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