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COLD FORMED THIN GAUGE MEMBERS

COLD FORMED STEEL MEMBERS AND SHEETING

1.1 IntroductionThe cold-formed thin gauge sections gather together into one of the main families of steel

profiles used in the construction field. They have various shapes- sheet, strip, plates or flat bars,fabricated in roll-forming machines or by press brake operations. The thickness of the steel sheetsor strips excluding the coating, generally ranges from 0.5 mm to 4 mm for sheeting and from 1 mmto 8 mm for profiles, respectively, according to E. C.3. Also, steel plates and bars as 25 mm may becold formed into structural shapes

Cold-formed thin gauge sections are used for the various elements in the steel structuresoffering some important advantages for the constructions:

a) in comparison with thicker hot rolled shapes, cold formed light members may bemanufactured for relatively light loads and/or short spans;

b) various and intricate sectional configurations may be produced economically by coldforming operations and consequently, favourable strength-to-weight ratios may be obtained;

c) nestable sections may be produced, allowing for compact packaging and shipping;d) load carrying panels and decks are able to provide useful surfaces for floors, roofs and

wall constructions, and in other cases they can also provide enclosed cells for electrical and otherconduits;

e) panels and decks not only withstand loads normal to their surfaces, but they can also actas shear diaphragms to resist force in their own plans if they are adequately interconnected to eachother and to the supporting members.

1.2 Industrial production of cold formed thin gauge sectionsTwo procedures are used to produce these elements:I) continuously processing: for more important series of sections, by continuous

forming, in rolling mills. Thus, the coil is unrolled and the steel sheet passes through successivepairs of roles and after that the sections are cut at the desired length (fig.1.2 axinte). Depending onthe possibilities of pressing and on its characteristics, stripped steel may be processed withthickness between 0.3 mm and 18 mm and width between 20 mm and 2000 mm.

II) with adiscontinuous process: for small series of sections, either a leaf press brake(folding) of the steel sheets or a coin press brake (press braking) are commonly used (fig.1.1.axinte) for pressing the steel strip in a mould. The thickness of the of the shapes obtained by pressfolding is relatively small, under 3 mm, and the length of the elements is between 1.5 m and 4.0 m.The shapes obtained by pressing in moulds have the thickness under 16 mm and 6 m length.

Cold-formed structural members can be classified into two major types (see fig. 1.1 EC 3Part 1.3:

-individual structural framing members (fig. 1.1. a, b, c);-panels and decks (fig.1.1.d).Individual members are used in buildings as beams, columns, trusses, and in the workshop

design as purlins, skylights, bracing, structural elements for walls transmission towers, etc. Thepanel decks and corrugated shells are used for facades- as external layer for curtain walls,diaphragms, roofs, floors and permanent shuttering.

1.3. The steel used for cold formed thin gauge members. Characteristics for designAccording to EC 3 Part 1.3. the design thickness of the steel is considered as the nominal

core thickness (tolerances under 5%), tc,nom.

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Fig. 1. Continuous process of fabrication of the cold formed sections (with rolling mill or pressing)

Fig. 2. Discontinuous process of fabrication of the cold formed shapes- successive stages of bending: a- withthe leaf press brake (folding); b- by pressing in mould.

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Fig. 3. Examples of profiled sheeting and members (EC3-P 1.3): a- basic elements; b- structural elementssuitable for axial loading; c- structural elements suitable for bending

For continuously hot-dip metal coated sheeting with nominal thickness mm5 suppliedwith half of the normal standard tolerances, the design thickness t may be taken as the nominal corethickness, tc,nom.

In case of continuously hot-dip metal coated steel sheet and strip the core thickness is

znomc ttt = , where tz is the thickness of the zinc protection, usually 0.04 mm both sides of thesheet and 275 g/m2.

