Earthquake-resistant Design.pdf

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Earthquake-resistant design Francisco López Almansa

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Objectives  Earthquake-resistant design of buildings and bridges

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Index Effects of seismic inputs on buildings Effects of seismic inputs on bridges Conceptual seismic design of buildings Estimation of fundamental period Types of seismic analyses Single-mode linear static analysis Multi-mode linear static analysis Nonlinear static analysis Performance-based design Nonlinear dynamic (time-history) analysis Nonstructural components Bibliography Internet Sites

4 13 14 36 43 45 55 59 74 91 98 101 103

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Earthquake-resistant design. Francesc López Almansa. Barcelona

Effects of seismic inputs on buildings (1) 

Effect of horizontal components is more severe; vertical analysis is only necessary for long span-length, long cantilever, interrupted columns and prestressed concrete xg: ground displacement (input, excitation) y: absolute displacement x: relative displacement with respect to the base Relative displacement between adjoining stories is termed “interstory drift” Relative displacement and interstory drift report about structural damage Absolute acceleration report about human comfort and non-structural damage Relative displacement and absolute acceleration cannot be minimized simultaneously : structural damage is If buildings are designed very stiff, x  0 and minimized but non-structural damage is not 0: non-structural damage If buildings are designed very flexible, x   xg and is minimized but structural damage is not

        

x xg

Stiff

y xg

xg

Normal

x y

x xg

xg Earthquake-resistant design. Francesc López Almansa. Barcelona

x Flexible xg 4

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Effects of seismic inputs on buildings (2)  Effects of gravity forces on moment-resisting frames  Common design criteria: – – – –

Alike beams. Beam sections depend only on load and span-length Columns are strongest in lowest floors In lowest floors, central columns are strongest In highest floors, alike columns in each floor

Def.

V

N

M

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Earthquake-resistant design. Francesc López Almansa. Barcelona

Effects of seismic inputs on buildings (3)  Effects of lateral forces on unbraced moment-resisting frames  Common design criteria: – Strongest beams and columns in lowest floors – Alike columns in each floor

  

Moment/shear inversion on beams: this effect is higher in bottom levels, outer joints and inner frames Moment inversion precedes shear inversion Shear inversion can lead to tensioned columns and even to uplift

Def.

N

V

Earthquake-resistant design. Francesc López Almansa. Barcelona

M

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Effects of seismic inputs on buildings (4)  Signs of moments in joints without moment inversion:

 Signs of moments in joints with moment inversion:

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Earthquake-resistant design. Francesc López Almansa. Barcelona

Effects of seismic inputs on buildings (5)  Lateral behavior of moment-resisting frames is “awful” and “un-natural”, with huge interstory drift  Bending of beams and columns is an un-natural behavior; axial behavior is much better since strength and stiffness are higher  Strategy of avoiding bending, leads to the concept of bracing  For building frames, there are two major types of braces: diagonal and chevron  In both cases, interstory drift causes only axial tension/compression in braces  Pushing forces are distributed between main frame and bracing: since braces are much stiffer, take most of the force  In buckling analysis of a braced building, non-sway behavior is commonly assumed if interstory drift is reduced more than 80%  Diagonal braces perform slightly better than chevron ones (they are more horizontal), but chevron are frequently preferred for architectural reasons Earthquake-resistant design. Francesc López Almansa. Barcelona

No bracing

Diagonal bracing

Chevron bracing 8

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Effects of seismic inputs on buildings (6)  Gravity loads have no effect on braces (even their own weight)  With this aim, chevron braces are connected to the top beam once most of the load is present  Separate (?) behavior: frame for gravity loads and bracing for lateral actions (wind and seismic)  Braces are always steel-based, but bracing can be used both for concrete and steel buildings  In diagonal bracing, if the compressed brace buckles (bends), the remaining tensioned one can still resist  In chevron bracing, if the compressed brace buckles, the remaining tensioned one can not resist since additional bending is generated in beam (undesired behavior)

No bracing

Diagonal bracing

Chevron bracing Earthquake-resistant design. Francesc López Almansa. Barcelona

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Effects of seismic inputs on buildings (7)  In multi-story buildings, separation between main frame and bracings is not complete, since braces transmit axial forces to columns  Braces in the same bay: huge overcompression in a given column

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Effects of seismic inputs on buildings (8)  If braces are distributed among several bays (mainly in lower stories), axial overcompression is distributed among several columns  Although this solution is better than the one in the previous slide, braces transmit important shear forces to columns; this can generate brittle failure

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Earthquake-resistant design. Francesc López Almansa. Barcelona

Effects of seismic inputs on buildings (9)  In concrete buildings, structural walls (also termed “shear walls”) can play a similar role than braces, although without the localized shear forces transmitted to columns  “Shear buildings”: their lateral behavior is shear-like

Shear behavior

 “Shear-wall buildings”: their lateral behavior is momentlike  Both behaviors are quantitatively and qualitatively different  Walls are better tan frames, but openings are necessary: intermediate solutions are preferred Flexural behavior

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Effects of seismic inputs on bridges (1)  In seismic areas, commonly bridge deck is continuous (hyperstatic) and is rigidly connected to the supporting members (piles and abutments)  Deck big inertia forces are transmitted to piles (piers) and abutments  Broadly speaking, bridges are equivalent to single-story buildings (piles and abutments: columns; deck: slab; no infill walls)  Spatial variation of seismic input is relevant in long bridges  Vertical input is not more relevant than in buildings (except in long-span bridges)  Strong deck / weak pile  Pounding between adjoining segments of deck is relevant

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Conceptual seismic design of buildings (1) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

Lateral resistance and rigidity Plan (mechanical) symmetry Regularity (mechanical and geometrical) along height Compact plan configuration Lightweight (mainly in top stories) Torsion strength and stiffness In-plane rigidity of slabs (rigid diaphragm effect) Ductility Damping Structural redundancy Strong column-weak beam No “short columns” Subjection and strengthening of non-structural elements Tying of footings and pile caps No long cantilevers, no interrupted columns Simple structural behavior Separation to adjoining buildings Earthquake-resistant design. Francesc López Almansa. Barcelona

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Conceptual seismic design of buildings. Lateral resistance (2)  Buildings should be provided with bidirectional lateral strength and rigidity (i.e., in two directions); strength is useful to resist the seismic forces, and rigidity ensures that there are no excessive relative displacements, thus preventing P- effects and collision with adjoining buildings  In framed structures, lateral strength and rigidity are provided both by columns and beams; however, weak columns cannot be compensated with over-resistant beams  In framed structures, lateral strength and rigidity rely on the rigidity of the connections; therefore, the seismic behavior of precast concrete buildings is doubtful  Braces or structural walls are preferred to frames, but are less ductile

Flexural behavior

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Earthquake-resistant design. Francesc López Almansa. Barcelona

Conceptual seismic design of buildings. Plan symmetry (3) Non-structural cladding masonry wall

●R

●G

R●G

Asymmetric!

