialsdoalsohave veryclosecoecients of thermalexpansionunder

normaltemperature.

Planesectionremainplane )strainis proportionalto distancefromneutralaxis.