Seismic Design of Steel Structures - College of Engineering 9 (2013 filled-in... · Seismic Design...

CE470 (2013 S16-09) IX - 1

Chapter 9

Seismic Design of Steel Structures_________________________________________________________________________________

9.1 S16-09: Clauses Clause 27: Seismic Design

(ductility of frames)27.1 General Rd Ro27.2 Type D (ductile) moment-resisting frames 5.0 1.527.3 Type MD (moderately ductile) moment-resisting frames MRFs 3.5 1.527.4 Type LD (limited-ductility) moment-resisting frames 2.0 1.327.5 Type MD (moderately ductile) concentrically-braced frames 3.0 1.327.6 Type LD (limited-ductility) concentrically-braced frames Braced 2.0 1.327.7 Type D (ductile) eccentrically-braced frames Frames 4.0 1.527.8 Type D (ductile) buckling-restrained braced frames 4.0 1.227.9 Type D (ductile) plate walls 5.0 1.627.10 Type LD (limited-ductility) plate walls 2.0 1.527.11 Conventional construction 1.5 1.327.12 Special seismic construction. -tbd -tbd

Annexes: Annex J: Ductile moment-resisting connections Annex L: Design to prevent brittle fracture

NBCC-2010: Division B: Section 4.1.8. Earthquake Load and EffectsCE-321 Class Notes Chapter 3 (2013)Reference publications:

FEMA (2000) Recommended seismic design criteria for new steel moment framebuildings, FEMA 350, Federal Emergency Management Agency, Washington, DC. Hamburger, Ronald O., Krawinkler, Helmut, Malley, James O., and Adan, Scott M.(2009). "Seismic design of steel special moment frames: a guide for practicingengineers," NEHRP Seismic Design Technical Brief No. 2 available from:

http://www.nehrp.gov/pdf/nistgcr9-917-3.pdf

THESE NOTES ARE SUBJECT TO CHANGE WITHOUT NOTICE. REPORT ERRORS AND OMISSIONS to : [email protected]

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9.2 Review of concepts in Earthquake Engineering

9.2.1 Basic definitionsEarthquake Engineering deals with applying civil engineering design principles toreduce life and economic losses due to earthquakes, (i.e. to mitigate seismic risk).Seismic risk can be defined as the probability of losses incurred by earthquakes withinthe lifetime of a structure. The two main components of seismic risk are:

a) Seismic hazard : This component of risk is determined by nature and cannot bereduced. There are several damaging effects due to earthquakes including: groundshaking, landslides, surface ruptures and liquefaction. The level of seismic hazardcan vary from having frequent low intensity earthquakes to having rare severeearthquakes.

b) Structural vulnerability : This component depends on the structuralconfiguration and properties and thus can be reduced by proper seismic design ofstructures. Steel structures have several inherent characteristics that areadvantageous for seismic design. At the top of the list is the high ductility of steelcompared to other construction materials. Ductility is the ability of the structure todeform past yielding without significant strength deterioration. However, to makeuse of the advantages of steel as a construction material for seismic design, thedesign engineer has to be familiar with the code design and constructionprovisions. In essence, code provisions are set to avoid different sources ofstructural vulnerability which include: inappropriate detailing inappropriate design poor connections irregularities in structural configuration (in plan and/or in elevation) soft storey (laterally) pounding against nearby structures failure to conform to the intent of the design

9.2.2 Nature of EarthquakesThere are several causes for earthquakes: Some are caused by volcanoes which may be atriggering factor for earthquakes, or there can be induced seismicity resulting fromunderground explosions. However, a cause which is believed to be the main reason formost earthquakes is referred to as plate tectonics. Compared to the radius of the earth,the thickness of the earths crust is relatively thin. The earths crust is composed ofseveral tectonic plates which move relative to each other about 50 mm per year.


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The roughness of the surfaces and edges of tectonic plates, and the huge pressuresinvolved, cause potential sliding and slipping movements to generate friction forces largeenough to lock-up surfaces in contact. Instead of sliding past each other, rock in a plateboundary area absorbs greater and greater compression and shear strains until it suddenlyruptures. At rupture, the accumulated energy (strain energy) within the strained rock massreleases in a sudden manner with a violent jarring motion. This is an earthquake.

Most earthquakes are caused by movement between tectonic plates: 70% around theperimeter of the pacific plate; 20% along the southern edge of the Eurasian plate and 10%cannot be explained by plate tectonics, some of which are intra-plate (within the plate).

The surface along which the crust of theearth fractures is an earthquake fault.The point in the fault plane surface areaconsidered the centre of energy release istermed the focus. The projection of thefocus up to the earths surface is called theepicenter. The distance between the focusand the epicenter is known as the focaldepth.


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When a fault ruptures, seismic waves propagate in all directions from its focus. The twotypes of underground waves which are generated by a fault rupture are: P waves (Primary waves), also known as compression waves; they push and pull

the soil through which they pass. S waves (Shear waves); they move soil particles side-to-side either horizontally or

vertically. This shear effect is of most concern and damaging to buildings.There is also a surface-rippling wave known as a Rayleigh wave.The response of the soil affects the features of the earthquake waves felt by the buildings.For example: deep layers of soft soil, as may be found in river valleys, significantlyamplify shaking and also modify the frequency content of seismic waves by filtering outhigher frequency excitations.

9.2.3 Earthquake Magnitude (Richter) and Intensity (Mercalli)Earthquake magnitude defines the amount of energy released by the earthquake. Thus,earthquake magnitude is a quantitative measure of earthquake severity, commonlymeasured by the Richter scale (1935). Each earthquake is assigned only one magnitudevalue. This is determined by seismologists from seismograph records. The Richter scaleis a magnitude scale for earthquakes which relates logarithmically to the amount ofenergy released. This means that an increase of 1 in the number on the Richter scalerepresents a ten-fold (101) increase in amplitude and a 30-fold increase indischarged energy.