 Symmetric / asymmetric buildings: the centers of mass G and rigidity R are approximately coincident / clearly eccentric in each floor  Symmetric buildings provide better performance  Centers of mass G of each story refer to the supported (above) weight Earthquake-resistant design. Francesc López Almansa. Barcelona

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Conceptual seismic design of buildings. Uniformity along height (4)  Vertical regularity ensures that damage is uniformly distributed along height  Regular does not mean alike!

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Conceptual seismic design of buildings. Uniformity along height (5)  Non-uniform buildings

Weak first floor

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Conceptual seismic design of buildings. Uniformity along height (6)  Damage concentrated in one story

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Conceptual seismic design of buildings. Compact plan configuration (7)  Plan configuration close to square is preferred  Longer plan size should not exceed shorter one by more than about four times  Seismic joints can be used; are similar to expansion joints but should accept wider motions in two directions  Can be used for bridges and for buildings

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Conceptual seismic design of buildings. Lightweight (8)  Since seismic forces are proportional to mass, lightweight buildings are less affected by earthquakes  Conclusions:   

NO

Timber better than any other material Steel better than concrete Prefabricated concrete awful

 Heavy masses are more dangerous in top part of the buildings:  

No roof swimming pools! (very romantic but hazardous) No “big-top” buildings

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Earthquake-resistant design. Francesc López Almansa. Barcelona

Conceptual seismic design of buildings. Torsion strength and stiffness (9)  Even symmetric buildings can experience torsion (twist) motion, because of both accidental eccentricities and torsion excitation  Therefore, stiffening elements (braces or structural walls) should be located as separated as possible  Centrally-located staircases (typical of tall buildings) do not provide usually enough torsion strength and stiffness

        

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Conceptual seismic design of buildings. Rigid diaphragm (10)  Slabs and roofs should be infinitely rigid in its own plane; this guarantees joint cooperation of all vertical resisting members (columns, braces, walls) and provides a simple and regular structural behavior  Light steel roofs do not posses this quality unless they contain horizontal trusses (in-plane bracing)  Any building slab with a reasonably compact plan configuration behaves as a rigid diaphragm  In-plane rigidity of timber slabs is controversial  ASCE 7-10 (12.10.1 Diaphragm Design) proposes design forces for diaphragm design

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Earthquake-resistant design. Francesc López Almansa. Barcelona

Conceptual seismic design of buildings. Ductility (11)  Ductility (resilience, tenacity) is the capacity of further resistance after the onset of damage (end of linear behavior)  Ductility can be measured in terms of force, displacement or product of both (energy)  Since earthquakes are indirect actions (imposed displacements), force ductility is only of little interest  Ductility can be defined at sectional, member or structural level  Since earthquakes are highly unpredictable, ductility is a convenient quality

Brittle

Ductile Brittle Earthquake-resistant design. Francesc López Almansa. Barcelona

Ductile 24

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Conceptual seismic design of buildings. Damping (12)  Damping is always beneficial  Damping is spread along the building; therefore, it is difficult to provide damping  A convenient strategy is to install energy dissipators; this will discussed in the corresponding part of the course  In base isolated buildings, it is easier to provide damping

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Conceptual seismic design of buildings. Structural redundancy (13)  Statically redundant structures with high degree of hyperstaticity are preferred  Redundant members provide additional safety

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Conceptual seismic design of buildings. Strong column-weak beam (14)  In rigid beam-column connections, failure of beams should precede (by a given factor) failure of columns  In other words, beams protect columns as “structural fuses”  This condition is based on the assumption that columns are more crucial, to structural integrity, than beams  Conclusion: if beams are strengthened, columns should be also strengthened by, at least, the same factor

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Conceptual seismic design of buildings. No “short columns” (15)  Short columns have less capacity to absorb interstory drift than normal ones

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Conceptual seismic design of buildings. Non-structural elements (16)  Non-structural elements (appliances, appendages, antennae, etc.) should be rigidly connected to the main structure as to avoid detaching, falling and overturning  Infill masonry walls can be either detached from the main structure or fixed to it, as to provide stiffness and strength; some design codes (e.g. New Zealand) consider the cooperation of masonry walls

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Conceptual seismic design of buildings. Tying of foundation (17)  Because of the spatial variation of the seismic action, footings and pile caps should be tied together  Foundation slabs usually fulfill this condition  Bottom basement pavement can be considered for this purpose  Usually, seismic design codes indicate the design values of axial forces

xg

x’g

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Conceptual … buildings. No long cantilevers, no interrupted columns (18)

 At risk because of vertical inputs

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Conceptual seismic design of buildings. Simplicity (19)  Complex structures are difficult to comprehend  There can be hidden failure modes  Commonly, software codes are not helpful

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Conceptual seismic design of buildings. Separation (20)  Pounding between colliding buildings (or between several parts of a building separated by joints) is dangerous  Risk is higher is slabs are unaligned  Solutions: separation (gap) or bumpers  Separation should be equal to the sum of both displacements  Displacements must be calculated from nonlinear analysis without accounting for ductility  Torsion should be considered

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Conceptual seismic design of buildings. Wrong? (21) Rem Koolhaas building in Beijing (CCTV Headquarters)

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Conceptual seismic design of buildings. Exercise (No. 8) (22) Provide sketches or pictures (better) of actual buildings fulfilling the following requirements. You can either browse on the Internet, take your own pictures or draw or use sketches. 1. 2. 3. 4. 5. 6. 7. 8. 9.

Buildings with low lateral strength (in one or two directions) Buildings with plan asymmetry Buildings with soft first story Buildings with interrupted columns Adjacent pounding buildings with aligned/unaligned slabs Light steel roofs with and without in-plane bracing Buildings with complex structural system but adequate seismic-resistant configuration Slabs with dubious rigid diaphragm effect Masonry infill walls separated from the main structure

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Estimation of fundamental period (1)  Seismic design depends on many building characteristics, but mainly on fundamental period (in any direction), since it influences spectral ordinates  Therefore, design codes include empirical expressions providing preliminary estimations of the fundamental period  Fundamental period depends on mass and stiffness parameters: (K – 2M) = 0; stiff and light buildings have short periods while flexible and heavy buildings have long periods  Fundamental period depends mostly on building height, being little correlated to horizontal size  The most simplified criterion is TF = N / 10 s (N: number of floors)  This criterion can be only applied to modern and regular concrete or steel frame buildings y designed for seismic regions  In wall or braced buildings, period is shorter  In buildings designed for non-seismic regions, period is longer  In tall buildings, this expression yields too long periods

10 9 8 7 6 5 4 3 2 z

1

x

TFx  1 s; TFy < 1 s

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Estimation of fundamental period (2)  Design spectrum by EC-8

