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Structure loaded by the seismicity effects
Daniel Makovička, Assoc. Prof., D.Sc., C.E.
Czech Technical University in Prague, Klokner Institute,
CZ-166 08 Praha 6, Šolínova 7, Czech Republic,
E/mail: [email protected]
&
Daniel Makovička, C.E.
Static and Dynamic Consulting,
CZ-284 00 Kutná Hora, Šolínova 7, Czech Republic,
E/mail: [email protected]
Purpose:
1) Principles of earthquake analysis Example of a ventilation stack of a reactor building
2) Comparison of earthquake and other loading effects Cooling tower under combination of design loading states
3) Vibrobase isolation of building
Example of administrative building
The goal of the paper:
the methodology of the simplified numerical earthquake analysis of the structure,
the response of the very sensitive structure to seismic loads (the spectrum of the lowest natural frequencies corresponds with the frequency spectrum of excitation),
the participation of individual response frequency components in the overall stress and strain state,
comparison of the recommendations of relevant standards and codes.
DESCRIPTION OF STACK STRUCTURE Location: on the roof of reactor building
double-skin steel segment structure (height 52.550 m),
consisting of: foundation element 1.550 m high
+ 5 segments 10.200 m high
2 platforms – 20.550 m and 49.130 m
exterior cylindrical segment (part 3, 5):
the inside diameter ... 3.000 m,
the wall thickness ... 12 mm in the first segment,
the others 8 mm.
inside cylindrical segment (part 4, 6):
the inside diameter ... 1.600 m
the wall thickness ... 4 mm.
annular stiffeners ... between exterior and inside
segment steel walls ... 16 mm thick.
Methodology of the simplified earthquake analysis
MVʽʽ + CVʽ + KV = P(t) = MVgʽʽ
M, C, K .... mass, damping and stiffness matrices
Damping C ... D 3 to 5 %
Vʽʽ, Vʽ, V ... acceleration, velocity and displacement vectors Vgʽʽ... earthquake acceleration or P(t) .... excitation function
The whole system: the building foundation sub-base - the building - the stack
2 calculation steps:
1st Subsystem:
foundation sub-base - the building and the mass affect of stack on the roof
(without stack stiffness)
output: Response Spectrum of Reactor Building Roof
2nd Subsystem:
elastic foundation of stack on the roof – stack structure
(with stack mass and stack stiffness)
output: Stack Structure Response
The degree of justification
of the application of simplification methodology
The solution accuracy depends
– on the difference between the natural frequencies of the
stack and the natural frequencies of the building as a
whole structure;
– on the roof structure natural bending mode
(the top of building where the stack is anchored.
The 1st Subsystem: Floor Response Spectrum of Reactor Building Roof
(Input Data for Stack Analysis)
Stack Location:
The 2nd Subsystem:
Natural modes of stack structure
The dominant frequencies
for vibration:
a) in horizontal direction:
in the vicinity of 1.0 / 5.1 / 14.516.0 / 26.5 Hz;
b) in vertical direction:
in the vicinity of
18.5 / 22.5 Hz.
Principles of analysis: - dynamic linear elastic solution: - steady-state solution for dominant frequency components,
- nonharmonic solution for time course of acceleration,
- determination of maximum response value for individual dominant frequency peaks … as vector sum
(RMS superposition in frequency and coordinate domains),
- ductility factor utilisation,
- combination of static and dynamic load states.
Ductility factor is usually given in the respective codes and standards
in dependence on the importance of the structure and its structural design.
• Eurocode 8 uses the ductility factor to correct the seismic load before the
computation start and permits to use this factor „for standard structures, unless the design brief provides differently“ on the basis of type of structure usually at the rate of 2.0 regardless of structural design,
• The US guideliness (for power plant structures – Kennedy, 1990) enables a more discerning application according to the type of structure (design of joints of structural members, material, importance of the structure, etc.); the ductility factor to steel structures is within the limits of 2.5 and 3.3.
• US codes (Kennedy + ANSI/ASCE 7-93) permit the correction of the computed response and only for structural members loaded in bending and not for those loaded in compression or tension for which they stipulate the ductility factor of 1.0.
Used for stiffeners, only (conservative value: 1.6)
which are loaded
by a combination of the normal force and bending moments.
