Post on 29-Mar-2015
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
Steel Lab., Sejong University, Seoul, Korea
Linear Elastic Analysis of System
Member Capacity Check by Design Equation Developed on
Nonlinear Inelastic Concept
Analysis Methods
Introduction
Steel Lab., Sejong University, Seoul, Korea
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.
Steel Lab., Sejong University
Introduction
Load-Displacement
Steel Lab., Sejong University
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
Steel Lab., Sejong University, Seoul, Korea
Nonlinear Inelastic Analyses
2-D Beam-Column
Steel Lab., Sejong University
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
Steel Lab., Sejong University
Nonlinear Analysis
Stability Functions
Nonlinear Analysis
Steel Lab., Sejong University, Seoul, Korea
)( 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
Steel Lab., Sejong University, Seoul, Korea
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
Steel Lab., Sejong University, Seoul, Korea
Nonlinear Inelastic Analysis
Inelasticity Associated with Residual Stresses
Steel Lab., Sejong University, Seoul, Korea
EEt 0.1 yPP 5.0
)1(4yy
t P
PE
P
PE
yPP 5.0
for
for
Nonlinear Inelastic Analysis
Inelasticity Associated with Flexure
Steel Lab., Sejong University, Seoul, Korea
for
for
0.1 5.0
)1(4 5.0
Nonlinear Inelastic Analysis
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
Steel Lab., Sejong University, Seoul, Korea
Nonlinear Inelastic Analysis
Force-State Parameter()Orbison (1982)
242622422 65.40.367.315.1 yzyzyz mmmpmpmmp
yPPp
pzzz MMm
pyyy MMm
Where,
(strong-axis)
(weak-axis)
Steel Lab., Sejong University, Seoul, Korea
Nonlinear Inelastic Analysis
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
Steel Lab., Sejong University, Seoul, Korea
Nonlinear Inelastic Analysis
Column
Verification
Steel Lab., Sejong University, Seoul, Korea
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
Steel Lab., Sejong University, Seoul, Korea
Load-Displacement
Verification
Steel Lab., Sejong University, Seoul, Korea
Proposed Modeling
Modeling and Design Principles
Steel Lab., Sejong University, Seoul, Korea
요소수 : 10 개
ABAQUS Modeling
요소수 : 50,000 개
Modeling and Design Principles
Steel Lab., Sejong University, Seoul, Korea
Geometric Imperfection
Braced Member Unbraced Frame
Modeling and Design Principles
Steel Lab., Sejong University, Seoul, Korea
Design Format
AISC-LRFD : member
Proposed : system
m
iniin QrR
1
Modeling and Design Principles
Steel Lab., Sejong University, Seoul, Korea
Twenty-Two Story Frame
Design Example
Steel Lab., Sejong University, Seoul, Korea
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
Steel Lab., Sejong University, Seoul, Korea
Member Sizes of 22-Story Frame
Beams
Columns (1-11 story) Columns (12-22 story)
Design Example
Steel Lab., Sejong University, Seoul, Korea
Load-Displacement
Design Example
Steel Lab., Sejong University, Seoul, Korea
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
Steel Lab., Sejong University, Seoul, Korea