Improved Design Assessment LTB I-Section Members Modern ... Design Assessment... · Improved Design Assessment of LTB of I-Section Members via Modern Computational Methods 4/20/2016

Improved Design Assessment of LTB of I-Section Members via Modern Computational Methods

4/20/2016

2016 NASCCD. White, Georgia Tech 1

IMPROVED DESIGN ASSESSMENT OF LTB OF I-SECTION MEMBERS

VIA MODERN COMPUTATIONAL METHODS

Improved Design Assessment of LTB of I‐Section Members

via Modern Computational Methods

Donald W. White (with credits to Dr. Woo Yong Jeong & Mr. Oguzhan Toğay)

School of Civil and Environmental Engineering

Georgia Institute of Technology

Atlanta, GA USA

2016 NASCC The STEEL Conference2


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IMPETUS FOR THIS WORK

• Efficient, more rigorous assessment of

Web‐tapered members with

Multiple taper

Steps in the cross‐section (CS) geometry

Doubly‐ & singly‐symmetric CS geometry

Ordinary frame members

including

• Impact of general lateral & torsional bracing

• Benefits of end restraint & member continuity across braced points

• Influence of general moment gradient and other load & displacement boundary condition effects 3

IMPETUS FOR THIS WORK

• Lack of sufficient rigor of Direct Analysis (DM) type approaches for assessment of 3D member limit states & stability bracing requirements

• Lack of sufficient computational efficiency of advanced (plastic zone) analysis methods

• Difficulty of correlation between advanced analysis results and Specification resistances

• Desire for improvement upon traditional K & Cb factor approximations

• Desire for improvement upon traditional strength interaction eqs.4


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INTRODUCTION

• Column inelastic effective length factors have been used extensively in the past to achieve improved accuracy and economy in the design of steel frames

• Using a buckling analysis with inelastic stiffness reduction factors, , the following effects can be captured quite rigorously & efficiently for columns, beams & beam‐columns:

Loss of member rigidity due to the spread of plasticity

Various end restraints

Various bracing constraints and other load & displacement boundary conditions

Continuity across braced points 5

6

AISC a FOR COLUMNS W/ NONSLENDER ELEMENTS

. ( . ) . ( . ) c n e a eP P P0 9 0 877 0 9 0 877 e a eP P

.

a y

e

P

Pc n

c y

P

P0 658 for .

40 390

9e c n

y c y

P P

P P

.

ne

PP

0 877

.

.a y

n

P

Pc n

c y

P

P

0 877

0 658a y

n

P

Pc n

c y

P

P

0.877

ln ln 0.658

ln 0.877 ln 0.658c yc na

c y c n

PP

P P

2.724 lnu u

a

c y c y

P P

P P

for 0.390u

c y

P

P

a 1for 0.390u

c y

P

P


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ANALYSIS STEPS

• Build a model of the structure

• Apply the desired LFRD factored loads. These loads produce the internal axial forces Pu

• Reduce EIx, EIy, ECw and GJ by SRF = 0.9 x 0.877x a• Solve for the inelastic buckling loadVary the applied loads by the scale factor Calculate τa at the current load level

Iterate until the assumed in the calculation of a is the same as that determined from the buckling analysis

The resulting Pu is a rigorous calculation of cPn accounting for all member continuity, bracing and/or end restraint effects 7

EXAMPLE COLUMN INELASTIC BUCKLING ANALYSIS

8

• SABRE2 (using the inelastic reduction factor a) gives

cPn = 1153 kip

• This result matches with a traditional iterative calculation (Yura 1971) using an inelastic K = 0.861, based on a = 0.633


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COLUMN STIFFNESS REDUCTION FACTORS (SRFs)

9

/u yP P

4 1u ub

y y

P P

P P

2.724 lnu ua

c y c y

P P

P P

Net SRF

10

BEAM ltb MODEL, COMPACT & NONCOMPACT WEB MEMBERS

0.9b n b e ltb eM M M For where uL

yc b yc

MFm m

F M

.For b max LTBL

yc b yc

MFm

F M

4 2

2

2 2 26.76 2

ltb

yc

Y X

FX m Y

E

.max LTB pc ycM R M

11

1.951

pc p p ycr

t t tL

pc yc

m

R L L FLY m

r r r EF

R F

2 xc oS hX

J

where:

1ltb


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COLUMN VS. BEAM FACTORS FOR A W21X44

