Seismic System Factors and System Overstrength

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Copyright 2009

Opening Slide

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Seismic System Factors and System Overstrength

Patrick J. Fortney, Ph.D., P.E.Manager and Chief EngineerCives Engineering CorporationCives Steel Company

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AgendaWhat are Seismic System Factors/Coefficients:

• Response Modification Factor, R• Overstrength Factor, W0

• Displacement Amplification Factor, Cd

• Ductility Reduction Factor, Rd

Load Combinations• Basic• Seismic• Seismic with Overstrength

LFRS Specifics• Nonlinear response history analysis of a 20-story HCW system – Wall

overstrength• Load Path in a CBF – Ensuring development of brace forces

4

ELF

ASCE 7-05 form of the Equivalent Lateral Force procedure

WCV s EQ. 12.8-1, ASCE 7-05

R

ISC DS

s EQ. 12.8-2, ASCE 7-05

where,

LLD

LD

s

TTRT

TIS

TTTR

IS

C

for

for ofsmaller

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1

5

The General Linear-Elastic EQ Procedure

1. Obtain the mapped MCE spectral accelerations, SS and S1

2. Modify the MCE spectral accelerations to account for site specific soil characteristics (SMS and SM1)

3. Convert the MCE parameters to the DBE (2/3) (SDS and SD1)(a specified design ground motion 1/1.5 of MCE)

5. Implement the ELF procedure to determine the vertical distribution of the design base shear

Note: Judgment must be used at each step based on performance level and analysis objectives

4. Factor the DBE base shear based on Use and LFRS type (factor by I/R)

(I varies from 1 to 1.5 presumed margin of 1.5 to 1.52)

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Performance LevelsPerformance Description

Immediate Occupancy

•No significant damage to structure. Retains nearly all of its pre-event strength and stiffness•Non-structural components operate for the most part, if utilities are available•Building can be used for intended use, under impaired conditions

Life Safety

•Significant damage to structural elements; substantial reduction in stiffness•However, safety margin exists against collapse•Non-structural components are secure, but not operational•Occupancy not ensured until repairs are made

Collapse Prevention

•Substantial structural and non-structural damage•Stiffness and strength significantly degraded•Little margin against collapse•Falling debris hazards may have occurred

Although ELF appears to be a strength-based design, it really isn’t! Although, using current methods, we evaluate only one performance level at a single event

Minimum strength is based on a fraction of the theoretical strength demand assuming the structure would remain elastic. AND…

Assumes some level of performance based on Importance

That fraction (or coefficient) is I/R.

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Design Response Spectrum

Period, T (sec)

Spectral Response Acceleration, Sa (%g)

T0 Ts TL

SD1

SDS

T=1sec

T

SS D

a1

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T

TSS LD

a

a v d0.4SDS

DSDS

a STT

SS 4.06.0

0

valuemapped

2.0

10

10

L

DS

D

DS

D

T

S

ST

S

ST

8

Response Spectrum Parameters

So what exactly do the terms S1, SS, SD1, and SDS represent?

SD1 and SDS are “factored” ground accelerations

• Defines the DBE• Accounts for site specific soil properties• 2/3 of the MCE• Statistically represents a 10% chance of exceedence in 50

years (500 year return period)

S1 and SS are the mapped ground accelerations (produced by the USGS) for 1-second and short period motions

• Defines the MCE• Assumes a Class B soil site, and 5% damping• Statistically represents a 2% chance of exceedence in 50

years (2,500 year return period)

Note that this is different from the 1997 UBC which used an MCE of 2% chance of exceedence in 100 years

(1,000 year return period)

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Response Spectrum Parameters (USGS)

http://earthquake.usgs.gov/hazards/design/

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11


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System Seismic Factors/Coefficients

Allow us to capture nonlinear behavior using linear-elastic model

Allow us to select the performance level of our building

• Immediate Occupancy

• Life Safety

• Collapse Prevention (not considered for new buildings)