“Singlestory” buildings

Low-rise buildings

High-rise buildings

Mid-rise buildings

Long–span, high–rise bridges

Short–span, low–rise bridges

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Estimation of fundamental period (3)  EC-8. Art. 4.3.3.2.2.(3)  T1 = Ct H ¾; H: height (m) (H  40 m)    

Ct = 0.085 in steel frames Ct = 0.075 in concrete frames and eccentricallybraced steel frames Ct = 0.050 elsewhere; or Ct = 0.075 / Ac1/2; Ac =  [Ai (0.2 + (lwi / H))2] (concrete or masonry walls)

 T1 = 2 d 1/2; d is the top floor lateral displacement (m) under “horizontal gravity forces”  This result arises from assuming that the building behaves as an equivalent SDOF (1st mode) with the period of the first mode and all the mass of the building: 2

2



2

10 9 8 7 6 5 4 3 2 z

1

x y

TFx = 0.085 (31)¾ = 1.12 s TFy = 0.050 (31)¾ = 0.66 s

2

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Estimation of fundamental period (4)  ASCE 7-10, 12.8.2.1  Ta = Ct hnx; hn: height (m)    

Ct = 0.0724, x = 0.8 in steel frames Ct = 0.0466, x = 0.9 in concrete frames Ct = 0.0731, x = 0.75 in steel eccentrically-braced frames or with buckling-restrained braces Ct = 0.0488, x = 0.75 elsewhere

10 9 8 7 6 5

 TF = N / 10 s (N  12, h  3 m)  For masonry or concrete shear wall structures:

4 3 2 z

1

x y

TFx = 0.0724 (31)0.8 = 1.13 s TFy = 0.0488 (31)0.75 = 0.64 s

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Earthquake-resistant design. Francesc López Almansa. Barcelona

Estimation of fundamental period (5)  For estimating the higher mode periods: Ti = TF / (2 i  1) (expression from NCSE-02)  Infill walls. Former EC-8 (part 1.3, art. 2.9.4) proposed empirical expressions for reducing TF because of stiffening effect of non-structural infill walls (provided they are not detached from the main structure): T’1 = (T1b + T1i) / 2  T’1: effective period (to be used for design); T1b/T1i: fundamental period without/with infill walls  Two expressions are provided: 0.065 0.080 1

16

0.075

¾

 Aw: area of walls per story, G: shear modulus of walls, H/B: building height/length (m), W: building weight, n: number of stories  EC-6 states that G = 0.4 E; E = 1000 fk = 1000 K fb fm (MPa)  fb and fm are brick and mortar strength, coefficient K ranges between 0.25 and 0.8, depending on the type of brick units and mortar, for ordinary situations  = 0.7,  = 0.3 Earthquake-resistant design. Francesc López Almansa. Barcelona

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Estimation of fundamental period (6)  Once the building is modelled with the usual software codes, the fundamental period is obtained from eigenvalue (or Ritz vectors) analysis  The obtained values should be similar to the preliminary estimations (15% at most); this can be used for checking modelling errors and for calibrating the model  For severe inputs, damage progresses along the input duration and the fundamental period of the buildings elongates significantly  This circumstance is commonly taken into consideration when generating the design spectra  This is also relevant when evaluating the performance of damaged buildings under expected aftershocks Sd(T)

B

agS0/q

agS TA = 0

C

D A

TB

TC

T

TD

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Estimation of fundamental period (7)  Once the building is modelled with a software code, periods can be approximately obtained by the Rayleigh-Ritz method   . Since modal vectors are orthogonal to  Eigenvalue problem:   mass and stiffness matrices (    0, i  j): ω   ∑   ; fi is the vector that contains the forces that generate i ∑    shape deformation (fi = K i)  This expression can be used to estimate any natural frequency (without knowing the stiffness matrix), provided that we “guess” the modal shape; for the first mode (i = 1), we can assume that fi correspond to the equivalent static forces  Example: 0 0 m 0 0 k   3 1 ω m 0.463 0 0 14 k   2 0 1 2 m 2 3 k 0

 The error is not very relevant (actually, ω  Excess error!

0.445

/ )

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Types of seismic analyses (1)  Linear static analysis (after absolute acceleration response spectra) – Single-mode – Multi-mode

 Nonlinear static analysis (pushover) – Ordinary pushover analysis – Multimodal pushover analysis – Adaptive pushover analysis

 Nonlinear dynamic analysis – Ordinary dynamic analysis – Incremental Dynamic Analysis (IDA)

 Energy-based formulations  Commercial software codes: ETABS, GSA, MIDAS, PERFORM-3D, RISA, ROBOT, SAP, SOFISTIK, STAAD, STRAND7, TEKLA  Advanced commercial software codes: ABAQUS, ANSYS, DIANA, NASTRAN  These lists are non comprehensive  Scientific software codes: OPENSEES, SEISMOSOFT (several programs), ZEUSNL, RUAUMOKO, IDARC

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Types of seismic analyses (2)  Types of seismic analysis according to EC-8:

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Single-mode linear static analysis (1)

W S  ag S a ζ, TF   The dynamic effect of a given V horizontal ground motion in each R direction is represented by static P SU Z C equivalent forces Fk determined to V R generate displacements equal to the m z maximum dynamic ones (“actual”) Fk  V N k k  V: base shear mk z k   W: building weight k 1 Fk  S: soil coefficient  : importance factor m φ m φ  ag: seismic acceleration Fk  V N k 1k  V Tk 1k φ1 M r  Sa(,TF): spectral ordinate mk φ1k   R: response modification k 1 (reduction) factor  Grey coefficients have been already N described V   Fk Earthquake-resistant design. Francesc López Almansa. Barcelona

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Single-mode linear static analysis. Building weight (2)

W S  ag S a ζ, TF   Building weight (“seismic weight”) corresponds to the level of V occupation that is expected when earthquake arises R  European regulations consider permanent (G), variable (Q) and accidental (A) actions; obviously, earthquakes are accidental  In America G/Q are D/L (dead/live)  In Europe there are safety factors for actions (G, Q, A) and for strengths of materials (M, c, s); the  coefficient that is employed in America (playing the same role) is not considered in Europe  In Europe, under normal conditions in ULS: G = 1.35, Q = 1.5, A = 1, M = 1.05 (higher values for connections), c = 1.5, s = 1.15  In Europe, there are combination coefficients (for variable actions): 0, 1, 2 (0 ≥ 1 ≥ 2)  Combination coefficients () depend on the type of action (people for housing, people on a pedestrian bridge, snow, wind, etc.)  For ordinary occupation buildings: 0 = 0.7, 1 = 0.5, 2 = 0.3 (except in congregation areas)  Seismic building weight corresponds to the combination G + E Q  E = 2  (art. 4.2.4 EC-8) 0.5    1  Seismic combinations: G + E Q + EX + 0.3 EY; G + E Q + 0.3 EX + EY. This applies to Europe, America and everywhere Earthquake-resistant design. Francesc López Almansa. Barcelona