Standard grades of steel shall have the properties that conform to the required suitabilityfor cold forming, welding and galvanising. The ratio of the specific minimum ultimate tensile

strengthfuto the specific minimum yield strength satisfies: 2.1yu ff , see fig.4.

The nominal (characteristic) values of the yield strength fyb and tensile strength fu for thespecified steels are presented in table 1.

The basic material used for fabrication of the steel sections consists in flat sheet steel stripsand the Romanian standards available are: STAS 908-90, STAS 1945-90, STAS 9236-80, STAS9150-80, STAS 10896-80. Generally, all these grades of steel will have the elongation at tear, A(%)>20%. Also, supplementary measures will be adopted for the stripes of 0.28 mm thickness

considering cold forming process and sensibility to brittle fracture.1.4.Influence of cold hammeringThe manufacturing process plays a governing role in modifying the mechanical properties of

the profiles. First of all, it leads to an alteration of the stress-strain curve of the steel. Cold

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hammering provides an increase of the yield strength and sometimes, of the ultimate strength that isimportant in the corners and still appreciable in the flanges, while press braking lets thesecharacteristics unchanged in these zones.

Fig.4. The effects of cold hammering upon the mechanical characteristics of the steel

Tabel 1. Nominal values of yield strength of basic material fyb and tensile strength fu according to the relevant codesType of steel Standard fabrication Grade f yb

[N/mm2]fu[N/mm2]

Hot rolled steel sheet of

structural quality

EN 10025:1993;

SR EN10025+A1:1994

S235JR;S235JO;S235J2 235 360

Hot rolled steel sheet ofhigh yield stress ofstructural quality1)

EN 10025:1993;SR EN10025+A1:1994EN 10113:1993;EN 10137:1993

S275JR;S275JO;S275J2;S275N;S275NL;S275M, S275ML

S355JR;S355JO;S355J;SR355K2;S420N; S420NL; S420M; S420ML;S460N; S460NL; S460M; S460ML

275

355420460

370

470500530

Cold-reduced steel sheet ofstructural quality

ISO 4997 CR 220CR250CR 320

220250320

300330400

Continuous hot dip zinccoated carbon steel sheet ofstructural quality

EN 10147 S220GS250GS280GS320GS350G

220250280320350

300330360390420

High yield strength steels

for cold forming

EN 10149

Note: According to ENV 1993-1-1:1992/A1:1994 the following criteria should be accomplished inchoosing the appropriate steel in the case of cold forming:1) Material in both delivery conditions M and N may be cold formed;2) During cold forming the higher tensile and resilience properties of S 460 or S 420 steel,compared to S 355 should be taken into account.3) If after cold forming a stress relief treatment has to be carried out, the following conditions shall

be both satisfied for delivery conditions M and N:a) temperature range: 5300C to 5800C;

b) holding time: 2 minutes/mm of material thickness, but at least 30 minutes; The grades of steels used for cold formed shapes according to the Romanian standards stillavailable are: OL 32, OL 34, OL 37, OL 42, OL 52- STAS 500/2-80; RCA37, RCB52- STAS500/3-80; B1, B2-STAS 9724-90; A1, A2, A3- STAS 9485-80; OLC10 and OLC20- STAS 880-88. The cold-formed shapes are made of steel strips obtained under the Romanian standard

prescriptions: STAS 908-90; STAS 1945-90; STAS 9236-80; STAS 9150-80; STAS 10896-80.

The ratio: 2.1y

u

ff

must be respected and also ultimate elongation A5>20%.

Maximum Width-to-Thickness RatiosThe cold-formed shapes may be considered as several independent sheets (plane walls)

interconnected with rounded corners; the internal radii depend on the thickness of the walls. Theratios width-to-thickness, b/t may not exceed certain values, representing the field of experienceand verified by testing. If these values are still exceeded, the strength of these walls shall be tested.

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Table 2. Maximum b/t ratios and modelling of the static behaviour

The thickness of the material considered during the process of design depends on thetolerance limits and on the type of the coating (see table 3).