Dynamic
stress
(high values)
part 1: foundation element
part 2: vertical foundation
element stiffeners
part 3: exterior skin plates
between found.element
and middle platform
part 4: interior skin plates
between found.element
and middle platform
part 5: exterior skin plates
between middle platform
and stack top
part 6: interior skin plates
between middle platform
and stack top
Displacements (high values)
part 1: foundation element
part 2: vertical foundation
element stiffeners
part 3: exterior skin plates
between found.element
and middle platform
part 4: interior skin plates
between found.element
and middle platform
part 5: exterior skin plates
between middle platform
and stack top
part 6: interior skin plates
between middle platform
and stack top
Seismic analysis requirements – Standard comparison
Eurocode 8 does not deal with the analysis of individual frequency components, but
according to the Art. 4.1, para. 4 it characterizes the design acceleration of 0.1g for a
building with a chimney stack as „a low seismicity domain“ for which „the
application of a simplified method of seismic design is permitted“ and understimates
the significance of seismic load for such a sensitive structure.
National Standard prescribes the assessment of internal forces while taking into
account the effect of the basic dominant frequency of the natural vibrations of the
structure in superposition, but with half (older) or full (new) the weight of higher
natural frequencies. The preceding analysis has revealed that in case of such a
seismically sensitive structure as the ventilation or chimney stack the response of the
structure to the basic bending natural frequency need not be always dominant for the
overall stress state of the structure.
Response reality – dominant in displacements … first bending modes (about 1Hz)
in stresses … higher bending and axial vibration
modes (about 5.1 Hz)
Superposition of seismic effect with dead load
• ČSN EN 730032: the dead load due to the weight of the structure with a load factor >1,0
(by ČSN EN 1990)
is superposed on seismic load with a load factor 1.0 (corrected by the
duktility).
• US standard (ANSI/ASCE 7-93): the dead load incl. the weight of the structure appears in this
combination with the load factor 1.0.
The effects of seismicity are included in the combination with the
factors of from 0.65 to 1.2 according to the type of material and the
loading of the structure, further corrected by the ductility
characteristics of the structure.
Conclusions to the stack analysis
The goal of the paper was to show:
• The seismic response results of the simplified analysis of ventilation stack,
• The advantages of modal analysis with particular reference to the specific characteristics of a cantilever stack structure which is very sensitive to low-frequency seismic excitation,
• The comparison of selected codes requirements for structure assessment.
In the structure of this type:
· • The lowest natural vibration mode need not be the dominant mode for the design of the structure, but may be replaced with one or several higher modes which determine the seismic resistance of the structure.
• Particularly in the structures the seismic load of which is mediated by the transfer characteristics of another structure (in this particular case the building on top of which the stack is mounted) this modal analysis is very useful for:
¨ the correct design,
¨ to analyze potential reserves
¨ and improve the seismic resistance.
(2) Comparison of earthquake and other
loading effects
Cooling tower under combination of
design load states
RC structure of twin cooling tower unit
with fans 6m in propeller diameter for an Oil Refinery Basra
(Basic static and dynamic design: ANSI/ASCE 7-95: Minimum Design Loads for
Buildings and Other Structures)
Concrete: Grade 25
(equivalent to B30)
Reinforcement:
Grade 400 (10 425 V)
External and internal
walls 250 mm,
roof 150 mm,
diffuser 65 mm,
baseplate 800 mm.
Loads Temperature:
– During construction … +35.0 C,
– Normal air operating temperature (inside) … +35.0 C,
– Winter period … -5.0 C,
– Summer period … +55.0 C.
Wind:
– Basic wind velocity ... V = 50 m/s,
– Topography factor ... S1 = 1.0,
– Wind pressure variation with height ... S2 = 0.99 (for h < 15 m),
– Statistical factor ... S3 = 1.0,
– Design wind velocity ... Vs = 49.5 m/s,
– Dynamic wind pressure ... q = 0.613 × 49.52 = 1.502 kPa
Earthquake:
– Importance factor … I = 1.25,
– Seismic area … 1,
– Seismic area factor ... Z = 0.075,
– Seismic wave velocity … vs = 360 m/s,
– Seismic coefficient ... Cv = 0.18, Ca = 0.12,
– Damping ratio ... D = 5%,
– Acceleration (foundation plate) … 2.5 × Cv = 0.3 g. Design elastic response spectrum
Natural modes and frequencies
2.19 Hz 2.57 Hz 3.28 Hz
Rotating around x Rotating around y Vertical vibration in the direction of z
3.31 Hz 4.95 Hz 5.25 Hz
Torsional vibration around z Higher mode of rotation around x Higher mode of rotation around y
Displacements in direction x
Displacements in direction z
Earthquake response (ductility factor 3.6
excitation in directions x and z)
Displacements in direction y
Displacements in direction z
Earthquake response (ductility factor 3.6
excitation in directions y and z)
Conclusions to the design of the cooling tower unit
1) The dominant effect with reference to structure safety is temperature effect
together with the design wind load.