11

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Beam LTB TauFactor

Column TauFactor

0.223

,max

u u

c ye b

P M

P M

REQUIREMENTS FOR INELASTIC LTB ANALYSIS

• The software must rigorously include ECw in addition to EIx, EIy & GJ in the context of doubly‐symmetric I‐section members

• For singly‐symmetric members, the behavior associated with the monosymmetry factor, βx, also must be included

• The 0.9 x ltb factor should be applied equally to the member elastic stiffness contributions EIy, ECw and GJ for the execution of the buckling analysis

• Required number of elements:

At least 4 elements per unbraced length are required to capture the behavior for frame elements based on cubic Hermitian interpolation of the transverse displacements and twists along the element length 12


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GENERAL PURPOSE THIN‐WALLED OPEN‐SECTION FRAME ELEMENT

13

Implemented in SABRE2 (available at white.ce.gatech.edu/sabre)

ELASTIC LTB BENCHMARK

14


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ELASTIC LTB BENCHMARK

15

Typ.14 dof prismatic element (10 elem) stepped using avg. depth in ea. elem.

Typ.14 dof prismatic element (10 elem) stepped using smallest depth in ea. elem.

BASIC BEAM‐COLUMN EXAMPLE USING SABRE2

16

Dimensions:

At left end:

bft = 6 intft = 0.2188 inbfc = 6 intfc = 0.3125 in h = 12 intw = 0.125 in

At right end:

bft = 6 intft = 0.2188 inbfc = 6 intfc = 0.3125 inh = 24 intw = 0.125 in

Fy = 55 ksi

Simply-supported end conditions

1800 kip-in

11.3 kips

From AISC/MBMA Design Guide 25

144 in90 in

Point Brace, i = 0.825 k/in

SABRE2 available at: white.ce.gatech.edu/sabre


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SRF DIAGRAM

17

SABRE2 VS DG25

18

vs

1.173 DG25 Solution A

1.138 DG25 Solution C


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0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Mn /M

p

Lb /Lp

BEAM ltb MODEL – RESULTS (W21X44 BEAMS)

19

Moment Gradient(Cb = 1.75)

AISC Specification Chapter F

Uniform Moment

Moment Gradient,Inelastic Buckling Analysis (SABRE2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Mn /M

p

Lb /Lp

BEAM ltb MODEL – RESULTS (W21X44 BEAMS)

20

Moment Gradient(Cb = 1.75)

AISC Specification Chapter F

Uniform Moment

Moment Gradient,Inelastic Buckling Analysis (SABRE2)


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W21X44 BEAM LTB RESISTANCE VS. POINT BRACING STIFFNESS

(Flexurally & torsionally simply-supported end conditions, Uniform Moment, One intermediate point brace at compression flange, Lbr1 = 8.1 ft, Lbr2 = 4.9 ft )

21

Inelastic Buckling Analysis

AISC 2016 Commentary Provisions including “Lq”



22




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23



TRANSFER GIRDER ASSESSMENT

24

465.1D2

D,413.3

D

D,32

t

D2,109

t

D2,160

t

D,40.1

M

M

ccp

c

w

cp

w

c

wy

p

P

3 at Lb = 45 ft = 135 ft

Lateral brace (TYP)

xx

xx

xx

xx

0.5P

Critical Middle Unbraced Length: Cb = 1.10 K = 0.848

Girder Factored Load Capacity: Pmax = 361 kip … from manual calcs.


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INELASTIC BUCKLING MODE

25

Pmax = 376 kip

MOMENT & SRF DIAGRAMS

26

MOMENT

SRF


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CROSS‐SECTION UNITY CHECK

27

BEAM‐COLUMN SRF

• Calculate the UC value with respect to the cross‐section strength from Eqs. H1‐1

UC = Pu /c Pye + 8/9 Mu /b Mmax for Pu /cPye > 0.2

UC = Pu /2c Pye + Mu/b Mmax for Pu /cPye < 0.2

• Use the UC value in the a & ltb eqs. instead of Pu /c Pye & Mu /bMmax

• Determine the angle

• Calculate the net SRF applied to ECw , EIy & GJ as

28

max

/tan

/

u c ye

u b

P Pa

M M

ea b ltbo o

g

ASRF x x R

A0.9 0.877 1 0.9

90 90


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BEAM‐COLUMN ltb MODEL – W21X44 RESULTS