Table 3.Design values of the thickness of the steel sheetConditions imposed by the manufactory process Design thickness, t [mm]

Tolerances under 5% tc, nomTolerances greater than 5% 1.05(tc, nom-t)

Tolerances under normal tolerances, thickness 1.5mm, continuous hot-dip coating prEN 10143

tc, nom

Continuous hot-dip coating EN 10147 tc= tN - tz; tz= 0.04 mm, bothsides, 275g/m2

Along with the verifications presented in the table above, the end stiffener must be providedwith a sufficient stiffness to avoid primary buckling. For this purpose, the following limits of theratios c/b and d/b should be taken into account: 6.0/2.0 bc and 3.0/1.0 bd .

An increase of the ultimate strength is related to the strain ageing accompanied by adecrease in ductility and depends on the metallurgical properties of the material. A superiormechanical strength perpendicular to the cold-hammering direction is the characteristic of the

corners determined by the folding process and as a result in certain situations the design values ofthe strength will be increased wilt almost 45%.

According to NP 017/97 that replaces the standard 10108-1/80 an averaged value of

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strength will be determined either experimentally or by calculations, on the basis of the followingrelationship:

(1) ( )ybuybya ffA

Cntff

+=

2

where:

ufybf , - yield strength, respectively ultimate tensile strength, N/mm

2;

t- thickness of the steel plate;A - gross area of the cross section (mm2);C=7 for cold rolling and 5 for other methods of cold forming;n - number of folders at 900 having the internal radius r


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Fig. 5. Determination of the folding numbern: a- members axially loaded; b- members subjected to bendingabout major axis.

2. Specific Features of the Cross Sections of Cold Formed Thin Gauge ShapesZ, , C and I profiles are the usual shapes used in the design. Their heights are between 80mm and 250 mm and the widths of flanges between 20 mm and 150 mm. Closed sections, ashollow circular, square or rectangular sections are used often for the design of the steel elements.In appendix A some shapes are presented with their catalogue characteristics.

The walls of the cold-formed shapes are classified into two categories: stiffened walls that have their edges bound with another wall or with a folded end stiff enough

as to prevent from its deformation in a direction perpendicular to the plane of the element: un-stiffened walls that have one edge fee to displace (rotate) in a plane normal to the plane of

the element

Fig. 5. Stiffened walls of the cold formed shapes: a)- external wall with end stiffener; b) internal walls withintermediate stiffeners

A certain shape may be considered as a profile with intermediary stiffeners, like the one infigure 5.b., if the following relationship is available:

(5) 42

411min 4.1826600066.3 t

RtbtI p

The end stiffeners, as the one presented in the figure 5.a. are considered active if:

(6) 42411min 2.9

266000)(83.1 t

Rt

btI

p

Also, the end stiffener must respect the following condition for the minimum height, amin in order tobecome active:

(7) t

Rt

ata

p8.4

266000)(8.2 62

min =

The end stiffeners of and C shapes must respect also the condition: amin from the totalwidth (excluding the rounded corners) of the wall that is stiffened.

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a-

b

Fig. 1. Cold formed shapes with stiffened walls: a)- intermediate stiffeners; b)- with lip and clip (end stiffener)

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Fig. 6. Shapes with or without stiffeners, their geometric characteristics and mechanical behaviour, according to EC 3.

The calculation of the sectional properties1. Gross cross section and net cross sectionThe mechanical properties of the cross section are determined on the basis of the elements

(flat portions) that form it. When calculating the gross section properties, holes for fasteners neednot be deducted but allowance shall be made for large openings.

