Special Steel Structures - Courses - 2013

PARTICULAR ASPECTS IN THE DESIGN OF COLD FORMED

STEEL MEMBERS AND SHEETING

1.1 Introduction

1.2 Industrial production of cold formed thin gauge sections

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

1.4. Effect of cold forming

1.5. Maximum Width-to-Thickness Ratios

2.1.Specific Features of the Cross Sections of Cold Formed Thin Gauge Shapes

2.2. Calculation of Sectional Properties

Cold formed sections are made in various shapes: 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.

1.1. INTRODUCTION

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, etc

b)- panels and decks (corrugated shells); used in facades as external layer for curtain walls,

diaphragms, roofs, floors and permanent shuttering.

1.2. COLD FORMING OF THIN GAUGE SECTIONS

Manufacturing by folding Manufacturing by press braking

Discontinuous manufacturing process

Continuous manufacturing process

Cold rolling

Specific shapes made of cold-formed thin gauge

members (Trebilcock, 1994)

1.3. THE STEEL USED FOR COLD FORMED THIN GAUGE MEMBERS

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 EN 1993-1-1, 3/2006.

The basic material used for fabrication of the steel sections consists in flat sheet steel stripes Generally, all these grades of steel will have the elongation at failure, A (%)>20%.

Also, supplementary measures will be adopted for the stripes of 0,28 mm thickness

considering cold forming process and sensibility to brittle fracture.

2.1yu ff

znomc ttt

Examples of profiled sheeting and members (EN 1993-1-3)

SHEETING

BASIC

ELEMENTS

ELEMENTS

USED FOR

AXIAL

LOADING

ELEMENTS

USED FOR

BENDING

1.4. EFFECT OF COLD FORMING. STRAIN HARDENING

The continuous manufacturing process modifies the mechanical

properties of the profiles; the result is the alteration of the stress-

strain curve of the steel (see on the diagram).

Strain hardening provides an increase of the yield strength

and sometimes, of the ultimate strength; it is important in the

corners and still appreciable in the flanges.

Press braking lets the characteristics unchanged in these arii.

The increased value of strength is taken into account only if the

gross cross section is equal with the effective cross section:

ybu

g

2

ybya ffA

kntff

902n i

i 090i

uybya fff 5.0

fyb, fu - yield strength, respectively ultimate tensile strength, N/mm2;

t - thickness of the steel plate;

Ag - 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

The cross section of a cold formed element may be divided in a number of plane walls and for every wall a separate

value of the increased yield limit, fyi may be determined if the following relationship is respected:

Ag,i is the gross transversal section of the plane element i

DETERMINATION OF THE NUMBER OF RELEVANT CORNERS

Note:

The increased value of the strength is not considered if welding is placed in the

strain hardened area or thermal treatments

were performed with 0 >520 0 C.

The increased value of the strength is not considered on the web of a bended

profile.

Stages of cold-forming of an section (Rhodes,1992)

Equippment for continuous process in workshop

THE WALLS OF COLD FORMED SHAPES

Cold formed shapes are obtained from several walls. The walls are internal or external, stiffened

or un-stiffened, according to their end (edge) conditions.

the stiffened walls 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:

the un-stiffened walls 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)- wall with edge stiffener; b) walls with intermediate stiffeners: 1- stiffened wall; 2-un-stiffened wall

Conditions are imposed for the stiffness of the walls:

-for intermediate stiffeners:

-for edg stiffeners:

4

2

411

min 4,18266000

66,3 tRt

btI

p

42411

min 2,9266000

)(83,1 tRt

btI

p

tRt

ata

p 8,4

266000)(8,2 6 2min

Cold formed shapes with stiffened walls:

a)- intermediate stiffeners; b)- with lip and clip (edge stiffener)

Maximum b/t (slenderness) ratios and modelling of the static behaviour

1.5. MAXIMUM WIDTH-TO-THICKNESS RATIOS

THE INFLUENCE OF ROUNDED CORNERS

UPON THE DETERMINATION OF BP

The middle of the median line of the corner or fold

(b) Plan width of the wall bp for the

flanges and edge stiffeners

(c) Plan width bp for the web of the cross

section

bp = tilted line sw

(d) Plan width bp for wall attached to

the intermediate stiffeners on the

flanges

X-the intersection of the median lines

P-middle of the median line of the corner

The plane width bp is measured from the midpoint of the corner.

In the case when a cross section is made 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:

SHAPES WITH OR WITHOUT STIFFENERS.

GEOMETRIC CHARACTERISTICS AND MECHANICAL BEHAVIOUR,

ACCORDING TO EC 3 (SR EN 1993-1-1.3)

INSTABILITY 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

Winters 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: c cr where the critical stress is ([N/mm2])

3

22

2

2

10190112

pp

crb

tk

b

tEk

The coefficient k depends 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: k =0.425;

- stiffened walls: k=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 fy, is reached in the extreme

zones, a bigger portion in the internal part of the wall already isnt working anymore (where = 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:

-the stiffened compressed elements (walls) are 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;

-the non-stiffened compressed elements (walls) are flat elements in compression which are stiffened only

at one edge parallel to the direction of the stress.

BUCKLING OF THE THIN WALLS-WINTERS GRID MODEL

Local buckling in compression and bending

of the thin walled elements

Consecutive stages of stress distribution

in stiffened compressed elements

Winters model (grid)

Effective width of a plate in compression

Stiffened walls- EDGE and intermediate

Buckling is reached for a critical value of the normal stress: c cr where the critical stress is determined with the known relationship:

3

22

2

2

10190112

pp

crb

tk

b

tEk

The coefficient k depends 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: k =0.425; stiffened walls: k=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.

[N/mm2]

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 isnt working anymore (where 0, the deformations being very important.

The width of the wall reaches its minimum value, called the effective width beff.

CLASSIFICATION OF THE WALLS OF A COLD FORMED SECTION

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 cr,eff reaches the maximum stress in the plate in post-critical

domain, that is: max = fy. Then the former relationship becomes:

22

2

2

,112

eff

p

cr

eff

effcrb

b

b

tEk

From this relationship it results that the effective width of

the wall depends on the ratio cr/max :

max

crpeff bb

In buckling stage, the averaged stress on the whole width of the wall is u, the equivalence between the stresses will impose the following equation:

upeffupyeff bbbfb max

Von Karman determined the following relationship for the effective wall:

max

2

2

2 1

112

p

peffb

tEkbb

In the case of the plate articulated all around and uniformly compressed, k = 4.0: max

9.1

Etbeff

in order to simplify the further design specifications EC3 uses the following relationships:

relative slenderness (of the plate) referred to bp:

k

t

b

fp

cr

y

p

4,28

reduction factor: y

u

p

eff

fb

b

influence of the elastic limit: yf

240

11

andp

The slenderness of a wall, p is the ratio between the flat width of the wall, bp and its thickness, t.

It results that:

Winter proposed a semi - empirical relationship, derived from that of von Karmans that takes into account the imperfections:

maxmax

415.019.1

E

t

b

Etb

p

eff

This is used by EC3 in the design of the strength of very slender sections.

The following annotations are used:

673.0p 1

673.0p

pp

22.01

1

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 before. 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 table.

For:

For:

DIFFERENCIES BETWEEN BUCKLING OF IDEAL SLENDER MEMBER,

HOT ROLLED SECTION MEMBERS AND COLD FORMED SECTIONS

STRESSES DEVELOPED IN THE WALLS OF A COLD FORMED SECTION

SUBJECTED TO BUCKLING

Thin walled C section in compression

Buckling ranges depending on slenderness

EUROCODE buckling curves

BUCKLING MODES OF COLD FORMED SECTIONS

Local Flexural+ Flexural Torsional

interactive buckling

a) Flexural + Flexural-Torsional

interactive buckling;

b) b)- Local+Flexural Torsional

interactive buckling Simple buckling modes for a C column (thin walled section)

DISTORTION OF OPENED SECTIONES WITH THIN WALLS

Combined modes of buckling leading to distortion of thin walled opened sections

(wavelength is considered as buckling length in the case of a column)

Buckling forms, critical buckling forces and resistances

depending on the length of the element

Buckling forms depending on the buckling half-wave :

a)- local buckling; b)- distorsion; c) overall buckling

THE EFFECTIVE WIDTH OF THE WALLS IN COMPRESSION

DOUBLY SUPPORTED COMPRESSION ELEMENT OUTSTAND COMPRESSION ELEMENT

THE EFFECTIVE WIDTH AND EFFECTIVE AREA OF THE WALLS IN BUCKLING

BUCKLING BY DISTORSION

Distorsion of a Z shape: (a) in compression; (b) in bending

Critical elastic stress for a slender element in compression having an elastic support with a stiffness

coefficient K is determined with the relationships of Timoshenko and Gere (1961).

