July 2013 Update Direct Strength Prediction of Cold-Formed ... · PDF filebiaxial bending, in...

July 2013 Update Direct Strength Prediction of

Cold-Formed Steel Beam-Columns S. Torabian, B. Zheng and B.W. Schafer

July 2013

Buffalo,NY American Iron and Steel Institute Meetings

Objective Development and verification of a design method for

CFS beam-columns that explicitly and directly considers the applied actions, including axial loads and biaxial bending, in uniquely determining the stability and strength of a CFS member under those actions.

Outcomes •  Improved and increased capacity predictions •  Improved understanding of stability and collapse

behavior under multiple actions •  Enable accurate CFS member and system collapse

analysis in beam element programs (MASTAN, SAP, STAAD, etc.) through stress resultant yield surfaces

Methods(1.  New formulation for DSM that can account for

stability and strength under multiple actions 2.  Targeted testing under P-M-M loadings to

explore the beam-column stability space explicitly and find capacities (Phase 1 and 2)

3.  Nonlinear FEA analysis to expand the studies and flesh out issues in final design methods

4.  Technology transfer to ease the use of the develop method and its related tools

1.(Year(one(Reports(Summary(•  “Cold-formed steel beam-column applications in residential and

commercial midrise buildings and design method comparisons.” TWG-RR01-12, Thin-walled Structures Group Research Report, Johns Hopkins University, Y. Shifferaw, July 2012.

•  “Towards optimization of CFS beam-column industry sections.” TWG-RR02-12, Thin-walled Structures Group Research Report, Johns Hopkins University, Y. Shifferaw, July 2012.

•  “Identifying targeted CFS beam-columns for testing.” TWG-RR03-12, Thin-walled Structures Group Research Report, Johns Hopkins University, Y. Shifferaw, July 2012.

•  “Development of DSM Direct Design Formulas for Beam-Columns (Year 1 Proposed).” Letter report, Thin-walled Structures Group, Johns Hopkins University, B Schafer, July 2012.

Targeted(Tes7ng(–(rig(July(2012(

Bo?om(of(test(fixture,(pin(can(be(rotated(so(that(axis(of(bending(is(at(an(angle,(crea7ng(biaxial(bending(in(specimens.(

Scu?led(August(2012(aGer(feedback(

2.(Experimental(Program(New(test(rig(details(

7

ey

Point(Load ex

Clamping(bolts Slider6x

Slider6y

End(plate

Specimen

Clamping(bolts

Slider

Clamping(boltsSlider

Specimen

Loading(plate

Loading(plate

Loading(plate

End(plate

Z

x

ex

ez

Test(Setup(Top$Hinge$

Bo+om$Hinge$LabView:$•  MTS$Load$•  MTS$Displacement$•  Loading$Plate$Displacement$and$rota=on$•  Cross?sec=onal$Deforma=on$@$Mid?point$

Loading$Plates$

Specim

en$

Clamps$

Instrumenta7on(

Specim

en$

Posi=on$Transducers$for$Top$Plate$

Posi=on$Transducers$for$Bo+om$Plate$

PTs$for$right$flange$deforma=ons$

PTs$for$leE$flange$deforma=ons$

PTs$for$web$deforma=ons$

Phase(1(Specimen�

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��θ ��θ

��θ ��θ

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Parameters( Nominal(Measured(specimen(

No.(1( No.(2( No.(3,…(H((in.)( 5.9434& 6.0147& 6.0017& …&

t((in.)( 0.0566& 0.0562& 0.0563& …

B1((in.)( 1.3184& 1.3947& 1.4137& …

B2((in.)( 1.3184& 1.3624& 1.3164& …

D1((in.)( 0.3467& 0.3677& 0.3897& …

D2((in.)( 0.3467& 0.4094& 0.3904& …

RB1((in.)( 0.1132& 0.1562& 0.1562& …

RB2((in.)( 0.1132& 0.2031& 0.2031& …

RT1((in.)( 0.1132& 0.1406& 0.1406& …

RT2((in.)( 0.1132& 0.1406& 0.125& …

θB1((deg.)( 90& 89.4& 91.4& …

θB2((deg.)( 90& 94.3& 90.1& …

θT1((deg.)( 0& 1.62& 1& …

θT2((deg.)( 0& 7.67& 7.67& …

600S137Q54([50ksi](

Local(at(short(lengths(Distor7onal(at(intermediate(likely(LocalQglobal(at(long(lengths(

PQMQM(Space(

Consider the P-M-M Space defined in z-x-y and in Cartesian or Spherical coordinates