The plates provided for battens or for splices shall not be included.The net area of an element or of the whole section shall be taken as its gross area less the

deductions for all openings. The deduction of the holes should be done according to the followingrules:

The hole has the dimension of the nominal hole diameter, not the diameter of the fastener; The area that shall be deducted in the case of the countersunk holes should be the gross

area of the hole, including the countersunk portion, in the plane of its axis; In the case of the holes that are not staggered, the area to be deducted from the gross

sectional area should be the maximum sum of the sectional areas of the holes in any crosssection, at right angles to the direction of stress in the member;

In the case of staggered holes, the area to be deducted should be the greater of:(a) the deduction for non-staggered holes;(b) the sum of the sectional areas of all holes in any zigzag line extending progressively

across the member or part of the member, less: s 2t/4g, but not more than 0.6s for eachgauge space in the chain of holes (see figure 2.1. EC3).Where:s- staggered pitch (also called spacing), that is the distance measured parallel to the

direction of stress in the member centre-to-centre of holes in consecutive lines;

t- the thickness of the holed material;g- the gauge, that is the distance measured at right angles to the direction of stress in the

member centre-to-centre of holes in consecutive lines.

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(c) for angles with holes on both legs, the gauge should be measured along the centre ofthickness of the material.

Fig. 7. Disposition of the staggered holes in the web a of a cold formed profile

Rounding of cornersIn the calculation of the geometrical properties the configuration of the cross section will beconsidered according to fig. 1.3. The plane widths bp shall be measured from the midpoint ofthe corner.

Fig. 8. Design conditions for the rounding corners of the cold formed shapesIn the case when a cross section is made up from plane elements with sharp cornerswith r5t and r/bp0.15, rounding of corners is ignored.

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All the sectional properties may be calculated based on an ideal section according tofig. 2.3 and the following approximations:

(8)

( )

( )

( )

41

21

1

'

'

'

=

=

=

uu

gg

gg

II

II

AA

where:

''',, ugg IIA are the reduced properties taken into account due to rounding corners;

=

==m

i

i

n

i

i

b

r

1

143.0

with the annotations:n- number of corners;m- number of flat widths;

bI- length of the mid line of the flat widths.

Fig. 9. Example of an idealised cross section

Determination of the sectional characteristics of the cold-formed shapesThe specific feature of these shapes lays in the fact that the compressive forces applied on the

cross section lead to a certain diminishing of the net area that sustains the effort. An effective area,

smaller than the net area is determined, depending both on the geometrical characteristics and on thenature and the value of the stresses. In the same time, certain shapes will loose their stability not bysimply flexural buckling, but by torsional and flexural-torsional buckling. The calculation of themechanical properties for these sections implies the determination of the torsional centre and the

polar radius of gyration, also St. Venant constant and warping constant.The calculation of the sectional properties is based on the study of warping .In figure 10.a. a pointMis identified in the proximity of the C shape. From this point that we

will call the sectorial pole an origin vector-radiusMA is traced and after that, another radius Mb, thepoints A and b being placed on the median line of the profile. The surface obtained from theintersection of the vectors with the median line, doubled, represents the sectorial surface or the

sectorial co-ordinate of the point b: MrbA = .

Fig. 10. Sectorial surfaces and coordinates- basic notations

The sectorial surface has an algebraic sign, if the rotation of the vector is clockwise, then the

sign is positive and if the rotation is counter clockwise, then the sign is negative.In figure 10.b the vector intersects the median line and in this situation the sectorial surface is

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the algebraic sum of two surfaces: ( )yrh

M =+=2

21 .

We choose the torsional centre of the profile, named also sectorial principal pole. The pointson the cross section where the normal sectorial stress is zero and also =0 are named points ofzero. The point a determines the origin vector and for this reason is chosen to be the closest pointto the torsional centre, namedprincipal vectorial point of zero

This last point which is the torsion centre is determined with the help of the principalsectorial point of zero as it follows:

A shape is considered with its principal sectional axes of symmetry as in figure 3.9; for thisshape a poleMis chosen as to determine easily the sectorial surfaces M .

