MULTI-STOREY STEEL STRUCTURES

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SHORT HYSTORY

Reliance Building, Chicago -designers Burnham &Root (extended 14 storeys), 1890

1801- Salford-Manchster, U.K, 7 storeys building with beams and columns made of cast iron, designed by Boulton&Watt;

1845- William Fairbanks uses iron I sections for a several storey factory; 1879- Chicago, Willim La Baron Jenney designes “Leiter Building”, 7 storeys and Home Insurance Building,

11 storeys; In the same period Monadnock Building is designed by Burnham & Root : 16 storeys, brick masonry.

• Structures that are placed in down town where the price of land is high so the surface on the ground is restricted.

• The homeland-America, associated with the economic boom from the end of XIX-th century to the middle of the XX-th.

• Most reprezentative:

Leiter Building, Chicago, 1879, architect William le Baron Jenney; 11 storeys

Monadnock, Chicago, Burnham & Root, 16 storeys

1890 Industrial producing of steel with Thomas and Siemens-Martin kilns

Invention of the elevator (Ottis)-important moment

Empire State Building, New York, 1931, Al Smith, 381m, 102 storeys

World Trade Center, New York, 1963, 411m , 110 storeys

John Hancock Center, Chicago, 1968, 337 m

Sears Tower, Chicago, 1974, 442 m, 120 storeys

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SHORT HYSTORY

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Empire State Building, New York, 102 storeys, 381 m-1931

John Hancock Center, Chicago, 337 m

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Sears Tower, Chicago, 1972, 442 m, 120 storeys Tower Montparnasse, 210 m, 50 storeys

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Chrysler Building New York, 1928-1930 Rchard Daley Center, 1965, scoala arh. Ludwieg Mies van Der Rohe, Chicago, 215 m

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Petronas Towers Cesar Pelli, Kuala Lumpur, Malaysia, 1998 Taipei 101, by C. Y. Lee & Partners, Taipei, 2003 to 2004

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Turning Torso, Malmo, 2001, 240 m

30, St. Mary Axe, (“Gherkin Building”), London, 2000-2004, 41 floors, 180 m

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9 Cartier La Defense, Paris, 560 hectares (5.6 million square metres) area, 72 glass and steel buildings and skyscrapers, 180,000 daily workers, and 3.5 million square metresof office space. Around its Grande Arche and esplanade ("le Parvis"), La Défense contains many of the Paris urban area's tallest high-rises, and is home to no fewer than 1,500 corporate head offices, including those of 15 of the top 50 companies in the world

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STRUCTURAL SYSTEMS

Rigid frames both directions-unbraced;

Braced frames with articulated connections between beams and griders-vertical and horizontal and on both principal directions directions

Frames with rigid connections on one direction and articulated connection on the other;

Structures with rigid core (steel or reinforced concrete) and suspended columns on periphery

Tubular structures

1- Rigid joints: 20-25 storeys; 2, 3, 4- rigid joints and vertical bracing: 70-80 storeys; 5- external rigid tube made of columns closely placed and internal rigid core: 80-90 storeys; 6- articulated joints and vertical bracing externally placed: 90-100 storeys (John Hancock Centre, Chicago); 7- external and internal tubes , columns placed very closely and rigid connection- (World Trade Centre) :100-110 storeys; 8- frames with rigid joints and vertical plus horizontal bracing both directions: 110-120 storeys (Sears Tower, Chicago)

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PLANE-SHAPES • Regular shapes: rectangular or compound from several rectangles (Other shapes are

used also); • In plane: • a - symmetry necessary to avoid torsion effect under horizontal actions; • b- distance between columns on both directions 4...10 m.

Optimization of the distances between the axes of the columns: L-spans; Wc- weight of columns; Wb - weight of beams; Wt – total weight

Plane shapes of the high-rise buildings and in plane grid

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EXAMPLES OF STRUCTURAL SOLUTIONS

Rigid core of reinforced concrete and rigid connections between columns and beams both directions

Rigid core that takes and transfers the loads from floors to the foundations; columns are in tension

Beams very close placed transversally, longitudinal beam rigidly connected to the columns and horizontal bracing externally and internally

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BRACED FRAMES

Braces in tension dissipation in lower part, close to the interface with the column

V shape braces in tension and compression

Eccentric braces – dissipation in the bottom flange of the beams ; Braces in K –rigid, non-dissipative

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EFFICIENT SOLUTIONS FOR TOLERANCE DISTANCES

• Preventing the effects of temperature variation: a- limitation in plane length: 70...100 m; b- tolerance between the structural elements of the building on the whole height or at least at the top of the structure

(reduces the cumulative linear deformations of beams); c- Design the walls at the first storey independent: avoid the shear stresses in the external walls at the first floor level

due to the variations in dimensions. • Preventing the effect of uneven settlements of the foundations-two adjacent buildings with different weights and/or

heights or laying on different ground soils, will settle differently at the foundations level: - the foundations will be designed separately (soil cannot take important stresses); - the foundations will be designed as a common rigid plate.

