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2/3/2017

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PRACTICAL USES OF NONLINEAR PUSHOVER ANALYSIS

Jerod G. Johnson, PhD, SE

SEAU Education Conference February 22, 2017

SEAU: 2017 Education Conference

Disclaimer

This presentation is meant to neither explicitly endorse nor discourage

the use of the nonlinear pushover analysis method for any given design

scenario. As with any method, nonlinear pushover has its benefits and

limitations. Whether nonlinear pushover analysis is appropriate lies at

the discretion of the engineer in responsible charge.

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Presentation Outline1. What is Nonlinear Analysis?

2. What is Nonlinear Pushover Analysis?

3. Why Use Nonlinear Pushover Analysis?

4. What are the Common Perceptions?

5. Embracing Innovation.

6. Embracing Nonlinearity.

7. Nonlinear Pushover Analysis – A Good First Step.

8. Nonlinear Element Modeling

9. Examples

10. Nonlinear Pushover Limitations

11. Time History – Quick Summary

12. Software


1. What is Nonlinear Analysis?

Simple Definition of Nonlinearity:

An alteration of material, element or system modeling properties as a function of load (including direction of load), displacement, deformation or velocity.

Wikipedia:

In physical sciences, a nonlinear system is a system in which the output is not directly proportional to the input.

Simple example – a tension only element.

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Types of Nonlinearity

• Geometric Nonlinearity – Also known as P-Delta.

• Rate Dependent Nonlinearity – Properties change as a function of rate

(e.g. viscous damper)

• History Dependent Nonlinearity – Properties change as a function of

repeated load (cumulative ductility or fatigue).

• Cyclical Dependent Nonlinearity – Change of hysteretic properties

(e.g. tension only braces).

• Contact Nonlinearity (e.g. footing/soil interface, pounding)

• Material Nonlinearity – e.g. yielding of steel.


1

P

F2

3

P

θ2θ3

F 24EI/L3 6EI/L2 6EI/L2 -6P1/5L-6P3/5L -P1/10 -P3/10 u1

0 = 6EI/L2 8EI/L 2EI/L + -P1/10 -2P1L/15-2P2L/15 -P2L/30 θ2

0 6EI/L2 2EI/L 8EI/L -P3/10 -P2L/30 -2P2L/15-2P3L/15 θ3

Basic Stiffness Matrix:

Stiffness reduction matrix due to geometric nonlinearity:

Forces: Displacements:

Axial loads in members (1, 3) change as a result of load F.

This example is for illustrative purposes and assumes equal member lengths and section properties

Note: The P1, P2 and P3 forces are the developed frame forces which are resolved through iterative processes.

u1

Geometric Nonlinearity

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Rate Dependent Nonlinearity


History/Cyclical Dependent Nonlinearity

Slen

derIntermediate

StockyConcentric Braces

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Contact Nonlinearity

-1

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30

Footing Deflection

Pounding


Material Nonlinearity

Some materials are more ductile than others….Some materials behave better when confined….

Structural Steel – Fy = 50ksi Rebar– fy = 60ksi

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Material Nonlinearity (cont.)

Some materials are less ductile than others….Some materials behave better when confined….

Unconfined Concretef’c = 4000psi

Confined Concretef’c = 4000psi

Mander Concrete Model



“Ductile” systems are driven to enable material nonlinearity.

This is the basis behind:• Ties and confinement in “Special”

reinforced concrete sections.• Lateral bracing of moment frame beams in

SRMF and OMF.• Lateral bracing of beams in other BF

systems.• The casing and grout of a BRB.• Definitions of seismic compactness.

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“Ductile” systems are driven to enable:

Element Nonlinearity

Repeated cycles of stable (material) nonlinearity are preferred and even encouraged in the codes. This is reflected in the R factors. Let’s observe…

R R R R R R R R R R R R??Non-Degrading Stiffness Degrading Pinched Buckling

∆

F F F F

∆ ∆ ∆

BRB/SRMF SCSW OCBF

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2. What is Nonlinear Pushover Analysis?

Piecewise monotonically displacing a structure consistent

with a rational loading pattern while explicitly accounting for

nonlinearity of specific lateral force resisting elements

(plastic hinges). The displacement magnitude of the

structure is compared against the reactions that develop as

nonlinear mechanisms develop.


What is Nonlinear Pushover Analysis?

∆

rxnrxn

0

200

400

600

800

1000

1200

0 2 4 6 8 10

Base S

hear

Rooftop Displacement

Base Shear vs. Displacement

Nonlinear

Linear

∆

��

4��

How is this performed?

