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MODELLING AND ANALYSIS OF BASE ISOLATED STRUCTURES THROUGH IPERSPACE MAX
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D.M. 14/01/2008 (Italian Technical Construction Regulation)
Phd Ing. Stefano Ciaramella Technical Consultant R&D
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Seismic isolation
The approach to the earthquake-resistant construction problem:
CAPACITY DEMAND
where:
the demand depends on the seismic event, which generates inertial forces in the structure. These forces are equal to the product of the masses of the structure and the accelerations due to the vibration induced by the event itself.
the capacity depends on the strength and on the non-linear deformability of the structure.
Seismic Isolation: is an alternative design approach that acts on demand drastically limiting the accelerations
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a) increase of the fundamental period of the building to bring it in the field of lower responses to accelerations
b) limitation of the maximum horizontal force transmitted
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a) Increase of the period (and dissipation) b) Limitation of the force (and dissipation)
Seismic isolation strategy
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Model of a base isolated building
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Superstructure Substructure
Isolation Interface
Seismic isolation system
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Benefits of seismic isolation
Economically acceptable and convenient structures
Drastic reduction of the story drift which allow to create structures that do not suffer damage for devastating earthquakes
High protection of structural content
The people in the building have a minor perception of the seismic event
Great savings for repairs after high intensity earthquakes If the building has strategic importance the earthquakes does not cause the
interruption of the service.
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Definition of the characteristics of the isolating system:
Stiffness
Dissipative capacity
Identification of the period-damping couple (Tis, esi).
Compared to the configuration of fixed-based structure (FB), this approach determines a better balancing between a satisfactory reduction of the seismic effects and horizontal displacement of the superstructure.
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System pre-dimensioning
Case Configuration T
1 Structure (FB) 0.47 sec 5%
2 Structure (BI) 1.50 sec 10%
3 Structure (BI) 2.00 sec 10%
4 Structure (BI) 2.50 sec 10%
5 Structure (BI) 1.50 sec 15%
6 Structure (BI) 2.00 sec 15%
7 Structure (BI) 2.50 sec 15%
3/4
1 0.47secfbT C H
fixed-based structure (FB) base-isolated structure (BI)
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System pre-dimensioning
2 isois
esi
MT
K
2
2esi iso
is
K MT
,iso e is esiF M S T
2,
,2
iso e is esi isdc e is esi
esi
M S T Td S T
K
Horizontal equivalent stiffness of the isolating system:
Equivalent period of the isolating system:
Resultant of horizontal forces applied to the isolated system:
Displacement of the stiffness centre of the isolating system:
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Response Spectrums
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Period [sec]
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Acceleration Displacement Response Spectrum
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Case Configuration T
[sec]
[%] ddc
[mm]
2 Structure (BI) 1.50 10% 156
3 Structure (BI) 2.00 10% 218
4 Structure (BI) 2.50 10% 280
5 Structure (BI) 1.50 15% 135
6 Structure (BI) 2.00 15% 189
7 Structure (BI) 2.50 15% 242
2
,2
dc e
Td S T
Stiffness Centre Displacement
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Response Spectrums
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Elastic Spectrum
Structure
Project Spectrum
Structure (FB)
Period [sec]
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Case Configuration T
[sec]
[%] Shear Force
[KN]
1 Structure (FB) 0.47 5% 1550
2 Structure (BI) 1.50 10% 1260
3 Structure (BI) 2.00 10% 960
4 Structure (BI) 2.50 10% 740
5 Structure (BI) 1.50 15% 1100
6 Structure (BI) 2.00 15% 770
7 Structure (BI) 2.50 15% 630
,
600
eF M S T
M t
Shear force at the bottom of the superstructure
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Case Configuration T
[sec] Kesi
[KN/m] ki
[KN/m]
2-5 Structure (BI) 1.50 13861 770.0
3-6 Structure (BI) 2.00 7896 438.7
4-7 Structure (BI) 2.50 5053 280.7
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2
2
790
esi iso
is
iso
K MT
M t
Horizontal stiffness
pillarsofnKk esii /
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Case Configuration T
[sec]
[%] ddc
[mm] Shear Force
[KN] Kesi
[KN/m] ki
[KN/m]
1 Structure (FB) 0.47 5% - 1550 - -
2 Structure (BI) 1.50 10% 156 1260 13861 770.0
3 Structure (BI) 2.00 10% 218 960 7896 438.7
4 Structure (BI) 2.50 10% 280 740 5053 280.7
5 Structure (BI) 1.50 15% 135 1100 13861 770.0
6 Structure (BI) 2.00 15% 189 770 7896 438.7
7 Structure (BI) 2.50 15% 242 630 5053 280.7
Seismic Effects: 50% reduction compared to the FB configuration
Summary of the results
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d =189 mm + 30% =246 mm Ko = 0.439 kN/mm
Preliminary Analysis
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1. Go to the section Isolatori (“Isolator”) in the widget Elementi e click on Nuovo (“New”).