Shear of the external wall at the ground level: t he first storey is designed independent from the others in order to avoid this phenomenon

Effects of the variation of temperature upon the structural elements: a) line O of horizontal displacements in the middle of the building and cumulative deformations at the edges; b) reducing the cumulative linear deformations by introducing internal tolerances at the top level

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16 Foundations need tolerance distances when the structural units weight differ or the ground foundaton condtions are different

POSITION OF THE CONFERENCE HALLS IN PLAN • at the ground level as an independent structure ► enables the access and the evacuation easily

(needs a bigger surface of terrain); • at the top level ► the structural in plane shape undisturbed and doesn’t increase the surface of

ground affected (the evacuation of the people from inside is much more difficult); • at intermediary level ► insures a quicker evacuation the continuity of the columns being

interrupted and the structure is provided with a powerful truss in some cases on the height of a storey taking over and transferring the stresses from the columns above).

The position of the conference halls

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VARIATION OF THE CROSS SECTION OF THE BUILDING

Alternatives for the variation of the cross section of the high-rise buildings: constant

cross section and variable in steps; a- elastic part; b- rigid part.

Anti-seismic provisions The most important provisions are:

1. Design of a structure with a high degree of redundancy that insures an important reserve of loading capacity in plastic domain and consequently allow its accommodation to a new static scheme which results in certain cases of collapse;

2. The adoption of a symmetric shape in plan parallel with avoiding of the unequal repartition of the weight for reducing the torsion effects;

3. Design of a rigid base for the building;

4. Gravity centre lower to the ground level (by compensating the weight of the underground level);

5. Steels with high performances of strength and ductility must be used- the ration fu/fy≥1,2 and elongation under ultimate stress ≥ 15%;

6. Structural connections with mechanical fasteners will be done with high strength bolts (group 8.8…10.9).

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ACTIONS AND COMBINATION OF ACTIONS •Vertical actions

1.Permanent actions: self-weight of the structure, including

the weight of the floors and of the walls an empirical formulae

being used for a preliminary evaluation:

• [daN/m3]

where:

•G- the total weight of the structure;

•n - total number of the storeys;

•K – amplifying coefficient (influence of bracing system, stairs,

lifts, building services (K=1,10...1,15);

2.Variable actions:

2.1. Live loads, usually uniformly distributed, in [daN/m2]

according with the function of the building (e.g., residential

building, hotel, etc.) and in particular with the destination of

every space inside this building (rooms, halls, lobbies, stairs

etc.);

2.2. Snow on the roof (terrace)-uniform distributed.

•Horizontal actions

•Variable actions - wind on the envelope of the building;

•Accidental actions – earthquake, fire, explosions.

The distribution of the variable actions in various schemes is

presented, the most familiar cases of loading being considered

in the static computation of the multi-storey buildings.

2

n12K10G

Simplification of the static computation

Separation of the spatial structure into plane frames: 1- transversal frame; 2- longitudinal structural element

(girder); 3- longitudinal frame

Loading schemes of vertical and horizontal actions on multi-storey buildings: a)- permanent actions; b)- variable actions (live loads); c) variable actions (wind); d) accidental actions (earthquake)

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Wind Dynamic Action

Different loading diagrams for wind action and for combined gravitational and wind loading on structure

Classification of the steel structures considering the wind dynamic effects

HzH

1004,0n

5,1

0

HzH

n40

0

202

1

ii

ii

ym

yWn

HzH

dn

1,01 4Hm

Enr

r=1 r=2

r=3

r=4

r=5

r>5

=3,52 =22,4 =61,7

=121,0

=200

*

22/12* r

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STATIC ANALYSIS

•Slope-deflection method- smaller number of unknown elements; whenever is possible the advantages of structural symmetry (geometric, elastic, mechanic) must be taken into account. • Some assumptions are prior set off: 1.-moments of inertia- constant along the bars; 2.-influence of shear forces neglected; 3.-in the first order computation the effect of axial forces upon the deformations of the bars is neglected; Computer design of the structure implies that the elastic characteristics of the cross section of the elements are known. These characteristics may be determined with the help of approximating methods.

