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( a ) ( b )

Fig. 1.2. Examples of type S.C. construction works

2. Type S. (Construction work = Structure only)

This type (Fig. 1.3) is represented by all kind of civil engineering works when

cladding is not necessary, like:

transmission towers (Fig. 1.3a);

pipe-lines (Fig. 1.3b) etc.

( a ) ( b )

Fig. 1.3. Examples of type S. construction works

Cladding

Structure

Cladding

Structure

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3. Type C. (Construction work = Structural cladding)

This type (Fig. 1.4) is represented by all kind of civil engineering works when

cladding is structural, like:

tanks (Fig. 1.4a);

spherical vessels (Fig. 1.4b);

chimneys (Fig. 1.4c);

silos etc.

( a ) ( b ) ( c )

Fig. 1.4. Examples of type C. construction works

1.2. DESIGN. FABRICATION. ERECTION

A steel structure results by assembling on site a number of various structural

members, like beams, columns etc. (Fig. 1.5) prefabricated in fabrication shops.

Fig. 1.5. Examples of structural members

Truss Beam

Beam-column Column

H

pp

p

NN

M

M M

N

H

QQQ

M

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The main steps to realise a steel structure are:

design of the structure;

fabrication of structural members in fabrication shops (using plates and

profiles which are produced in steel works); transport of structural members on site;

erection of the structure by assembling structural members on site.

All the technical activities involved, meaning design, production of shapes and

plates, fabrication of the structural members and erection must comply with

requirements contained in principles and application rules provided by the codes.

1.3. BASIS OF DESIGN

A structure shall satisfy the following requirements during its intended lifetime:

1. It must sustain with appropriate degrees of reliability all actions to occur during its

construction and intended use.

2. It must remain fit for its required use.

This usually leads to two types of requirements to be checked:

strength requirement in order to resist all actions to occur during its intended

lifetime;

stiffness requirement in order to remain fit for its required use (allowable

displacements).

Fig. 1.6. Main steps to create and analyse the model of a structure

Actualconfiguration

Calculation scheme

Actions

Effects of actions

h h

L L

IC IC

IB

p

H x

y y

z

z

x

Q+M+

N+

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The strength requirement is expressed by

dd CE ( 1.1 )

In eq. (1.1) and in figure 1.6:

Ed is the design value of that effect of actions:N axial force (+ tension; - compression);

M bending moment;

Q shear force;

Mt torsion moment.

N, M, Q, Mt are efforts and they are effects of external forces.

Cd is the design capacity of the structural member, for the considered effort N, M,

Q orMt.

The stiffness requirement is expressed by:

a ( 1.2 )

where:

the calculated deformation;a the allowable deformation.

Example

Fig. 1.7. Example

Strength requirement

8

LpME

2

Sdd

== (calculated)

RWMC Rdd == (calculated)

p

L

f

MSd

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dd CE RdSd MM RW8

Lp 2

Stiffness requirement

EILp

3845f

4

== (calculated)

300

Lfaa == (allowable)

a aff 300

L

EI

Lp

384

5 4

In the above relations:

W section modulus of the cross-section;

R design strength of the steel grade that is used;

EI stiffness of the cross-section of the member.

The strength requirements and the stiffness ones can be found in codes of

practice as principles and application rules.

Principles comprise:

general statements and definitions for which there is no alternative;

requirements and analytical models for which no alternative is permitted.

Appl ication ru les , usually called recommendations in the codes, are recognised

rules that follow the principles and satisfy their requirements. It is allowed to use

alternative rules, different from the recommendations (application rules) given in the

codes, provided that it is proved that the alternative rules comply with the principles

and provide at least the same reliability.

1.4. STRUCTURAL MEMBERS

Structural members are prefabricated in fabrication shops using a large range

of products for steel construction produced in steel works:

standard profiles (shapes)

angle I shape (W shape) channel steel pipe etc.

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rolled plates.

Some built-up elements like plate girders or box sections are fabricated in

fabrication shops, usually by welding.

The main structural members can be classified with respect to the dominant efforts N

(axial force), M (bending moment), Q (shear force), as follows:

1. Beam is a structural member whose primary function is to carry loads transverse

to its longitudinal axis (Fig. 1.8). The dominant effort is M (bending moment).

Fig. 1.8. Beam

Equilibrium relations

Fig. 1.9. Typical stress distribution for a beam

NSd = 0 T C = 0 T = C ( 1.3 )

MSd 0 MSd = T z MRd ( 1.4 )

where:

MSd action (bending moment produced by external forces);

MRd capacity (resistant bending moment);

C resultant of compression normal stresses on the cross-section;

T resultant of tension normal stresses on the cross-section.

