Seismic Response Analysis using R es po pons ns e Spe S pectrum ctrum Me Metthod hod,, S ei eiss mi micc C oeffi oefficc i ent Met Method hod & Interpr Inte rpret eta ati on of res r esul ultts Illus Ill us trat ratii ve Ex E x ampl ples es As per IS:1893- Part-1, Part-1, 2002 & Part-4, 2005
Agenda
• Preamble to Theoretical Background • Flow-chart for seismic analysis • Illustrative Example-1: Industrial building, Cat:3, I:1.5, DBE • Illustrative Example-2: Industrial building, Cat:1, I:2.0, MCE • Illustrative Example-3: Commercial building, Cat:4, I:1.0, DBE • General Guidance • Closure
START
Civil / structural unit Non-Industrial structures (Part-1) of IS: 1893
Industrial structures (Part4) of IS: 1893
Non-buildings Non-buildings under Categories 1-4
Qualifies for Detailed analysis ?
Yes RSM / THA
Buildings under Part-1 of IS:1893
Buildings under Category-4
SCM as per Part-1 of IS:1893
No Yes Simplified analysis RSM
Qualifies for Detailed analysis ?
Enhancement of RSM results Load-combinations with non-seismic Design calculations Drawings
No
Flow-Chart : Seismic Analysis Building Site-specific seismic parameters
Geometry / layout of structure A, MI, L
Foundation: Type of soil: Rock, Hard / medium / soft
Structure RCC / Steel Mass-distribution, density (loading for mass-matrix)
Material-properties E, G, Poisson’s Ratio
Damping in structure
Frequency / time-period calculations (modal analysis) Spectral-acceleration, Sa/g (spectrum analysis)
DBE / MCE
Zone for site, Z factor
Hazard category: Importance factor, I
Seismic Coefficient, Ah = (Z/2).(I/R).( Sa/g)
Ductility in structure: R factor
Illustrative examples Example-1: Industrial structure (e.g. Workshop building)
• • • • • •
Site: Guwahati Site-seismicity: IS1893 code-specified Spectra to be used • Seismic Zone: V (Very severe earthquake intensity) • Zone factor: 0.36, (i.e. PGHA in g) Foundation Stratum : Type-2 (Medium Soil) • (SS=2 for STAAD) Design Earthquake : DBE Building; RCC framed structure • Hence ST=1 for STAAD
Equipment / System-hazard Category : 3 • hence Importance factor : 1.5 Damping for DBE: 5% • • Response Reduction factor, SMRF • R: 5.0 (RF in STAAD terminology) RSM to be used for calculations of seismic response
Illustrative examples Example-2 Industrial structure (e.g. Control-building)
• •
Site: Guwahati Site-seismicity: IS1893 code-specified Spectra to be used • Seismic Zone: V (Very severe earthquake intensity) • Zone factor: 0.36 (i.e. PGHA in g) • Foundation Stratum : Type-2 (Medium Soil) • SS=2 in STAAD terminology Design Earthquake : MCE • Control Building; RCC framed structure • • Hence ST=1 for STAAD terminology Equipment / System-hazard Category: 1 • • hence Importance factor, I : 2.0 Damping for MCE: 7% • • Response Reduction factor for SMRF • R: 5.0 (RF in STAAD terminology) RSM to be used for calculations of seismic response
Illustrative examples Example-3 Non-industrial building (e.g. Commercial building)
• •
• • • • •
Site: Bhuj Site-seismicity: IS1893 code-specified Spectra to be used • Seismic Zone: V (Very severe earthquake intensity) • Zone factor: 0.36 (i.e. PGHA in g) • Foundation Stratum : Type-2 (Medium Soil) • SS=2 in STAAD terminology Design Earthquake : DBE Control Building; RCC framed structure • Hence ST=1 for STAAD terminology Equipment / System-hazard Category: 4 • hence Importance factor, I : 1.0
Damping for DBE : 5% Response Reduction factor for SMRF • R: 5.0 (RF in STAAD terminology) Both SCM & RSM to be used for calculations of seismic response
Summary Example-1 Earthquake Hazardcategory
Example-2
Example-3
DBE
5% damp
MCE
7% damp
DBE
5% damp
Cat-3
I = 1.5
Cat-1
I = 2.0
Cat-4
I = 1.0
RSM
SCM
Method
RSM
RSM
Direction of EQ
x
z
x
z
x
z
x
z
Base-shear (kN)
106
104
254
251
71
69
81
81
Tips for novice
• Familiarize with the input-command format fully well… be aware of limitations of software
• Work on simpler models for testing the overall procedure …then move on to larger / complex models …manual calculations provide better insight. For simple models compute time-periods with closed-form solutions
• In case model has RC & steel members use Modal-damping & different damping. Refer to FAQ folder for justification.