Simply‐supported members, moment gradient loading

29

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

cPn/

cPy

cMn /cMp

Fully‐Effective Cross‐Section Plastic Strength

L = 7.5 ft

L = 15 ft

L = 10 ft

/b n b pM M

ROOF GIRDER EXAMPLE (ADAPTED FROM AISC 2002)

30

(G' = 1 kip/in)

2 in


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ROOF GIRDER EXAMPLE

31

= 0.921b Mn = 230 kip‐ftc Pn = 18.4 kips

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70

Net SRF

Position along girder length (ft)

SRF, GRAVITY LOAD CASE AT BUCKLING LOAD

32


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CLEAR‐SPAN FRAME EXAMPLE

33

SYM

BUCKLING MODE & CONTROLLING LIMIT STATE INFORMATION

34

1.2 (Dead + Collateral + Self-Weight) + 1.6 Uniform Snow


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AXIAL FORCES AT STRENGTH LIMIT

35

MOMENTS AT STRENGTH LIMIT

36


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SRF VALUES AT STRENGTH LIMIT

37

bMmax VALUES AT STRENGTH LIMIT

38


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cPye VALUES AT STRENGTH LIMIT

39

CROSS‐SECTION UNITY CHECKS AT STRENGTH LIMIT

40


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ADVANTAGES OF BUCKLING ANALYSIS APPROACH

• More general and more rigorous handling of all types of bracing, end restraint & continuity effects

• Substantially cleaner, more streamlined & less error prone member strength calculations

• Consistent bracing stiffness & member strength assessments

• More accurate capture of

Moment gradient and other load & displacement b.c. effects

Tapered & stepped member geometry effects

via a continuous representation of the corresponding SRF values along the member lengths

41

COMPLEMENTARY RESEARCH

• Trahair, N.S. and Hancock, G.J. (2004). “Steel member strength by inelastic lateral buckling,” Journal of Structural Engineering, ASCE, 130(1), 64–69.

• Trahair, N.S. (2009). “Buckling analysis design of steel frames,” Journal of Constructional Steel Research,65(7), 1459-63.

• Trahair, N.S. (2010). “Steel cantilever strength by inelastic lateral buckling,” Journal of Constructional SteelResearch, 66(8-9), pp 993-9.

• Kucukler, M., Gardner, L., Macorini, L. (2014). “A stiffness reduction method for the in-plane design ofstructural steel elements”, Engineering Structures, 73, 72–84.

• Kucukler, M., Gardner, L., Macorini, L. (2015a). “Lateral–torsional buckling assessment of steel beamsthrough a stiffness reduction method”, Journal of Constructional Steel Research, 109, 87–100.

• Kucukler, M., Gardner, L., and Macorini, L. (2015b). “Flexural-torsional buckling assessment of steelbeam-columns through a stiffness reduction method”. Engineering Structures, 101, 662-676.

• Kucukler, M., Gardner, L., and Macorini, L. (2015c). “In-plane design of steel frames through a stiffnessreduction method”. Journal of Constructional Steel Research. in press.

• Gardner, L. (2015). “Design of Steel Structures to Eurocode 3 and Alternative Approaches”. Proceedings,International Symposium on Advances in Steel and Composite Structures, Hong Kong, 39-51.

42


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DESIGN METHOD REQUIREMENTS

• Traditional Methods

Effective Length Method (ELM)

∅ , ,

∅ , ,

2nd‐Order Elastic Analysis

– Joint out‐of‐alignment ∆(gravity only load cases)

• Advanced Methods

AISC (2016) App. 1.2 (Elastic Analysis)

∅ ∅

∅ , ,


– Stiffness reductions 0.8 & 0.8

– Joint out‐of‐alignment ∆– Member out‐of‐straightness

– For TWOS members, 43

INELASTICBUCKLINGANALYSIS

} Direct Analysis Method (DM)

∅ , ,

∅ , ,


– Stiffness reductions 0.8 & 0.8

– Joint out‐of‐alignment ∆

AISC (2016) App. 1.3 (Inelastic Analysis)

2nd‐Order Inelastic Analysis

– 0.9 & 0.9

– Spread of yielding including residual stress effects

– Joint out‐of‐alignment ∆– Member out‐of‐straightness

– For TWOS members,


}


}

THANKS FOR YOUR ATTENTION!

I will be happy to address any questions

44

SABRE2 available at: white.ce.gatech.edu/sabre

Documents

Improved Design Assessment LTB I-Section Members Modern ... Design Assessment... · Improved Design Assessment of LTB of I-Section Members via Modern Computational Methods 4/20/2016