Development of Software for Practical Nonlinear Inelastic Analysis S.E. Kim Department of Civil and...

Development of Software for Practical Nonl

inear Inelastic Analysis

S.E. Kim

Department of Civil and Environmental Engineering Sejong University

Seoul, Korea

Steel Lab., Sejong University, Seoul, Korea

Contents

Introduction

Nonlinear Analysis

Nonlinear Inelastic Analysis

Verification

Modeling and Design Principles

Design Example

Conclusions

세종대학교 Steel Lab

Incompatibility of Conventional Design Procedure

Introduction


Linear Elastic Analysis of System

Member Capacity Check by Design Equation Developed on

Nonlinear Inelastic Concept

Analysis Methods

Introduction


P

a aPP

Design Methods

Steel Lab., Sejong University

Introduction

Benefit of Nonlinear Inelastic Analysis

• Accounts for geometric and material nonlinearities.

• Not necessary for separate member capacity check.

• Overcomes the difficulties due to incompatibility.


Introduction

Load-Displacement


Introduction

• FEM(ABAQUS, ANSIS, etc.)– Accurate but not practical

• Plastic – Zone– Accurate but not practical

• Second – Order Modified Plastic Hinge – Acceptably accurate and practical

Introduction


Nonlinear Inelastic Analyses

2-D Beam-Column


Nonlinear Analysis

2-D Force - Displacement

1 2

2 1

0

0

0 0

A A

B B

M S SEI

M S SL

P A e

I

:, 21 ss Stability Functions


Nonlinear Analysis

Stability Functions

Nonlinear Analysis


)( 3s

2

1 2

sin( ) cos( )0

2 2cos( ) sin( )

cosh( ) sinh( )0

2 2cosh( ) sinh( )

if P

S

if P

)( 4s

2

2 2

sin( )0

2 2cos( ) sin( )

sinh( )0

2 2cosh( ) sin( )

if P

S

if P

),//( 22LEIP positive in tension:P

3-D Force - Displacement

Nonlinear Analysis


zB

zA

yB

yA

zz

zz

yy

yy

zB

zA

yB

yA

L

GJL

EIS

L

EIS

L

EIS

L

EIS

L

EIS

L

EIS

L

EIS

L

EIS

L

EA

T

M

M

M

M

P

00000

0000

0000

0000

0000

00000

34

43

12

21

:),(,,, 4321 EIPfssss Stability Function

Inelastic Nonlinear Force - Displacement

0 0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0 0

t

yA yAiiy ijy

yB yBijy jjy

zA zAiiz ijz

zB zBijz jjz

E AP LM k k

M k k

M k k

M k k

T GJ

L

22

11

( (1 )) t yiiy A B

E ISk S

S L 2

t yijy A B

E Ik S

L

22

11

( (1 )) t yjjy B A

E ISk S

S L

24

33

( (1 )) t ziiz A B

E ISk S

S L 4

t zijz A B

E Ik S

L

24

33

( (1 )) t zjjz B A

E ISk S

S L



Inelasticity Associated with Residual Stresses


EEt 0.1 yPP 5.0

)1(4yy

t P

PE

P

PE

yPP 5.0

for

for


Inelasticity Associated with Flexure


for

for

0.1 5.0

)1(4 5.0


Force-State Parameter()

AISC-LRFD (Kanchanalai 1977)

zp

z

yp

y

y M

M

M

M

P

P

9

8

9

8

zp

z

yp

y

y M

M

M

M

P

P

9

2

9

2

zp

z

yp

y

y M

M

M

M

P

P

2

zp

z

yp

y

y M

M

M

M

P

P

9

2

9

2

for

for



Force-State Parameter()Orbison (1982)

242622422 65.40.367.315.1 yzyzyz mmmpmpmmp

yPPp

pzzz MMm

pyyy MMm

Where,

(strong-axis)

(weak-axis)



Modification of Element Stiffness for the Presence of Plastic Hinge at End A

2

2

0 0 0 0 00

0 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

t

ypcA

ijy ijy ypcAyA yAjjy

iiy iiyyB yB

zA zA zpcA

zB zBijzjjz

iiz

E A

L

MP

C C MMC

C CM

M M

M CC

T C

GJ

L

0

ijz zpcA

iiz

C M

C

2

2iiy jjy ijy iiy sz

iiyiiy jjy ijy sz

k k k k A GLC

k k k A GL

2

2iiy jjy ijy ijy sz

ijyiiy jjy ijy sz

k k k k A GLC

k k k A GL

2

2iiy jjy ijy jjy sz

jjyiiy jjy ijy sz

k k k k A GLC

k k k A GL

2

2iiz jjz ijz iiz sy

iiziiz jjz ijz sy

k k k k A GLC

k k k A GL

2

2iiz jjz ijz ijz sy

ijziiz jjz ijz sy

k k k k A GLC

k k k A GL

2

2iiz jjz ijz jjz sy

jjziiz jjz ijz sy

k k k k A GLC

k k k A GL



Column

Verification


Orbison’s Six-Story Space Frame

Material property

Yield Stress 36 ksi

Young’s modulus 30,000 ksi

Shear modulus 11,500 ksi

Load

Uniform floor pressure 100 psf

Wind load 6 kips (in the Y-direction)

Verification


Load-Displacement

Verification


Proposed Modeling



요소수 : 10 개

ABAQUS Modeling

요소수 : 50,000 개



Geometric Imperfection

Braced Member Unbraced Frame



Design Format

AISC-LRFD : member

Proposed : system

m

iniin QrR

1



Twenty-Two Story Frame

Design Example


Material property

Yield Stress 36 ksi

Young’s modulus 30,000 ksi

Shear modulus 11,500 ksi

Load

Uniform floor load 115 psf

Wind load 7. 8 kips (in the Y-direction)

Plan and Elevation of 22-Story Frame

Plan Elevation

Design Example


Member Sizes of 22-Story Frame

Beams

Columns (1-11 story) Columns (12-22 story)

Design Example


Load-Displacement

Design Example


22.1

0.1

36.19.0

nii

n

Qr

R

Conclusions

A practical inelastic nonlinear analysis of three-dimensional steel fram

es has been developed

Stability functions enable only one or two element per member to capt

ure nonlinear effects

The CRC tangent modulus and softening plastic hinge model predict i

nelastic behavior reasonably well

The proposed analysis can be used in lieu of the costly FEM analysis

The proposed design method overcomes the difficulties due to incomp

atible of ASD and LRFD


Development of Software for Practical Nonlinear Inelastic Analysis S.E. Kim Department of Civil and...

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