• Take full advantage of SCM for gauging order of magnitude of forces • SCM is useful for obtaining a fair idea about sizes of footings, rafts, piling • Compare base-shears in SCM & RSM • Look out for suspicious results such as inadequate supports, in-ordinately high / low forces, reactions, displacements
• Check units …. Are they consistent … • Use templates of existing data-files with caution
Design Categories (7.1) and I factor Seismic Category (7.1) 1
2
Consequences of Failure of system functionality (7.1) Extensive loss of life, property to population at large in areas adjacent to plant Fire-hazard / damage within plant-area
Importance factor, I (8.3.2, Table2) 2
1.75
Few examples of system / industrial structure (Table-5)
•
Process column (on elevated structure or low RC pedestals)
•
Control building (blast-resistant)
•
Cryogenic storage tanks (C 2H4)
• Pipe-rack, pipe-supports including anchors • Process building (closed) • H2 plant, caustic tanks, Process water storage tank, Tanks for refrigerated liquefied gases. • FO storage tanks, Fire-station • Horizontal vessels, HEX • Sub-station,
3
4
Not leading to serious hazard in plant complex Any other structure
1.5
warehouse
• Tunnels and trenches • Generator transformer, start-up transformer,
1
Laboratory building, work-shop, administration building
Application to Analysis For Raft Foundations on soil
1. 2. 3. 4. 5. 6.
Generate structural model (in STAAD-PRO) Generate mass-distribution on model (lumped-weights) Analyze structure for SCM in X-direction, followed by RSM In case any force-enhancement on RSM is needed, carry it out. Obtain sets of support-reaction at raft-level using SCM and RSM Attach signs of SCM’s support -reactions to those of RSM. i. ii. iii.
7. 8. 9.
Due to this, vertical forces to generate maximum overturning moment bending moments, shears at column-base will have signs of SCM Check sum-totals of applied forces Fx through Mz.
Create load-cases in the form of load-combinations with non seismic and seismic loads using set as in 6 above. Perform analysis of raft for the load-combination and not individual load-case, since there may be lift-off from soil. Repeat the steps 3-8 for Z-direction
Analysis Method Recommendations Seismic Hazard
Seismic zones
Least
II III
Seismic Category of utility Cat-1 RSA or THA (10.2)
Moderate
Highest
Cat-2
Cat-3
Cat-4 Structures
Cat-4 buildings
Simplified method may be Simplified Refer Part-1 used (10.3) method may be used Refer Part-1 RSA or RSA or (10.3) THA THA
IV
RSA or THA
RSA or THA
Refer Part-1
V
RSA or THA
RSA or THA
Refer Part-1
Equipment failure hazard
Highest
Earthquake level
MCE
DBE
DBE
Least
Nil or Least
DBE
DBE
Seismic Response Calculations
• Following methods are permitted by engineering standards – Seismic Coefficient Method (SCM) is applicable for simple buildings, such as
• Nearly uniform mass distributions in plans and elevations • Nearly uniform stiffness distributions • Regular framing patterns, • Symmetrical buildings • Less important structures, buildings – When building not qualifying for SCM, then first choice is RSA – Though RSA is involved it is more rational than SCM – But RSA is not sophisticated as much as Time History Analysis (THA) •
To arrive at a reasonably adequate mathematical model, the engineer ought to visualize physics of the system such as …
– Deflection pattern of structure as a whole, to facilitate… • Primarily for design of columns, Elevation-bracings, anchor-bolts and foundations – Deflection pattern at local heavy masses, enabling him carry out … • Local design of floor-level beams (secondary and tertiary) in horizontal plane • Design of Plan-bracings
Seismic Coefficient Method (SCM).. An overview
h
Seismic Coefficient Method .. An overview
Response Spectrum Analysis (10.2.5) Terminology … • Response / modal response
– Internal forces in members, storey-shears, stress-resultants – Nodal displacements – Support reactions
• Degrees of Freedom – Displacement Co-ordinates needed to express the behavior of structure
• Mode-shapes – Characteristic deflected shape in a vibration mode
• Modal mass – Mass participated in a mode (fraction of total mass of the structure)
• • • • •
Mass participation Factors Response Spectrum Seismic Weight / mass Damping Frequency / Time-period
Response Spectrum Analysis (10.2.5)
Basic Concepts …
• RSA is a numerical simulation devised for …. – Prediction of only Maximum response of members during seismic excitation – Time-instant wise variation is not expected from calculations
• Real response of a structure is perceived as ….. – Combination of responses of several modes of vibration (at least significant modes)
– Real life behavior is expected to be closer to combined effect obtained using • Absolute sum of modal responses • SRSS or CQC combinations of modal responses
• Modal response could be … – Bending-moments, shear-force, axial-force in members, storey-shears – Displacements (translations, rotations)
• A typical modal response is a function of … Sa/g from Spectrum – Frequency / time-period, damping of that mode Modal-mass, Modal participation – Mode-shape coefficients, mass matrix factor
Response Spectrum Analysis (10.2.5)
• SDOF : Single Degree Of Freedom system …. – Shear-beam model with base-excitation (earthquake).