C0 – SDOF to MDOF Modifier.C1 – Elastic to Inelastic Modifier.C2 – Pinched Hysteresis Modifier.C3 – P-Delta Modifier

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3. Why Use Nonlinear Pushover Analysis?

• Explicit accounting of nonlinearity.

• More accurate prediction of member forces.

• More accurate prediction of base shear.

• More direct prediction of displacements.

• Offers consideration of multiple performance

scenarios.

• Provides a rational methodology for higher ductility

demand and/or irregular structures (per ASCE 41)

• Does not require input ground motions.

• Credit where credit is due (ASCE 41).


Why Use Nonlinear Pushover Analysis? (cont.)

• Direct accounting of performance (as opposed to

prescriptive design).

• Less conservative than ELF, Lower construction cost.

Is the cost of construction proportional to the

complexity of the design approach?

$ C

on

str

uctio

n

Design Complexity ($)

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Performance can be better than expected:

“…observed seismic performances of three existing buildings in

Christchurch subjected to the 2011 Lyttleton event were compared

to the predicted performance of the analytical nonlinear models of

the subject buildings. In general, the observed performance of the

buildings was found to be better than that predicted by the

analytical models.”


Performance can be better than expected (cont.)

If performance is better than predicted by the most sophisticated of

nonlinear analysis procedures then how conservative are the

provisions using equivalent lateral force static methods?

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If performance is often better than expected, then the tools

for analysis and design may be too conservative.

Does it make sense to embrace a design methodology that

is more complex but produces a less conservative design?

A more complex design approach is more costly but can

yield major savings in construction along with a more

reliable (targeted) outcome. This is especially relevant in

today’s discussion regarding resiliency.

.

Performance can be better than expected (cont.)


4. What are the common perceptions?

March 2014 Issue of Structure Magazine reported the following results of

a survey of Academician/Research Engineers, Industry Professionals,

Consultants and others…

• More than 75% of respondents said that guidance for most of these topics [nonlinear

analysis and design] was ambiguous.

• Claims of inadequate software (21%), too complicated (29%), not practical/time

consuming (61%), lack of research (22%), lack of guidelines (43%).

• More guidance is needed for: Modeling NL Elements (42%), NL Procedures (18%),

Benchmark problems with solutions (35%).

Head, Dennis, Muthukumar, Nielson, Mackie – StructureMagazine, March 2014

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What are the common perceptions? (cont.)

“…there is a need to be able to communicate to the importance of doing nonlinear analysis

to the owners, as the apparent gain to pay for a more extensive analysis is not always clear.”

“Nonlinear analysis can be used when owners request ways to reduce costs (for new

construction) by optimizing material use, more likely though as demonstrating a building

retrofit is perhaps not even necessary (or if it is, that only minor changes/systems are

needed rather than what the code would require), or even as a way of quantifying

performance for owners, insurance and risk managers that may look at inventories of

structures. So, the major question to the owner is whether they’d prefer to pay now or pay

later?”


From the Experts… (March 2016 Structure Magazine)

When to conduct NL Analysis

• Irregular building type

• Assumptions of code-based linear are not valid

• Retrofitting

• Viscous dampers, isolators or new type of LFRS

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From the Experts… (March 2016 Structure Magazine)

• NL Procedures are “time consuming, computationally demanding and required added

cost of a peer review” Not to mention the added cost of design.

• Pushover analysis should not be used as the sole measure and not be needed if one is

performing a nonlinear time history.

• Pushover is less useful for drift/ductility, but rather to help proportion the structure to

activate any intended ductile mechanism.

• Pushover not appropriate for multi-mode buildings.

• “…the need for more education and training on advanced topics like nonlinear analysis

cannot be overstated.”

• “Pay now or pay later?”

Head, Pathak, Muthukumar, Mackie– StructureMagazine, March 2016

5. Embracing Innovation

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A Tip Calculator?

Much more than a tip calculator!....

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What do we do…fundamentally?

Design Buildings?

How?

Mathematical Models…

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What was the basis of these equations?:

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∑ ��

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Mathematical Models:

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We Use Mathematical Models to:

• Predict behavior of structural systems with respect to theoretical load.

• Ensure structures are sufficiently strong to resist the anticipated load.

• Reliably predict loads a structure may experience.• Reliably predict the minimum strength of structural elements.