(ref: mathworld) + annotated

M1,M2,P→

x = M1

My1

y = M2

My2

z = PPy

β = x2 + y2 + z2

θMM = tan−1 y / x( )

φPM = cos−1(z / β)

β,θMM ,φPM →x = β cosθMM sinφPMy = β sinθMM sinφPMz = β cosφPMM1 = xMy1

M2 = yMy2

P = zPy

M1

My1

M2

My2

PPy

MM

PM

Test(across(PQMQM(space(and(develop(experimental(bounding(strength(surface(

Phase(1(Test(Matrix(

Eccentricitiesex ez θ

MMφPM ex ezT'Average θ

MMφPM

(in.) (in.) (deg.) (deg.) (in.) (in.) (deg.) (deg.)S600'12'ex(0)'ez('1.0) S600'12'1 0.00 '1.00 270 79 0.00 '1.075 270 80 1S600'12'ex(0)'ez('0.5) S600'12'19 0.00 '0.50 270 69 0.00 '0.541 270 70 2S600'12'ex(0)'ez('0.15) S600'12'4 0.00 '0.15 270 38 0.00 '0.185 270 44 3S600'12'ex(0)'ez(+0.15) S600'12'5 0.00 0.15 90 38 0.00 0.109 90 29 4S600'12'ex(0)'ez(+0.35) S600'12'6 0.00 0.35 90 61 0.00 0.308 90 58 5S600'12'ex(0)ez(+1.0) S600'12'8 0.00 1.00 90 79 0.00 0.950 90 79 6S600'12'ex('1.0)'ez(0) S600'12'9 '1.00 0.00 0 31 '1.00 '0.043 20 33 7S600'12'ex('3.5)'ez(0) S600'12'10 '3.50 0.00 0 65 '3.50 '0.013 2 65 8S600'12'ex('7.5)'ez(0) S600'12'11 '7.50 0.00 0 78 '7.50 0.001 0 78 9S600'12'ex('1.5)ez(+0.1) S600'12'2 '1.50 0.10 30 47 '1.50 0.107 31 47 10S600'12'ex('5.0)'ez(+0.34) S600'12'13 '5 0.3397 30 74 '5 0.338 30 74 11S600'12'ex('0.8)'ez(+0.17) S600'12'14 '0.8125 0.1656 60 45 '0.8125 0.166 60 45 12S600'12'ex('3.0)'ez(+0.6) S600'12'15 '3 0.6115 60 75 '3 0.628 61 75 13S600'12'ex('1.5)ez('0.1) S600'12'16 '0.8125 '0.1656 300 45 '0.8125 '0.161 301 44 14S600'12'ex('5.0)'ez('0.34) S600'12'17 '3 '0.6115 300 75 '3 '0.614 300 75 15S600'12'ex('0.8)'ez('0.17) S600'12'3 '1.5 '0.1019 330 47 '1.5 '0.100 331 46 16S600'12'ex('3.0)'ez('0.6) S600'12'20 '5 '0.3397 330 74 '5 '0.337 330 74 17