Reduction factor (buckling coefficient) by distorsion depends on the value of the reduced slenderness is

determined with the following relationships:

where the relative slenderness for distorsional buckling is:

where:

- As, Is area and moment of inertia of the edge stiffener;

- - slenderness of the stiffener.

ELEMENTS WITHOUT STIFFENERS (PLANE ELEMENTS)

I step

The reduction factor for the determination of the effective widths for stiffened or un-stiffened walls shall be obtained as

we have already seen. The value of relative slenderness is determined with:

where:

com effective stress of compression on the extremities of the wall, 1, determined with respect to the effective area of the transversal section and multiplied with the safety factor, M1;

k buckling coefficient.

II step

The design for the limit state of serviceability, 1-fy: The value of the reduction factor is determined with the relative slenderness obtained as in the I step, where com = 1 M1 and the effective stress calculated is 1 < fy/M1.

The following relationships are used:

-For : =1;

-For: , 1;

After determining the values:

III step

In the tables the geometrical width of the flat wall is bp. In the case of the lateral webs without intermediate stiffeners

(the folders of the sheeting), the annotation sw is equivalent with bp.

kEt

bcomp

p

052.1

673.0pd 0.16.018.0

22.01

pu

pdpu

pd

pd

kEt

bcomp

pd

052.1

kE

f

t

b yppu

052.1

673.0pd

PLANE ELEMENS WITH STIFFENERS- EDGE AND INTERMEDIARY STIFFNERS

Determination of the transversal deformation of the walls

Stiffness to rotation of a stiffener is calculated by applying a unit force on length, u, normal to the wall. The rigidity of

the spring on unit length, K is obtained by the relationship:

where is the deflection of the stiffener as effect of u acting in the centroid of the effective part (placed at the distance b1 )

Real system

Equivalent system

Deflection of the compressed stiffened walls of C and Z cold formed sections

Modeling the deformations as effect of compression and bending:

a) and b) C section subjected to compression and bending; c) and d) Z section subjected to

compression and bending

a) b) c) d)

Edge stiffeners

with lip with lip and clip

In the case of a intermediary stiffener, C1 and C2 will be conservatory annulled, deflection being thus determined:

3

2

21

2

2

2

1

Et

112

)bb(3

bbu

The reduction factor due to distorsional buckling is determined considering the relative slenderness of the wall , and imperfection coefficient according to the table of classification the cross sections by buckling curves, (curve a0)

cr,s the critical stress of the stiffener (without imperfections).

scr

ybf

,

d

TRANSVERSAL DEFLECTION OF THE WALLS IN COMPRESSION

(IMPERFECTION EFFECTS)

A rectilinear section will have an initial bend shape equal with the deflection u, where:

A curved element in bending (beam) will have a maximum deflection:

where:

u bending of the flange (hogging); bs- half of the distance between the webs for closed sections or or, the part of the flange extended on the flange

depth;

z distance from N.A. to the flange in compression; r - radius of the curve;

a mean value of the stress in flange, determined on the gross area

The design is based on the assumption that the stiffener works as a beam on elastic foundation represented by a spring

stiffness, depending on the bending stiffness of adjacent parts of plane elements and on the boundary conditions of the

element.

The determination of the spring stiffness is illustrated separately for intermediate and edge stiffeners respectively.

The significance of the terms are:

- the deflection of the stiffener due to a force equal with 1;

fs and fr are taken as in the figure.

For the rotational stiffness in the supports C, C1 and C2 , the effects of other stiffeners are considered if there is the case, for

any element that forms the cross section in compression.

For an edge stiffener, the deflection is determined with the relationship:

where:

In the case of C and Z sections with edge stiffeners the rigidity at rotation K1, the stiffness to rotation of the flange 1 is

determined by placing the unit force u =1 in the position according to figures.

3

22

p

ptE

112

3

bub

C

bu p

where:

b1 distance between the web and the flange intersection and the centroid of the effective area of the end stiffener of the flange 1 (including the effective width be2 of the flange);

b2 distance between the web and the flange intersection and the centroid of the effective area of the end stiffener of the flange 2 (including the effective width be2 of the flange);

hw height of the web; kf= 0 if the flange 2 is in tension; Kf=As2/As1 if the flange 2 is in compression; kf =1 for a cross section symmetrical in compression;

As1, As2 effective section of end stiffeners (including the effective area of the flange be2 of the flange 1 and 2 respectively.

In order to determine the effective widths that split into several sections a stiffened wall the general method applied

follows 7 successive steps; it also may be simplified in a restrained form by imposing initial conditions.

Both methods may be developed iteratively.

General method:

. An initial effective area of the edge stiffener is determined, based on the fact that it will act as an element infinite rigidly supported and subjected to a stress:

. The reduction factor will be determined for this stiffener but this time, the elastic spring will be considered;

. The reduction factor will be improved by iteration. The initial values of the effective widths bef,1 and bef,2 are obtained from the indications in the table, considering that the wall is an intermediary one;

The initial values of the effective widths cef si def are obtain as it follows:

I. Lip: in the relationship, and are prior determined and the values of the local buckling coefficient, k is determined as it follows:

If: k=0,5;

If

II. Lip and clip: The same relationships except the value of k are determined for a doubly supported wall (table).

Then determine:

1,

M

ybEdcom

f

35,0,

p

cp

b

b

6,035,0,

p

cp

b

b3

2

, 35,083,05,0

p

cp

b

bk

c,peff bc

d,peff bd

where is determined as for the lip stiffener before.

Then the characteristics of the effective section of the stiffener will be:

- The area:

- The moment of inertia with respect to the neutral axis of the effective section, Is

. Critical stress of the edge stiffener is determined with:

. Effective reduced area of the stiffener:

. The reduced thickness of the wall used for the effective area:

Reducing factor , for edge stiffener is determined based on the value of cr,s obtained priory but its value may be improved via iteration method if

Simplified method:

If the following condition is satisfied by the wall of which the width is bp:

where : - h - depth of the web adjacent to the wall, on the opposite edge to the end stiffener;

- As- effective area of the edge stiffener, that is:

determined for an even distributed stress , , with be2, cef, def, determined according to

the general method and ; - r =0,31.

Effective area of the stiffener is obtained with :

but and = 0,5.

Effective cross section characteristics are determined based on the reduced thickness of the wall, ts,red.

In the case when =1 and r=4,86, the stiffener plays the role of a support for the adjacent wall.

32

2 5,1

t

b

E

f

b

hAI

pyb

p

srs

efefes dcbtA 2

1

,

M

yb

Edcom

f

predp,

Edcom

Myb

sreds

fAA

,

1

,

sreds AA ,

INTERMEDIARY STIFFENERS

Stiffness to rotation C1 and C2 are conservatively assumed to be equal with 0 and the deflection is obtained with the following relationship:

cr,s critical elastic stress in buckling of the stiffener

STAGES OF DESIGN OF THE EFFECTIVE SECTION OF A FLANGE WITH EDGE STIFFENER

Stiffness coefficient k and reducing factor according to EN 1993-1-3/2006

COMPOSITE BEAMS

HOT ROLLED SHAPES OR PLATE GIRDERS (BUIL-UP SECTIONS) ARE USED FOR THE STEEL ELEMENT OF THE SECTIONS

Steel beams and reinforced concrete slab with constant or variable thickness of the slab (barrel volt). Steel beams encased partially in the concrete and reinforced concrete slab

Steel beams and composite slab

Steel beams encased partially in the concrete and composite slab

1

2

COMPOSITE BEAMS

The composite beams are structural elements in bending made of a steel shape acting together with a concrete slab. The slab may have just a light mesh reinforcement (fire reinforcement that reduces severe cracks at the supports) or on the contrary, it may be a reinforced concrete section or even pre-stressed.

