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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
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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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Cross-section
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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
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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