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: daniel.makovicka@klok.cvut.cz

&

Daniel Makovička, C.E.

Static and Dynamic Consulting,

CZ-284 00 Kutná Hora, Šolínova 7, Czech Republic,

E/mail: d.makovicka@worldonline.cz

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

(1) Seismic resistance of a ventilation stack

of a reactor building

NPP Temelin – A case study

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

Anchoring - Screw support forces [kN]

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

Comparison of design moments in plate elements

Comparison of design internal forces in beam elements

Comparison of the design axial forces in plate elements

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).

(3) Vibrobase isolation of building Example of administrative building

(technical seismicity)

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

With

vibroisolation,

maximum 1.572

Computation of peak vertical displacements (3D calculation)

Maximum of peak vertical displacements (normalized)

Maximum of peak horizontal displacements (normalized)

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.

Dynamic response of building - vertical excitation

Nonisolated structure Isolated structure

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.

Thanks for your attention