Mathematical Models:

Mn=FyZx Mn=Asfy(d-a/2)

T� 2�"

#

F 24EI/L3 6EI/L2 6EI/L2 u1

M2 = 6EI/L2 8EI/L 2EI/L θ2

M3 6EI/L2 2EI/L 8EI/L θ3

$%& ' (%) ' *% � +,-.

φPn,max = 0.80φ[0.85f ’c(Ag-Ast) + fy(Ast)]

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Tools of the Trade…Today:

� � ��

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��

��

��

�

∑ ��

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Evolution of Computer Power:

Moore’s Law: The number of transistors in a dense integrated circuit doubles approximately every two years.-Gordon E. Moore – co-founder of Intel Corporation and Fairchild Semiconductor.

This law is now used in the semiconductor industry to guide long-term planning and to set targets for research and development.

What does this say about the advancement of computer power over the last 20 years?

Increase = 210 = 1,024

How about the last 40 years?

Increase = 220 = 1,048,576

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Moore’s Law:https://en.wikipedia.org/wiki/Moore%27s_law

Embracing Nonlinearity

It can do more than equivalent lateral forces!

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6. Embracing Nonlinearity

Re: ASCE 41, FEMA P695, Others

Lumped Plasticity Models


Professor Ed Wilson:

“The enormous increase in speed and memory capacity of inexpensive personal computers and the development of new numerical methods allow structural engineers to conduct earthquake response analysis of large and complex three-dimensional structures. Therefore, I am

optimistic many structural engineers will

realize linear and non-linear time-history

dynamic analysis of structures is not difficult

and performance based design is now a

reality.”

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Professor Ed Wilson (cont.):

“After fifty years of conducting linear and non-linear earthquake analyses of many different types of structures, I am concerned with the increase in use of the approximate Response Spectrum Method. The fundamental equilibrium equations are not satisfied for systems over one-degree-of-freedom. In addition, the application of the method to

nonlinear structural analysis has no theoretical or physical

justification.”

So, what is Dr. Wilson Talking About?

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Higher Mode Response

Multi-Degree of Freedom Systems

1.4 Seconds 0.67 Seconds


91% Mass

Activation



Multi-Degree of Freedom

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The simple calculation of story drifts is not appropriate when using dynamic response spectrum analyses because combined modal displacements can be less than the combined modal story drift (signs are lost). This is a consequence of simplified approaches.



“…..the application of the method to nonlinear structural analysis has

no theoretical or physical justification.”

In other words, what happens to these mode

shapes when yielding occurs?


91% Mass

Activation


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7. Nonlinear Pushover Analysis – A Good First Step

• A good ‘first step’ into the larger world of nonlinear analysis.

• A good ‘first step’ into the advanced capabilities of the tools we use.

• A good tool for helping us understand the basis behind many code provisions.

• Primary Shortcoming; how to handle higher mode effects.


A Nonlinear Model:

• Includes explicit modeling of mechanisms (ductile and brittle) that are likely to occur as material limit states are reached and surpassed.

• Remember, a material or element reaching to a limit state doesn’t necessarily mean collapse. A system failure means collapse.

What has been asked in regions of low seismicity?

Why would you want something to yield?-Targeted nonlinearity, fuse, system control, reduction of forces.

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A Nonlinear Model

Nonlinear models explicitly include nonlinear mechanisms or nonlinear material behaviors that become activated upon reaching a theoretical load or displacement threshold.

Linear

Nonlinear

Linear:

σ = εE

Nonlinear:

σ = ??


Consider a Beam Approaching it’s Flexural Limit State:

Mn=FyZx

Fb=M/S

Elastic Elasto-Plastic Plastic

Stress Diagrams

Fy Fy

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Strain Diagrams

How do the strain diagrams correlate?

Stress Diagrams


Consider a Concrete Beam:

Mn=Asfy(d-a/2)

σc

Stress Diagrams

0.85f’c

σs


fy

σc

fy

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Strain Diagrams

How do the strain diagrams correlate?

Stress Diagrams


εcu=0.003

εt>0.00207εt>0.00207εs

εc εc


Comparing Strain and Curvature

Strain(ε)

d/2

φCurvature: φ = ε/(d/2)

N.A.

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Consider Load vs Curvature Diagram:

Moment Curvature Chart

0

50

100

150

200

250

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Curvature (1/in)

Mo

men

t (k

-ft)

Mn




0

50

100

150

200

250

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Curvature (1/in)

Mo

men

t (k

-ft) What if the beam is not ductile?

e.g. an over-reinforced or under-reinforced concrete beam?e.g. a steel MF beam w/ lack of lateral bracing?

