COLD FORMED STEEL MEMBERS AND SHEETING

1.1 Introduction 1.2 Industrial production of cold formed thin gauge

sections1.3. The steel used for cold formed thin gauge members.

Characteristics for design1.4. Influence of cold hammering 1.5. Maximum Width-to-Thickness Ratios2.1.Specific Features of the Cross Sections of Cold

Formed Thin Gauge Shapes 2.2. Calculation of Sectional Properties

1.1 INTRODUCTION • Sheet, strip, plates or flat bars, fabricated in roll-forming machines or by press brake

operations;• The thickness of the steel sheets or strips excluding the coating 0.5 mm to 4 mm for

sheeting and from 1 mm to 8 mm for profiles; also, steel plates and bars as 25 mm may be cold formed into structural shapes

• Some important advantages:• a) cold formed light members are manufactured for relatively light loads and/or short

spans;• b) various and intricate sectional configurations are produced economically by cold

forming operations favourable strength-to-weight ratios may be obtained;• c) nestable sections are produced 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 other conduits;

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

1.2 INDUSTRIAL PRODUCTION OF COLD FORMED THIN GAUGE SECTIONS

A. Continuous process: important series of sections, by continuous forming, in rolling mills. The coil is unrolled and the steel sheet passes through successive pairs of roles and after that the sections are cut at the desired length. Stripped steel may be processed with thickness between 0.3 mm and 18 mm and width between 20 mm and 2000 mm.

B. Discontinuous process: small series of sections, either a leaf press brake (folding) of the steel sheets or a coin press brake (press braking) are commonly used for pressing the steel strip in a mould. The thickness of the of the shapes obtained by press folding 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.

Types of structural elements: Cold-formed structural members can be classified into two major types a)- individual structural framing members; used in buildings as beams, columns, trusses, and in the workshop design as purlins, skylights, bracing, structural elements for walls transmission towers, etcb)- panels and decks (corrugated shells); used in facades as external layer for curtain walls, diaphragms, roofs, floors and permanent shuttering.

COLD FORMING OF THIN GAUGE SECTIONS

1.3. The steel used for cold formed thin gauge members. Characteristics for design

Continuously hot-dip metal coated sheeting with nominal thickness supplied with half of the normal standard tolerances, the design thickness t may be taken as the nominal core thickness, tc,nom.

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

tz, the thickness of the zinc protection, usually 0.04 mm both sides of the sheet and 275 g/m2.

“Standard” grades of steel shall have the properties that conform to the required suitability for cold forming, welding and galvanising. The ratio of the specific minimum ultimate tensile strength fu to the specific minimum yield strength satisfies:

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

The basic material used for fabrication of the steel sections consists in flat sheet steel strips and the Romanian standards available are: STAS 908-90, STAS 1945-90, STAS 9236-80, STAS 9150-80, STAS 10896-80. Generally, all these grades of steel will have the elongation at failure, A (%)>20%. Also, supplementary measures will be adopted for the stripes of 0,2…8 mm thickness considering cold forming process and sensibility to brittle fracture.

2.1yu ff

znomc ttt

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

Influence of cold forming (hammering)

The manufacturing process modify the mechanical properties of the profiles alteration of the stress-strain curve of the steel.

Strain hardening provides an increase of the yield strength and sometimes, of the ultimate strength that is important in the corners and still appreciable in the flanges, while press braking lets these characteristics unchanged in these zones.

ybuybya ffACntff

2

902 in

i 090i

uybya fff 5.0

fyb, fu - yield strength, respectively ultimate tensile strength, N/mm2; 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<5t on the whole perimeter of the cross section; for different angles from 900 the number n is determined with:

where:n - relevant number of folders that increase the strength;

-internal angle of the folder, between 900 and 1350; for values under 900, we will use:

and for values bigger then 1350 the folder will not be considered anymore.A superior limit value is imposed also for the average limit yield strength:

DETERMINATION OF N –NUMBER OF RELEVANT CORNERS

STRUCTURE OF COLD FORMED SHAPES-WALLS

Cold formed shapes are obtained from several walls. The walls may be internal or external, stiffened or un-sitffened, according to their end (edge) conditions. • 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 .

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

Conditions are imposed for the stiffness of the walls:

-for intermediary stiffeners:

-for end stiffeners:

42

411min 4.18

26600066.3 t

Rtb

tI p

42411min 2.9266000)(83.1 t

Rtb

tI p t

Rta

ta p 8.4266000)(8.2 6 2min

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

OBSERVATION: The end stiffeners of Ω and C shapes must respect also the condition: amin≥ ¼ from the total width (excluding the rounded corners) of the wall that is stiffened.

Maximum b/t ratios and modelling of the static behaviour

Shapes with or without stiffeners, their geometric characteristics and

mechanical behaviour, according to EC 3 (SR EN 1993-1-1.3)

Rounding the corners

The plane widths bp is measured from the midpoint of the corner.In the case when a cross section is made up from plane elements with sharp corners with r≤5t and r/bp≤0.15, rounding of corners is ignored. All the sectional properties may be calculated based on an ideal section and the following approximations:

41

21

1

'

'

'

uu

gg

gg

II

II

AA

m

ii

n

ii

b

r

1

143.0n- number of corners;m- number of flat widths;bi- length of the mid line of the flat widths.

