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OVERVIEW OF THE COLD FORMED STEELSTRUCTURAL SYSTEMS AND FUNDAMENTALS OF

DESIGN OF COLD FORMED PLATED ELEMENTS

S.Arul JayachandranStructural Engg. Research Centre

CSIR Campus, TaramaniChennai 600 113

E-mail:[email protected]

[email protected]

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Production of cold formed steel sections

Basically there are three methods(a) folding

(b) press braking

(c ) cold rolling

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Cold rolling from sheet steel

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Mass production and uniform quality

Because CFSS productsare formed on high-speed sequentialmachinery or on

continuous formingequipment, costs areminimized and quality isconsistent.

We live in an era of timecompression hence massproduction helps therace against time(Example: Housing)

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Ease of prefabrication

Because sheet steel building products areuniform, their fabrication in large numbersbecomes easy.

Working in a central fabrication shop the

contractor can reduce on-site operations withsignificant labour savings

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High strength to weight ratio

Reducedconstruction costsand loweredweight per square

meter

Reducedfoundation costs

Material saving.

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Economy in transportation and Handling

The lightweightproducts reduceshipping costs andsimplify handling

Nesting of partsminimises the taskof transportationand subsequent on

site handling of thecomponents.

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Cold formed steel products

Light weight

frames

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Typical framedetail

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Innovationsare hallmark

of coldformed steelstructures

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Innovationsare hallmark

of coldformed steelstructures

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Framing using X-bracings

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Virendeel type offraming

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Walls

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Walls asDiaphragms

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Constructionof Cassette

walls

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Decks

Floors

Roofs

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Light weight steel floor construction

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A dry floor on a cold formed steel deck

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Most popularapplication

Composite decks

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Most popularapplication

Compositedecks

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Steel roof decking for Swimming pool complex in the U.K

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A cold formed steel floorsub-system consisting of

C-purlins for 35 houses inMelbourne (1999)

Builders want to usequality product that can

be erected on site quicklywith minimum fuss and

maximum accuracyAndrew Allen

Sub-floor expert.

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Quick and simple installation

Easy handling combinedwith simple connectionmethods help speed oferection.

Most building productsare shipped from themanufacturer in exactsizes, onsite cutting is

avoided resulting infurther reduction oflabour costs.

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Self tapping and selfdrilling screws

Blind rivets

Fired pins

Plug welds

Typical connectioncomponents in CFSS

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Punched connections

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Cold formed steel framedstructure under construction

A sub panel is about to be erected

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Cold formed steel framedstructure under construction

Combination of trusses and wall studs

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Cold formed steel is used extensively inmetal building industries

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Steel Multi storey flats on the Tenth street-Atlanta

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Tenth and Home, Atlanta

3 / 4 storey flats under construction

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Tenth and Home Details of services

Data cables takenaround a column

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Electrical cables and junction boxes

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Series of Cold waterpipes with hot water

pipes

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Tenth and Home Details of servicesView of the bent pipe networks

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Durability

Cold-formed steel building can have varietyof decorative and protective coatings thatoffer visual, handling, storage andmaintenance advantages

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FIRE !

All types of structural steels areincombustible

So do cold formed steels

Nothings happens to the strength ofthe steel up to 2150C

Even after a fire many sections canbe salvaged

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Cost per tonne of cold formedsteel is costly !

The real cost involves in life cyclecosting

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The design provisions areiterative and not designer

friendly !The design provisions have been

simplified

Computer programs are available forsection property calculation

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The IS:801(1975) provisionsare sometimes irrational and

uneconomical !The designer has a valid pointHis point need to be redressed!

Changes are needed ineffective width concept forunstiffened elements

Limit state philosophy and

section classification isneeded for flexural members

Rational methods such as reffmethod are needed for

columns

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The most difficultthing in promotion ofsteel construction inIndia is the mind set.

New ideas cannot beplanted unless is

mindset is changed!

Indian Designers and

contractors views

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Now Indian businessunderstands that time is moneyas we are living in an era of

time compressionIn such a scenario steelstructures both, hot rolled and

cold formed structures have agood promise

The best example is mineral water

Summary (1st Part)

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Section synthesis

Plate buckling concepts

Postbuckling Principles

Special phenomena in cold formedsteel structures

Fundamentals of cold formed steel design

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Variety of cold formed steel sections

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How codes view cold formed sections?