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0

50

100

150

200

250

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Curvature (1/in)

Mo

men

t (k

-ft)

Some other unstable behavior may occur before stable hysteretic nonlinearity develops.


8. Nonlinear Element Modeling

• Lumped (Concentrated) Plasticity

• Distributed Plasticity (forced based fiber nonlinearity)

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Nonlinear Building Modeling

• Lumped (Concentrated) Plasticity vs• Distributed Plasticity (forced based fiber

nonlinearity)

+

• Nonlinear Static Analysis (Pushover) vs• Nonlinear Dynamic Analysis


Nonlinear Static vs. Nonlinear Dynamic?

Key Differentiators:• Geoseismic Input• Time• Complexity• Project Needs• $$• Software

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Beam Rotation (rad)

Beam

Fo

rce (

kip

-in

)

Nonlinear Static Pushover Curve

0

50

100150

200250

300

350400

450500

0 10 20 30 40 50 60

Roof Displacement (inches)

Base

Fo

rce (

kip

s)

Element Hysteretic Response

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Nonlinear Analysis

• Explicitly includes either lumped plasticity elements or distributed plasticity elements to predict a system’s response

to an input function.

• May use either piecewise static analysis (pushover) or a full response-history analysis.


Lumped (Concentrated) Plasticity:

Mn=FyZx

Fy

Mn=Asfy(d-a/2)

0.85f’c

fy

These very familiar models represent the ultimate strength limit state of these beams.

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Lumped Plasticity Example:

Plastic flexural hinge will develop at the support

W14x159


Lumped Plasticity Example

Force

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Nonlinear Pushover:

Force

Reaction

Pattern

∆

Force


Nonlinear Pushover:

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Nonlinear Pushover:


Nonlinear Pushover:

The ‘flat’ nonlinear region is simply a reflection of the flat hysteretic backbone of the input

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Nonlinear Pushover:

The ‘flat’ nonlinear region is simply a reflection of the flat hysteretic backbone of the input

Why displacement vs. reaction and not moment vs. rotation or curvature?


Distributed Plasticity:Reinforcement

Confined Concrete

Unconfined Concrete

Note: this column may require at least 7 layers of material to effectively model

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Distributed Plasticity Example:



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Distributed Plasticity Example – Pushover:

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Comparison:

Distributed Plasticity Lumped Plasticity


Strain Hardening?

Distributed Lumped

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Comparison

Distributed Lumped

2 Min. 52 Sec. 0.14 Sec.


Key Differentiators:• Time• Complexity• Project Needs• $$• Accuracy• Software

Lumped Plasticity vs. Distributed?

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Nonlinear Dynamic – Distributed Plasticity


Nonlinear Pushover

Can use either lumped (discrete) plasticity models, sometimes called “links” or “hinges” or the elements may be included with

specific material nonlinearities with explicit modeling using nonlinear fiber or shell type elements.

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Nonlinear Pushover

Can, in more explicit terms than elastic analysis, identify and quantify specific mechanisms and the order in which they are

expected to occur.

Nonlinear Pushover Larger Application:

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Base Reaction

Roof Displacement

Nonlinear Static Analysis (Pushover)


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Knowing the order of hinge occurrence may or may not be important, but knowing that beam hinging is likely to dominate the nonlinear behavior is important



050

100150

200250300

350400

450500

0 10 20 30 40 50 60


Ba

se

Fo

rce

(k

ips

)

��

4��


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050

100150

200250300

350400

450500

0 10 20 30 40 50 60


Bas

e F

orc

e (

kip

s)

Imm

ed

iate

Occu

pan

cy

Lif

e

Safe

ty

Co

llap

se

Pre

ven

tio

n

Dam

ag

e

Co

ntr

ol



Nonlinear Pushover

• Can help us understand the basis behind code provisions.

• Can help us understand the consequences of element failure (e.g. brace buckling).

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Nonlinear Pushover

Braced Frame – Unbalanced Forces:AISC 341-10 F1-4a, F2-3.

In ‘V’ and inverted ‘V’ configurations, beams in braced frames must account for unbalanced effects of braces reaching full yield strength and post-buckled compression strength.