Fig. 11. Geometric construction for the determination of the coordinates of the warping centre

IfB is the torsion centre that determines the sectorial surfaces we may draw the axes y1Mz1parallel to the central principal axes of symmetry. For the element ab the tangent (t) to the profilewill be drawn and also from the two poles the perpendiculars rB and rM to the tangent. The length ofthe element ab being expressed as ds then the elementary sectorial surfaces will be expressed also:dM=rM ds and d=r ds. The polar radius will be expressed in the following form:

(9) sincos ++= BBM zyrr

If we amplify the relationship with ds we will have:

(10) sincos = dszdsydsrrds BBMwith the annotations:

(11)

sin

cos

==

dsdy

dsdz

It results that:

(12) dyzdzydd BBM += And integrating, we obtain:

(13) Cyzzy BBM +++=

where Cis the constant after integrating andy andzare according to fig. 3.9, the distances ofthe point a from the principal axes of inertia OXand OY.

The sectorial linear moment area must be a null value:

(14) ==== AA yz xdASydAS 0;0 So:

(15) =++= A A ABBA A M dAyCdAyydAyzydAydAy 02

and

=++= AABABA A M dAzCdAzyzdAzzzdAdAz 02

Also, considering the central principal axes of inertia, the following integrals must be zero:

(16) ===A A A dAzdAydAzy 0;0;0

Then finally the co-ordinates of the torsion centre are:

(17)y

AM

B

z

AM

BI

dAzy

I

dAyz

== ;

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wherey, z, respectivelyIy andIz are determined with respect to the central principal axes ofinertia of the cross section, and Mwill be determined with respect to a random pole Mwhich mayvery well coincide with the gravity centre G of the section and also any pointB in the plane.

The integrals are calculated with Veresceaghin rule.The sections with one axis of symmetry have the torsion centre on this very axis, and the

sections with two axes of symmetry have the torsion centre in the same point as the gravity centre.

Considering the condition that the sectorial moment area of the whole section to be zero wemay write:

(18) == A dAS 0and from this the position of the principal sectorial point of zero is determined.The sectorial second moment of area I is determined with the relationship:

(19) dAIA

= 2In the case of the particular situation in figure ., which represents the most common case of a

corner in the cross section of the cold-formed shapes, the sectional characteristics will be determinedwith the help of the coefficients k in table above, depending on the ratio r/t.

Fig. 12. Geometric elements for determination of the sectorial characteristics of a rounding corner

The following geometrical characteristics will be considered:

-the length of the element: lc=k1t;

- the area of the curved element:Ac=k1t2;

- sectorial linear moments area: Sy0=Sz0=k2t3;

- co-ordinates of the gravity centre:y0G=z0G=k3t;- moments area:Iy0=Iz0=k4t

4;Iy0z0=k6t4

Foropen sections, the stiffness for torsion is determined with an equivalent moment area fortorsion (St. Venant constant):

(20) == 3333

tLtlIt

where:- coefficient determined experimentally for each profile:- angles: =1;- I and C sections: =1.12;- T sections: =1.21.3.

l- width of the leg of the section;t- thickness of the leg;L- total length of the profile.Second moment area for torsion ofclosed (hollow) sections is determined with the relationship:

(21)U

tAIt

24

=

where:

A area determined by the median line (closed) of all the walls of the section:

(22) 22

12215.0 tt

rbhA

=

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D length of the median line:

(23) ( ) tt

rhbU

++= 1286.02

The sectorial characteristics for the most important sections are presented in table 3.3The following relationships are common for all the profiles:- distance from the gravity centre to the torsion centre:

(24) Gcc eey +=- radii of gyration with respect to the principal axes:

(25)A

Ii

A

Ii zz

y

y == ;

- polar radius of gyration with respect to torsion centre:

(26) 2c

zy

c yA

IIi +

+

=

- radius of gyration for torsion:

(27)2

c

tiA

Ii

=

- the warping constant:

(28)

I

Ik t62.0=

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Cold Formed1