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Single-mode linear static analysis. Importance factor (3)  : importance factor depending on the use of building or bridge (also for nonstructural elements)  EC-8 classifies buildings in four importance classes: I (minor), II (ordinary), III (crowded), IV (essential); I = 0.8, II = 1, III = 1.2, IV = 1.4  EC-8 classifies bridges in three importance classes: I (not critical), II (ordinary road and railway), III (crowded and essential); I = 0.85, II = 1, III = 1.3  ASCE 7-10 considers four risk categories (I, II, III, IV); importance factors (Ie) are 1, 1, 1.25, 1.5, respectively  Risk Category and seismicity determine the Seismic Design Category (A, B, C, D)  There are also categories E and F (highest)  The importance factor can be considered linked to the return period of the seismic action to be considered W S  ag S a ζ, TF  V R

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Single-mode linear static analysis. Response modification factor (4)  If the base shear was obtained as V = W S  ag Sa, design forces would be enormous  Our aim is that building is not damaged under a severe shake (475 years return period); unfortunately, this objective is overambitious  Being more realistic, we need to accept some degree of damage  Then, simulating the actual behavior of damaged building would be cumbersome  Solution: to divide the design forces by a factor ( 1) and recover W S  ag S a ζ, TF  the original design objective (linear analysis!) V R  R: response modification (reduction) factor  R is commonly obtained after easy empirical criteria in terms of the type of structure (even its material), plan symmetry, vertical uniformity and overall quality (ductility)  Using R = 1 corresponds to not accept any damage (ambitious objective); the greater R, the higher the accepted damage  Commonly, R ranges between 3 (low ductility) and 8 (very high ductility)  EC-8 states that q  1.5 (even for highly non-ductile structures) Earthquake-resistant design. Francesc López Almansa. Barcelona

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Single-mode linear static analysis. Response modification factor (5)  We should keep in mind that the use of R is merely a “design strategy”; in other words, it is not real, and we cannot “believe our own lie”  For instance, lateral displacements and other similar calculations should be performed “without R” (i.e. R = 1); see art. EC-8 art. 4.3.4  EC-8 considers “behavior factor” q; there are three levels of quality (“ductility classes”): L (“low”, DC L), M (“medium”, DC M) y H (“high”, DC H)  In the American regulation, they correspond to ordinary, intermediate and special structures, respectively  Important warning: expression V = W S  ag Sa / R should not be understood literally (it is not found like that in any design code)  For instance, if the design spectra have an initial growing branch, the value of the initial ordinate is usually kept (except in the EC-8, see eqn. 3.13)  This is equivalent to say that R is not actually constant Sd(T)

B

agS0/q

agS TA = 0

C

T0 corresponds to TB in the EC-8

D A

TB

TC

TD

T

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Single-mode linear static analysis. EC-8 and ASCE 7-10 (6)          

W S  ag S a ζ, TF  EC-8 considers two spectra: Se (q =1) and Sd (q >1) V R EC-8 (art. 4.3.3.2.2): Fb = Sd(T1) m  Fb is the base shear force (V) Sd(T1): ordinate of the design spectrum; it includes the influence of S, , ag, Sa and q (it plays the same role than R) Correction factor :  = 0.85 if T1  2 Tc and N > 2; otherwise,  = 1  accounts for the fact that in buildings with at least three stories, the effective modal mass of the fundamental mode is smaller, on average by 15%, than the total building mass Apparently, the effect represented by  is over-simplified (small change of period can generate huge effect on base shear) Be aware that Sd(0) = 2/3 ag S (instead of ag S) ASCE 7-10: V = Cs W Cs: seismic response coefficient; it includes the influence of S, , ag, Sa and R Earthquake-resistant design. Francesc López Almansa. Barcelona

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Single-mode linear static analysis. Vertical distribution (7)  The base shear force has to be distributed ∑ among all the stories:  EC-8: ∑ ; si is the displacement of i-th story in the fundamental mode shape  ASCE 7-10:



∑



; hi is the

“cumulated” height of i-th story, and exponent k = 1 (straight configuration) if TF ≤ 0.5 s or k = 2 if TF ≥ 2.5 s (parabola). For periods in between 0.5 and 2.5, linear interpolation for k is suggested  Some codes (e.g. New Zealand, Chile) state that the force in the top floor should be bigger; this accounts, in a simplified way, for the higher-mode effects

V

Fk  V

W S  ag S a ζ, TF  R mk φ1k N

m k 1

k

φ1k

V

mk φ1k φ1T M r

Fk

N

V   Fk Earthquake-resistant design. Francesc López Almansa. Barcelona

k 1 51

Single-mode linear static analysis. Horizontal distribution (8)  Single-mode method can be used only for buildings with plan symmetry, therefore, static forces are applied in the centroid of each story  However, accidental torsion effects must be taken into consideration:  

If the building is represented by a 3-D model, 5% accidental eccentricity between centers of gravity and rigidity must be considered (EC-8, ASCE 7-10). This operation is performed inside the software If the building is represented by 2-D models, uniform distribution among equal-rigidity frames is corrected with factor 1 + 1.2 x / Le; outer frames receive 60% more (art. 4.3.3.2.4(2) EC-8). This operation is performed outside the software

 If most of the members providing torsion rigidity (walls and bracings) are concentrated in façades, these criteria are conservative; in the opposite case, they are under-conservative

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Single-mode linear static analysis. P- effects (9)  If the top floor displacements are important, second order analysis might be necessary (P- effect)  General criterion: P- analysis is necessary if, in the columns, the 2nd order moments exceed the 1st order ones more than 10% (as to classify structures sway or non-sway)  Following verifications should be carried out for each story (commonly, first and second are the most critical) ∆

0.1. Where, Px: unfactored  ASCE 7-10 art. 12.8.7: θ gravity force, : interstory drift, Ie: importance factor, Vx: seismic shear force, hsx: story height, Cd: coefficient similar to R (Table 12.2-1)  The objective of Cd is to neutralize the effect of R  Remarkably,  is to be obtained “without R” (e.g. with Cd)  EC-8 art. 4.4.2.2(2): θ



0.1

 EC-8 art. 4.4.2.2(3): if 0.l <  ≤ 0.2, second-order effects may approximately be taken into account by multiplying the relevant seismic action effects by 1 / ( 1  )  EC-8 art. 4.4.2.2(4): coefficient  shall not exceed 0.3  Vtot and dr should be “q free”: ds = qd de (art. 4.3.4, qd = q) 53