The two materials steel and concrete participate with their characteristic properties, optimizing the complex behavior.

The concrete has a very good behavior in compression but its resistance for tension may be ignored. The steel acts evenly in tension and compression still, the slenderness of the elements affects the parts in compression.

The design calculations are based on the concept that the slab, or almost all of it is in compression. The top flange of the steel beam is prevented from instability phenomena and, depending on the position of the Neutral Axis, the steel is almost exclusively subjected to tension.

CREEP AND SHRINKAGE

The effect of creep may be taken into account by using the modular ratio nL for the concrete, this ratio depending on the type of loading (L) and is given by: where: n0 ratio Ea/Ecm for short term loading; Ecm- secant modulus for short term loading ;

t creep coefficient (t,to) depending on the age of the concrete at the moment t0 of loading;

L creep multiplier (0,55 for primary and secondary effects of shrinkage, 1,5 for prestressing , 1,1 for permanent loads.

GRINZI MIXTE OEL-BETON

3

COMPOSITE BEAMS

tL0L 1nn


Based on these observations is may be put into evidence that if there were any bond between

the steel beam and the concrete slab, the two elements will act independently, the part of the

slab in tension cracking and the steel beam limiting its strength capacity because of the overall

buckling phenomenon. If a connection between the two elements is insured, then the

distribution of strains in the two materials will be in equilibrium and the composite section will

behave as a whole.

4

COMPOSITE BEAMS

Stress distribution on

the depth of a

composite beam:

a) no connection in the

interface;

b)- with connectors

placed on the steel

surface

Fundamental criteria for the Limit States Design of the composite beams:

1. The steel beams are mono-symmetric in the plane of the web, the bending being in this plane;

2. The design bending moment capacity is determined with a plastic calculus only if the effective cross section is in the class 1 or 2;

The steel beam is subjected to tension or compression ;

The concrete cross section in the compressed area may cope with a maximum stress level of constant on the whole depth, between the Neutral Axis and the most compressed fiber;

The longitudinal reinforcement may be stressed up to a level of

if the bars are fixed in the supports.

The bars of reinforcements in the compressed area may be neglected and also the steel decking if it finds itself in the compressed area. The steel decking in the tensioned area may be subjected to a stress equal with

if the trough is parallel with the steel beam.


ya a ydf = f

ck c cd0.85f = 0.85f

sk s sdf = f

yp apf

5

COMPOSITE BEAMS

In order to classify the section of the composite beams, along with the verification of the slenderness of the walls, the following are considered:

If the steel flange in compression is connected to the concrete slab with an adequate number of studs, then the beam is in class 1;

If the concrete slab is in the compressed area and the steel beam is in the class 1, then the composite beam is in the class 1 if the Neutral Axis is cutting the reinforced concrete slab or the compressed flange of the steel beam; if not, then the composite beam is considered in the class 2.

Composite beam section Neutral axis position Class of the cross section

Neutral axis cuts the

slab class 1

Neutral axis cuts the

web

clasas2

(n general)

COMPOSITE BEAMS

OBSERVATIONS

In the design of the composite beams the effect of temperature variations is neglected.

The action of the contraction and expansion of the concrete may also be neglected in the case of Ultimate State Verifications, excepting the beams in the class 4.

The transversal section of a composite beam is made of a steel beam and

a concrete slab. Between the slab and the flange of the beam a barrel volt may be designed in order to insure the anchor length of the connectors. This part of the cross section is not taken into account during the computation but it might increase the strength capacity by increasing the depth of the composite beam.

When the Neutral Axis cuts the slab, the concrete in the tensioned area is not taken into account.

In the case when the slab is composite, the depth of the trough is not taken into account.


7

COMPOSITE BEAMS


The static system finally adopted may be different from the one used to describe the preliminary stage of execution, for ex.: removal of the

props used as temporary supports during the drying of the concrete

increase the span of the girder in the final stage; also the flexible

reinforcement in the slab begins to work, changing the stiffness and

the strength of the connections with the steel beam. We may

conclude that:

- if the connections of the steel beam are considered as perfect

articulated during the mounting stage, the participation of the flexible

reinforcement to the growing stiffness will result in a partial restraint

determining a semi-rigid connection and a partial full strength section

in the final stage (of exploitation);

- if the connections of the steel beam are considered as fully restraint

during the mounting stage, the reinforced concrete slab will increase

this stiffness, along with the ultimate strength on the support.

The composite girder obtained from a steel beam statically

determined will become in the final stage a partially restraint girder;

the composite girder obtained from a steel beam fully restraint during

the mounting stage will become a continuous girder.

8

COMPOSITE BEAMS

ULTIMATE LIMIT STATE VERIFICATIONS

OF THE COMPOSITE BEAMS

9

VERIFICATION OF COMPOSITE BEAMS

IN CRITICAL SECTIONS

VERIFICATIONS IN THE CRITICAL SECTIONS

I-I STRENGTH AGAINST BENDING AND SHEAR II-II STRENGHT AGAINST COMBINED EFFECT OF M-V III-III LONGITUDINAL SHEAR OF THE CONNECTORS IV-IV LOCAL PRESENCE OF LONGITUDINAL SHEAR FORCES IN THE CONCRETE SLAB V-V LONGITUDINAL SHEAR OF THE CONCRETE IN THE TOP OF THE COMPOSITE BEAM VI-VI FLEXURAL-TORTIONAL BUCKLING OF THE STEEL BEAM

10

Composite beams shall be checked for:

- Resistance of critical cross sections;

- Resistance to lateral torsional buckling;

- Resistance to shear buckling and transverse forces on webs;

- Resistance to longitudinal shear

Critical cross sections include:

- Sections of maximum bending moment; - Supports;

- Sections subjected to concentrated loads or reactions;

- Cross sections with sudden geometric variations, others than changes due to cracking of

the concrete;

For checking resistance to longitudinal shear, a critical length consists of a length of the

interface between two critical cross sections. For this purpose the cross section includes:

- free ends of cantilevers;

- tapering members.

SECTIONS FOR VERIFICATION AND TYPES OF VERIFICATIONS

Class of

the steel

section

Method of analysis Moment capacity

1 Rigid-plastic or elastic analysis with the

redistribution of the bending moments

2 Elastic analysis with the redistribution of the

bending moments

3

Elastic analysis with the redistribution of the

bending moments 4 Local buckling on the cross section

pl,RdM

pl,RdM

el,RdM

ef

el,Rd

Relationship between analysis method and the determination of the moment capacity

METHODS OF ANALYSIS

OF THE COMPOSITE BEAMS

12

HYPOTHESIS FOR THE ELASTIC ANALYSIS The composite beams are made of steel beams fixed at the top flange continuously by the slab; the connection between the two elements is sufficient for preventing the slip between the steel and the concrete surfaces; The steel sections remain plane after developing strains inside the material; Steel and concrete are materials acting linear elastic ( ), ) no matter the stress level might be; The concrete in the tensioned area is not considered during the verifications nor the area of increased depth above the beam, whenever it exists. Also, the concrete in the tensioned area is not taken into account nor in the case when the N.A. cuts the slab.

a c =

ELASTIC DESIGN OF THE COMPOSITE BEAMS

13

Elastic design of a continuous beam with constant moment of inertia is not taking into account the cracking of the slab in the internal support area and a redistribution of the bending moment from the support to the middle of the span is not possible. As redistribution in a certain degree is favorable leading to optimization of the properties of the component materials and using simplified methods for design, the effects of concrete cracking and the elastic-plastic behavior of the materials will be considered.

