reliability analysis of steel smrf and scbf … · reliability analysis of steel smrf and scbf...
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RELIABILITY ANALYSIS OF STEEL SMRF AND SCBF STRUCTURES CONSIDERING THE
VERTICAL COMPONENT OF NEAR-FAULT GROUND MOTIONSInvestigators:
1) Jawad Fayaz; Graduate Student 2) Farzin Zareian; Associate Professor
Performance Based Earthquake Engineering Laboratory, University of California Irvine
Estimate Type II Parameters
u & k
Type II Distribution-
Curve Fitting - EQ Load
Setting up Limit State Equations
𝒁𝑪𝑨 = 𝑹𝑪𝑨 − 𝑫𝑪𝑨 − 𝑳𝑪𝑨 − 𝑬𝑪𝑨 BEAMS & BRACES
𝒁𝑪𝒐𝒍𝒖𝒎𝒏 = 𝟏 −𝑫𝑨𝒙𝒊𝒂𝒍+ 𝑳𝑨𝒙𝒊𝒂𝒍+ 𝑬𝑨𝒙𝒊𝒂𝒍
𝑹𝑨𝒙𝒊𝒂𝒍−
𝑫𝑴𝒐𝒎𝒆𝒏𝒕+ 𝑳𝑴𝒐𝒎𝒆𝒏𝒕+ 𝑬𝑴𝒐𝒎𝒆𝒏𝒕
𝑹𝑴𝒐𝒎𝒆𝒏𝒕COLUMNS
D, L, E and R represent random variables for EDP due to Dead Load, Live Load,
Earthquake Load and corresponding Resistance, respectively. The subscript CA
denotes the respective component action
Calculate:
µ𝑬 & 𝝈𝑬
𝐺𝐸 𝑒 = 1 − exp 𝜆𝐸𝑡
𝐹𝐸 𝑒 = 1 – 𝐺𝐸 𝑒𝜆𝐸 = 𝑘0 Τ
𝑒𝑎
−𝑘𝑒𝑥𝑝1
2
𝑘2
𝑏2𝜎 𝐿𝑁 𝐸 |𝑆𝑎
2
Analysis Case Effective Nominal Resistance (Rn) Analyzed Under
Case I Τ𝟏. 𝟐𝐃𝐧 + 𝟎. 𝟓𝐋𝐧+𝟏. 𝟎𝑬𝐧 𝟎. 𝟗 2-D Ground Motions
Case II Τ𝟏. 𝟐𝐃𝐧 + 𝟎. 𝟓𝐋𝐧+𝟏. 𝟎𝑬𝐧 𝟎. 𝟗 3-D Ground Motions
Case III Τ𝟏. 𝟐 + 𝟎. 𝟐𝐒𝐃𝐒 𝐃𝐧 + 𝟎. 𝟓𝐋𝐧+𝟏. 𝟎𝑬𝐧 𝟎. 𝟗 3-D Ground Motions
Case IV 2% Drift Based Design 3-D Ground Motions
CASES OF ANALYSIS1
SMRF 2-, 4-,
8- & 12- Story
SCBF 3- & 6-
Story
140 feet
10
0 f
eet
180 feet
120 fe
et 1
20
feet
180 feet
SCBF 12- & 16-
Story
𝑬
𝑬
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 100 200 300 400 500EDP due to Earthquake Load
E
RotD50 Spectral Acceleration (Sa)
0k
a a a aH S P S s k s
0k
a a a aH S P S s k s
Dead Load - Normal Distribution
𝐌 𝐚𝐧
𝐍𝐨𝐦𝐢𝐧𝐚𝐥=
µ𝑫𝑫𝒏
C.o.V 𝑽 =𝝈𝑫µ𝑫
Calculate:
µ𝑫 & 𝝈𝑫
Live Load- Gamma Distribution
𝐌 𝐚𝐧
𝐍𝐨𝐦𝐢𝐧𝐚𝐥=
µ𝑳𝑳𝒏
C.o.V 𝑽 =𝝈𝑳µ𝑳
Calculate:
µ𝑳 & 𝝈𝑳
Resistance – LogNormal
Distribution
𝐌 𝐚𝐧
𝐍𝐨𝐦𝐢𝐧𝐚𝐥=
µ𝑹𝐑𝒏
C.o.V 𝐕 =𝛔𝑹µ𝑹
Calculate:
µ𝑹 & 𝝈𝑹
Limit State Equation FORM b
4
5
6
𝜸𝑫+ 𝟎. 𝟐 + 𝒙 𝑺𝑫𝑺 𝑫𝒏,𝑪𝑨 + 𝜸𝑳𝑳𝒏,𝑪𝑨 + r𝑬𝒏,𝑪𝑨
2
3
Current b of SMRF Members
Current b of SCBF Members
Empirical values to upgrade seismic load combinations
Empirical values of ‘x’ for the
seismic load combinations can
be derived from this figure
depending on what percentage
of members are required to
attain Reliability = 1.75 (i.e.
Probability of Failure = 4%)
CASE I CASE II CASE III
Reliab
ilit
y I
nd
ex (
b )
fo
r B
races
1.0
1.2
1.4
1.6
1.8
2.0
CASE I CASE II CASE III
Reliab
ilit
y I
nd
ex (
b )
fo
r C
olu
mn
s
1.0
1.2
1.4
1.6
1.8
2.0
1.0
1.2
1.4
2.2
2.4
2.6
2.0
1.8
1.6
Reliab
ilit
y I
nd
ex (
b )
fo
r B
eam
s
CASE:
MOMENTS SHEAR
I II III IV I II III IV CASE III CASE IV1.0
1.2
1.4
2.2
2.4
2.6
2.0
1.8
1.6
Reliab
ilit
y I
nd
ex (
b )
fo
r C
olu
mn
sCASE IICASE I
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
0
0.1
0.2
0.3
0.4
0.5
0.6 1.2 1.8 2.4 3 3.6
Frequency
Bin
Probability Mass Cumulative Probability0.5
PM
F
0.0 0.6 1.2 1.8 2.4 3.0 3.6
CD
F
x - Values
0.4
0.3
0.2
0.1
0.0
1.0
0.8
0.6
0.4
0.2
0.0