Frame 1 Frame 2 Frame 3

Simple Frame ComparisonsA case study in the consequences of buckling


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Frame 1


Frame 1

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Frame 1


Frame 1

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Frame 1


Frame 1

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Frame 2


Frame 2

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Frame 2


Frame 2

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Frame 2


Frame 3

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Frame 3


Frame 3

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Frame 3


Frame 3

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Pushover Curves Superimposed

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14

Ba

se S

he

ar

(kip

s)

Rooftop Displacement (inches)

Frame 1

Frame 2

Frame 3

1

2

3


A Caveat…

While this example corroborates the requirements of AISC 341, research by Sen, Roeder, Lehman & Berman at University of Washington shows much better performance in braced frames when quasistatically loaded under a fully reversed increasing amplitude cyclical protocol…

See Structure Magazine – July 2015

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Nonlinear Pushover

Strong column/weak beam:AISC 341-10 E3-4a

Requires that the sum of nominal flexural strengths of columns at a joint must be greater than the sums of the flexural strengths of the beams (with over-strength included) at the same joint.

Why?

Beam mechanisms are preferred over column mechanisms.


The Stability Issue

1

P

F 2

3

Pθ2 θ3

What happens if the geometric nonlinear stiffness matrix overpowers the initial matrix?

24EI/L3 6EI/L2 6EI/L2 -6P1/5L-6P3/5L -P1/10 -P3/10

6EI/L2 8EI/L 2EI/L + -P1/10 -2P1L/15-2P2L/15 -P2L/30

6EI/L2 2EI/L 8EI/L -P3/10 -P2L/30 -2P2L/15-2P3L/15

The effects of geometric nonlinearity can become greater than the effects of strain hardening.

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Pushover Analysis:

Base Reaction

Roof Disp.

0

50

100

150

200

250

300

350

400

0 2 4 6 8 10B

ase S

hear




The Stability Issue

What is happening here?:

0

50

100

150

200

250

300

350

400

0 2 4 6 8 10

Base S

hear



W/O P-delta

W/ P-delta

Residual column forces create reduced stiffness which creates increased displacements which create even more residual column forces.

This is a consequence of columns which yield in flexure before beams yield in flexure.

1

P

F2

3

Pθ2 θ3

Geometric nonlinearity

controls over strain hardening

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Problems with Beam/Column Strength Ratios

Base Reaction

Roof Disp.

0

50

100

150

200

250

300

350

400

0 2 4 6 8 10B

ase S

hear



W/O P-delta

W/ P-delta


Nonlinear Pushover

A more elaborate demonstration.

Nonlinear Pushover can help us understand the effectiveness of a reinforcement scenario…

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North-South Pushover



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Failure occurs at 38 inches rooftop displacement


North-South Pushover Curve

Pushover Curve

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25 30 35 40

Displacement (in)

Base S

hear

(kip

)

Approximated displacement for a quake can be calculated using classical methods, adjusted to account for altered stiffness (and other factors).

��

4��

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Nonlinear Pushover

Can help us understand alternate load paths that may develop as members are pushed to failure…


Nonlinear Pushover

Consider a multi-tiered braced frame with pseudo-static lateral forces:

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Nonlinear Pushover

Member forces based strictly upon the input loads would be:

Do these forces really reflect the design level earthquake?


What are the consequences of braces buckling in compression?

Nonlinear Pushover

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A typical brace hysteretic backbone:

What happens in the frame as these axial mechanisms begin to form?

-400

-300

-200

-100

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5Axi

al F

orc

e (

kip

)

Axial Deformation (in)

Brace Hysteretic Backbone

Nonlinear Pushover


-400

-300

-200

-100

0

100

200

300

400

500

600

-2 0 2 4 6

Axi

al F

orc

e (

kip

)

Axial Deformation (in)

Brace Hysteretic Backbone

Concept courtesy of Brent Maxfield, SE

Nonlinear Pushover

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A ‘pseudo’ nonlinear approach?

Nonlinear Pushover


Can help us demonstrate the validity of a new approach…

Nonlinear Pushover

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Bennett Federal BuildingSalt Lake City

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Buckling Restrained Brace Concept

Images Courtesy of Corebrace

tension

compression

Axial force-displacement behavior

unbondedbrace

typicalbuckling

brace

displacement

-80

-60

-40

-20

0

20

40

60

80

-3 -2 -1 0 1 2 3

Str

ess

(k

si)

Strain (%)

Unbonded Brace Hysterisis Backbone

Fye=51.7 ksi

Fmax=62.8 ksi

Fye=-51.7 ksi

Fmax=-65.2 ksi

TENSION

COMPRESSION

Intermediate

Local buckling less criticalthan inelast ic buckling

-60

-40

-20

0

20

40

60

80

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

Str

ess

(ksi

)

