Draft

9.3UltimateStrengthMethod 165

 < all=

yld

F:S:

(9.1)

whereF:S:is thefactorof safety.

10 Majorlimitationsof thismethod

1. Anelasticanalysiscannoteasilyaccount forcreepandshrinkageof concrete.


2. For concretestructures,stressesarenotlinearlyproportionalto strainbeyond 0 : 45 f

0

c.

3. Safety factorsarenotrigorouslydeterminedfroma probabilisticapproach, butarethe

resultof experienceandjudgment.

11 Allowablestrengthsaregivenin Table9.1.

Steel,AISC/ASD

Tension,GrossArea Ft= 0: 6 Fy

Tension,Eective NetArea



Ft= 0: 5 Fu

Bending Fb= 0: 66 Fy

Shear Fv= 0: 40 Fy

Concrete,ACI/WSD

Tension 0

Compression 0 : 45 f

0

c



Eective netareawillbe denedin section??.

Table9.1:AllowableStressesforSteelandConcrete

9.3 UltimateStrengthMethod

9.3.1 TheNormalDistribution

12 Thenormaldistributionhasbeenfoundto be anexcellent approximationto a largeclassof

distributions,andhassomeverydesirablemathematicalproperties:

1. 
   

   f(x) is symmetricwithrespectto themean.

   
   


2. 
   

   f(x) is a \bellcurve" within
   ectionpoints atx=.

   
   


3. 
   

   f(x) is a validprobabilitydistributionfunctionas:

   
   

Z

1

1

f(x) = 1 (9.2)

4. Theprobabilitythatxmin< x < xmaxis givenby:

P(xmin< x < xmax) =

Z

xmax

xmin

f(x)dx (9.3)