Allow us to take advantage of decreases in force demands as yield sequencing occurs (i.e., as structure period lengthens)

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Brief Background on Response Factor, RPrior to the 1970’s, “nearly” all beam-column connections were designed to be moment-resisting providing complete or nearly complete frame systems

This level of high redundancy justified having “large” R-values

Current R-values remain nearly the same as was intended for the now-gone highly redundant systems

• At the time, building codes recommended that lower R-values be used where such redundancy was not present, but provided no direction how to do this

• Economic pressures eventually resulted in less redundant systems. However, designers were still taking advantage of the large R-factors

Lack of redundancy is now accounted for through the redundancy factor (r), effectively reducing the R-factor

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System Seismic Factors/Coefficients (cont.)

Lateral Displacement

Lateral Force

Vy Full Plasticity

dxe=dx/Cd

Actual Response

Elastic Response

Vs DesignDesign

Rd

0

R

V

V

y

E

R

0 ds

E RV

V

W0

s

y

V

V

VE

Shear Developed in a Linear-Elastic SystemDBE

yds VRRV

dxCd

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System Seismic Factors/Coefficients (cont.)Response Modification Factor, R

The ratio of the level of force that would develop in a system at DBE motions, in a linear-elastic system, to the level of force required in design (e.g., ASCE 7 design base shear)

Overstrength Factor, W0

The ratio of the maximum strength that can be developed in a system to the design base shear

Ductility Reduction Factor, Rd

A measure of the combined effect of:

As yield sequencing progresses, the effective period of the response decreases, resulting in a reduction in strength demand

As inelastic deformation occurs, hysteretic damping (energy dissipation) occurs

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System Seismic Factors/Coefficients (cont.)Displacement Amplification Factor, Cd

• Amplifies the lateral displacement of the linear elastic model to account for actual displacement in the nonlinear-inelastic system

• Actual displacement, dx, is dxeCd

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More on Overstrength, W0

Introduced in the UBC in 1997

Was intended to be a rational approach to estimate the maximum force that a system may deliver to isolated or individual members whose loss would result in a complete loss of:

• The LFR system,

• Stability, or

• Collapse Prevention Mechanisms

Also intended for the design of elements that could fail in an undesirable manner when subjected to loads significantly larger than those for which they were proportioned

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More on Overstrength, W0 (cont.)


Lateral Force

WD

Wm

Actual Response

WS

dE

Elastic Response

dxe=dx/Cd

Design

VE

Vd

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WD is the overstrength provided by the design engineer

Even in the most efficient design controlled by strength, load and resistance factors ensure some degree of design overstrength

When design is controlled by stiffness, the design overstrength can be even greater

It’s also possible that architectural requirements result in design overstrength

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Wm is the overstrength provided by using specified minimum material properties

Structural systems have inherent overstrength resulting from actual strength values and potentially strain hardening

Ws is the overstrength that results from system characteristics such as:

Redundancy

The degree to which elements not considered part of the LFR system participating in lateral resistance after LFR elements have yielded

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More on Overstrength, W0 (typical ranges)

Structural System

DesignOverstrength

Wd

MaterialOverstrength

Wm

SystemOverstrength

Ws

W0

Special Steel Moment Frames

1.5 - 2.5 1.2 – 1.6 1.0 – 1.5 2.0 – 3.5

Intermediate Steel Moment

Frames1.0 – 2.0 1.2 – 1.6 1.0 – 2.0 2.0 – 3.5

Ordinary Steel Moment Frames

1.0 – 1.5 1.2 – 1.6 1.5 – 2.5 2.0 – 3.5

Braced Frames 1.5 – 2.0 1.2 – 1.6 1.0 – 1.5 1.5 – 2.0

Values reported in FEMA 369 (NEHRP 2000)

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More on Ductility Reduction, Rd


Lateral Force

Vb (R=5)