2) The effects of natural seismicity (without reducing of this load by ductility factor)
are comparable with the dynamic wind load within the interval of design wind
velocities. However, seismicity may become dominant for the reliability of the
structure when there is vibration of selected parts, such as joints, measuring probes
for technological purposes, etc.
3) For structural design, static loads were there combined with wind effect. The wind
effect is greater than the reduced seismic load.
4) The reinforced concrete structure of the towers must also have sufficient reserves
for ductility strain at seismic load. In order to enable this ductility strain, the structure
must be appropriately reinforced especially by shear reinforcement.
5) When using the ductility factor for sizing the dimensions of the structure, it must
be taken into account that after an earthquake the structure will be damaged and must
be repaired (ductility strain assumes the occurrence of cracks).
Spectrum and time history of excitation (transport effects)
Building structures in the vicinity of
transport lines are loaded by
vibrations excited by the passage of
trains, tracks, busses etc.
These vibrations propagate as
technical seismicity effects through
the soil to the foundations of
buildings in the vicinity of their
source.
Due to its tuning, the building
structure usually amplifies or, in
better cases, reduces the effects of
technical seismicity.
An effective method for reducing the
vibration level of the protected
structure is to spring it from the
foundations. The effectiveness of the
springing is determined by the
frequency tuning of the sprung
structure.
Vertical excitation
Elastic support of the structure at its foundation level
The vibroprotection is usually effected
by placing the whole upper part of the
structure on individual springs or
sprung layers.
The lower the tuning of the structure
based on springs (the lower the
dominant natural frequencies), the
greater the decrease in the higher
vibration frequencies and acoustic
frequency effects propagating into the
structure from its geological
environment.
The normalized time course of the measured acceleration can be used as a time function of the force load.
Calculation model
Location of elastomer on the bottom foundation plate
The lower foundation plate is based on
large diameter piles mutually connected
by reinforcement.
On top of this plate an antivibration
layer of elastomer has been designed.
Above the elastomer there is an upper
foundation plate in which the cast-in-
place skeleton building structure is
constrained.
Elastomer: rubbergranulated materials, plates:
50050030 mm.
Stiffness was verified in laboratory conditions.
Used properties of the material (its stiffness):
related to static prestress. Elastomer layout
Interaction of foundation plate and elastomer
signal modification / effect of imposed load
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0Time [s]
Dis
plac
emen
t [m
im]
Lower foundation plate
Upper foundation plate
The lowest natural modes – structure tuning
Natural frequency [Hz]
Natural mode shape without with
vibroinsulation
1,22 1,03 Rotation of the whole building round the z axis
1,70 1,42 Rotation round the z axis and bending of the whole
structure in direction y
1,98 1,49 Bending of the whole structure in direction x
4,52 4,32 Rotation round the z axis and floor slab bending of the
higher storeys
6,29 5,44
Higher modes of floor slab bending
6,34 5,74
6,91 6,14
6,98 6,52
6,99 6,82
7,03 6,91
Computation of peak vertical displacements (3D calculation)
The history of the
response displacement
was normalized, to the
maximum of the
displacement of the
baseplate, where the
seismic load acts.
Thus, if the response is
smaller than value one,
the vibration in this
location of a storey is
smaller than the vibration
of the maximally vibrated
point of the baseplate,
and vice-versa if it is
greater than one the
vibration is amplified.
Without
vibroisolation,
maximum 3.2799
Time response history of above-ground storeys and normalized history of excitation - isolated structure
The most intensive vibrations can be observed in the proximity of columns and structural
parts situated on the underground side. With increasing building height, the vibration
intensities are smaller and lower frequencies are dominant.
Conclusions to the vibroisolation
• The using of elastomer for vibro-base isolation is advantageous way
to decrease excessive vibrations of the building foundation (seismicity
from the soil structure).
• The loading of the building structure by the time history of
acceleration makes possible to respect the real properties of subsoil
and its interaction with building foundation and decrease of loading
intensity (damping) with distance of foundation parts from the source
of vibration (for technical seismicity).
• 3D analysis is accurate enough for response prediction of any floor
configuration and for its result combination with other design load
effects.
• The variability of input dates (material properties of elastomer,
structure conditions, type of supports etc.) may be respected in the
process of analysis.