CALCULUL ELASTIC

AL GRINZILOR MIXTE OEL-BETON

a 1E I

a 1E I

a 2E I

ELASTIC DESIGN OF THE COMPOSITE BEAMS

EaI2

L1/L2>0.6 and L1,cr (L2,cr)>15%L1(L2)

EQUIVALENT SPANS FOR THE ACTIVE EFFECTIVE WIDTH

OF CONCRETE FLANGE OF THE COMPOSITE BEAMS

15

EQUIVALENT SPANS FOR THE ACTIVE EFFECTIVE WIDTH

OF CONCRETE FLANGE OF THE COMPOSITE BEAMS

Position of N.A. Aa, Ia, Ac, n, Ab, Ib

On the span 1. In the slab:

2. In the steel beam:

On the support

2)( cccaba

h

n

AhzhA

2

h

n

A)hhzh(A ccbaccaa

3beff2

baaab

a

a

eff

eff

ab

zhn

b

12

1zzAII

zhAn

b211

b

Anhz

2bb2

cc2

baaab

ccba

ca

b

zhAhn

A

3

1zzAII

2

hh

n

AzA

n

AA

1z

22

1

sbsbaaab

ssaa

sa

b

zzAzzAII

zAzAAA

z

STRENGTH ON THE CROSS SECTIONS OF THE COMPOSITE BEAMS

CROSS SECTION SUBJECTED TO

ELASTIC HOGGING BENDING MOMENT

yd

a

b

b

fW

Mz

I

M

c

ck

c

b

b

f85.0

W

Mz

In

M

b

bcs

cb

bci

cbacb

bas

bb

bai

z

InW

hz

InW

;hhz

IW

;hz

IW

Elastic hogging moment N.A. in the steel beam

steel

r.c.

Maximum Stresses

1. zb


ELASTIC HOGGING BENDING MOMENT

Elastic hogging moment N.A. in the concrete slab

2. zb>hc

ccbacaa

ef

eff

ab h1hhznA

b21

b

nAz

n

hbA

n

AAA

;hbA

ceffa

cab

ceffc

3beff2

baaab zhn

b

12

1zzAII


ELASTIC SAGGING BENDING MOMENT

sssis

sam

AAA

AAA

The concrete is cracked

Steel

sa

isissscbacaab

AA

dAdAhhzAz

2sbss2

ibsi

2

bcbacaaab dzAdzAzhhzAII

3max

b

s

sk)3(

Rd,el

1

max

1

a

ya)1(

Rd,el

)2(

Rd,el

)1(

Rd,elRd,el

y

IfM

y

IfM

M,MminM

ib

bsi

dz

IW

sb

bss

dz

IW


PLASTIC DESIGN

partial safety factor for concrete, partial safety factor for flexible reinforcement, partial safety factor for steel section, partial safety factor for the steel connectors,

1.5c c

1.15s

s 1.10a a

1.25v v

21


PLASTIC DESIGN

In the case when the steel grade is greater than S420 and the distance xpl between the plastic NA and the extreme fiber

of the concrete slab in compression exceeds 15% of the overall depth of the member, the design moment resistant

shall be Mpl,Rd

STRENGTH ON THE CROSS SECTIONS OF THE COMPOSITE BEAMS PLASTIC DESIGN

The ductile shear connectors may determine the calculation of the bending moment with a full plastic theory but the

compression flange will be subjected to a reduced force Nc instead of Ncf. The ratio = Nc/Ncf represents the degree of shear connection. The cross section will have a new plastic N.A. which shall be

used for the classification of the web.

The relationship between MRd and Nc is given by the convex curve ABC where Mpl,a,Rd and Mpl,Rd are the plastic

resistance to sagging bending of the steel section and of the composite section with full shear connection.

A conservative value of the moment resistant MRd may be determined on the straight line AC:

PLASTIC RESISTANCE MOMENT OF SECTIONS WITH PARTIAL SHEAR CONNECTION

Both for sagging and for hogging moments zones partial shear connection may be used. In hogging moments

sections appropriate shear connection will ensure yielding of the reinforcing bars in tension.

PLASTIC RESISTANCE MOMENT OF SECTIONS WITH PARTIAL SHEAR CONNECTION

Plastic design and verifications of the composite beam Plastic design and verifications of the composite beam

Position of N.A. Aa, Ia, Ac, n, Ab, Ib

On the span In the slab:

In the top flange of the steel beam:

In the web of the beam:

On the support

In the top flange:

In the web:

n

AA ca

ac

a An

ActA 4

n

ActA ca 4

2

2

1;

ef

aabab

ef

abb

b

AnzhAZ

b

Anhz

222;4

1baaac

cba

cab zhczAz

n

AZA

n

A

chz

222

4

2

2

1

baaaacc

b

aac

b

zdthdt

hctzAzn

AZ

thd

ctA

n

A

dz

ac

a An

ActA 4

s

sa

n

ActA 4

222;4

1baaas

s

sba

s

sab zhczAz

n

AZA

n

A

chz

222

4

2

2

1

baaaas

s

sb

aa

s

sb

zdthdt

hctzAzn

AZ

thd

ctA

n

A

dz

Cross section subjected to plastic hogging bending moment

Equilibrium Relationships

Cross section subjected to plastic hogging bending moment


ef

a

k

ckef

a

ya

a

bb

An

f85.0b

fA

z

bb hz

bb hz

k

ckbefc

f85.0zbF

a

y

aa

fAF

2

zh

fAz

fAM bs

a

y

a

a

y

aRd,pl

cbacsic hhthz

a

y

i

a

y

tscdcef

a

y

a

ic ft

fAfhb

fA

h

2

285.0

Cross section subjected to plastic sagging bending moment


Cross section subjected to plastic sagging bending moment


VERIFICATION FOR ULTIMATE LIMIT STATES PLASTIC DOMAIN

The methods of obtaining the efforts during a global plastic analysis may be either rigid plastic or elastic-plastic.

Rigid plastic analysis asks for the following amendments:

Transversal cross section of the steel beam must be symmetric with respect to the vertical principal axis;

The steel beam must be designed in such a way that to prevent from local buckling the flange in compression;

Active cross section of the composite beam in the plastic hinges are in class 1 and the other transversal cross sections are in class 1 or 2, excluding the active part of the webs;

The adjacent spans must respect the following conditions:

In all the bays, where more than half of the design load is concentrated on a length smaller than 1/5 from the bay and also placed in the plastic hinge area, the slab being in compression, the depth of the area in compression on the cross section of the beam must not exceed with more than 15% the total depth of the element;

In the case when the plastic hinge is the last that will affect a certain bay, the beam must not be particularly insured transversally.

1 2 2 1 1

L < L : L - L 0.50L

1 2 1 2

L > L : L 1.15L

PLASTIC STRENGTH OF THE SECTIONS OF COMPOSITE BEAMS

29

HYPOTHESES REGARDING THE PLASTIC MOMENT RESISTANCE

The existence of a complete interconnection between the steel beam and the concrete slab (concrete and reinforcement) in order to reach in the same time a limit strength;

The whole section of the steel beam is considered plasticized. Tension and compression in steel will be equal with elastic limit,

The tensions in the active section of reinforced concrete in compression have a limited value , constant on the whole cross section placed between the plastic N.A. and the most compressed fiber of concrete. The partial safety factor is ;

In the flexible longitudinal reinforcement the stresses will be equal with limit elastic design stress , where . The flexible reinforcement in the part of the slab in compression will be neglected in the design.