R=

5R

d (R

=5)

W0

(R=

5)

Vb (R=3)

R=

3

Rd

(R=

3)

W0

(R=

3)

DBE

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Comparison of System FactorsCode/year

Steel System Type R 0 Cd R

0 Cd R 0 Cd

Ordinary Concentric Braced Frames

5.60 2.20 - 5.00 2.00 4.50 5.00 2.00 4.50

Special Concentric Braced Frames

6.40 2.20 - 6.00 2.00 5.00 6.00 2.00 5.00

Eccentrically Braced Frames

7.00 2.80 - 7.00 2.00 4.00 7.00 2.00 4.00

Ordinary Moment Frames

4.50 2.80 - 4.00 3.00 3.50 4.00 3.00 3.50

Intermediate Moment Frames

- - - 6.00 3.00 5.00 6.00 3.00 5.00

Special Moment Frames 8.50 2.80 - 8.00 3.00 5.50 8.00 3.00 5.50

Code/yearSteel System Type R

0 Cd R 0 Cd R

0 Cd


5.00 2.00 4.50 5.00 2.00 4.50 5.00 2.00 4.50


6.00 2.00 5.00 6.00 2.00 5.00 6.00 2.00 5.00


7.00 2.00 4.00 7.00 2.00 4.00 7.00 2.00 4.00


3.25 3.00 3.00 3.50 3.00 3.00 3.25 3.00 3.00


4.25 3.00 4.00 4.50 3.00 4.00 4.25 3.00 4.00

Special Moment Frames 8.00 3.00 5.50 8.00 3.00 5.50 8.00 3.00 5.50

Code/yearSteel System Type R

0 Cd R 0 Cd R

0 Cd R 0 Cd


5.00 2.00 4.50 3.25 2.00 3.25 5.00 2.00 4.50 3.50 2.00 3.25


6.00 2.00 5.00 6.00 2.00 5.00 6.00 2.00 5.00 6.00 2.00 5.00


7.00 2.00 4.00 7.00 2.00 4.00 7.00 2.00 4.00 7.00 2.00 4.00


3.25 3.00 3.00 3.50 3.00 3.00 3.25 3.00 3.00 3.50 3.00 3.00


4.25 3.00 4.00 4.50 3.00 4.00 4.25 3.00 4.00 4.50 3.00 4.00

Special Moment Frames 8.00 3.00 5.50 8.00 3.00 5.50 8.00 3.00 5.50 8.00 3.00 5.50

FEMA 450 2003 ASCE 7 2005 NYCBC 2008 ASCE 7 2010

UBC 1997 ASCE 7 1998 IBC 2000

FEMA 368 2000 ASCE 7 2002 IBC 2003

If R is taken as 3 for an OCB would special seismic detailing be required

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Basic Load Combinations

ASCE 7-05, Section 2.3

What is E?

LRFD ASD

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Seismic Load CombinationsASCE 7-05

For Basic Load Combination 5

vh EEE For Basic Load Combination 7

vh EEE

Eh QE

DSE DSv 2.0

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Seismic Load Combinations (cont.)

Substituting E into Basic Load Combinations, you get the Seismic Load Combinations as presented in ASCE 7

vh EEE

HQDS

SLQDS

EDS

EDS

6.12.0-0.9 .7

2.02.02.1 .5

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Seismic Load Combinations w/ Overstrength

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Seismic Load Combinations w/ Overstrength (cont)

Substituting Emh into Basic Load Combinations, you get the Seismic Load Combinations as presented in ASCE 7

vh EEE

HQDS

SLQDS

SLQDS

EDS

EDS

EDS

6.12.0-0.9 .7

2.05.02.02.1 5a.

2.02.02.1 .5

0

0

0

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So When Do We Use What Combination?

Basic Load Combinations in Chapter 2

Always

Seismic Load Combinations

Always

Except when overstrength is used

Seismic Load Combinations w/Overstrength

Only for the following:

Except when redundancy is used

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So When Do We Use What Combination?

