MainProject NameBURJ DUBAI TOWERJob NoSheet NoDX001741ClientEMAARPrepared ByChecked ByPO Box 52750 Dubai United Arab EmiratesSection of ProjectEARLY-AGE CRITICAL STEEL RATIODateDateISO 2394 STANDARDISED FORM ANALYSIS7 Dec 10REFERENCECONTENTSOUTPUTSAFETY MARGINCIRIA C660Tbl A10.2Basic Equation, crit =kis.ka.ks.fct3/fykwhere kis =in situ strength factorka =age at loading factorks =sustained loading factorfct3 =mean concrete tensile strength at 3 daysfyk =characteristic strength of reinforcementFor reliability analysis, the above equation is re-arranged in the form of the safety margin, M:M =crit - kis.ka.ks.fct3/fyk and, at failure, M = 0BASIC VARIABLES (EC2 & CIRIA C660)The basic variables are assumed to be normally distributed random variables. Note that the 3-day tensile strength of concrete is derived overleaf to allow ease of use with different concrete grades.VariableUnitsMeanStd DevCOV/Tbl A10.2kis0.900.0820.091ka1.000.1360.136ks0.700.0400.057fykMPa53032.10.061SENSITIVITY FACTORS (-VALUES)The following standardised -values are suggested in ISO 2394.ISO 2394Variable, XiSensitivity Factor, iTable E.3Dominant resistance variable0.80Other resistance variables0.32Dominant load variable-0.70Other load variables-0.28A variable is a load variable if failure is more likely when it takes values higher than the mean.A variable is a resistance variable if failure is more likely when it takes values less than the mean.Note that -values are +ve for variables that provide safety and are -ve for variable that are hazardous.The procedure is described in ISO 2394 and was used for the probabilistic verification of the Eurocodes. However, to limit the error in using table E.3, it is usually required that:0.16 < S/R < 6.6whereS is the dominant load variableR is the dominant resistance variable

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CalcProject NameBURJ DUBAI TOWERJob NoSheet NoDX001742ClientEMAARPrepared ByChecked ByPO Box 52750 Dubai United Arab EmiratesSection of ProjectEARLY-AGE CRITICAL STEEL RATIODateDateISO 2394 STANDARDISED FORM ANALYSIS7 Dec 10REFERENCECONTENTSOUTPUTINPUT DATA (EC2 & CIRIA C660)Concrete Grade=C40/50C40/50 ConcreteCharacteristic Cylinder Strengthfck =40 MPa3-Day Tensile Strengthfck =40MPaMean 28-Day Tensile strengthfctm =3.55 MPafctm =3.55MPaMean 3-Day Tensile strengthfct3 =2.12 MPafct3 =2.12 MPafct3 =2.12MPaVariableUnitsMeanStd DevCOV/fct3MPa2.120.390.184Probability of failure,pf =5.0%Reliability IndexISO 2394Reliability Index, =-1(pf) =1.645 = 1.645 for 5.0% probability of failure =1.645E.4.3.AISO 2394 suggests =1.5 for irreversible serviceability limit states, which corresponds to pf = 6.7%.RELIABILITY ANALYSISCheck fct3/fyk =0.39/32.1=0.012< 0.16 Therefore Table E-3 may not applyNotwithstanding the above, a full iterative FORM analysis has been carried out in accordance with ISO 2394 and this gives similar results to that obtained from this analysis. Therefore the error using the standardised procedure in this analysis is small.Using Standardised ISO 2394 FORM Procedure is OKThe "design point" values, Z*i, are first calculated in standard normal space and then transformed to basic variable space.. Note that the variables have a mean, i = 0, and a standard deviation, i = 1, in standard normal space.Dominant Load VariableDominant Load Variable is fct3 because its COV is highest and all of the load variables vary linearly with the safety margin, M.Z*fct3 =fct3. =-0.70 x 1.645=-1.152Other Load VariablesZ*kis =kis. =-0.28 x 1.645=-0.461= Z*ka = Z*ksDominant Resistance VariableZ*fy =fy. =0.80 x 1.645=1.316Transforming the design points from standard normal space to basic variable space gives the following design values:k*is =kis - Z*kis.kis =0.90 + 0.461 x 0.082 =0.938k*a =ka - Z*ka.ka =1.00 + 0.461 x 0.136 =1.063k*s =ks - Z*ks.ks =0.70 + 0.461 x 0.040 =0.718f*ct3 =fct3 - Z*fct3.fct3 =2.12 + 1.152 x 0.390 =2.57MPaf*yk =fyk - Z*fyk.fyk =530 - 1.316 x 32.1 =488MPaFor 5% Failures, C40/50 Concrete & 500 MPa SteelFor Safety Margin, M = 0, Critical Steel Ratio, crit:crit =k*is.k*a.k*sf*ct3/f*ykcrit =0.938x1.063x0.718x2.574/488=0.378%crit =0.378%

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