pl,RdM

ya af

ck c0,85( f )

a = 1,0

c = 1,5

sk sf

s = 1,15

PLASTIC STRENGTH OF THE COMPOSITE STEEL BEAMS

30

Interaction curve shear force-bending moment

PLASTIC STRENGTH OF THE COMPOSITE STEEL BEAMS

a

ya

elplEd

fWM

)(

a

ya

vRdplEd

fAVV

3,

a

ya

plLT

Edf

W

M

cr

ypl

LTM

fW

2

32,1

hL

IEtbM

yff

cr

STRENGTH VERIFICATIONS

STABILITY VERIFICATIONS

DESIGN OF THE CONNECTIONS IN COMPOSITE BEAMS

ELASTIC AND RIGID CONNECTIONS

COMPLETE AND PARTIAL SHEAR CONNECTIONS

DESIGN OF THE CONNECTIONS IN COMPOSITE BEAMS

ELASTIC AND RIGID CONNECTIONS

COMPLETE AND PARTIAL SHEAR CONNECTIONS

Classification of the connectors

Elastic (ductile) - with deformations >6mm -studs with d=1622 mm and h>4d welded at the top

flange of steel beams or on the steel decking

Rigid (non-ductile) - steel profiles (angles, tees, thick plates anchor and hoop) welded on the top flange of beams

Sliding direction of the reinforcing bars

rigid connections

DESIGN OF THE CAPACITY OF SHEAR OF THE CONNECTORS DESIGN OF THE CAPACITY OF SHEAR OF THE CONNECTORS

Angle connector Elements for the definition of the frontal surfaces Af1 and Af2

Dimensionarea unei conexiuni partiale cu conectori ductili

Complete connection: N> N f

Partial connection: N

DESIGN RESISTANCE OF THE CONNECTORS

),min( )2()1( RdRdRd PPP

v

uRd

fdP

48,0

2)1(

v

cmck

Rd

EfdP

2)2( 29,0

Design resistance of studs:

Shear strength of a stud

Shear resistance due to concrete crushing

Rigid connectors

Steel thick plates c

ckRd

fAfP

1

Angles v

ckRd fbhP

110 4/3

TYPES OF STRUCTURAL COMPOSITE ELEMENTS

COMPOSITE ( STEEL-REINFORCED CONCRETE ) STRUCTURES

1

ELEMENTE MIXTE OEL-BETON

2

COMPOSITE ( STEEL-REINFORCED CONCRETE ) STRUCTURES

COMPOSITE STEEL BEAMS

1)-hot rolled universal beams or plate girders

2)-reinforced concrete slabs

COMPOSITE SLABS

1)-hot rolled universal beams or plate girders

2)- steel decking and reinforced concrete

COMPOSITE COLUMNS

1)-hot rolled sections

2)-reinforced concrete

1. The two elements act well (complementary) together under exploitation loading;

2. The steel consumption is reduced in comparing with

steel beams acting alone and in the same time, the self-weight reduces in comparing with the reinforced concrete beams;

3. The deflection diminishes drastically; 4. The depth of the current level is reduced leaving a

wider space for the building services facilities-ducts, equipments, etc.

ADVANTAGES OF COMPOSITE STRUCTURAL ELEMENTS

3

MATERIALS

USED FOR THE COMPOSITE STRUCTURAL ELEMENTS

4

STEEL GRADES used for composite elements according to EC4

MATERIALE

PENTRU ELEMENTE MIXTE OEL-BETON

Steel grade

Nominal thickness of the element [mm]

[N/mm2]

[N/mm2]

[N/mm2]

[N/mm2]

S235 235 360 215 360

S275 275 430 255 410

S355 355 510 335 470

mmt 40 mmtmm 8040

yf ufyfuf

Mechanical characteristics of steel used for composite elements according to Romanian regulations SR EN 10025-2

Characteristics of the structural steel: Youngs elastic modulus [N/mm2]: Transversal modulus [N/mm2]: Poissons ratio: ; Density [kg/ m3] :

aE = 210.000

a

a

a

EG =

2 1+ a = 0,3

a =7850

5

MATERIALS

USED FOR COMPOSITE STRUCTURAL ELEMENTS

STEEL DECKING-profiled steel sheeting Modern deck profiles are in the range of 4580 mm height and 150300

mm trough spacing, like the dovetail profile or the trapezoidal profile with web indentations. The steel is galvanized 0,9 to 1,5 mm thick; the thickness of the galvanizing is G275 (275 g/mp), equivalent of 0.02 mm for each face.

EUROCODE 4 recommends the thickness of the steel sheet to be between 0,75 mm2 mm (usually 1,0 mm 1,25 mm).

The most efficient spans are 6501000 mm but also bigger, like 2,7 m3,6 m and the lengths 1020 m. Steel yield strengths of 280 N/mm2 and 350 N/mm2 are commonly met.

Quality classes JR, JO, J2 i K2 used for these elements, the difference being in different welding quality criteria and the toughness.

MATERIALE


6

MATERIALS


CONCRETE - type and grade

Normal and lightweight concrete are both used. The concrete grade may be specified in terms of cylinder or cube strength (ex: C25/30 is the grade for 25 N/mm2 cylinder strength and 30 N/mm2 is the cube strength.

MATERIALE


Grade of concrete

NE 012-99

Concrete

Strngth

C12/15 C16/20 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60

Class: C 140-86 Bc15 Bc20 Bc25 Bc30 Bc35 Bc40 Bc50 Bc60 Bc60

Grade B200 B250 B300 B400 B450 B500 B600 B700 -

[MPa] 12 16 20 25 30 35 40 45 50

[MPa] 1.6 1.9 2.2 2.6 2.9 3.2 3.5 3.8 4.1

[MPa] 1.1 1.3 1.5 1.8 2.0 2.2 2.5 2.7 2.9

[MPa] 2.0 2.5 2.9 3.3 3.8 4.2 4.6 4.9 5.3

[N/mm2] - - 0.26 0.30 0.34 0.38 0.42 0.45 0.48

ckf

ctmf

ctk0,05f

ctk0,95f

Rd

7

MATERIALS


Equivalence between the cube strength and cylinder strength for the concrete

MATERIALE


8

> C 20/25; LC 20/25 < C 60/75; LC 60/75

MATERIALS


In elastic domain the alteration of the elastic properties of the concrete due to contraction, expansion and cracking may be estimated by different values of the elastic modulus,

This estimation is, in the current situations done by replacing the area of the concrete cross section, , with an equivalent steel area, , where is the nominal equivalence coefficient determined with:

where: is the elastic longitudinal modulus of the steel, is the equivalent modulus of the concrete. In most common situations a simplified, averaged value

is accepted in the equilibrium equations on the cross sections

cE

cA cA n

n

'

a cn = E E

aE

'

cE

'

c cmE = E 2

9

MATERIALE

PENTRU ELEMENTE MIXTE OEL-BETON MATERIALS


SYSTEMS FOR ELECTRICITY

TRANSMISSION ON LINES

1. Introduction. General elements

2. Elements of the Electric Transmission Lines - Conductors (Wires) and Insulators

2.1. Specific features. a. Metals used for conductors; b. Classification of the conductors based on their design; c. Design strength of the conductors 2.2. Requirements for the disposition of the conductors on the towers

2.3. Insulators-types, minimum design distances

2.4. Actions and groups of actions on the conductors and on insulators

2.5. Specific situations for the design of electric transmission lines

3. Towers and cross-arms

3.1. Types of towers

3.2. Actions and groups of actions in the tower design

4. Design of the Electric Transmission Lines

4.1. Specific climatologic and meteorological conditions for the E.T.L. 4.2. Design values of the actions

4.3. Design hypotheses

Design of the steel towers

Single wall columns

Tower with square or rectangular section

Solutions for the internal members and connections

The foundations of the towers

S.E.T.L. is an independent system that transmits and distributes the electric energy in the territory. This system is made of: conductor wires, insulation units, clamps, fittings, towers and their foundations, also various devices necessary to tie to the earth.

The transportation and distribution of electric energy from the producer (electric plants) to the consumer (cities, plants, etc.) is a system developed similarly with "a cascade", from higher voltages, of more than 750 kV to lower voltages: 110, 220, 400, 500 kV. The electric current transported may have one phase (continuous) and two or three phases (alternative).

According to the code for practice PE 104/1993, the structures and systems that sustain nominal voltage of more than 750kV are the objects of the specific recommendations in PE 151/1993.