Seismic Load Combinations with Overstrength

Only for the following:

• Elements supporting discontinuous walls (12.3.3.3)

• Collectors and their connections (12.3.3.4; 12.10.2.1)

• Batter Piles (12.13.6.4)

• Pile Anchorage (12.13.6.5)

• Pile Splices (12.13.6.6)

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Example of Using Overstrength, W0

Consider a 20-story coupled core wall

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Coupled Core Wall SystemLATERAL LOAD

L

T C

M1 M2

Coupled Core Wall System - Elevation LFRS Mechanism CB Shear & Moment Dist.

M

M

V V

0

V

M

M

0

Shear

Moment

L

L/2 L/2

V

TW CW

TW CW

Note that T and C are S(Vb)

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Beam Design

Beam Shear Distribution

Beam Shear (kips)

Flo

or L

evel

Demand (C) Nominal (C) Factored

Design shear demand versus nominal shear capacity gives rise to contributing to the Wd portion of W0

Note that beam is desired to be “shear-critical”

n

Pb V

ML

6.1 i.e.,

Thus, significantly flexural overstrength

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Example of Using Overstrength, W0 (cont.)

Currently, US model codes/specifications do not require overstrength for wall piers in CCW systems

CSA has required this overstrength since mid ’90’s

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Normalized Beam Hysteresis

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-12 -8 -4 0 4 8 12

Chord Rotation (%)

V/V

n

Normalized ratio accounts for measured material properties

Overstrength attributed to • Strain hardening• Stress interaction phenomena (shear-moment uncoupled

in strength calculations)This would contribute to the Wm portion of W0

Note very little, if no, strength or stiffness degradation

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How is this Helpful?

Why should we concern ourselves with such things?

What does this mean in terms of evaluating system overstrength?

So, who cares about beam hysteretic characteristics?

Who cares about available strength versus required strength?

Do we need to consider the axial load beams are capable of delivering to wall piers?

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Design Wall Piers for Beam Overstrength

nDS VDSLDP 2.05.02.1

nDS VDSDP 2.09.0Tension Wall:

Compression Wall:

Wall design axial forces calculated as:

Wall pier design forces increased by wall overstrength factor calculated as:

f

nwall V

V

where,Vn is nominal capacity of the coupling beam; Vf is the design beam shear demand.

gwall is analogous to W0

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Design Wall Piers for Beam Overstrength

Capacity DemandFloor Beam Cap. (includes ) Accum. Accum.

Level Vn V Vn V Wall

(kips) (kips) (kips) (kips)

20 238 83 238 83 2.8619 238 99 475 182 2.6118 238 114 713 295 2.4117 238 129 950 424 2.2416 356 189 1307 613 2.1315 356 203 1663 816 2.0414 356 215 2020 1031 1.9613 356 224 2376 1255 1.8912 480 281 2856 1536 1.8611 480 289 3336 1825 1.8310 480 299 3816 2124 1.809 480 308 4296 2432 1.778 556 348 4852 2780 1.757 556 358 5408 3138 1.726 556 366 5964 3504 1.705 556 370 6520 3874 1.684 546 361 7066 4235 1.673 546 338 7613 4574 1.662 546 288 8159 4861 1.681 546 187 8706 5049 1.72

8706

Wall Overstrength

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Nonlinear Analysis – Evaluate Need for Overstrength

0.00

0.250.50

0.75

1.001.25

1.50

1.752.00

2.25

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Period (seconds)

Sa

(%g)

North Ridge

10% in 50

2% in 50

El Centro

Design SCB: T=2.31secDCB: T=2.63sec

Spring

1231 2427 1829 2427 1231

6683

Spring

SpringBeamRigid

BeamRigid

BeamRigid

BeamRigid

BeamRigid

BeamRigid

Wall P

ierWa

ll Pier

Wall P

ierWa

ll Pier

2743

Typic

al

Location of "Column"Representing Wall Pier,

Typical

Equivalent 2-DFrame

Core Wall,Typical

Properties of Springs andWall Piers Vary Over

The Height of the Building

“Link” modeled as spring with hysteresis model based on measured hysteretic characteristics