Response Spectrum Analysis (10.2.5)
• What is Acceleration-RS …. – Plot of maximum response acceleration of SDOF oscillator against various frequencies for specific damping.
Response Spectrum Analysis (10.2.5)
• •
Carry out SCM to get a feel of expected base-shears in X, Z-directions
How to carry out RSA… – Mass-modeling – Stiffness-modeling, i.e. structure / building modeling in STAADPRO – Damping constants for material and DBE / MCE – Mode-frequency analysis as a starter – Spectrum loading application in X, Y, Z directions independently – Vertical spectra are 2/3 of Horizontal (8.4, 6.4.5 of Part-1) – Extract minimum no. of modes in each direction (cumulative 90 % mass – –
excitation or extraction of modes up to 33 Hz) 10.2.5.1; 7.8.4.2 of Part-1 Missing mass correction with Sa corresponding to cut-off frequency (33 Hz) Modal response combinations (CQC, SRSS) 10.2.5.2 • On peak response quantities (e.g. member-forces, displacements, baseshears)
• For widely spaced modes ….SRSS is specified by IS • For closely spaced modes ….Absolute-sum is specified by IS
Mathematical Modeling (9.1)
• •
All elements contributing to lateral load resistance shall be modeled. Structural Analysis is carried out with following (6.2c)
• •
• • •
•
Ec = 5000 √fck (MPa) for RCC
Es = 200,000 MPa for Structural Steel Effect of spatial distribution of mass and stiffness be simulated Choice of 2-D or 3-D modeling is correlated to the behavior of structure Mass modeling to include all the following – Equipments masses • Exchangers, Tanks etc • Electrical panels – Cable-tray, piping accessories – 25 % imposed load as distributed (9.1) – Two mass-models to be used (with and without imposed loads) Damping modeling to include all the following – Damping ratios for RCC, Steel elements modeled as follows
Response Spectrum Analysis (10.2.5)
• Stiffness Modeling… – Study the building layout – Visualize beforehand …vibration patterns during earthquake motion – Can the behavior be simulated by simple models such as …. • Cantilever model (1-D) – e.g. Symmetrical, minor buildings, chimney, stacks
• Plane frame (2-D)
–
– Pipe-racks, regular framing patterns Last recourse may be
• Space frame (3-D)
–
– Asymmetrical, important buildings – Model all lateral load-resisting members e.g columns, primary beams Use empirical / simple formulae for time-period estimation
• Structure without infills • Structure with masonry-infills
– For 2-D / 3-D models : Base-fixity or hinged – Effect of including RC pedestals in modeling steel-frameworks – Calculate base-shear by SCM, empirical formulae on periods
Response Spectrum Analysis (10.2.5)
•
Mass Modeling… – Lumped mass approach suits well with most industrial buildings / structures – STAAD expects weights to be provided – Important locations of mass points are • Beam-column junctions • Major equipment-load-points on primary beams • Major loads fro secondary-beams to Primary beams – In 3-D models, the Masses should be ACTIVE in all three directions Particularly significant for un-symmetrical frameworks, where .. – Coupling between lateral and torsional modes may effect final response • Self-weight of modeled members should be active for mass calculations • Compute total mass in the model by either – Manual calculations, or – PRINT STATIC CHECK command
Mass-Modeling
Loading for mass calculations as under (clause 7.2) 1. 2.
3.