The electric transmission lines (E.T.L.) are classified into three categories according to their importance:

I category - electric transmission lines for high voltage that transport high electric power to cities or important industrial area, with continuous services;

II category - electric transmission lines for high voltage that transport low electric power to small towns or ordinary factories and also they may be distribution lines for high voltage lines;

III category - electric transmission lines for low voltage.

The elements of these systems are:

conductors;

insulating units and fittings;

towers with cross-arms;

foundations.

SYSTEMS FOR ELECTRICITY TRANSMISSION ON LINES

GEOMETRIC ELEMENTS OF AN ELECTRICITY SUPPLY TRANSMISSION LINE

The definitions of the geometric elements are:

the alignment, comprising a number of spans in straight line, at both ends being placed end towers and/or corner towers;

tension panel formed by a number of spans in straight line, at both ends being placed anchor towers;

effective span of the conductor, ai, represents the horizontal projection of the distance between the two fixing points that form one span (fig. 1);

the sink (out of level of one tower from previous one, hi, which represents the difference of level between the fixing points of the conductor with the columns that mark the span;

virtual span, ah, between two towers situated at different levels of ground, is the horizontal distance between one point where the conductor is fixed and the intersection with the effective curve of the cable or with its extension, depending whether this last point is placed lower or upper to the fixing point;

nominal span, an, is the conventional distance where the fixing points are in the same plane, In the nominal span, the terrain is plane and for the maximum deflection, the clearance gauge to the ground has the minimum value. The nominal span is obtained according to technical and economical evaluations and for this value, the nominal height of the towers is determined.

the span afferent to wind pressure, aw,, represents the average between the effective spans placed both sides of one single tower;

vertical (gravitational) span due to the weight of the cable, ag, representing the average of the virtual spans afferent to a single tower.

virtual span, ah, between two towers situated at different levels of ground, is the horizontal distance between one point where the conductor is fixed and the intersection with the effective curve of the cable or with its extension, depending whether this last point is placed lower or upper to the fixing point;

nominal span, an, is the conventional distance where the fixing points are in the same plane, In the nominal span, the terrain is plane and for the maximum deflection, the clearance gauge to the ground has the minimum value. The nominal span is obtained according to technical and economical evaluations and for this value, the nominal height of the towers is determined.

the span afferent to wind pressure, aw,, represents the average between the effective spans placed both sides of one single tower;

vertical (gravitational) span due to the weight of the cable, ag, representing the average of the virtual spans afferent to a single tower;

deflection, f, represents the distance between any point on the cable in its curved shape and the straight line that link the two towers marking one span; it may have maximum, minimum and average values and fn is the nominal deflection;

suspension (or fixing) height of the conductor, the height from the points where the cable is fixed on the tower, or it is suspended from the chains of insulators to the ground level

clearance gauge, hg , is the minimum distance from the conductor to the terrain.

GEOMETRIC ELEMENTS OF AN ELECTRICITY SUPPLY TRANSMISSION LINE

Fig. 1. Graphical representation of the basic elements of the electric transmission lines- 19 towers

Specifications

alignment: part: of the line between the towers 13 and 39; panel: part of the line between the towers 13; 36; 69 where towers 1, 3, 6, 9 are anchor towers;

an nominal span; ai(i=1n)=ar -effective spans;

av span afferent to wind pressure on the conductors; ag- vertical span corresponding to gravitational actions from the conductors; ah virtual span; hi(i=1n) out of level between two current towers; fn the deflection of the cable corresponding to nominal span; hc height from the ground to the point of fixing (or suspension) of the cable; hg clearance gauge from the ground level.

TYPES OF ELECTRIC CIRCUITS AND TOWERS

Different constructive solutions of E.T.L. for alternative current with one circuit

Different solutions for the E.T.L. with alternative current in two circuits

Wires for E.T.L. with one single phase: a- simple circuit; b, c- double circuit

METALS USED FOR CONDUCTORS

They may be active conductors that transfer the electricity from a tower to the next one and passive or protection conductors that prevent the electric system from the direct thunderbolt.

The conductors are made of different materials that insure their electric and mechanical properties: copper and its alloys, aluminum and its alloys, steel and steel wires combined with one of the materials mentioned especially with aluminum.

Copper conductors - very good conductivity, mechanical strength (small stresses , small spans ),big specific weight .

Bronze conductors alloys of copper, tin and silicium , big mechanical strength, smaller conductivity .

Aluminum conductors basic type of conductors, mainly in Europe; good, conductivity, small specific weight, important mechanical strength. Its highest performance lies in its high purity, the alloying elements (Fe, Cu, Si, Zn) not exceeding 0.5%.

Aldrey conductors alloy based on Al, with 0.63%Si, 0.4%Mn and 0.3%Fe; good conductivity and specific weight almost equal with Al while the strength is 100% bigger than the strength of Al. Both aluminum conductors and Aldrey conductors form on their surface a thin layer of oxide that protects the wire against corrosion.

Steel conductors reduced conductivity, good mechanical strength (increased carbon percentage) and they are galvanized on their surface (corrosion conditions).

Steel- aluminum conductors combination between two metals, which influences the mechanical strength and the electric conductivity of the conductor. Although the two metals have different elastic linear deformations and different specific elongation, they act homogeneously due to their inter reaction at the interface because of friction.

1

n

n

A

AA olalololalal

METALS USED FOR CONDUCTORS

ololalal AAA

ol

ol

al

alolal

EEE

1

n

EEn

AA

EAEAE olal

olal

ololalal

olal

ololalal

ololalal

olololalalal

EEn

EEn

EAEA

EAEA

ol

al

AA

n Ratio between aluminum and steel section

Specific weight of the combination

The equilibrium of efforts in the whole conductor

Ideal (theoretic) elastic modulus

Ideal (theoretic) coefficient of linear dilatation

Conductors with tubular section:

-With more layers;

-With one layer.

Single and multi-threaded

conductors

Classification of the conductors based on their design Single threaded conductors small cross sections, small lengths: - spans smaller than 70 m; - aluminum and its alloys are not allowed; - steel is not allowed also for line in the categories I and II; - copper and its alloys are admitted only when the cross sections are > 16 mm2; - minimum cross section of the conductor: 25 mm2 for aluminum, steel-aluminum and steel with aluminum

alloys conductors, 16 mm2 for steel.

Multi-threaded conductors cross section like rope, a material with good conductivity or steel wires; may be mono- metallic or bimetallic.

Conductors with tubular section - electric current with more than 220 kV, bigger diameter, 2530 mm and two types of sections:

- two or more layers of wires or special shapes of sections are twisted together in opposite

direction and they represent the wall of the tube; another element that sustain them is made of coiled

steel stripe or a steel spiral thin wire;

- one single layer of special steel shapes without any support, the shapes being assembled one

by one in tongue and groove system.

The steel-aluminum conductors are designed according to STAS 3000/1,2-1986 and their

protection against corrosion is made with the a zinc layer, thicker or thinner according to the

prescriptions of STAS 3732/1,2-1985.

Design strength of the conductors

The design strength of the wire = percentage from the ultimate tensile strength of the cable, prc, (ratio between the ultimate force and the effective section of the cable);

Minimum tensile strength -the physical and mechanical characteristics of the wires used for the electric transmission lines are presented in tables.