Note that the DBE correlates well with the Design Response Spectrum

Fortney, P.J., Shahrooz, B.M., Rassati, G.A., (2008) “Seismic Performance Evaluation of Coupled Core Walls with Concrete and Steel Coupling Beams,” Steel and Composite Structures Journal, V. 7, No. 4, pp. 279-301

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Response History – Wall Piers

-60,000

-40,000

-20,000

0

20,000

40,000

60,000

80,000

-200,000 -100,000 0 100,000 200,000

Moment (kN-m)

Axi

al (

kN

)

NL Response (LW)

NL Response (RW)

CW: Elastic Analysis Demand

TW: ElasticAnalysis Demand

-60,000

-40,000

-20,000

0

20,000

40,000

60,000

80,000

-200,000 -100,000 0 100,000 200,000

Moment (kN-m)

Axi

al (

kN

)

NL Response (LW)

NL Response (RW)



(a) Base wall demands - El Centro (b) Base wall demands - Northridge

-60,000

-40,000

-20,000

0

20,000

40,000

60,000

80,000

-200,000 -100,000 0 100,000 200,000

Moment (kN-m)

Axi

al (k

N)

NL Response (LW)

NL Response (RW)



-60,000

-40,000

-20,000

0

20,000

40,000

60,000

80,000

-200,000 -100,000 0 100,000 200,000

Moment (kN-m)

Axi

al (

kN

)

NL Response (LW)NL Response (RW)



(c) Base wall demands - ASCE 7 (10%) (d) Base wall demands - ASCE 7 (2%)

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Wall Overstrength Compared to System Overstrength

Capacity DemandFloor Beam Cap. (includes ) Accum. Accum.

Level Vn V Vn V Wall

(kips) (kips) (kips) (kips)

20 238 83 238 83 2.8619 238 99 475 182 2.6118 238 114 713 295 2.4117 238 129 950 424 2.2416 356 189 1307 613 2.1315 356 203 1663 816 2.0414 356 215 2020 1031 1.9613 356 224 2376 1255 1.8912 480 281 2856 1536 1.8611 480 289 3336 1825 1.8310 480 299 3816 2124 1.809 480 308 4296 2432 1.778 556 348 4852 2780 1.757 556 358 5408 3138 1.726 556 366 5964 3504 1.705 556 370 6520 3874 1.684 546 361 7066 4235 1.673 546 338 7613 4574 1.662 546 288 8159 4861 1.681 546 187 8706 5049 1.72

8706

Wall Overstrength

20

f

nwall V

V

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Recommendations Coming Soon

Wall pier design axial forces will be:

1.1Ry accounts for material overstrength (including strain hardening), WM

ny VR 1.1

• Recommendations made in HCW report;

• Adopted by AISC Seismic Specification committee for the soon-to-be-released supplement to the 14th Ed.

SVn accounts for design overstrength, Wd

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How Can This be Applied to CBFs

AISC requires connections in SCBFs to transfer RyFyAg

This is a relatively “huge” demand on the connections

However, the braces and columns, and supports are not required to transfer this force

25'

13'

13'

BR,2

F BR,1

R R,x

F

2

F1

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How Can This be Applied to CBFs

Let’s evaluate this a couple of different ways.