SpeccimenSpecimen,in,the,test

Minor

Major

Bi'Axial

Target MeasuredEccentricities Angles Angles

Eccentrici7es(were(measured(while(seYng(the(specimen(in(the(test(rig(

Minor(Axis((Lip(in(TensionQθMM=270o)(

S600Q12Qex(0)Qez(Q1.0)(:(S600Q12Q1(

Minor(Axis((Lip(in(TensionQθMM=270o)(

WLB( WLB( WLB(

Minor(Axis((Lip(in(Compression(QθMM=90o)(

S600Q12Qex(0)Qez(+0.35)(:(S600Q12Q6(

Minor(Axis((Lip(in(CompressionQθMM=90o)(

FDB( FDB( FDB(

Major(Axis((θMM=0o)(

S600Q12Qex(Q3.5)Qez(0)(:(S600Q12Q10(

Major(Axis((θMM=0.0o)(

FDB( FDB( FDB(

BiQaxial(Bending((θMM=60o)(

S600Q12Qex(Q3.0)Qez(Q0.61)(:(S600Q12Q15(


FDB( FDB(


WLB( WLB(


FDB( FDB(

3.(Nonlinear(FEA((Verifica7on)�•  Parameters used in FEM

Geometry Dimension: mid-thickness

�

�

��

��

��

��θ ��θ

��θ ��θ

��

��

Parameters( Nominal(Measured(specimen(

No.(1( No.(2( No.(3,…(H((in.)( 5.9434& 6.0147& 6.0017& …&

t((in.)( 0.0566& 0.0562& 0.0563& …

B1((in.)( 1.3184& 1.3947& 1.4137& …

B2((in.)( 1.3184& 1.3624& 1.3164& …

D1((in.)( 0.3467& 0.3677& 0.3897& …

D2((in.)( 0.3467& 0.4094& 0.3904& …

RB1((in.)( 0.1132& 0.1562& 0.1562& …

RB2((in.)( 0.1132& 0.2031& 0.2031& …

RT1((in.)( 0.1132& 0.1406& 0.1406& …

RT2((in.)( 0.1132& 0.1406& 0.125& …

θB1((deg.)( 90& 89.4& 91.4& …

θB2((deg.)( 90& 94.3& 90.1& …

θT1((deg.)( 0& 1.62& 1& …

θT2((deg.)( 0& 7.67& 7.67& …

600S137Q54([50ksi](

FEM(modeling(method(

Model in ABAQUS Test rig

P

Ref. node

Ref. node

P

Rotation Center

Specimen

Rigid Length

Rotation Center

Rigid Length

Element(and(Mesh(

•  Element : S9R5

•  Integration points: 7

•  Element in the Corner: 4

•  Element in the Lip: 2

•  element in the flange: 2

•  element in the web: 10

•  MPC TIE constrain for rigid link modeling

Material(property(

Mises yield rule / Associated flow rule / Isotropic hardening

Imperfec7on(Local buckling mode from CUFSM

(1) Load : axial loading

(2) Boundary : simple support (S-S)

Positive (Scale factor=+50%)

Negative (Scale factor=-50%)

Residual(stress(for(Corners(

Moen, C.D., Igusa, T., Schafer, B.W. (2008). “Prediction of residual stresses and strains in cold�formed steel members.” Thin�Walled Structures, 46(11), 1274�1289

��

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��−0.05σ

��−0.5σ

��+0.5σ

��−0.5σ

��+0.5σ

�ε

�ε

��

��Transverse Longitudinal Plastic strain

Valida7on(of(FEA(model(

8 model variations examined for comparison to tests

Valida7

on(of(FEA

(mod

el�

Nominal

Negative

With residual stress

Realistic

Negative

With residual stress

Geometry:

Imperfection:

Residual stress:

��Ptest/PFEM�

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1� 0.946� 0.907� 0.975� 0.936� 0.929� 0.893� 0.956� 0.919�2� 0.839� 0.816� 0.868� 0.848� 0.844� 0.820� 0.877� 0.842�3� 0.864� 0.841� 0.902� 0.880� 0.850� 0.827� 0.887� 0.865�4� 0.978� 0.947� 0.952� 0.935� 0.963� 0.931� 0.934� 0.916�5� 0.923� 0.885� 0.926� 0.885� 0.909� 0.871� 0.909� 0.870�6� 0.914� 0.870� 0.909� 0.791� 0.925� 0.879� 0.920� 0.799�7� 0.901� 0.873� 0.965� 0.939� 0.880� 0.852� 0.939� 0.913�8� 0.948� 0.925� 0.975� 0.948� 0.928� 0.904� 0.962� 0.938�9� 0.981� 0.956� 0.978� 0.945� 0.988� 0.968� 0.999� 0.972�10� 0.981� 0.950� 0.964� 0.929� 0.989� 0.960� 0.976� 0.941�11� 1.104� 1.066� 1.061� 1.020� 1.121� 1.084� 1.080� 1.039�12� 1.029� 0.998� 0.981� 0.948� 1.026� 0.994� 0.979� 0.946�13� 0.984� 0.949� 0.968� 0.935� 0.948� 0.918� 0.943� 0.913�14� 0.943� 0.915� 1.000� 0.974� 0.916� 0.888� 0.966� 0.940�15� 0.977� 0.945� 1.027� 0.992� 0.947� 0.915� 0.991� 0.957�16� 0.882� 0.853� 0.948� 0.921� 0.858� 0.830� 0.917� 0.891�17� 0.968� 0.937� 1.041� 1.010� 0.936� 0.904� 0.998� 0.967�

MAX.� 1.104� 1.066� 1.061� 1.020� 1.121� 1.084� 1.080� 1.039�MIN.� 0.839� 0.816� 0.868� 0.791� 0.844� 0.820� 0.877� 0.799�AVG.� 0.951� 0.920� 0.967� 0.931� 0.939� 0.908� 0.955� 0.919�STD.� 0.063� 0.061� 0.049� 0.057� 0.069� 0.067� 0.049� 0.056�

