1. STEEL STRUCTURES

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Chapter 1

STEEL STRUCTURES

1.1. TYPES OF CONSTRUCTION WORKS WITH STEEL STRUCTURES

Construction works is the general term including both buildings (apartment houses, offices, schools, etc.) and civil engineering works (TV towers, tanks, etc.). In the European code EN 1990 [10] it is defined as everything that is constructed or results from construction operations. It accords with ISO 6707-1 [35]. Structure (Structural system) is an assemblage of load carrying structural members joined to provide the required strength, stiffness and ductility of a construction work. EN 1990 [10] (def. 1.5.1.6) defines the structure as organised combination of connected parts designed to carry loads and provide adequate rigidity and the structural system as load-bearing members of a building or civil engineering works and the way in which these members function together. In the American code ANSI/AISC 360-10 [34], the structural system is defined as an assemblage of load-carrying components that are joined together to provide interaction or interdependence. Cladding is the exterior covering of the structure (ANSI/AISC 360-10 [34]). By cladding (roof + side wall) a certain volume is separated from the atmosphere. This separation is made to create in the interior all the conditions required by a human activity that can not be developed in open air. Construction works with steel structures can be classified in three types, depending on the presence or role of cladding: 1. Type S.C. (Construction work = Structure + Cladding) This is the most general type (Fig. 1.1). This type (S.C.) of construction works is largely represented by all kind of buildings: one storey industrial buildings (Fig. 1.2a); apartment houses, offices, hotels, schools, colleges etc. (Fig. 1.2b); sport halls, theatres etc.

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Fig. 1.1. Type S.C. construction work

( 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.

Side wall Roof Structure Cladding

Cladding Structure

Cladding Structure

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( a ) ( b ) Fig. 1.3. Examples of type S. construction works

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

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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 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:

Truss Beam

Beam-column Column

H

p p

p

NEd NEd

MEd

MEd MEd

NEd H

VEd VEd VEd MEd

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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 The strength requirement is expressed by

dd RE (EN 1990 [10], rel. (6.8)) ( 1.1 ) In eq. (1.1) and in figure 1.6: Ed is the design value of that effect of actions:

NEd axial force (+ tension; compression); MEd bending moment; VEd shear force; TEd torsion moment. NEd, MEd, VEd, TEd are efforts and they are effects of external forces.

Rd is the design capacity design value of the corresponding resistance of the structural member, for the considered effort NEd, MEd, VEd or TEd. The stiffness requirement is generally determined by serviceability criteria (the proper use of the structural member or structure) and it is usually expressed by:

a ( 1.2 ) where:

the calculated deformation;

Actual configuration

Calculation scheme

Actions

Effects of actions

h h

L L

IC IC

IB

p H x

y y

z

z

x

VEd+ MEd+

NEd+

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a the allowable deformation.

dd CE (EN 1990 [10], rel. (6.13)) ( 1.2 ) where: Ed the design value of the effects of actions specified in the serviceability

criterion, determined on the basis of the relevant combination; Cd the limiting design value of the relevant serviceability criterion.

Example

Fig. 1.7. Example

Strength requirement

8LpME

2

Edd

== (calculated)

0M

yRdd

fWMR

== (calculated)

dd RE RdEd MM 0M

y2 f

W8Lp

Stiffness requirement

EILp

3845fE

4

d

=== (calculated)

300LfC aad === (allowable)

dd CE a aff 300L

EILp

3845 4

In the above relations: W section modulus of the cross-section;

p

L

f

MEd

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R design strength of the steel grade that is used; fy the yielding limit of the steel grade that is used; M0 partial safety factor for resistance of cross-sections to excessive yielding, including local buckling; 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. Application rules, 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.

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), V (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). In the

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American code ANSI/AISC 360-10 [34] it is defined as nominally horizontal structural member that has the primary function of resisting bending moments.

Fig. 1.8. Beam

Equilibrium relations

Fig. 1.9. Typical stress distribution for a beam

NEd = 0 Ten C = 0 Ten = C ( 1.3 ) MEd 0 MEd = T z MRd ( 1.4 ) where:

MEd effect of actions (bending moment produced by external forces); MRd resistance capacity (resistant bending moment); C resultant of compression normal stresses on the cross-section; Ten resultant of tension normal stresses on the cross-section.

Remark: The cross-section must be developed (Fig. 1.10) in the plane of the acting bending moment MEd in order to increase the resistant bending moment MRd, i.e. in the plane of the acting forces (greater h greater z greater MRd = Ten z).

M

L

p

C

Ten z

z

x

z

z

y y MEd0

NEd=0

VEd0

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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

MEd 0 MEd = MRd = C h (or MRd = Ten h) ( 1.5 )

h

h

Top chord

Web members

Bottom chord

L

M

C

T

D

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NEd = 0 Ten + D cos C = 0

=

cos

TCD ( 1.6 )

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. In the American code ANSI/AISC 360-10 [34] it is defined as nominally vertical structural member that has the primary function of resisting axial compressive force.

( 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.

P P

buckling buckling he

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

( )2e2

RdEd h2EIPP

pi= ( 1.7 )

External force Critical force 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. In the American code ANSI/AISC 360-10 [34] it is defined as structural member that resists both axial force and bending moment.

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).

P

P

NEd MEd H

h MEd = H h

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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

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

y y y y y y

z

z

z

z

z

z

lip

H

P

H P P P P P P

H H

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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 in reinforced concrete, brick or timber.

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

x

h

P point A

y

h

P

A

B

NEd = P

O

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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.

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.

x

O y

h

H

point A

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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 to carry the same force acting vertically P = H. 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

h

H A

B

VEd = H

MEd = H h

H

h

Ten C

a

==

=+

=

cos2HTenC

HcosTencosCTenC

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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 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 Teninit 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 )

x

y O

h

H

P

point A

H H H H P P P P

Ten C Compressed bar

Pretensioned cables Teninit > CH

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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

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 it consists of:

1 1

2 2 3 3 4 4

1 1

2 2

3 3

4 4

C C

A

A

L VB

B H P

B

A A

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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 L acting 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.

Remarks The 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

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).

H I P

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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 resistance to the forces S (NEd, MEd, VEd, TEd 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

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

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

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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 MEd 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 the longitudinal direction;

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 their P and H forces to the MRF and L forces to the VB.

Remark:

TRANSVERSE SECTION SIDE VIEW PLAN VIEW

H P

P H

HLB

crane CRG

Pr HTB VB CRG

L

Pr VB

L

RHB

MRF

HTB

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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

Specific terms: crab crucior hoist palan corrugated plate tabl cutat (ondulat)

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 runway girder (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 1.38a shows one of the tallest building in the world, Taipei 101, situated in Taipei, Taiwan. Present day (2015) tallest building in the world is Burj Khalifa (Fig. 1.38b), previously known as Burj Dubai, placed in Dubai. It was built between September 21st 2004 and January 4th 2010.It is 828 m high and it has 163 floors; the total built surface is 334000 m2 (source Council of Tall Buildings and Urban Habitat (www.ctbuh.org)).

Taipei 101 Burj Khalifa 509m 101 floors 2004 828m 163 floors 2010

( a ) ( b ) Fig. 1.38. Present-day tallest buildings in the world