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Structural systems for the high rise buildings: 1-rigid joint; 2- column; 3-floor; 4- horizontal bracing; 5-vertical bracing; 6- hinged joints

Rigid frames both transversally and longitudinally; the connections are designed to the moments induced by the vertical and horizontal loads. These structures have rather a small number of stories (20 to 30 storeys) and a big amount of maneuvre at the building site is necessary.

Rigid frames transversally with braced frames articulated with vertical braces longitudinally; the frames take over vertical loads and the horizontal forces are transferred to the vertical bracing of the structure;

Frames with both rigid and articulated joints, for ex. transversal rigid frames and longitudinal braced frames with articulated joints which have at the lower part of the structure articulated joints and the frames are provided with vertical bracing; rigid frames are used at the top of the structure;

Rigid frames braced both directions: used for up to 70-80 storeys

Bracing system may also be adopted for the limitation of the horizontal displacements. If braces are missing, then important horizontal displacements due to horizontal actions (wind, earthquake etc.) have to be taken into account affecting the joints of the structure.

RIGID AND HINGED FRAMES IN VARIOUS COMBINATIONS

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Cross sections of steel buildings with rigid core and dual core

Design of the rigid core: a)made of reinforced concrete; b) made of steel trusses

Rigid core structures with columns and/or tensioned elements on the perimeter; external core made of columns closely situated and connected to very stiff girders and internal columns sustaining the floors; VI Rigid cores and pendulum columns: vertical bracing are placed in the external walls all the height of the building and the columns inside the perimeter sustain the floors; VII Dual core tubular structures: two concentric tubes formed of columns closely spaced connected at every level with stiff girders; the internal core may be made of reinforced concrete or steel columns; VIII Other combined systems

HIGH RISE BUILDINGS WITH RIGID CORES

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THE STIFFNESS OF THE STRUCTURAL FRAMES

•P- effect – analysis that allows the structural classification into two categories: non-sway (stiff, rigid) and sway (flexible) frames

•rigid steel frame: during the evaluation of the structural response to horizontal actions the additional stresses due to horizontal translations of the connections may be neglected.

•V- vertical total reaction determined at the bottom of the columns in a certain level;

•H- horizontal total reaction;

• - horizontal relative translation of the storey determined in a I order computation, based on the vertical and horizontal actions on the structure and in addition horizontal equivalent forces due to imperfections.

•Imperfections: ENV 1993-1-1:

•-global;

•-local geometrical imperfections and residual stresses variation of the yield strength

1,0H

V

h

Types of structures considering the classification of the stiffness: a- structures for which the relationship is relevant; b- structures for which the relationship is not relevant

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PRINCIPAL ASPECTS OF BRACING SYSTEM DESIGN

ai – horizontal translations at the i level in the braced system due to horizontal force H;

si - horizontal translations at the i level in the un-braced system due to horizontal force H.

•In other words, the stiffness of the braced frame is 5 times greater than the stiffness of the un-braced frame:

5

i

si

a

sa R5R

sR

- stiffness of the un-braced structure.

- stiffness of the braced structure;

HRa

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Braced steel frame is considered: if the horizontal translations of the joints are reduced in a 80% proportion due to the presence of braces

The bracing system is a plane girder, fixed in foundations (at the ground level). The connection between any vertical bracing and the adjacent columns is obtained with longitudinal elements- girders that are considered with infinite stiffness. Under this supposition, the horizontal forces acting in the joints of the vertical bracing system at a certain level will determine translations of the ends of the columns identical with the joints of the bracing elements.

