Two Calculation Methods for Overall Stability Coefficients of Stainless … · 2016. 11. 13. · Stability typical problem of stainless steel structural members Experimental investigation

Two Calculation Methods for Overall

Stability Coefficients of Stainless Steel

Welded I-section Beams

Stainless Steel in Structures

Lu Yang, Yuanqing Wang*, Bo Gao

Yongjiu Shi, Huanxin Yuan

6 DEC 2012

Fourth International Experts Seminar


Contents

Introduction

Experimental investigation

Numerical simulation

validation & parametric analysis

Proposed formulae for the overall stability coefficient


Introduction

Advantages of stainless steel

Research background stability: typical problem for stainless steel structural members

lack of reseach on stainless steel beams with built-up sections

the design code for stainless steel structures is underway in China

Research framework

Experimental tests

Parametric analysis

8 specimens

315 cases

validating

Proposed method I

Proposed method II

modification

regression

Comparison with EC3

Specimen Test result PExp(kN)

S-1 184.17

S-2 236.54

S-3 262.92

S-4 333.92

S-5 397.04

S-6 442.68

S-7 346.91

S-8 428.32


Test program

Test set-up

Coupon test

Deformed shapes Ultimate loads



Stress-strain relationship

Ramberg-Osgood expressions(Gardner, Quach)

Welded residual stress distribution

(Gardner and Cruise, 2009)

1.5tf

1.3fy

fc

1.3fyfc

3tw

1.5tw

+

+

+

+

1.5tf1.5tf



FE model

initial imperfection(scaled)

Initial imperfection The first buckling mode with

an amplitude of L/1000

σ/MPadistribution of residual

stresses


Validation of numerical models

test results

Failure mode

FEA results

Load-deformation curves

S-2 S-5


Validation of numerical models

Ultimate loads

Specimen Test result

PExp(kN)

FEA result

Prs(kN) PExp/Prs

FEA result

Pnr(kN) PExp/Pnr

S-1 184.17 175.02 0.95 187.08 1.02

S-2 236.54 230.57 0.97 226.31 0.96

S-3 262.92 246.59 0.94 257.48 0.98

S-4 333.92 342.88 1.03 351.63 1.05

S-5 397.04 400.45 1.01 407.70 1.03

S-6 442.68 447.43 1.01 453.58 1.02

S-7 346.91 335.14 0.97 347.28 1.00

S-8 428.32 443.95 1.04 460.82 1.08

Mean 0.99 Mean 1.02

with residual stresses without residual stresses


Parametric analysis

FE model a total of 315 cases with typical sections, different slenderness ratios,

and different load conditions

1

1

2 2 2 22

3

3

3

4

4

3

4

4

(a) (b) (c) (d) (e)cross-sections

load conditions


Proposed method I

Basic idea Based on the provisions for carbon steel structures, considering the

strength reduction for the material non-linearity of stainless steel

193000

205

4.41

4646 0

2.0

2

1

2

E

fh

t

W

Ah yb

xy

bb

1

1+ 1.0n nb b bm m=n=0.8

elastic theory

GB 50017-2003

material non-linearity modified

Proposed method I


Proposed method I

Calculation results

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Section (a)

Calculated results of φb by proposed method I

FE

A r

eslu

ts o

f φ

b

Reference line with unit slope

Section (b)

Section (c)

Section (d)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Section (a)

Section (b)

Section (c)

Section (d)


FE

A r

eslu

ts o

f φ

b


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2


FE

A r

eslu

ts o

f φ

b


Section (b)

Section (c)

Section (d)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8


FE

A r

eslu

ts o

f φ

b


Section (a)

Section (b)

Section (c)

Load situation a) Load situation b)

Load situation c) Load situation d)


Proposed method I

Calculation results

Load situation e) Load situation f)

Load situation g)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4


FE

A r

eslu

ts o

f φ

b


Section (b)

Section (c)

Section (d)

Section (e)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6


FE

A r

eslu

ts o

f φ

b


Section (b)

Section (c)

Section (d)Section (e)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4


FE

A r

eslu

ts o

f φ

b


Section (b)

Section (c)

Section (d)

Section (e)


Proposed method I

Comparison with EC3

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4


Cal

cula

ted

res

luts

of φ

b b

y E

C3


Both results are close to each other and the results predict

ed by proposed method I are relatively conservative.


Proposed method II

Basic idea •normalized slenderness ratio

•combined with plenty of FE modelling cases

•regression analysis


Proposed method II

0 1 2 3 40.0

0.4

0.8

1.2

1.6

FEA results

Calculated results by Eqn(9)

Calculated curve by Elastic theory

λ2.2

φ'b

0 1 2 3 4-3

-2

-1

0

1

FEA resultsLower envelope curve Average curve Elastic curve

b

ln

2 3

1.9516 2.1917 0.8993 0.1199b cr yM M

λ≤2.2 2

1b cr yM M λ>2.2

natural logarithm

0.1097153580 λ..eb

0.1102.126610 λ.eb

average

lower

envelop

Proposed method II


Proposed method II

Comparison with FEA and with EC3

Comparison with FEA

0.0 0.2 0.4 0.6 0.8 1.00.0

0.4

0.8

1.2

1.6

Calculated results of φb by proposed method II

FE

A r

eslu

ts o

f φ

b


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Cal

cula

ted

res

ult

s o

f φ

b b

y E

C3

Calculated results of φb by proposed method II


Comparison with EC3

The predictions are conservative


Conclusions

Stability typical problem of stainless steel structural members

Experimental investigation

8 full-scale test sepcimens

FE parametric analysis

315 FE modelling cases

Proposed methods for the overall stability coefficient I: modification of existing design code for steel structures

II: regression analysis based on FEA results

Thank you for your

attention


Documents

Two Calculation Methods for Overall Stability Coefficients of Stainless … · 2016. 11. 13. · Stability typical problem of stainless steel structural members Experimental investigation