2. Insert the code for the new isolator.
3. In the property widget (“Proprietà”) through the section Generici, insert the vertical and horizontal stiffness taken from the catalogue.
Adding an isolating element to the program library
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Inserting isolators in the model of the structure
1. Selecting one or more pillars in the substructure.
2. Click on Crea (“Create”) Isolatore sui selezionati (“selected isolators”)
3. Choose the isolator type, define its high and confirm (√)
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Structural analysis: fixed-based structure
1st mode
2nd mode
3rd mode
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Structural analysis: fixed-based structure
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T = 0.47 sec Preliminary Analysis
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Structural analysis: fixed-based structure
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F = 155000 daN Preliminary Analysis
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Use of isolation devices “FIP INDUSTIALE” series SI-S 400/125 Reduction of the elastic spectrum for T 0,8 Tis = 1.6 sec Assumes = esi = 15% for T 0,8 Tis and = 5% for T < 0,8 Tis
Structural analysis: base-isolated structure
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For the ultimate limit state verification, the needed resistance of structural elements of the superstructure can be met by considering the seismic effects reduced by the factor of 1/q=0.6667, where q=1.5 is the structure factor.
Structural analysis: base-isolated structure
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Structural analysis: base-isolated structure
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T = 2.0 sec Preliminary Analysis
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Structural analysis: base-isolated structure
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F = 77000 daN Preliminary Analysis
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The following figure shows the deformation of the structure due to a seismic event aligned with the x-axis.
The isolator maximum horizontal displacement is d = 221 mm, not far from our preliminary prediction (246 mm) and however under the limit of the isolator (250 mm).
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Limit State Verification
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Ultimate Limit State Verification Damage Limit State Verification
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Ultimate Limit State Verification
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The superstructure and substructure should be designed with reference to construction details related to the non seismic zone (Geometric and Reinforcement Limitations)
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Ultimate Limit State Verification
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Damage Limite State Verification
For the superstructure, the verification must be carried out controlling that the story drift, obtained from the analysis, is under the 2/3 of the Damage Limite State limits of conventional structures. This verification is carried out by setting k(*h) = 0.005x2/3 = 0.00333333 into the “Impalcati” section of the property widget and finally checking the results.
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However, it remains to be performed the verification for the parts involved in the non-dissipative function. These should remain in the elastic range even under the conditions of maximum stress, according to the rules relating to the materials they are made. For this verification, also a safety factor (≥1.5) have to be taken into account.
For the replacement of isolators, the lifting by hydraulic jacks could be required. Therefore it is necessary to evaluate the dimensions of the concrete squat above the isolation interface and calculate an additional bottom reinforcement.
In order to prevent or reduce traction in the seismic isolation devices, the vertical load design "V“, due to seismic actions, should be compressive or zero (V ≥ 0).
In the case that V < 0, the modulus of the tensile stress should be minor both of 2G and 1 Mpa into the isolators (G is the shear modulus).
For further examinations regarding these issues, the reader can refer to the specific publications available.
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Further Verifications
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