Dead load (7.2.1) of structure SIDL : Super-imposed Dead Load (7.2.2) constituted by • Equipment weight (from MQ, Vendor information) • Associated auxiliaries (e.g. valves) • Accessories that are permanently mounted (e.g. operating / access platforms) • Piping with its accessories (e.g. insulation, stools) Imposed Load (7.2.3) : IS-875 (Part-2) depending on • Type / nature of industrial unit, occupancy of the floor / platform • Refer to GES / CN for clarity on portion of Imposed load to be used as fixed (which would be clubbed with SIDL above)
Response Spectrum Analysis (10.2.5)
• Modal Analysis – Mode-shapes for 3-DOF model (2-D frame) as below
Response Spectrum Analysis (10.2.5)
Response Spectrum Analysis (10.2.5)
Response Spectrum Analysis (10.2.5)
Mass Modeling 2-D frame
3-D frame
Mathematical Modeling
• Damping for dynamic analyses (Table-4, 9.4) – Energy dissipation in structures such as • Internal friction at joints, slipping / sliding at joints • Cracking in RCC, yielding at joints / stressed regions Material of construction as under
DBE
MCE
Structural steel, Aluminum
2%
4%
Reinforced concrete
5%
7%
• In hybrid / structures with different materials (Table-4, note) – Use of lowest damping among all the materials (conservative measure) – Use modal damping (more rational) based on • Weighted strain-energy principle • Also termed as composite damping
Seismic Zoning Of India (Z factor) (Table-2 of Part-1) Seismic Zone
II
III
IV
V
Intensity
Low (VI)
Moderate (VII)
Severe (VIII)
Very severe (IX)
Z (g) PGHA (g)
0.1
0.16
0.24
0.36
Town
Jamshedpur
Mumbai, Pune, Nasik
Delhi, Amritsar
Bhuj, Guwahati
– (Zone-1 is merged with Zone-2)
Aseismic design Concept (R effect)
• A well designed structure can withstand a horizontal force several times the design force due to:
– Over-strength – Redundancy – Ductility • Ductility :As the structure yields, two things happen: – There is more energy dissipation in the structure due to hysteresis
– The structure becomes softer and its natural period increases: implies lower seismic force to be resisted by the structure
– Higher ductility implies that the structure can withstand stronger shaking without collapse
Over-strength Effect (R effect)
• The structure higher load-carrying capacity than the design load due to all the following … – Partial Safety Factors as multipliers on … • seismic loads • gravity loads • materials – Material Properties • Member size or reinforcement larger than required • Strain hardening in materials • Confinement of concrete improves its strength • Higher material strength under cyclic loads – Strength contribution of non-structural elements – Special ductile detailing adds to strength also
Design-Horizontal Load (R effect) Δ Total Horizontal Load
Maximum force if structure remains elastic F el d a o L l a t n o z i r o H l a t o T
Linear Elastic Response
Maximum Load Capacity F y Load at First Yield
F s
Due to Ductility Non linear Response Due to Redundancy
First Significant Yield
Due to Overstrength
Design force F des
0
Δw
Δy
Δmax
Roof Displacement (Δ) Response Reduction Factor
Maximum Elastic Force (Fel ) Design Force (Fdes )
Horizontal Seismic Force (8.3)
If code-specified spectra CSS (8.3.2) are used then Ah = (Z/2).(Sa/g)/(R/I) …… for DBE Ah = (Z/1).(Sa/g)/(R/I) …… for MCE
If SSS (8.3.1) to be used then
Ah = (Sa/g)/(R/I) Ah = 2.(Sa/g)/(R/I)
……for DBE ……for MCE
Where Z : Zone factor (Annex-A or Table-2 of Part-1) Sa/g : (Annex-B or Table-1 of Part-1) I : importance factor for various categories (Table-2, 8.3.2) R : Response reduction factor (Table-3, 8.3.2)
Code Specific Spectra (8.3.2)
Steps to be followed for RSA… • • • • • •
•
Categorization of Structural system (Category 1-4) Basic seismic parameters : – Zone-factor, Importance factor, Response Reduction factor, SSS or CSS ? Stiffness modeling : 2-D or 3-D or even 1-D as an expedient Mass-modeling Mode-frequency analysis: Eigen-value extraction
– Frequency and mode-shape calculations (mode-wise) – Mass-participation factors (Pk ) calculated (mode-wise) Response-Spectrum loading application : as support excitations – DBE and MCE as per Category – Seismic Coefficient Ak for each mode – Modal forces (Qk ) at floor-levels / mass-points Modal-combinations : for internal forces – Mode-wise internal forces extracted – Missing mass correction (Rigid mode) – Modal combinations
• •
Shear-ratio as multiplier on RSA forces Torsional correction : by static method
• • •
Load combinations with non-seismic loads Structural design: Factored load-combinations Serviceability design : Un-factored load combinations
I llustrative E xample of RSA M1 = 0.4141kN
M3
MASS
M2 = 0.3882kN M3 = 0.2558kN
K3
SPRING
calculations.pdf
K1 = 89.506kN/m K2 = 209.78kN/m
TECHNICAL SPECIFICATION.pdf
M2
STAAD-OUTPUT.pdf
K3 = 49.489kN/m K2
M1
MODE-1.avi MODE-2.avi
K1
ACTUAL BUILDING FRAME
MATHEMATICAL MODEL
MODE-3.avi