Earthquake-resistant design. Francesc López Almansa. Barcelona

Single-mode linear static analysis. Exercise (No. 9) (10)  Exercise (No. 9)  Obtain the equivalent static forces Fk at each story according to EC-8  Assume that the forces are proportional to the floor mass and height  4-story building with square plan layout 10  10 m2. Story height is 3 m (H = 12 m). Seismic acceleration is ag = 0.4 g  Moment-resisting concrete frames in both directions  Soil B; damping factor  = 0.05; S (T) G = 12 kN/m2; Q = 3 kN/m2; E = 0.5 (floors); E = 0 (roof); q = 4 (both directions) a S /q  Type 1 spectrum aS  Hint: easy exercise! (be careful with units) d

g

B

C

0

g

TA = 0

D A TB

TC

Earthquake-resistant design. Francesc López Almansa. Barcelona

T

TD

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Multi-mode linear static analysis. SRSS (1)  r: number of modes to be included in the Wi *  mi*g m1   mr  0.9 mT analysis (in each direction) Wi * S  ag S a ζ i , Ti   Usual criterion: the sum of the equivalent modal Vi  weights covers 90% of the total weight R  Wi*: equivalent modal weight of i-th mode mk φ ik m φ Fik  Vi N  Vi Tk ik  Sa(i,Ti): spectral ordinate for i-th mode φi M r  Quadratic combination (SRSS) mk φ ik  Commonly, higher modes (have small base k 1 shear) influence mostly top stories S  SRSS can be used only if modal periods are well Fik  Wk i S a ζ i , Ti  φ ik separated (Ti / Tj ≤ 0.90) T 2 *

*



mi* 

Vik  FiN    Fi k

(φ i M r ) φ iT M φ i

R

Vk  V    V 2 1k

10

10

10

9

9

9

8

8

8

7

7

7

6

6

+

5 4 3

4

x

y

6

=

5 4

3

z

2 1

5

2 rk

3

2

2

1

1

Fk  Vk 1  Vk 55

Earthquake-resistant design. Francesc López Almansa. Barcelona

Multi-mode linear static analysis. CQC (2) r  If modal periods are not well separated (ratio > 0.90), the possibility of having almost Vk    ij VikVjk simultaneous maxima is higher, and SSRS might i, j1 become unconservative 3  CQC (Complete Quadratic Combination)  Ti   Ti  2 criterion results of incorporating “cross terms” 2 8ζ 1   into the combination  T  T  j  j    ij = ji  ij  2 2 2  If Ti = Tj, ij = 1 (therefore, ii = 1)  T   1   i    4 ζ 2 Ti 1  Ti   Since ij  0, VjkVik must be positive too  T   Tj  Tj   This criterion is just necessary in irregular   j  buildings  Another version (CQC-4) has been proposed

1 10

9

9

8

8

7

7

6 4 3

5 4

y

0.6

2 x

1

10 9 8 6

0.2

4

0

 = 0.05

7

0.4

=

3

z

2 1

6

+

5

0.8

ij

10

5 3 2

0.51

0.6

0.7 0.8 Ti / Tj

Earthquake-resistant design. Francesc López Almansa. Barcelona

0.9

1

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Multi-mode linear static analysis. EC-8 and ASCE 7-10 (3)  EC-8 (4.3.3.3 Modal response spectrum analysis): apart from the usual criterion, any mode with more than 5% modal participation factor (m*i / m) cannot be excluded  If this requirement cannot be satisfied (e.g. in buildings with a significant contribution from torsional modes), the minimum number (k) of modes to be included should satisfy k  3 N ½ (N: number of floors) and Tk  0.2 s  ASCE 7-10 (12.9 Modal response spectrum analysis): where the combined response for the modal base shear (Vt) is less than 85% of the calculated base shear (V) using the equivalent lateral force procedure, the forces shall be multiplied by 0.85 V / Vt (Vt is the base shear from the required modal combination). Therefore, the reduction will not be lower than 0.85  Where the calculated fundamental period T exceeds Cu Ta in a given direction, Cu Ta shall be used instead of T in that direction; Cu: coefficient for upper limit on calculated period (Table 12.8-1). This applies also for Equivalent Lateral Force Procedure

57

Earthquake-resistant design. Francesc López Almansa. Barcelona

Multi-mode linear static analysis. Asymmetric buildings (4)  Analysis of asymmetric buildings for excitation in x direction  Each mode contains components of horizontal displacement in x and y directions, and torsion rotations   The sum of the modal masses should exceed 90% of the total mass in each direction (x, y and )  Displacement vector corresponding to a generic mode i: 2  xi  T  Ti   i φ i q   y  Γ i  φTi M r q i  S a Ti , ζ   i i φi M φi  2π φ   i

Fx ik  Wk i S a Ti , ζ i  φ x ik

S R

r  (1,...,1, 0 ,...,0, 0,...,0)   

Fy ik  Wk i S a Ti , ζ i  φ y ik

N

S R

N

T

N

 φ xi    φ i   φ yi  φ   i 

S  Fx ik: Force in x direction, mode i, story k R  Fy ik: Force in y direction, mode i, story k  Tik: Torque, mode i, story k a2  b2 Wk  mk g I k  mEarthquake-resistant design. Francesc López Almansa. Barcelona k 58 12

Tik  I k i S a Ti , ζ i  g φ φ ik

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Nonlinear static analysis. Definition (1) 

  

Pushover analysis of a construction (building or bridge) consists of investigating its behavior under constant gravity loads and growing lateral forces Vertical forces correspond to seismic excitation (G + E Q) Horizontal forces grow keeping the same vertical variation pattern Common patterns: uniform, triangular or modal (1st mode shape)



V/W

Capacity curve

Vu / W

Fk

Vy / W /H

V   Fk

 Subindexes y and u account for yielding and ultimate, respectively  Damage and displacement are clearly correlated, force and damage not so clearly 59

Earthquake-resistant design. Francesc López Almansa. Barcelona

Nonlinear static analysis. Plastic hinges (2)

±

 Nonlinear behavior of structural elements is commonly represented by plastic hinges, usually located at their ends  There are plastic hinges of V, N, T, M, y “N + M”  Nonlinear behavior of plastic hinges is commonly described by moment-curvature (or rotation) or force-displacement laws Failure Plastification

Earthquake-resistant design. Francesc López Almansa. Barcelona

Residual strength

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Nonlinear static analysis. Plastic hinges (3)  Design codes (e.g. FEMA 356) propose moment-curvature (or force-displacement) laws for the most common situations  The initial branches of these laws are obtained from theoretical (local) analysis and the plastic branches are selected as the envelopes of the experimental hysteresis loops  These laws are implemented in the major software codes  For unusual or new members, there are no available experiments; therefore, tests and theoretical analysis are required (in this order)

61

Earthquake-resistant design. Francesc López Almansa. Barcelona

Nonlinear static analysis. Plastic hinges (4)  Typical moment-curvature law  Q / Qy: M / My; : rotation ( / l: curvature, where l is the hinge length)  AB: linear elastic branch; BC: plastic branch; CDE: residual branches (to be determined after testing)  Before yielding (B), rotation is zero; however, some rotation (y) is assumed for point B  For beams: y = My L / 6 E I; for columns: y = My L / 6 E I (1  N / Ny). This the “chord rotation”  Noticeably, the initial flexibility of the moment-rotation law (AB branch) should not be considered in the global analysis; fully rigid connection must be considered instead My

M / My

My Beam

 / y Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear static analysis. Plastic hinges (5)  Concentrated Plasticity. Plastic hinges can be either zero-length or a fixed length can be assigned to them; there are a number of simple empirical expressions fcm = fck + 8 (MPa)  Distributed Plasticity. Fiber Models  Average values of material parameters instead of characteristic ones  No safety factors!