P-M-M Space

P-Mz plane

(major axis)

Mx-Mz plane

(biaxial)

P-Mx plane

(minor axis)

Comparison(of(interac7on(curves(in(the(PQMQM(space…(

Interac7on(Curves((PQM(Major)(

All#results#in#good#agreement,#tradi1onal#

interac1on#expression#works#OK#here.#

Interac7on(Curves((PQM(Minor)(

Lots#of#inelas1c#reserve!#Surface#unique#to#sec1on.#

Experimental#strength#consistently#higher#than#

FEM#predic1ons.#DSM#implementa1on#needs#

some#cleaning#up.#

Interac7on(Curves((θMM=30°(biaxial(Q(slice(of(PQMQM)(

Major#axis#+#Minor#(lip#in#C)#Some#inelas1c#reserve#now!#

FSM#underlying#DSM#needs#some#cleaning#up.#Note##

that#DSM#>#first#yield#though#


More#inelas1c#reserve.#FE#model#working#well.#

DSM#cleanup#needed.#


Lip#in#tension#for#minor#axis#Bending.#Less#inelas1c#reserve#

FE#working#well.#FSM#underlying#DSM#needs#

some#cleaning#up.#


FE#working#well#DSM#cleanup#needed…#

Quick(and(dirty(comparison(to(tradi7onal(interac7on(expression(

(approximate)(

Interac7on(Curves((PQM(Major)(

All#results#in#good#agreement,#tradi1onal#

interac1on#expression#works#OK#here.#

Linear(interac7on(as(assumed(in(AISI(today(

Interac7on(Curves((PQM(Minor)(

Lots#of#inelas1c#reserve!#Surface#unique#to#sec1on.#

Experimental#strength#consistently#higher#than#

FEM#predic1ons.#DSM#implementa1on#needs#

some#cleaning#up.#



Major#axis#+#Minor#(lip#in#C)#Some#inelas1c#reserve#now!#

FSM#underlying#DSM#needs#some#cleaning#up.#Note##

that#DSM#>#first#yield#though#



More#inelas1c#reserve.#FE#model#working#well.#

DSM#cleanup#needed.#



Lip#in#tension#for#minor#axis#Bending.#Less#inelas1c#reserve#

FE#working#well.#FSM#underlying#DSM#needs#

some#cleaning#up.#



FE#working#well#DSM#cleanup#needed…#


TEST(vs(prelim.(DSM(Predic7on(

Test Local Distortional local/Test Distortional/Testex ez θ

MMφPM P/Py Pnl/Py PnD/Py Pnl/Py PnD/Py

(in.) (in.) (deg.) (deg.) 1 (in.) (in.) (in.) (in.)S6001121ex(0)1ez(11.0) S60011211 0.00 11.27 270.0 81.4 0.21 0.17 0.16 0.79 0.74S6001121ex(0)1ez(10.5) S600112119 0.00 10.66 270.0 73.7 0.34 0.28 0.30 0.83 0.86S6001121ex(0)1ez(10.15) S60011214 0.00 10.25 270.0 52.8 0.46 0.41 0.45 0.89 0.99S6001121ex(0)1ez(+0.15) S60011215 0.00 0.12 90.0 30.9 0.61 0.43 0.45 0.71 0.73S6001121ex(0)1ez(+0.35) S60011216 0.00 0.40 90.0 64.2 0.41 0.33 0.31 0.79 0.74S6001121ex(0)ez(+1.0) S60011218 0.00 1.06 90.0 79.7 0.21 0.19 0.16 0.91 0.79S6001121ex(11.0)1ez(0) S60011219 11.00 10.06 25.5 34.1 0.46 0.39 0.39 0.85 0.85S6001121ex(13.5)1ez(0) S600112110 13.50 10.02 2.8 65.0 0.29 0.26 0.26 0.90 0.88S6001121ex(17.5)1ez(0) S600112111 17.50 10.01 0.4 77.7 0.17 0.17 0.16 0.95 0.91S6001121ex(11.5)ez(+0.1) S60011212 11.50 0.12 35.0 48.2 0.41 0.36 0.33 0.88 0.79S6001121ex(15.0)1ez(+0.34) S600112113 15 0.3866 33.3 74.7 0.18 0.17 0.16 0.93 0.87S6001121ex(10.8)1ez(+0.17) S600112114 10.813 0.2053 65.0 49.6 0.44 0.39 0.34 0.87 0.76S6001121ex(13.0)1ez(+0.6) S600112115 13 0.7393 64.5 76.8 0.22 0.20 0.16 0.91 0.72S6001121ex(11.5)ez(10.1) S600112116 10.813 10.2099 294.5 50.2 0.40 0.38 0.39 0.94 0.96S6001121ex(15.0)1ez(10.34) S600112117 13 10.7041 296.6 76.3 0.22 0.20 0.19 0.92 0.87S6001121ex(10.8)1ez(10.17) S60011213 11.5 10.1314 323.3 48.8 0.41 0.34 0.35 0.84 0.86S6001121ex(13.0)1ez(10.6) S600112120 15 10.3762 327.4 74.6 0.21 0.19 0.19 0.92 0.90