NOTE

Limitation of the sway by placing vertical bracing on the height: left- sway to a frame with rigid joints and to a braced frame; middle- interaction between the two frames; right- deformation of the whole building

EFFECT OF VERTICAL BRACING SYSTEM

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P- EFFECT

• The joints of the bracing system suffer horizontal translations under a linear variation on the height of the structure:

• The force necessary to fix the elements in the connection will then be (the angle is very small):

•

• and at the level i the whole force acting on the bounded connections will then be:

• The real behaviour is presented, the variation of the horizontal translations being in fact different from level to level. The effect P- will then be described by the horizontal force at the level i:

• Then the real total force acting at the level i will be:

The P- effect

H

1

iiiiiii VtgVDDDDH 11 sin

ii VH

iiiii DDH 11

iiiii DDH 11 Systems of horizontal in-plane translations due to imperfections: a- braced frames; b- un-braced frames

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BRACING SYSTEM OF MULTI-STOREY STEEL STRUCTURES

• Vertical braces: placed in the plane of the vertical frames and insure the necessary stiffness on both directions and to take in plane torsion effects. • Horizontal braces: stiffness of the floor when it cannot insure a satisfactory bond between the vertical elements (trusses with simple ties or in X over the whole floor or only in certain zones). • Floors made of reinforced concrete or corrugated steel sheet (composite structure) insure enough stiffness. •Sometimes the horizontal bracing is placed at 3...5 storeys interval on the height of the structure, considering that the current floor insures its own stiffness.

Vertical bracing designed as a rigid core : actions of the horizontal forces

Different systems for the vertical braces

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ACTIONS ON RIGID FRAMES

• Vertical actions

Loading cases for maximum axial force and maximum bending moments for the marginal (A) and internal joints (B)

Distribution of the bending moments from vertical loading in the internal joints

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The loading schemes correspond to maximum axial force and maximum bending moments in the end bays and internal bays

Distribution of the bending moments from vertical actions and the static equilibirum in the

structural joint

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EVALUATION OF INTERNAL FORCES AND BENDING MOMENTS FROM HORIZONTAL ACTIONS

• In the elastic design it is assumed that the axial internal forces from each level, Nik, are directly proportional with the distances to the N. A. (rigidity center), dik, at every level; also, these forces are directly proportional with the cross section area of the columns, Aik. • We write the equations of equilibrium for the overturning moment under horizontal

actions for each of the current column, k, at the current level i :

ikikjj dNyW

1i1i

ikik

1i

ik

dA

dA

N

N

2

ikik

1i1i

1ijj dA

dA

NyW

jj2

ikik

1i1i1i yW

dA

dAN

n

1i

ji WV

ij

ikiik

I

IVV

2

hVM ikik

Horizontal actions from wind action on structures with rigid connections and the internal forces resulted under these forces: axial forces, shear forces and

bending moments

DESIGN OF HINGED STRUCTURES AND VERTICAL BRACING

• Vertical actions

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The structural joints are subjected to a reduced bending moment as a result of uneven reactions on the edge of the structural beams :

eRRM

2

lpR;

2

lqpR

21

11

Calculation of the bending moment resulted from un-even reaction from beam convergent in the structural connection

Forces and bending moments resulted from the distribution of horizontal forces to the bracing system

Horizontal actions

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The rigidity of the current stiffener i is Fi (equal with horizontal force acting on the bracing system that results in an unitary translation of the brace). If a reference stiffness Fo is considered, the stiffness of the current bracing i may be expressed in relation wih Fo by adopting a factor of proportion, ki:

Horizontal actions

0Fi

ki

F

2

Ac

y

n

1jij

n

1jj

xyj

k

n

1jyj

F

n

1jj

xyj

F

cx

Based on these stiffnness values, the rigidity center will be determined on each level:

Every bracing system parallel with the axis y-y will take the in plane force Nyi’ , component of the resultant force Ry, distributed based on its rigidity to the “n” braces)

yj

yik

yR

n

1jyj

F

yiF

yR

'yi

N

Force Nyi” resulted from from th distribution of the bending moment determined by the the eccentricity of the aplication of the reaction force Ry with respect to the rigidity center, My= Ry· ex to all “n” bracing systems depend on the rigidity of the braces and on the distance ax from the torsion center:

yixi

yjxj

''

yi

''

yj

Fa

Fa

N

N

yixi

yjxj''

yi

''

yjFa

FaNN

xj

n

j

''

yj aNM

But: xj

a

yiF

xia

yjF

xjan

j

''yi

NM

n

j yik

xia

yjk2

xja

''yi

NM

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n

1j

2xj

ayj

k

xia

yi

xe

yR

n

1jyj

k2xj

a

yik

xia

M''yi

N

It then results:

Forces that result acting at every level in the brace “i” are obtained by summarizing the two effects:

n

1j

2aj

ayj

k

xia

xe

n

1jyj

k

1

yik

yR''

yiN'

yiN

yiN

COMBINED SYSTEM- VERTICAL AND HORIZONTAL BRACING

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