M

L

p

C

T

z

z

x

z

z

y y

MSd0

NSd=0

QSd0

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Remark: The cross-section must be developed (Fig. 1.10) in the plane of the acting

bending moment M in order to increase the resistant bending moment MRd, i.e. in the

plane of the acting forces (greater h greater z greater MRd = T z).

Fig. 1.10. Typical development of the cross-section

Typical problem: The risk of lateral instability (lateral buckling) (Fig. 1.11a) or local

instability (local buckling) (Fig. 1.11b) is typical for metal (steel or aluminium alloy)

members subjected to bending moment.

( a ) ( b )

Fig. 1.11. Typical instability problems for metal members in bending

Depending on the practical solution adopted for a beam, the following ones are the

most commonly used cross-sections:

1.a. Rolled beam is a structural beam produced by rolling (hot rolling). The most

commonly used shapes (Fig. 1.12) for beams are the following ones:

IPE, HE, HL, HD, HP, W, UB, UC IPN UAP UPN

Fig. 1.12. The most commonly used hot rolled shapes for beams

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1.b.Plate girder (Fig. 1.13) is a built-up structural beam, usually made of welded

rolled plates (sometimes they may be bolted or riveted, especially in the case of

aluminium alloy).

Fig. 1.13. Typical plate girder cross-section

1.c.Lattice girder (Fig. 1.14) is a built-up structural beam made of a triangulated

system of bars subjected to axial forces. It is able to resist forces acting in its plane.

Fig. 1.14. Example of lattice girder

MSd 0 MSd = MRd = C h (or MRd = T h) ( 1.5 )

NSd = 0 T + D cos C = 0

= cos

TC

D ( 1.6 )

h

h

Top chord

Web members

Bottom chord

L

M

C

T

D

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Truss (Fig. 1.15) is a lattice girder used in the roof framing.

Fig. 1.15. Example of truss

1.d. Cold-formed shape (Fig. 1.16) is a cross-section obtained from plates by

bending or by rolling at normal temperature. They are especially used for purlins

(secondary beams of the roof structure).

Fig. 1.16. Examples of cold-formed cross-sections used for beams

2. Column (Fig. 1.17) is a structural member whose primary function is to carry

loads acting in its longitudinal axis. The dominant effort is N.

( a ) ( b )

Fig. 1.17. Examples of columns

Remark: The fact that practically all the compressed structural members are sized by

the buckling resistance of the member is typical for steel structures. In the concrete

structures the loss of stability is an uncommon phenomenon.

For the column in fig 1.17a the strength requirement (1.1) turns into:

( )2

e

2

RdSd

h2

EIPP

= ( 1.7 )

External force Critical force

P P

buckling bucklinghe

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As a result, in order to avoid buckling in any vertical plane, the cross-section

must be developed in its plane, like shown in figure 1.18.

Fig. 1.18. Examples of cross-sections for columns

3. Beam-column (Fig. 1.19) is a structural member whose primary function is to

carry both transverse to longitudinal axis and acting in its longitudinal axis forces.

The dominant efforts are M and N.

Fig. 1.19. Example of beam-column

Remark: The following are typical for the cross-sections used in metal structures:

the cross-section is preferentially developed in the plane of the acting bending

moment with regard to the strong axis y-y (Fig. 1.20a);

in the situations when it is necessary, the moment of inertia (second moment of

the area) with regard to the weak axis z-z is improved (Fig. 1.20c).

Beam Column Beam-column

Iy >> Iz Iy Iz Iz is improved by lips( a ) ( b ) ( c )

Fig. 1.20. Examples of cross-sections for beams, columns and beam-columns

P

P

N MH

h

M = H h

y y y y y y

z

z

z

z

z

z

lip

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4. Structural wall (Fig. 1.21) is a structural member whose primary function is to

carry both vertical and horizontal forces acting in the plane of the wall.

Fig. 1.21. Example of structural wall

4.a. Vertical bracing (Fig. 1.22) is a structural wall made of a triangulated system of

bars subjected to axial forces.

Fig. 1.22. Example of vertical bracing

1.5. STRUCTURAL SYSTEMS

1.5.1. Structural philosophy

The concept of steel structural system is largely influenced by some

particularities of structural steel as a material and of the behaviour of the structural

members. As a result, steel design is based on its own structural philosophy, which

presents some particularities in comparison with the concept of structural systems inreinforced concrete, brick or timber.