Strain (%)

Special Concentric Brace Hysterisis Backbone

TENSION

COMPRESSION

Fye=55 ksi

Fmax=68.8 ksi

27.5 ksi

-42.24 ksi

-8.45 ksi

Buckling Restrained Brace Concept

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05000

100001500020000250003000035000400004500050000

0 5 10 15

Base S

hear

-kip

s

Roof Displacement - Inches

Bennett Federal BuildingN-S Push-over V vs Roof Displacement

SCBF

BRBF

BRBF Braces Begin to Yield

SCBF Braces Begin to Buckle

Nonlinear Pushover

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Nonlinear Pushover

Can help us understand what happens with combinations of systems in a more explicit manner…


Horizontal Combinations

In the same direction, along the same line - Shear Wall and Moment frame:

12’

20’20’

w18x60

w1

4x1

20

w1

4x1

20

strut

12” thick wallf’c=4,000psiI = 0.35Ig

100k

w18x60

0.98k0.98k 98.04k

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In the same direction, along the same line - Shear Wall and HeavyMoment frame:

12’

20’20’

w30x261

w2

4x3

70

w2

4x3

70

strut

12” thick wallf’c=4,000psiI = 0.35Ig

100k

7.69k7.69k 84.62k



This demonstrates one immutable truth:

Loads follow the path of most resistance

Unless a stiffness compatibility exists, logic may predicate that the less

rigid system be abandoned entirely.


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What happens if the stiffness of the load path changes as a result of loading (or deforming)?

Dual System?



What does nonlinear pushover predict for this scenario?

• Let’s use ρ = ρmin (0.0015) for vertical reinforcement

• Let’s use lumped plasticity models


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Lumped Plasticity Approach:




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0

100

200

300

400

500

600

0 1 2 3 4 5 6 7

Base S

hear

(kip

)

Displacement (in)

Pushover Curve


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Nonlinear pushover demonstrates that the concrete wall does virtually all of the work and must literally become compromised before the steel frame begins to act.

Unless a stiffness compatibility exists, logic may predicate that the less rigid system be abandoned entirely.



Another Approach?

Use of distributed plasticity elements in lieu of lumped plasticity…

Account for nonlinearity of materials instead of nonlinearity of sections…


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concrete

reinforcement

12” thick wall with ρvert = 0.0015



Stress in Reinforcement

Stress in Concrete


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Stress in Concrete




Stress in Concrete


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Stress in Concrete




Stress in Concrete


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0

50

100

150

200

250

300

350

400

0 1 2 3 4 5 6 7

Base S

hear

(kip

)

Displacement (in)

Pushover Curves



Nonlinear Pushover

Can help us demonstrate that a system or geometry can work.

Large scale example – Combination of Systems

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Seismic Retrofit

Nonlinear Pushover

Nonlinear PushoverSeismic Retrofit

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Case Study – College of Nursing


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Seismic Retrofit

Pushover demonstrated that the existing core walls could satisfy performance objectives while working in concert with new braced frames.

Nonlinear Pushover

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10. Nonlinear Pushover Analysis Limitations…

• Does not directly account for cyclic behavior.

• Does not adequately capture higher mode effect.

• Does not have an explicit accounting for displacement.

• Does not account for highly transient effects (near field,

unidirectional pulse).

• No accounting for cumulative ductility or cumulative

energy.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

Time (sec)

Accele

ration (g)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70 80

Time (sec)

Accele

ration (g)


10. Nonlinear Time History – Quick Summary

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Nonlinear Dynamic Analysis - MF


Nonlinear Dynamic Analysis - MF

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Beam Rotation (rad)

Beam

Fo

rce

(kip

-in

)

Area within the enclosed force vs. displacement loop is energy dissipated

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Nonlinear Dynamic Analysis – BF/BRBF

Red = Yielding and/or Buckling


Keeping it Simple?

Successful & efficient nonlinear modeling requires a targeted

approach.

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So, why not use Nonlinear Time History?

• Time• $$• Ground Motions• Owner Objectives• Computing Power• Review


Software

• Hand 1.0 (by Ron Hamburger)• SAP 2000 Ultimate• ETABS Ultimate• Perform 3D• STAAD Pro• Opensees (Open System for Earthquake Engineering Simulation,

NEES)• ANSYS• LS Dyna• ANSR (proprietary)

• RISA?

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The End

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