Earthquake-resistant design. Francesc López Almansa. Barcelona

63

Nonlinear static analysis. Initial cracking (6)  In reinforced concrete, members are commonly cracked form the very beginning, i.e. for zero pushing forces  FEMA 356 indicates percentages of reduction of stiffness for beams, columns, slabs and walls

 Meaning of subindexes; c: concrete, g: gross, w: web, s: steel. Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear static analysis. Case (7)

    

“Strong column-weak beam” condition is basically fulfilled Hinges in the bottom section of the bottom columns might be not realistic Beams should not be uniform along height There is moment inversion in the bottom stories Since the behavior is nonlinear, the bending moment laws of the 1st floor columns are different than foreseen by linear analysis

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear static analysis. N-M (8)  N-M interaction diagram for reinforced concrete

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear static analysis. Example (9)  Single-bay single-story moment-resistant steel frame  Gravity load 30 kN/m (beam); steel S275 (fy = 275 MPa); beam IPE 450 (Wpl = 1702 cm3, My = 468.05 kNm); columns HEB 300 (Wpl = 1869 cm3, My = 513.96 kNm)  The structural behavior is linear, except for flexural plastic hinges at member ends  No reduction in yielding moment in columns due to interaction with axial force  In the top joints, hinges will appear earlier in beam than in columns  Simplified hinge behavior: infinite initial stiffness and horizontal plastic branch (no strain hardening)  First-order analysis; also members are assumed to be infinitely rigid in axial direction

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear static analysis. Example (10)  Bending moments laws under gravity and pushing loads  First two plastic hinges appear almost simultaneously at the right top and bottom joints

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear static analysis. Example (11)  Combined bending moments law under gravity and pushing loads  Horizontal pushing force and displacement are 283.7 kN and 45.48 mm, respectively

Earthquake-resistant design. Francesc López Almansa. Barcelona

69

Nonlinear static analysis. Example (12)  Bending moments law under pushing load; to be added to the previous law  Third plastic hinge appears at the left bottom joint  Horizontal pushing force and displacement are 54.95 kN and 21.9 mm, respectively

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear static analysis. Example (13)  Bending moments law under pushing load; to be added to the previous law  Fourth plastic hinge appears at the left top joint  Horizontal pushing force and displacement are 57.36 kN and 113.2 mm

71

Earthquake-resistant design. Francesc López Almansa. Barcelona

Nonlinear static analysis. Example (14)  Capacity curve

Force (kN)

400

300

and? 200

ASCE 7-10 does not consider pushover as a valid design strategy

100

0 0

50

100

150

Displacement (mm) Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear static analysis. R factor (15)      

First utility of pushover analysis: Equal-displacement approach Blue point: design force (theoretical onset of yielding) Purple point: design force (actual onset of yielding) Red point: collapse force (no stiffness) Capacity curves provide estimations of response modification factor (R or q) These calculated values of R will be higher than default ones

R

Fe Fe Fu Fe   Ω Fy Fu Fy Fu q

FEMA-356

αe αe αu  α1 α u α1

Earthquake-resistant design. Francesc López Almansa. Barcelona

EC-8

73

Performance-based design. Definition (1)  PBD (Performance-Based Design)  American regulations (FEMA 356) propose four Performance Levels: FO (“Fully Operational”), IO (“Immediate Occupancy”), LS (“Life Safety”) and CP (“Collapse Prevention”)  European regulations (EC-8 Part 3) propose three Limit States: DL (“Damage Limitation”), SD (“Significant Damage”) y NC (“Near Collapse”)  DL  IO, SD  LS, NC  CP  Performance Levels and Limit States have been proposed for retrofit but can be also used for new construction

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. FEMA 356 (2)  FEMA 356 2000 (“ ... seismic rehabilitation of buildings“)  FO (“Fully Operational”): no damage at all.  IO (“Immediate Occupancy”): only very limited structural damage, the construction remains safe to occupy, the structure essentially retains the pre-earthquake design strength and stiffness, the risk of life-threatening injury is very low, and there is no permanent drift.  LS (“Life Safety”): damage to structural components but retains a margin against partial or total collapse, the risk of life-threatening injury is low, and it should be possible to repair the structure.  CP (“Collapse Prevention”): damage to structural components such that the structure continues to support gravity loads but retains no margin against collapse. Structural damage potentially includes significant degradation in the stiffness and strength of the lateral-force-resisting system, large permanent lateral deformation, and (to a more limited extent) degradation in vertical-load-carrying capacity. The structure may not be technically practical to repair. Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. EC-8 Part 3 (3)

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. PBD vs T (4)  In EC-8, correspondence between Limit States and return periods: DL  225 years, SD  475 years, and NC  2475 years  In FEMA 356, three objectives are stated: Basic Safety, Enhanced and Limited  Basic Safety Objective cares only for LS (475 years) and CP (2475 years)  Enhanced Objectives care for LS (475 years), CP (2475 years) and FO and IO (72, 225 or 475 years); also FO, IO or LS alones (2475 years)  Limited Objectives care for LS (475 years) or CP (2475 years); LS (72 or 225 years) and CP (72, 225 or 475 years)

72 225 475 2475

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. PP (TD) (5)  Each “performance point” (or “target drift”) represents the effect on the building or bridge (in terms of force and displacement) of a ground motion whose severity corresponds to the return period associated with the limit state LS

IO CP

Performance points

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. Acceptability (6)  Research projects HAZUS (in America) and RISK-UE (in Europe) have calibrated damage in terms of yielding (y) and ultimate (u) levels  ND: No Damage; SD: Slight Damage; MD: Moderate Damage; ED: Extensive Damage; HD: Heavy Damage

SD

MD

ED

HD

ND LS

CP

IO

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. Sa Sd (7)  Absolute acceleration and relative displacement response spectra Sv(,T) = Sa(,T) (T / 2)

Sd(,T) = Sa(,T) (T / 2)2

Sd

TB

TC

TD

TB

TC

TD

Sa

T

2.50

1

Earthquake-resistant design. Francesc López Almansa. Barcelona

80 T

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Performance-based design. ADRS (8)  Demand is presented as spectrum  Instead of Sa(T) and Sd(T) vs. T, Sa(T) vs. Sd(T) (ADRS, Acceleration Displacement Response Spectrum)