H

P

H

P P PPPP

HH

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1.5.2. Structures with a single column

1.5.2.1. Structural philosophy

Problem 1 (Fig. 1.23)

Lead to ground (Fig. 1.23a) a vertical force P (gravitational) acting at the level

h from the ground in the plane xOy.

( a ) ( b )Fig. 1.23. Leading a vertical force to the ground

Solution

Use a vertical bar on the acting line of the force P to connect the point A to the

point B on the ground (Fig. 1.23b).

Remarks

1. This solution is the most economical, thanks to the following:

the path AB is the shortest one to carry the force P to the ground;

only the force P is to carry on the load path AB (according to a principle of

structural mechanics, a force translates on its acting line by its value).

2. This solution, corresponding to the case of a vertical force, can also be applied in

the case of an inclined force P.

Problem 2 (Fig. 1.24)

Lead to the ground a horizontal force H (wind, seismic action, etc.) parallel to

the ground, acting at the level h.

x

h

Ppoint A

y

h

P

A

B

N = P

O

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Fig. 1.24. Leading a horizontal force to the ground

General remark

In accordance with a principle of structural mechanics, a force H displaces

parallel to itself by its value H and a bending moment M. As a result, it is much more

expensive to carry a horizontal force to the ground than to carry a vertical one.

Solution a (Fig. 1.25)

Use a bar transverse to the acting line of the force H to connect the point A to

the point B on the ground.

Fig. 1.25. Solution a for leading a horizontal force to the ground

Remark a

Using this solution, the required area of material to carry a horizontal force H

could be 5 to 10 times (in some cases even more) greater than the required area tocarry the same force acting vertically P = H.

x

O y

h

H

point A

h

HA

B

Q = H

M = H h

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Solution b (Fig. 1.26)

Use a vertical bracing; the simplest one is a triangulated system.

Fig. 1.26. Solution b for leading a horizontal force to the ground

Remark b

This solution is more economical, because the force H is carried to the ground

by axial forces. For instance, if the force H = P the steel consumption is 2 to 3 times

greater than for the same force P acting vertically, depending on the distance a

between the supports. The greater the distance a is, the arm lever increases and, as

a result, the forces diminish.

Problem 3 (Fig. 1.27)

Lead to the ground a vertical force P and a horizontal force H parallel to the

ground, acting at the level h from the ground, in the plane xOy.

Fig. 1.27. Leading a horizontal force and a vertical force to the ground

H

h

T C

a

==

=+

=

cos2

HTC

HcosTcosC

TC

x

yO

h

H

P

point A

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Solutions (Fig. 1.28)

Four possible solutions are presented, based on the previously discussed ones:

(a) cantilever;

(b) structural wall (solved as a vertical bracing); (c) a triangulated system;

(d) guyed tower.

The solution (d) represents a combination between (a) and (c). The cables must be

in tension in any loading case so they need to be pretensioned. As a result, the initial

tension in the cables Tinit must be greater than the highest compression CH produced

by the force H. This solution is generally required by high rise TV towers.

( a ) ( b ) ( c ) ( d )Fig. 1.28. Solutions for leading a horizontal force and a vertical force to the ground

1.5.2.2. Structural systems

Some structural systems based on the solutions presented in figure 1.28 are

shown in figure 1.29. These solutions are developed in order to realise spatial

structures, required both by stability requirements and by the effects of horizontal

forces H acting on any direction.

Fig. 1.29. Structural systems with a single column

H H H HPP P P

T CCompressed bar

PretensionedcablesTinit > CH

1 1

2 2

3 3 4 4

2 2

3 3

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1.5.3. Structures with a number of columns in a line

Figure 1.30 shows a steel structure designed to support a pipe-line.

Fig. 1.30. Steel structure for sustaining a pipe-line

This solution is typical for steel structures and is characterized by:

cantilever columns (C) (Fig. 1.30), sized to resist the vertical forces P and the

horizontal forces H transverse to the line of columns; they also provide the

required stiffness in the transverse plane (each column resists its own P and H

forces); for this reason, their cross-sections are developed in the plane of the

acting bending moment produced by the transverse forces H;

a vertical bracing (VB) (Fig. 1.30), sized to resist all the horizontal forces Lacting in the longitudinal direction and to provide the required strength and

stiffness in the longitudinal direction;

two continuous beams (B) (Fig. 1.30), sized to resist the vertical loads P acting

between columns and to transmit them to the columns; at the same time, the

beams connect the columns in the longitudinal direction.

