stability of cold-formed elements

8/18/2019 Stability of Cold-Formed Elements

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STABILITY OFCOLD-FORMED ELEMENTS

Czech Technical University in Prague

2E12 Design of steel structures for renewable energy systems 1

21/11/2010


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Contents

21/11/20102E12 Design of steel structures for renewable energy systems

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Behavior features:local buckling of compression elements

plane elements

elements with stiffenersshear lagweb crippling

Cross-section checkBeams restrained by sheetingConnections


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Cross-section idealiseation

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C9 Design of steel structures for renewable energy systems


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Cross-section

21/11/2010C9 Design of steel structures for renewable energy systems

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Idealised section with radiuses r=0 when r


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Buckling in compression

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Buckling strength


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Local bucklingDistortional buckling

Section distortion

Global bucklingShear buckling

Sectional modes


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Buckling strength


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Buckling strength


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Local buckling


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Theory + calculation procedures(see local buckling of plates)

Elements:doubly supported

outstands

stiffenedplain

1,052com com

pcr

bt k Eσ

σ σ λ σ = = com y

f σ ≤


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Stress distribution on stiffened plate


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Calculation modelstiffener supports plane elementstiffener itself can buckle (as compression member on

elastic foundation)


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Buckling of edge stiffener


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V r a n y


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Spring stiffness of stiffener


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Stress distribution - idealisation


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- distortional buckling


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Calculation procedure


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1. Stiffener provides rigid support to the plate ⇒effective widths

2. K, As, Is3. Critical stress σcr4. for σcom = f y ⇒ χd (distortional buckling)5. σcom = χd fy6. Effective widths of parts adjacent to the stiffener7. As, Is8. iteration 3. – 7.9. tred = χd t


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(Vrany)

Interaction of local and distortional buckling

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http://www.ce.jhu.edu/bschafer/cufsm

Buckling modes

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Check – cross-sections, members


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EN 1993-1-3

Limits:members0,45 ≤ t ≤ 15 mmsheeting 0,45 ≤ t ≤ 4 mm


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Compression


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interaction of local and global buckling

=> χ

. 1b Rd eff y MN A f χ γ =

1

eff y eff R

cr g cr g

A f ANN A A

λ λ σ λ

= = =


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Buckling modes


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( D u

b i n a

)


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Flexural-torsional buckling


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uniaxial symmetrical profiles

torsional buckling:flexural-torsional buckling: …combination

buckling curve b

2w

cr,T t2 2g o T

1 EIGI

A iπ

σ = +

cr,TFσ cr,T cr,, yσ σ

( )22cr,y y yE iσ π =


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Members subjected to bending

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Bending


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Lateral-torsional buckling

Specific design of cold-formed members in bendingsubjected to lateral-torsional buckling

( ).eff Rd LT eff ydM W f χ =


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Behaviour - Z section in bending


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Slender section → local bucklingEdge stiffener – distortional buckling

Non-symmetry →distortion of cross-sectionOut-of-plane buckling of free flange in hoggingmoment areas


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Cross-section distortion


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C D

+

-

-

+

+

-

+

+

-

-Reality Idealized model


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Cross-section distortion


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Simplified model

K

C D

+=

y

z

y


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Calculation procedure EN1993-1-3


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Sagging moments:

Hogging moments:

,1

,

y EdEd yd y M

eff y

Mf f

Wσ γ = ≤ =

,

1,

y Ed fzEd yd y M

eff y fz

M Mf f W Wσ γ χ = + ≤ =


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Web crippling

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(Vrany)

Web crippling

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(Vrany)

Web crippling

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Web crippling


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Eccentric compression to webRw,Rd …equations derived experimentally


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Web crippling


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Cases:Single web

Two or more webs


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Web crippling


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Loading – cases:a) close to free endb) far from free end

a) from one sideb) from both opposite sides

Rw,Rd = f(t 2, r/t, f, s s …)product of individual factors


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Interaction

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Combination M+R


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Governing condition e.g. for corrugated sheeting,continuous beams

c,Rd w,Rd

1,25Ed EdM FM R

+ ≤


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Combination compression + bending


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,E d E d ,z N yM N e∆ =


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Shear lag

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Shear lag

21/11/2010Thin walled and composite structures / Michal Jandera /

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by elastic analysis (I. order) ⇒ both tension andcompressionfactor of ratio Le/ b 0 … to solve when Le/ b 0 < 50


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Shear lag


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for thin-walled sections, b 0:

Effective width:

( )0

max

b

eff

y dyb

σ

σ

=∫


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Shear lag


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Effective width:Effective width factor

0eff b b β = ⋅


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Connections

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Connections


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Weldsfillet

t ≥ 3 mm (automatic … t ≥ 2 mm)

MAG is bestlap connections

spot


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Connections


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Mechanical fastenersblind rivetsscrews 3 ≤ d ≤ 8 mm

self-drilling (self-tapping)thread-cutting

cartridge fired pinsbolts


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Blind rivets


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Screws


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Different failure modes compared with classic bolts


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New types of connections


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“Rossete” system

Adhesive bonding (problem of lifespan reliability)


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Design aids

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Design aids


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Tables

PRO IL

váha profilu řádek rozpětí pole L [m] rozpětí pole L [m]

číslo 5,0 6,0 7,0 8,0 9,0 10,0 5,0 6,0 7,0 8,0 9,0 10,01 3,41 2,34 1,70 1,29 1,00 4,91 3,03 2,09 1,54 1,192 3,41 2,34 1,70 1,15 4,91 3,03 2,09 1,54 1,19

Z 250/2,0 3 3,28 1,86 1,15 4,91 3,03 2,09 1,48 1,027,80 kg/m 4 2,49 1,63 1,12 3,95 2,48 1,70 1,25

5 -2,44 -1,65 -1,19 -0,89 -0,69 -3,95 -2,64 -1,90 -1,43 -1,116 -1,92 -1,29 -0,91 -0,68 -0,52 -3,16 -2,08 -1,48 -1,10 -0,851 4,61 3,17 2,31 1,74 1,36 1,08 6,59 4,10 2,84 2,11 1,64 1,30

2 4,61 3,17 2,28 1,50 1,02 6,59 4,10 2,84 2,11 1,64 1,30Z 250/2,5 3 4,25 2,42 1,49 0,97 6,59 4,10 2,84 1,92 1,329,70 kg/m 4 3,66 2,43 1,68 1,20 5,75 3,57 2,47 1,83 1,41 1,03

5 -3,31 -2,26 -1,63 -1,22 -0,95 -0,75 -5,29 -3,58 -2,59 -1,95 -1,52 -1,216 -2,81 -1,91 -1,37 -1,02 -0,78 -0,62 -4,53 -3,04 -2,19 -1,64 -1,27 -1,01

PROSTÝ NOSNÍK SPOJ ITÝ NOSNÍK S PŘES HY


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Design aids

2E12

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Software

stability of cold-formed elements

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