Channel

Stiffened

element

Un-stiffened

element

Section comprising of a

stiffened element and two

un-stiffened elements

RECTANGULAR PLATES ON FOUR SIDES

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Buckling of Plate under Uni-axial Compression

RECTANGULAR PLATES ON FOUR SIDES

Nx

y

z

b

a

A

B

C D

x

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2

2

3

2

4

4

22

4

4

4 )1(122

x

wN

Ety

w

yx

w

x

wx

,...3,2,1 ,....3,2,1

sinsinm n

mn

b

yn

a

xmww

2

22

3

2

4

44

22

422

4

44

)()1(12

2a

mN

Etb

n

ba

nm

a

mcrx

22

2

2

32

22

22222

2

32

)1(12/

//

)1(12)(

mb

an

a

mEt

am

bnamEt

N crx

2

22

321

)1(12

b

a

ma

bm

b

EtN

cr

22

2

)/)(1(12 tb

Ek

cr

CRITICAL BUCKLING STRESS

Equilibrium Equation

w can be assumed as (satisfies end conditions)

Lowest value for n=1

(Ncr= crt)

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b

a = 2b

b

a = 3b

Buckling Modes for Long Plates

INFLUENCE OF ASPECT RATIO ON PLATE BUCKLING

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m = 1 m = 2 m = 3k

4.0

1.0 2.0 3.0 a/b

k-values for a Simply Supported Plate

VARIATION OF PLATE BUCKLINGCOEFF. WITH ASPECT

RATIO

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21

2

2lim

)1(12

yf

Ek

t

b

DESIGN OF PLATE ELEMENTS

Limiting width-thickness ratio to ensure yielding before platebuckling

Codes prescribe limiting b/t ratios as C/fy

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(b)(a)

Local buckling of Compression Members

LOCAL BUCKLING

Beams compression flange buckles locally

Fabricated and cold-formed sections prone to local buckling

Local buckling need not lead to collapse

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Local buckling

Full Section Capacity Full section capacity

eroded by local Buckling

Vent

Vent

H i iff d l

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How can we get maximum stiffened elements

1. Channel section

2. Channel with a simple lip

3. Channel with compound lip4. Intermediately stiffened

Channel with compound lips

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Sections are identified by their elements

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Postbuckling strength of thin elements and

their design

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Which is Stronger ?An Elephant or an Ant

This signifies the capacity of thinelements to take larger stressesbeyond their critical stress

F F F

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S SD

Prebuckling

S D

Postbuckling

S

D

F FD

F

d

DS

S+D

F

D

Inplane

F

d

Out-of-plane

cr

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Postbuckling strength- thick or thin plate ?

y

d

Thick plate Thin plate

Postbuckled reserve

strength(Thin Plate)Postbuckled reservestrength(Thick Plate)

cr,thin

cr,thick

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Actual

paths

Secondary

path

Secondary

path

Funda

-mental

path

(a) Column

Actual paths

corresponding to

levels o f ini t ia l

imperfect ion

(b) Plate

P/PcrP/Pe

w0 w

1.0 1.0

w

Load versus Out-of-plane Displacement Curves

STABILITY OF PLATES

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Column and Plate Strength Curves

1.00

0.75

0.50

0.25

0 3.02.01.0 1.0

0.75

0.50

0.25

0 3.02.0

1.0

Test data(E/fy) (cr/fy)

fy/E fy/c r

Test d ata

(b)

f/fy f/fy

(a)

STABILITY OF PLATES - 2

M b b d diti t d

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Membrane boundary conditions encounteredin plate elements of structural members

Constrained towave in

Stiffened elements of coldformed membes

Internal panel of a largestiffened plate

x

x

b

a

t

Free to wave in

Hemp

x

x

b

a

t

Marguerre- Trefitz

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Shear buckling of a plate

BUCKLING OF WEBPLATES IN SHEAR

cr

UCE

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b

(a) Actual

beff/2

(b) Assumed

beff/2

Actual and Assumed Stress Distribution

in the Post-buckling Range(SCE)

POST-BUCKLING BEHAVIOUR & EFFECTIVE WIDTH

bbeff

b

(a) Actual

(b) Assumed

beff

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Concept of effective widthin cold formed steelstructures

bbeff

1

)22.0

1(1

George Winters equation

Eff ti ti d i l

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Effective section under axialcompression and bending

N A

Gross section Effective section-

Axial compression

Effective section-

Bending

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Typical modes in a thin-walled cold formed beams

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Lcr

Mcr

local buckling

I

. , .. , .

distortional buckling

I

. , .. , .

lateral-torsional buckling

I

. , .. , .

Typical modes in a thin-walled cold formed beams

Special phenomena in cold formed steel structures

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Flange Curling


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Web Crushing

Warping rigidity predominates in cold formed section

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Cold formed sections are open sectionsPure torsion and warping torsion

Torsion is avoided in most cases

Pure torsion

T

Th

u

Vf

VfTa

Ta

Z

X

Warping torsion

Warping rigidity predominates in cold formed section

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