PARTICULAR FEATURES FOR THE DESIGN OF THE COLD-FORMED THIN GAUGE SECTIONS

Cold-formed (thin gauge) sections may buckle under normal stresses smaller than the yield limit of the steel. The instability of the thin gauge flat sheets subjected to in-plane loading is due to imperfections.

The following assumptions are demonstrated to be inconsistent:I. The perfect planarity - the initial deformations of the sheets due to faults of fabrication must be between certain limits. Still, the real plane elements do have initial geometrical imperfections- initial deflection w0, which grows with the increase of loading. Due to the effect of membrane behavior, the ultimate strength of the sheet is bigger than the critical elastic force of buckling, Ncr. This reserve of strength clearly insures a post-critical behavior.

Plate in compression: conditions of supports and post-critical reserve

II. Reduced deformations out of the plane of the plate – this assumption is normally available in the theory of linear buckling in elastic domain. In reality, the ultimate strength of the plate exceeds the critical stress, the deformations being rather important;III. Axial loads - this assumption is impossible from the practical point of view, the planarity of the plate being an ideal assumption.

Measurement of residual stresses in a cold-rolled C shape:

a) – residual flower: b)- slicing method; c)- curvature method;

IV. Linear elastic behavior of the material – this condition is satisfied up to the yield limit. Still, due to residual stresses caused by rolling, welding, cutting etc, in some fibers the plastic stresses are reached for applied stresses lower than fy.

Local buckling in compression and bending of the thin walled elements

Consecutive stages of stress distribution in stiffened compressed elements

Winter’s model (grid)

The two distinct stages in the post-critical domain of the behavior of a plate are:Elastic- uniformly distributed stresses, under the critical force;Post-critic- below the critical force, the plate is deformed more and more, the stresses are not anymore uniform.

Buckling is reached for a critical value of the normal stress: σc ≥ σcr where the critical stress is determined with the known

relationship ([N/mm2])

3

22

2

2

10190112

ppcr b

tk

btE

k

The coefficient kdepends on the nature and the distribution of the stress on the width of the wall, on the boundary conditions, on the ratio between the dimensions of this wall.

-non - stiffened walls: kσ =0.425;-stiffened walls: kσ=4.0, the supports are considered articulated.

It is important to observe that: in the case of a wall under compression in its plane, the lost of strength capacity will not happen as

long as the longitudinal edges will remain rectilinear; the limits of strength capacity are much increased for certain types of walls. This remark leads to

the theory of effective width of the wall.

The design concept the grid model proposed by Winter (1959) for the instability phenomenon. The cross section for these profiles is made up from flat elements (walls) with constant thickness inter-connected, generating a grid.

In the post critical stage (post buckling strength) the central grid do not work anymore while the extreme grids, where the strains are smaller, are able to take over stresses that may reach the design value of strength. At the moment when the maximum strength value of the material R, is reached in the extreme zones, a bigger portion in the internal part of the wall already isn’t working anymore (where s = 0), the deformations being very important.

The width of the wall reaches its minimum value, called the effective width beff.From the point of view of the local buckling:

-stiffened compressed elements (walls) -flat elements in compression with both edges parallel to the direction of stress, which are stiffened by web elements, flanges or edge stiffeners of sufficient rigidity

-non-stiffened compressed elements (walls) -flat elements in compression which are stiffened only at one edge parallel to the direction of the stress.

Considering that in the situation of buckling in elastic of a wall having its effective width, beff, the stress σcr,eff reaches the maximum stress in the plate in post-critical domain, that is: σmax = fy. Then the relationship (1) becomes: (2)

From this relationship it results that the effective width of the wall depends on the ratio σcr/σmax : (3)

where:σcr – the critical stress of buckling in elastic of the plate, considering its total width; σmax - maximum stress on the edges of the plate.Considering that in the phase of buckling the averaged stress on the whole width of the wall is σu, the

equivalence between the stresses will impose the following equation: (4)

Von Karman determined the following relationship for the effective wall: (5)In the case of the plate articulated all around and uniformly compressed, kσ = 4.0 and: (6)

EC3 uses the following relationships in order to simplify the further design specifications:relative slenderness (of the plate) referred to bp: (7)reduction factor: (8)influence of the elastic limit: (9)table 2.

Based on von Karman’s relationship it will result that: (10)The slenderness of a wall, λp is the ratio between the flat width of the wall, bp and its thickness, t.Winter proposed a semi - empirical relationship, derived from that of von Karman’s that takes into account the imperfections: (11)This is used by EC3 in the design of the strength of very slender sections. The following annotations are used:for: we have: (12)for:we have: (13)Specifications:The effective width of a flat wall in compression and/or in bending is determined considering the relative slenderness referred to the width of the flat wall, bp and also, the limit of yield strength, fyb. In order to identify the way the cross section of a wall is working we have to compare the effective slenderness with the limit slenderness.

The recommended values of the maximum slenderness (limit slenderness) for different types of cold-formed sections are presented in table 1. The common experience and the tests in laboratory impose these values.

The limit slenderness is defined as the ratio between the width and the thickness of the wall in the case when the normal stresses are uniformly distributed on the whole cross section and equal with the design strength of the material. The values of the limit slenderness depend on the kind of the wall and the grade of the steel. The presence of the imperfections reduces the theoretical values of these limits over which buckling may occur anytime, see