Lecture 8 s.s.iii Steel Structures

MULTI-STOREYSTEELSTRUCTURES
C.Teleman_S.S.III_Curs8
1

2
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
3
SHORT HYSTORY

4
Empire State Building, New York, 102 storeys, 381 m-1931
John Hancock Center, Chicago, 337 m

5
Sears Tower, Chicago, 1972, 442 m, 120 storeys Tower Montparnasse, 210 m, 50 storeys

6
Chrysler Building New York, 1928-1930Rchard Daley Center, 1965, scoala arh. Ludwieg
Mies van Der Rohe, Chicago, 215 m

7
Petronas Towers Cesar Pelli, Kuala Lumpur, Malaysia, 1998 Taipei 101, by C. Y. Lee & Partners, Taipei,
2003 to 2004

8
Turning Torso, Malmo, 2001, 240 m
30, St. Mary Axe, (“Gherkin Building”), London,
2000-2004, 41 floors, 180 m

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

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)
12

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
13

EXAMPLESOFSTRUCTURALSOLUTIONS
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
14

BRACEDFRAMES
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
15

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

POSITIONOFTHECONFERENCEHALLSINPLAN
• 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
17

VARIATIONOFTHECROSSSECTIONOFTHEBUILDING
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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ACTIONSANDCOMBINATIONOFACTIONS
•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
n
12K10G
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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WindDynamicAction
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
 Hz
H
100
4,0n
5,1
0 






 Hz
H
n
40
0 
20
2
1
ii
ii
ym
yW
n




 Hz
H
d
n
1,0
1  4
Hm
E
nr




r=1 r=2 r=3 r=4 r=5 r>5
=3,52 =22,4 =61,7 =121,0 =200 *
  2
2/12*   r
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STATICANALYSIS
•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.
21

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
22

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
23

THESTIFFNESSOFTHESTRUCTURALFRAMES
•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
1,0
H
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
24

PRINCIPALASPECTSOFBRACINGSYSTEMDESIGN
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;

H
Ra 
25
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
26

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
27

BRACINGSYSTEMOFMULTI-STOREYSTEELSTRUCTURES
• 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
28

ACTIONSONRIGIDFRAMES
• 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
29
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

C.Teleman_CM3_Curs7
30
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
1i
jj dA
dA
N
yW 




 jj2
ikik
1i1i
1i yW
dA
dA
N


n
1i
ji WV


ij
ik
iik
I
I
VV
2
h
VM 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

DESIGNOFHINGEDSTRUCTURESANDVERTICALBRACING
• Vertical actions
C.Teleman_CM3_Curs7
31
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
l
pR;
2
l
qpR
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

C.Teleman_CM3_Curs7
32
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
0F
i
k
i
F 
2
A
cy
n
1j
ij
n
1j
jxyjk
n
1j
yjF
n
1j
jxyjF
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
yikyR
n
1j
yjF
yiFyR
'
yiN







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
''
yj
Fa
Fa
NN



xj
n
j
''
yj aNM  
But: xj
a
yi
F
xi
a
yj
F
xj
an
j
''
yi
NM 




 
 


n
j yi
k
xi
a
yj
k2
xj
a
''
yi
NM

C.Teleman_CM3_Curs7
33










n
1j
2
xj
a
yj
k
xi
a
yi
x
e
y
R
n
1j
yj
k2
xj
a
yi
k
xi
a
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
2
aj
a
yj
k
xi
a
x
e
n
1j
yj
k
1
yi
k
y
R''
yi
N'
yi
N
yi
N

COMBINEDSYSTEM-VERTICALANDHORIZONTALBRACING
34

Lecture 8 s.s.iii Steel Structures

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