Sa(T)

T < TB

T = TB

T = TC

2.50

T > TC

 < 0.05  = 0.05

 > 0.05 T = TD

1

Sd(,T) = Sa(,T) (T / Sd(TB;0.05)

Sd(TC;0.05)

2)2 Sd(TD;0.05)

Sd(T)

81

Earthquake-resistant design. Francesc López Almansa. Barcelona

Performance-based design. ATC-40 (9)

 Intersections between capacity curve and demand spectra are the “performance points” (or “target drifts”)  Conversion factors between both charts: Sa 

V/W

φ

V /W





2

V /W m1* / mT

Mr / rT M r φ M φ1 Capacity   S d  curve  φ1T M r 1 φ1T M φ1 φ1N  1 T 1 T 1

Iterative procedure:

/H

Sa(T)

 < 0.05  = 0.05

 = 0.05  = 0.08  = 0.10

 > 0.05 Sd(T) Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. ATC-40 (10) 1. 2. 3.

Procedure A (8.2.2.1.2) Trial performance point (api, dpi) Equal-energy bilinear approximation providing the yield point (ay, dy) Effective damping ratio corresponding to trial point (%): β 5 

4. 5. 6.

Coefficient  is described in Table 8-1 (0.33   1) If yield and trial points are coincident, eff = 5 Reduce the demand spectrum with factors SRA and SRV

7.

SR

.

. .



; SR

.

. .



8. If eff = 5, SRA = SRV = 1 9. Minimum values of SRA and SRV apply (Table 8-2) 10. If the new intersection point does not fit point (api, dpi) with 5% tolerance, return to step 1 selecting the intersection as new trial point 11. Repeat until convergence

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. ATC-40 (11)   

Procedure A (8.2.2.1.2) If trial and yield points are aligned with the origin, eff = 5 The higher the angle between both straight lines, the higher the value of eff In saw tooth capacity curves, the bilinear approximation is generated for the (degraded) branch the trial point belongs to

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. N2 (12)        

N2 method (EC-8) M ; N = 1 m∗ T M r r F* = m* g Fb = F* ; dn = d*  A: collapse point ∗ ∗ ∗  ½ ∗ ∗ ∗ is the area under the capacity curve

∗/  ∗ 2 π  Fy* = k* dy*



φT M r φT M φ

∗

85

Earthquake-resistant design. Francesc López Almansa. Barcelona

Performance-based design. N2 (13)  N2 method (EC-8) ∗

 d  ∗

Demanding ADRS

∗

∗

(short periods range): ∗ ∗ (elastic) If F ∗  ∗ ∗ d d ∗ ∗ If F ∗ (anelastic) ∗ d d∗ 1 1 ∗  d∗ ∗

Capacity curve

∗

Demanding ADRS

F∗ 

∗ 

(long and medium periods): d∗ d∗ ∗  d 3 d∗ Earthquake-resistant design. Francesc López Almansa. Barcelona

Capacity curve

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Performance-based design. N2 (14)

 N2 method (EC-8)  If d∗  d∗ (the considered input does not generate collapse), an iterative procedure might be used:  In the bilinear capacity curve d∗ is replaced by d∗ ; d∗ is accordingly modified

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. Examples (15)  Wide-beam buildings in Spain

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. Examples (16)  Thin-wall beam buildings in Peru

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Performance-based design. Examples (17)  Steel buildings in Colombia

Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear dynamic analysis. Definition (1)  Seismic design based on dynamic (time-history) analysis consists in representing expected seismic inputs by accelerograms  Since actual behavior of structures under severe inputs (i.e. corresponding to large return periods) is highly nonlinear, dynamic analysis must be also nonlinear  This formulation is the most natural one; also, apparently, is more accurate than using spectra  However, there are two major problems:  There is a big variety of expected inputs (amplitude, frequency content, pulses, duration, etc.)  Nonlinear dynamic analyses can be extremely costly, in terms of computational effort

 Design codes define the number and characteristics of the accelerograms to be employed  Since actual seismic excitations are 3-D (or even 6-D, if we account for rotational components of ground motion), dynamic analysis should consider, at least, the joint excitation of both horizontal components of input ground motion  For this purpose, both accelerograms should be exactly synchronized  The same accelerogram may not be used simultaneously along both horizontal directions (EC-8 3.2.3.1.1(2)) Earthquake-resistant design. Francesc López Almansa. Barcelona

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Nonlinear dynamic analysis. Accelerograms (2)  Accelerograms can be either recorded (historical), simulated (from the known seismogenic mechanism) or artificial (fitting design spectra)  Simulated accelerograms are (almost always) unfeasible  EC-8 3.2.3.1.3. Requirements for the artificial accelerograms: (i) stationary phase at least 10 s, (ii) minimum 3 accelerograms, (iii) the mean of the zero-period spectral ordinates (Sa(0)) should not be smaller than ag S, and (iv) in the range 0.2 T1  2 T1, no value should be under 90% of design elastic response spectrum  ASCE 7-10 16.1.3. Similar than (iv) from EC-8, but with 1.5 T1 instead of 2 T1  This range accounts for the influence of higher modes (range 0.2 T1  T1) and the period elongation during the shake (ranges T1  2 T1 or T1  1.5 T1)  Nowadays, nonlinear dynamic analysis is not yet widely employed, despite the powerful computational tools that are commonly available  A good spectrum-based analysis is better than a poor dynamic analysis  Dynamic analysis is only justified: (i) in research, (ii) for highly complex or very important structures, (iii) when required by design codes (e.g. in base isolation), and (iv) when the results from simplified analyses (i.e. spectra-based) are not acceptable

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Nonlinear dynamic analysis. Computational issues (3) Nonlinear equation of motion: Solution of this equation (and of the linear one) is known as “time-history analysis” Same models than for pushover analysis can be used Response should be obtained, in discrete time, by a step-by-step procedure; commonly, time step (discretization period or sampling period: t) is constant along the whole duration of analysis If structural behavior is linear (Q(x) = K x), response for next instant is obtained directly assuming an interpolation criterion in the interval; each criterion leads to a different calculation algorithm If structural behavior is nonlinear (Q(x) = Kt x, where is the Kt tangent stiffness matrix), stiffness at the beginning and at the end of interval is different and, therefore, response for next instant cannot be obtained directly (even assuming an interpolation criterion in the interval) and calculation must be iterative For both linear and nonlinear analysis, the most employed algorithm is Newmark Selection of time step is a crucial issue; usual criteria for linear analysis do not apply for nonlinear analysis; significantly shorter time steps are required The faster the excitation (high frequency) and the stiffer the structure (short period), the shorter the required time step The only valid rule for time step selection is to start with a coarse time discretization (t = 0.01 s) and then refine it (lowering t) until obtaining “time convergence”; values below 0.001 s are extremely frequent