The design values of the mechanical strengths of the wires must not be exceeded by more than 5% in the fixing points for any of the groups of actions in the serviceability state. The following situations will be checked:

1. maximum stress due to the self-weight, wind and ice altogether, the maximum design strength being 0.7 prc ;

2. minimum temperature, the self-weight acting on the conductor, maximum design strength being 0.5 prc ; 3. serviceability stress, due to the self-weight of the cable for which the design strength is 0.18prc, for spans

>120 m and 0.25 prc , respectively when the spans

Material of

the Wire

Electric Resistivity in

Continuous Current

Temperature

Coefficient of the

Electric

Resistance

Specific

Weight

Linear

Dilatation

Factor

Elastic

Modulus

Ultimate (Tensile)

Strength

mm2/m 0C-1 daN/dm3 0C-1 daN/mm2 daN/mm2

Aluminum

STAS

12486-86

0.028264 0.004 2.649 2.310-5 5500 -19.017.6 pt.1.758.5 mm;

-17.315.8 pt.2.755 mm

Alcora

(aluminum

alloy)

0.0328 0.0036 2.649 2.310-5 5600 29.40

Steel

category*

A

0.18180.1885 pt. =1.153.0 mm

0.0045 7.701 1.1510-5 18800 37.22

Steel

category*

B

0.25100.2493 pt. =1.453.2 mm

0.0045 7.701 1.1510-5 19600 117.6

Steel

category*

C

0.25100.2493 pt. =1.453.2 mm

0.0045 7.701 1.1510-5 19600 137.3

*- According to STAS 3732/1,2-1985

Physical and mechanical characteristics of the wires in threaded cables for S.E.T.L.

Requirements for the disposition of the conductors on the towers

A. Smaller voltage (under 35 kV), rigid fixing to the cross-arms, placed on supports;

B. Higher voltage- chains of several units of insulators (79 units), the number depending on the voltage level of the line.

Rigid insulators (support);

chain of insulators (suspension) Geometrical significance

of the parameters a and b

Distances: a- between the conductor and the

axis of the tower;

b- between the conductors

hg (hter) the distance between the lowest point of the conductor in its chain shape and the tangent to the ground level, tables.

The following distances correspond to the situations (Code for practice PE 105/ 1996):

t=+400 C;

t=-50 C and ice;

t=-50 C and ice with an increased value with 25% for terrain of category I.

The specificity of the terrain U


Crossing and maximum (limit) distances from the elements of the ETL and:

a)- buildings; b)- railroads

d - the minimum distance between two active conductors or one active and the other passive, in the

normal position measured at the suspension point: 150

Ulfkd i

f - maximum deflection of the conductor, in m, determined in the situation of maximum positive

temperature, or -50C and the white frost on the cable ;

li length of the chain of insulators, in m; in the case of anchor insulators or sustaining insulators, in V

shape, lI;

U - nominal voltage of the electric line, in kV;

k - coefficient considering the nominal voltage of the electric line and the characteristics of the

conductors(*)

* kh for horizontal disposition of the conductors, and kv for vertical disposition are taken from the table

below; for the other cases, k is obtained with the following formulae: 222

ba

bkkkk hvh

The material of the cable Tension in the line Un,kv

Steel Aluminum and

aluminum alloys

Steel-Aluminum 150 95150 0.75 0.62 0.85 0.65

7095 - 185300 0.70 0.60 0.75 0.62

>95 - >300 0.70 0.60 0.70 0.60

Values of coefficients kv, kh


Conductors with different cross sections the distance d between the conductors will be verified for

the case when the first conductor is subjected to a maximum wind pressure and the second to

a wind pressure diminished with 20% from the maximum value. The distance between the

conductors in this case must be greater than Un/150 but not smaller than 0.20 m.

The case when specific extreme wind manifestations may appear, like galloping, bounding of the

cables and a-synchronic oscillation will determine the adoption of some specific distances:

0.20 m for E.T.L. of 20 kV;

0.45 m for ETL of 110 kV;

0.95 m for ETL of 220 kV;

1.65 m for ETL of 400 kV.

Minimum distances must be kept also between the parts of the tower under tension and the ones

that are tied up to earth.

vcg

vcv

ga

gaarctg

5.0

vcg

vcv

ga

gaarctg

75.0

- the angle of inclination between the chains of insulators that sustain the conductors will be determined with the relationship:

for Un 110 kV

for Un= 220400 kV.


where av, ag - see fig. 1;

gc, gvc weight of the conductor itself and in the

combination with wind and ice.

cmin - the minimum distance between the conductors and the tower, in cm, may be determined starting from the

relationship and the geometry in the figure:

without wind action:

with wind action:

these minimum values are also tabulated in standard specifications, ex. table.

Uc 65.010

Uc 65.0

Meteorological conditions Voltage of E.T.L., in kV

110 220 400

Averaged temperature (100C150 C) and wind with speeds of 010 m/s

90 180 290

Averaged temperature (100C150 C) and maximum wind speed 2636 m/s

40 60 100

Minimum distances admitted between

the conductors and the tower, cmin, in

cm


2aced

where:

a- the width of the tower;

c- distance from the leg of the tower to the

balanced position of the reaction R;

Distances: a- between the conductor and the axis of the tower;

b- between the conductors

h the height of the tower above the ground, measured from the cross-arm placed at the lowest level and the

ground level, is determined with the relationship: rlfhh i 1

where:

f the maximum deflection of the conductor; li the length of the chain of insulators; r the length of the rigid part of the fixing device of the chain of insulators to the bottom part of the cross-arm.

Special situations: anchor towers - the chain follows the curved line of the conductor and then: rfhh t

rigid insulators : rhfhh izt

where:

hiz height of the rigid insulator; r - the same significance as above.

Height of the tower from the level of the cross-arm to the ground


tg - maximum balancing position of the conductor under the presence of the actions-both vertical and

horizontal:

2

ci

v

GV

Htg

where:

Hv reaction from wind action (fig. 16); V vertical reaction on the tower coming from both sides of the line; Gci weight of the chain of insulators;

The balanced position in its maximum geometric value: sin ile


ACTIONS AND GROUPS OF ACTIONS ON THE CONDUCTORS AND ON THE INSULATORS

ACTIONS ON CABLES

self-weight of the conductor: cgg 1

weight of the deposit of ice on the conductor:

[daN/m]

[daN/m]

where:

- b, do - the thickness of the ice layer, depending on the climatologic area and the diameter of

the cable, respectively;

-ice - the specific weight of ice, in daN/dm3;

32 10 icecdbbg

weight of the cable including the ice deposit: 213 ggg [daN/m]

wind pressure on the cable : 310 dpcg vctcvc

temperature effects for t=-50 C (the temperature of developing ice): a linear variation of the length of the cable;

[daN/m]

Combined value from self-weight, ice and wind on the cable: 223 vcggq [daN/m]

Combined load of self-weight and wind pressure: 22

1 vcggq [daN/m]

minimum temperature, t= -300C (wind and ice are missing); mean temperature (wind and ice are missing); mean temperature, wind speed of 10 km/s (without ice); mean temperature, maximum wind speed (no ice);

maximum temperature, t= 400C (wind and ice are missing); temperature of ice (t=-50C) and ice deposits on all the elements of the line (cables, insulators, cross-arms and towers); the wind is not considered at all;

temperature of ice (t =-50C) and wind simultaneously on all the elements of the line Note: The relationships used to determine the characteristic and design values of the actions on the

conductors are presented in the table

ACTIONS AND GROUPS OF ACTIONS ON THE CONDUCTORS AND ON THE INSULATORS

GROUPS OF ACTIONS

ACTIONS FROM THE CHAINS OF INSULATORS

Weight of the chains of insulators: - without ice deposit: Giz;

- with ice deposit:1.1Giz

24

2

16 ggg 2

5

2

37 ggg 2

5

2

37 aa ggg 2

4

2

16 ggg c 2

5

2

37 ccc ggg

Actions (daN) Normal Exploitation (Fundamental

Group of Actions)

Accidental Group of Actions

Characteristic

values of actions

Weight of the cable g1=gc

Ice on the cable g2=b(dc+b) ch10-3

Total weight of the cable loaded with ice g3=gc+b(dc+b) ch10-3

Wind pressure on the cable without ice g4=ctc c p(v) dc 10-3 -

Wind pressure on the cable loaded with ice g5=ctc c p(v+ch) (dc+2b) 10-3 g5a=a/n ctc c p(v+ch) (dc+2b)10

-3

Total weight of the cable with maximum wind

speed

-

Total weight of the cable with ice and wind

simultaneously

Design Values of

Actions

Weight of the cable g1=1.1gc ; g1=0.9gc*

Ice on the cable g2=1.8b(dc+b) ch10-3; g2c=1.0b(dc+b) ch10

-3*

Total weight of the cable loaded with ice g3c=1.1gc+1.8b(dc+b)ch10-3; g3c=0.9gc+b(dc+b) ch10

-3*

Wind pressure on the cable without ice g4c=nctc c p(v) dc 10-3 -

Wind frost on the cable loaded with ice g5c=nctc c p(v+ch) (dc+2b) 10- g5ac=actc c p(v+ch) (dc+2b)10

-3

Total weight of the cable with maximum wind

speed

-

Total weight of the cable with ice and wind

simultaneously

2

4

2

16 ggg

2

5

2

37 ggg 2

5

2

37 aa ggg

2

4

2

16 ggg c

2

5

2

37 ccc ggg

Actions and groups of actions for the design of the conductors

SPECIFIC SITUATIONS IN THE DESIGN OF E.T.L.