RemarksThe vertical bracing is typical for a steel structure. It is located in the middle of the

structure, to allow a good behaviour of the structure to the effects of temperature

variations. Built-up cross-sections able to resist bending moments in two planes like

those ones in figure 1.31 are to be avoided due to their high cost of fabrication.

Fig. 1.31. Cross-sections that are not very common for steel columns

C C

A

A

L

VB

B H

P

B

A A

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1.5.4. Structures with a number of orthogonal column lines

1.5.4.1. Structural philosophy

Problem 4

Lead to the ground vertical (P), horizontal (H) and inclined (I) forces acting on

the roof or on the floor of a building (Fig. 1.32).

Fig. 1.32. Leading to the ground forces acting on the roof

Solutions

Figure 1.33 shows three possible solutions, which are compared in table 1.1

from the point of view of their strength, stiffness and ductility properties.

Strength is the resistance to the forces S (N, Q, M, Mt) produced by the loads.

Stiffness is the resistance to the deformations , , produced by the loads.

Ductility is the capacity to dissipate energy by large plastic deformations.

Fig. 1.33. Possible solutions for leading forces acting on the roof

Solution 1: M.R.F. = Moment Resisting Frame

Solution 2: C.B.F. = Concentrically Braced Frame

Solution 3: E.B.F. = Eccentrically Braced Frame

1

1

plastic hinge

buckling

plastic zone

H I P

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Table 1.1. Comparison among possible solutions

Strength Stiffness Ductility

M.R.F. good poor very good

C.B.F. good very good poor

E.B.F. good good good

1.5.4.2. Single storey buildings

Figure 1.34 shows a typical structure of a single storey industrial building,

based on the structural philosophy discussed above.

Fig. 1.34. A typical steel structure for a single storey industrial building

The structure is composed of:

transverse MRF, sized to resist vertical (P) and horizontal (H) forces and to

provide the required strength and stiffness in the transverse plane; each MRF

resists its own P and H forces and their cross-sections are developed in the plane

of the acting bending moment M produced by the transverse forces H;

vertical bracing VB, sized to resist all longitudinal forces L acting in the

longitudinal direction and to provide the required strength and stiffness in thelongitudinal direction;

TRANSVERSE SECTION SIDE VIEW

PLAN VIEW

HP

P H

HLB

crane CRG

Pr HTB VB CRG

L

PrVB

L

RHB

MRF

HTB

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roof framing, consisting of roof horizontal bracing RHB, composed of horizontal

transverse bracing HTB and horizontal longitudinal bracing HLB , in order to

provide torsional rigidity of the structure and purlins Pr to resist vertical forces

acting on the roof and to transmit them to the MRF;

crane runway girders CRG, to resist the forces produced by cranes and to

transmit theirP and H forces to the MRF and L forces to the VB.

Remark:

Trusses are often used instead of girders for long span buildings. In this case

MRF is composed of columns and trusses, usually pin connected, like in figure 1.35.

Fig. 1.35. A steel structure for a single storey industrial building using trusses

1.5.4.3. Multi-storey buildings

Figure 1.36 shows a modern concept of a multi-storey steel structure

composed of two systems:

a frame system (F), resisting both vertical (P) and horizontal (H and L) forces; this

could be a moment resisting frame (MRF), a concentrically braced frame (CBF)

or an eccentrically braced frame (EBF);

a gravitational system, resisting only vertical forces (P).

Rigid diaphragm floors and side frame systems provide the torsional rigidity of the

whole building, which is fundamental for the good behaviour of the structure when

subjected to horizontal loads.

Figure 1.37 shows three very well known present-day performances in high-

rise skyscrapers construction.

Truss (T)

Crane runwaygirder (CRG)

Purlin (Pr)

Column (C)

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Fig. 1.36. A modern concept of a multi-storey steel structure

Petronas Towers Sears Tower Empire State

452m 88 floors 1998 442m 108 floors 1974 381m 1931

Fig. 1.37. Present-day performances in skyscrapers

PLAN

1 1

Frame system (F)

Gravitational system (G)

SECTION 1 1

MRF CBF EBF

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Figure 1.38 shows the tallest building in the world, Taipei 101, situated in

Taipei, Taiwan.

Taipei 101

509m 101 floors 2004

Fig. 1.38. Present-day tallest building in the world