     

   

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Nonlinear dynamic analysis. Computational issues (4) 0.01 (s)

0.001 (s)

0.0005 (s)

Storey

3

EXAMPLES OF SENSITIVITY TO t

2

1 0

10

20 Energy (kJ)

30

40

Pounding Force (kN)

4000 dt = 0.01 s dt = 0.001 s

Hysteretic energy and pounding force in a colliding building

dt = 0.0005 s

2000

Time (s) 0 8

8.05

8.1

8.15

8.2

8.25

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Nonlinear dynamic analysis. IDA (5)  IDA “Incremental Dynamic Analysis” is a kind of dynamic pushover analysis; a given structure undergoes inputs scaled with different (growing) factors  There are two types of IDA analysis: for a single input or for several inputs  IDA Curves are similar to capacity curves; vertical axis refers to any parameter characterizing input severity, and horizontal axis contains top floor displacement (or similar magnitudes)  In each dynamic analysis, the structure “is reset” (e.g. is undamaged)

Multi-input

Single-input

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Nonlinear dynamic analysis. Structural resurrection (6)

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Nonlinear dynamic analysis. Example (7) 100

NO WALLS

Displacement (mm)

LOW WALL DENSITY HIGH WALL DENSITY

50

0 0

2

‐50

4

6

8

10

Time (s)

Permanent displacement!

‐100 97

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Nonstructural components (1)  Non structural elements (appendages) can be antennae, façades, cladding panels, tanks, machinery, furniture, appliances, etc.  Those elements must be seismically designed  The seismic input of the device depends on its position in the building; the higher the worst (the seismic excitation is progressively amplified along the building height)  Therefore, the roof is the most critical (dangerous) location

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z

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Nonstructural components. EC-8 (2)  Article 4.3.5 (EC-8 1) specifies the seismic analysis of non structural elements  Fa = Sa Wa a / qa; Fa: seismic design force; Wa: element seismic weight; a = 1 or 1.5; qa = 1 or 2  Sa: floor spectra;  = ag / g; S: soil coefficient; z: height of the point the element is attached; H: building height; Sa ≥  S; T1 / Ta: fundamental period of building / element  The higher the point where the element is installed, the greater the seismic excitation; if z = H (roof appendage): (T Sa a) = Sa(2 T1  Ta); Sa(0) =  S 2.5; Sa(T1) =  S 5.5; Sa(4.32 T1) = 0; Sa() =   S 0.5 5

    3 1  z     H Sa  α S   0.5 2   1  1  Ta     T1 

Floor spectrum

4

Sa

3 2 1 0 0

1

2

3

Ta / T1

4

99

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Nonstructural components. ASCE 7-10 (3)  Chapter 13 (ASCE 7-10) specifies the seismic analysis of non structural elements  A list of nonstructural components which are exempt from verification is included .







1

2

; 0.3







1.6





 Fp: seismic design force; ap: component amplification factor (ranges between 1 and 2.5, plays the role of spectral ordinate); Wp: component operating weight; Rp: component response modification factor (1 to 12); Ip: importance factor  Alternative:





; 0.3







1.6





 Ax: torsional amplification factor; ai: acceleration at level i  In addition, the component shall be designed for a concurrent vertical force ±0.2

 Where the weight of a nonstructural component is greater than 25% of the building seismic weight, it shall be classified as a non-building structure and shall be designed (15.3.2) jointly with the building

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Bibliography. Books                 

Akiyama H. Earthquake-Resistant Design for Buildings. Tokio University Press 1988. Ambrose J.E., Vergun D. Diseño simplificado de edificios para cargas de viento y sismo. Limusa 1986. Bazán E., Meli R. Diseño sísmico de edificios. Limusa 2002. Bozorgnia Y., Bertero V.V. Earthquake Engineering: from Engineering Seismology to Performance-Base Engineering. CRC Press 2004. Bozzo L.M., Barbat A.H. Diseño sismorresistente de edificios. Ed. Reverté 2000. Chandrasekaran S. et al. Seismic Design Aids for Nonlinear Analysis of Reinforced Concrete Structures. CRC Press 2010. Datta T.K. Seismic Analysis of Structures. J. Wiley 2010. Dowrick D.J. Earthquake Resistant Design for Engineers and Architects. J. Wiley 1977. Fajfar P., Krawinkler H. Seismic Design Methodologies for the Next Generation of Codes. Balkema 1997. García L.E. Dinámica Estructural Aplicada al Diseño Sísmico. Universidad de Los Andes (Bogotá) 1998. Naeim F. The Seismic Design Handbook. Van Nostrand Reinhold 2002. Newmark N.M., Rosenblueth E. Fundamentos de ingeniería sísmica. Diana 1978. Paulay T., Priestley M.J.N. Seismic Design of Reinforced Concrete and Masonry Buildings. John Wiley 1992. Priestley M.J.N., Seible F., Calvi G.M. Seismic Design and Retrofit of Bridges. John Wiley 1996. Priestley M.J.N., Calvi G.M., M.J. Kowalski. Displacement-Based Seismic Design of Structures. IUSS Press 2007. Rosenblueth E. Design of Earthquake Resistant Structures. Pentech Press 1980. Wakabayashi M. Earthquake Resistant Design for Buildings. McGraw-Hill 1986. Earthquake-resistant design. Francesc López Almansa. Barcelona

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Bibliography. Codes

NCSE-02. Norma de Construcción Sismorresistente: Parte General y Edificación. Ministerio de Fomento 2002. NCSP-07. Norma de construcción sismorresistente. Ministerio de Fomento 2007. Seismic Provisions for Structural Steel Buildings. AISC (American Institute on Steel Construction) 2005. Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications. AISC (American Institute on Steel Construction) 2005. FEMA 356. Pre-standard and commentary for the seismic rehabilitation of buildings. Federal Emergency Management Agency 2000. ACI 318-11. Building Code Requirements for Structural Concrete. ACI (American Concrete Institute ) 2011. ASCE/SEI 7-10. Minimum Design Loads for Buildings and Other Structures. ASCE (American Society of Civil Engineers) 2010. Fardis M.N., Carvalho E., Elnashai A., Faccioli, Pinto Plumier A. Designers’ Guide to Eurocode 8. Thomas Telford 2005.

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Internet Sites            

http://www.asce.org/ http://www.concrete.org/ http://www.aisc.org/ https://www.atcouncil.org/ http://www.fema.gov/ http://peer.berkeley.edu/ http://earthquake.usgs.gov/ http://mceer.buffalo.edu/ http://eurocodes.org.ua/ http://www.roseschool.it/ http://mae.cee.illinois.edu/software_and_tools/zeus_nl.html http://www.civil.canterbury.ac.nz/eq/eqeng.shtml

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