The value of the maximum stress in the conductor: big spans the maximum stress from the most unfavorable combination of actions must be determined not in the lowest point of the curve, but in the section situated in the point of hanging, close to the tower.

AAor

HS

cos:

cos

1

cos

11 z

cos

z 1 fz max

The influence of the chains of insulators upon the amplitude of the deflection: uneven spans the

alteration of the loading conditions and of the temperature in the conductors induces different efforts

024

cos00

2

0

0

223

atta

E

aat

ttaa

E

aB

aA

t

0

2

0

0

23

0

232

24

cos

;24

cos

BE

aAa

21

nn

nn BE

aAa

BE

aAa

2

11

211

1.

1

01

n

r

ra

The critical span of the bimetallic conductors

SPECIFIC SITUATIONS IN THE DESIGN OF E.T.L.

RADIO AERIAL GUYED

MASTS

1. Introduction

2. General Provisions for Design

2.1. Actions.

2.2. Combinations of Actions

3. Structural computation of the masts

Lattice spatial systems obtained from hot rolled open sections or cold formed hollow sections supported (articulated) on foundations and guyed at different levels with wires. The number of guying levels may be from 16, depending on the technological necessities, the height of the mast and the dimensions of the transversal cross section. The wires are fixed with the help of insulators to anchor systems encased in concrete foundations. Masts are structures exclusively used for radio aerial transmission.

RADIO AERIAL GUYED MASTS

Central Florida broadcast stations: Broadcast Tower,WFTT-TV Tampa

Bay. Broadcasts on UHF channel 50 (the 442.550 m). The tower has a 7

foot wide face, which creates a null behind the antenna

The height must correspond to the criteria imposed by a perfect transmission;

A perfect insulation must be insured at the foundations level. In the case when the mast is radiating, the following complementary conditions must be considered:

1. the cross section must be the smallest possible;

2. the cross section must also be constant on the height;

3. the cross section must be the smallest possible at the supporting level (foundation level);

4. the length of the guying wires must be divided into several units by means of insulators; these units of length must not exceed the following limits:

a) in the case of short waves emissions;

b) in the case of long and medium waves emissions.

5. the number of wires must be the minimum possible, the triangular sections being the most advantageous; for the same reason, the number of guying levels must be also the smallest, this being in contradiction with the other conditions imposed.

As all these conditions are not possible to be rigorously respected, a compromise between all these must be searched during the design process

CONDITIONS IMPOSED BY EXPLOITATION CRITERIA

Masts: a) with constant cross section;

b)- with variable cross section guyed at the same level with several wires

Reducing the height by placing a horizontal ring at the top.

The efficiency lays in the fact that the height is fictively

enhanced with twice the diameter of this horizontal ring,

60 200 H

DDlD 3015

l < 34 b - triangular section;

l < 42 b - rectangular sections.

Masts are in carbon steel or low alloy steel; guying system is made of steel wires with diameters

Masts-common details in the design of the connections of different elements:

a, b, c- connection between leg, horizontal element (strut) and diagonals (pre-stressed rods), welded;

d-flange connection between two units of the leg and diagonals bolted in site;

e- cable anchored in separate foundation

1. Central articulation:

1)-vertical insulator; 2)- horizontal insulators; 3)- brackets; 4)-fixing frame; 5)- insulator;

2. Solutions for the central articulation:

a)- with plane base plate; b)- with spherical support

1 2

ACTIONS

Self-weight - in addition the vertical components of the pre-stressing forces in the cables Temperature effects have to be considered also as traction forces applied to the mast. Wind is the most important action, 90% of the maximum efforts ; on the mast and on the cables in the most unfavorable situation and combination of actions.

Wind on the cables - a constant value and equal with the pressure at 2/3 of the height of top edge of the wire. Wind

pressure on the mast is considered with a constant value on the distance between two anchorage points and it is

determined as the moderated value of mean pressures acting on this distance; the most unfavorable situation for the

mast is when wind pressure is considered at the maximum value, the outside temperature being +20oC.

The dynamic design must take into account the period of vibration of the anchored masts is: ( sec), (H in

m)

This relationship is sufficiently correct provided the mast is not charged with important concentrated masses that may

alter the static scheme.

Ice is also taken into account, both on the internal steel elements of the mast and on the cables. Here we remind that the density of the ice is 900 daN/cm3 and the thickness of the ice deposit, t, in cm depends on the region the

construction is situated, according to the regulations of STAS 10101/21-92.

Uneven settlements of the supports may have an important influence depending on the nature of the soil and must be considered in the case of redundant systems (masts anchored with cables at different levels).

Special (accidental) combination of actions, the effects of earthquake are considered in the situation of breaking of one wire.

HT 01.00

3.1. Efforts in the guying wire; wire length variation

3.2. Masts anchored at a single level;

3.3. Multi-level guying masts

Structural computation of the masts

GROUPS OF ACTIONS

Permanent actions + wind action + temperature effects, t=200C;

Permanent actions + ice + wind, moderated value, g w=0.3 kN/m2;

Permanent actions + effects of maximum temperature, t max= 400C , no wind;

Permanent actions + effects of minimum temperature, t min=-300C, no wind, no ice.

Special (accidental) groups of actions - either: earthquake effects + moderated wind

action + breaking of one cable, or, during the mounting stage: wind, maximum

value, alternatively wind, moderated value + ice.

Generally, it is presumed that the first combination is capital for the dimensions of the cross

sections of the structural elements. The second and the fourth combination are

important for the accidental case of breaking of one cable or cables on one side, and

the third is important for the computation of the maximum deflection.

STRUCTURAL COMPUTATION OF THE MASTS

WITH ONE LEVEL GUYING WIRES

888;

8

2222 l

A

lg

S

lgf

f

lgS

xl

fy

22 2 )

cos

3

81(

2

22

lflL

cos)()(cos

24

1

cos

)(02

0

2

0

2

2230 lttl

E

lt

232

222

1 cos24

1cos

3

8 l

lflLa

coscos2

lt

l

Ea t

coscos

24

1

cos

23

2

2

21

ltl

E

laaa t

Cl

tlE

lt

coscos

24

1

cos

23

2

2

)cos

cos24

1

cos( 0

23

2

0

2

00

ltl

E

lC t

GENERAL RELATIONSHIPS OF COMPUTATION OF THE

STRESSES IN THE WIRES

a) Wind normal to the wall of a square section mast

b) Wind on the diagonal of a square section mast

c) Wind normal to the wall of a triangular section mast

d) Wind along one guying wire of a triangular section mast

e) Wind parallel to one wall of a triangular section mast (normal to one wire)

Wires are pre-loaded initially with 0 so even if the wind action unloads the cable, it is still in tension. The value of 0 is considered as 0.350.5 from the design value of strength. Steel used for cables has usually the tensile strength Rt =12001600 daN/cm

2 and the elastic modulus E=1,51,8x105 daN/cm2.

ASASAS 002211 ;;

cos

Cl

tlE

lt

coscos

24

1

cos

23

2

Special Steel Structures - Courses - 2013

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