Average 0.87 0.84Standard9deviation 0.06 0.08

C.O.V 7.4% 9.8%

DSM9Prediction Comparison

SpeccimenSpecimen9in9the9test

Minor

Major

Bi1Axial

@9Peak9loadEccentricities Angles

TestQtoQpredicted(reciprocal(of(values(reported(above.(TestQtoQpredicted(is(conserva7ve((overly)(at(1.15(to(1.19…((

S1ll#working…#

4.(Technology(Transfer((•  Matlab extensions similar in spirit to CUFSM •  Load a general section •  Elastic buckling analysis in P-M-M •  Plastic section analysis in P-M-M •  Nominal strength surface in P-M-M •  Cross-section checker •  Output of Stress Resultant Yield Surface

–  Full point dump of discrete points –  Parameterized surface for general model

•  Global buckling complications still being worked out. That is, will we shrink the surface as a function of local-global interaction or handle another way

•  Current vision, on next slide…

Load(Sec7on(

Dump(PQMQM(points(

Calc(PQMQM(

crossQsec7on(checker(

Mr1(=(( Mr2(=(( Pr(=((

Fy(=((

xr(=(0.10(( yr(=(0.20(( zr(=((0.30(

βr(=(0.374(( θMM(=(33.69°(( φPM(=((35.82°(

βn(=(0.80(( φ(=(0.87((

φβn(=(0.696(>(0.374(=(βr(?(OK(

calculate(capacity(βn:(

calculate(demand(βr:(

Load(PQMQM(Consider the P-M-M Space defined in z-x-y and in Cartesian or Spherical coordinates

(ref: mathworld) + annotated

M1,M2,P→

x = M1

My1

y = M2

My2

z = PPy

β = x2 + y2 + z2

θMM = tan−1 y / x( )

φPM = cos−1(z / β)

β,θMM ,φPM →x = β cosθMM sinφPMy = β sinθMM sinφPMz = β cosφPMM1 = xMy1

M2 = yMy2

P = zPy

M1

My1

M2

My2

PPy

MM

PM

First(yield(Fully(plas7c(Local(buckling(Dist.(Buckling(Local(nominal(Distor7onal(nominal(Minimum(surface(✓(

✓(✓(✓(

1( 1(

2(

2(

Name(=((

Basic(proper7es(and(anchors(

A = Py= I11= I22= My+11= My+22= My-11= My-22= Mp+11= Mp+22= Mp+11= Mp-22=

views:(1(2(3([4](free(

Surface(Builder(XQray(

currently(construc7ng:(elas7c(local(buckling(

ΔθMM=(ΔφPM=((

Density(controls(

θMM(=(33.69°(( φPM(=((35.82°(

Summary(On the four major work areas 1.  DSM formulation

•  Complete, even integrates with inelastic reserve •  Compared to Test Results, Modification is underway

2.  Testing •  17 short specimens (12”) are done. (More focused on

local buckling) •  17 long (48” specimens) are underway this month. (More

focused on Distortional and local-global buckling) 3.  Nonlinear FEA

•  Verification analyses are done (Good agreement) •  Ready to do parametric analyses to extend the results

4.  Technology Transfer •  Clear vision, preliminaries can be started

Comparison(of(test(results(to(DSM(and(FEM(

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

P/PY

Specimen

Test.Results.vs.DSM.and.FEM.Analysis

Test0Results FEM DSM9Local DSM9Distortional

µ FEM/TEST(((((((((((((((((((((((((=0.97(((,(((c.o.v(=(5.1%(µ DSMQLocal/(Test((((((((((((((=0.87(((,(((c.o.v(=(7.4%(µ DSMQDistor7onal/Test(((=0.84(((,(((c.o.v(=(9.8%(

(

July 2013 Update Direct Strength Prediction of Cold-Formed ... · PDF filebiaxial bending, in...

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