First, we’ll look at the support reactions if the AISC connection requirement is satisfied (i.e., transfer RyFyAg)

Second, we’ll look at the support reactions if the connections are detailed using the seismic load combinations with overstrength (i.e., W0QE)

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How Can This be Applied to CBFs (RyFyAg)

225 kips

150 kips

312 kips312 kips

375 kips

422.7 kips

253.6 kips

Brace Size Pu fPnt fPnc RyFyAg

Upper W8x48 253.6 634 288 775.5

Lower W10x54 422.7 711 423 869

cos

cos

cos

,

2,1

,2

lBRx

lBR

uBR

FR

FFF

FF

Assume a frame laterally loaded as shown

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How Can This be Applied to CBFs (RyFyAg)

Brace Size Pu fPnt fPnc RyFyAg

Upper W8x48 253.6 634 288 775.5

Lower W10x54 422.7 711 423 869

771)47.27cos(869cos

83688)47.27cos(869cos

688)47.27cos(5.775cos

,

2,1

,2

lBRx

lBR

uBR

FR

FFF

FF

688 kips

83 kips

758.7 kips758.7 kips

771 kips

869 kips

775.5 kips

Column axial forces 2.4 times larger

Base horizontal reactions 2.1 times larger

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How Can This be Applied to CBFs (W0QE)

Brace Size Pu fPnt fPnc W0QE

Upper W8x48 253.6 634 288 507.2

Lower W10x54 422.7 711 423 845.4

750)47.27cos(869cos

300450)47.27cos(4.845cos

450)47.27cos(2.507cos

,

2,1

,2

lBRx

lBR

uBR

FR

FFF

FF

450 kips

300 kips

624 kips624 kips

750 kips

845.4 kips

507.2 kips

Column axial forces 2.0 times larger

Base horizontal reactions 2.0 times larger

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Support Reactions at Connection Strength Transfer688 kips

83 kips

758.7 kips758.7 kips

771 kips

869 kips

775.5 kips

225 kips

150 kips

312 kips312 kips

375 kips

422.7 kips

253.6 kips

Main Frame Design Forces at RyFyAg

Columns not sized to develop overstrength loadsConnection to supports not designed to transfer overstrength loads

Should philosophy used for wall piers in CCWs be used in main members of SCBFs? Should overstrength equations be used?

450 kips

300 kips

624 kips624 kips

750 kips

845.4 kips

507.2 kips

Forces at W0QE

Note that when using the RyFyAg method, the applied lateral loads get a little “goofy” when trying to keep the system in equilibrium.

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FYI ATC/FEMA P269

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ReferencesAISC, 2005. Seismic Provisions for Structural Steel Buildings (a supplement to AISC Manual of Steel Construction, 13’rd Edition), American Institute of Steel Construction.

FEMA-356 (2000), Prestandard and Commentary for the Seismic Rehabilitation of Buildings, FEMA 356/November 2000, Building Seismic Safety Council, Washington, D.C.

FEMA-450 (2003), NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, FEMA 450/2003, Building Seismic Safety Council, Washington, D.C.

ASCE 7, 2005. Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, Reston, Virginia 20191-440

ICC, 2003. International Building Code 2003, International Codes Council.

ICC, 2009. International Building Code 2009, International Codes Council.

ICBO, 1997. Uniform Building Code 2009, International Conference of Building Officials

Fortney, P.J., Shahrooz, B.M., Rassati, G.A., (2008) “Seismic Performance Evaluation of Coupled Core Walls with Concrete and Steel Coupling Beams,” Steel and Composite Structures Journal, V. 7, No. 4, pp. 279-301

FEMA-P369, 2009, Quantification of Building Seismic Performance Factors, FEMA 356/November 2000, Building Seismic Safety Council, Washington, D.C.

ASCE 7, 2010. Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, Reston, Virginia 20191-440

El-Tawil, S., Harries, K.A., Fortney P.J., Shahrooz, B.M., Kurama, Y., Hasson, M., Tong, S. (2009). “Recommendations for Seismic Design of Hybrid Coupled Wall Systems,” ASCE Special Publication, American Society of Civil Engineers, Reston, VA 20191.

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Copyright 2009

Closing Slide

Seismic System Factors and System Overstrength

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