( 103)


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On the other hand, earthquake intensity is a qualitative description of the earthquakeseverity. Accordingly, earthquake intensity varies according to the location whereshaking is felt. Factors affecting earthquake intensity at a certain location includes:earthquake magnitude, epicentral distance and soil conditions. The most recognizedintensity scale for earthquakes is the Modified Mercalli Intensity Scale summarized inthe following Table.

Intensity Description

I to III Not felt, unless under special circumstances.

IV Generally felt, but not causing damage.

V Felt by nearly everyone. Some cracked plaster. Some crockery broken oritems overturned.

VI Felt by all. Some fallen plaster or damaged chimneys. Some heavyfurniture moved.

VII Negligible damage in well designed and constructed buildings through toconsiderable damage in construction of poor quality. Some chimneysbroken.

VIII Depending on the quality of design and construction, damages rangesfrom slight through to partial collapse. Chimneys, monuments and wallsfall.

IX Well designed structures damaged and permanently racked. Partialcollapses and buildings shifted off their foundations.

X Some well-built wooden structures destroyed along with most masonryand frame structures.

XI Few, if any masonry structures remain standing.

XII Most construction is severely damaged or destroyed.


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Performance levels

Fully operational Collapse

Hazardlevel

Very rare

Frequent

Performance objective(s)

Risk Vulnerability PBEE Quantif ication Response SpectrumEQ. Eng. Hazard

Minor

Severe

Performance Based EarthquakeEngineering

9.2.4 Philosophy of Seismic-Resistant DesignGiven the uncertainties in determining the degree of severity of earthquakes and forobvious economical reasons, it is unrealistic to design a structure to respond elasticallyduring a major earthquake. Thus, the philosophy of seismic design for major earthquakesis collapse prevention rather than damage prevention.For less severe earthquakes, lowerlevels of damage are accepted. Asthe importance of the structureincreases, the criteria of acceptedperformance are more stringent asshown in the next figures taken fromSEAOC (Structural EngineersAssociation of Northern California).

Operational Immediateoccupancy

Life safety Structuralstability

Fullyoperational

Operational Life safety NearCollapse

Frequent

(Low Intensity)

Occasional

Rare

Very rare

(Severeintensity)

Performance levels

Seismichazardlevels

Vision 2000 (SEAOC 1995)

Risk Vulnerability PBEE Quantif ication Response SpectrumEQ. Eng. Hazard

Performance Objectives

Hazard

Level

Seismic

Hazard

Levels


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9.3 Seismic Forces on Buildings9.3.1 Nature of Seismic-Induced ForcesThe ground motion caused by earthquakes is experienced by the building as accelerationat the base. The masses of the building resist the ground motion acceleration and inertiaforces are generated. The inertia force can be quantified using Newtons second law ofmotion aMF where M is the mass of the building, and a is the acceleration ofthe mass caused by ground motion acceleration. Inertia forces are generated throughoutthe building on every element and component. However, most of the mass of the buildingis concentrated in its floors and roof. For this reason and for simplicity of design,engineers assume inertia forces act at the center of mass of the roof and floors aslumped masses.It is worth noting the similarities and differencesbetween seismic-induced and wind-induced forces:

Seismic-induced forces Wind-induced forcesmainly lateral- some earthquakes have

significant verticalcomponents ( ofhorizontal motion).

mainly lateral- near-vertical wind-induced

suction forces acting on roofsnormally have little impact onthe building behavior

dynamic- peak seismic-induced forces

act for fractions of a second

dynamic- strong wind gusts can last for

several seconds- act within the building mass - act external to the building

Seismic:InertiaForces

Loading

Wind Seismic


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9.3.2 Factors affecting Seismic-Induced Forces(a) Building weight:When an object is subjected to a dynamic action, the inertia force is proportional to itsmass according to Newtons second law of motion. Thus, as the weight of an objectincreases, the inertia force increases for a given level of acceleration. Buildings withheavier-weight structural materials are subjected to higher levels of seismic-inducedforces than lighter ones. It is therefore advisable to use lighter weight construction inseismic prone areas (less mass gets excited).(b) Natural periods of vibration:A natural period of vibration is the time for one complete vibration cycle that a structurewould undertake when subjected to an initial dynamic stimulus and then left to oscillatefreely. The lowest frequency has the largest natural time period of vibration and is calledthe 1st mode or fundamental mode of the structure. Depending on the structural andgeometrical configuration of the structure, there may be other periods corresponding tohigher-order (2nd, 3rd, ...) modes. It is noteworthy that the contribution of the first(fundamental) mode of vibration is the most prominent and important for low-rise andmedium-rise buildings.

(c) Damping:Damping is a resistance to free vibration and defines the energy-dissipation mechanismwhich steadily diminishes the amplitude of vibration. Damping in structures is mainlycaused by internal friction within building elements. The type of construction materialaffects the degree of damping. There are many forms of damping. Viscous damping isvelocity dependent. Currently, the most popular form is proportional damping (massand stiffness dependent); it is also known as: Rayleigh, classical, orthogonal ormodal damping. For additional information on damping refer to Tedesco et al.(1999).


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9.3.3 *** Response Spectrum concept ***Response spectrum is a powerful response vs. time graphical analytical tool used to

quantify effects of natural periods of vibration on responses (acceleration, velocity ordisplacement) of buildings to an earthquake. Design codes use this response spectrum todevelop design spectra.


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9.4 Lateral Load Resisting Systems

9.4.1 Lateral Load ResistanceThe two main types of gravity load resisting systems are:

o skeleton type structures: consisting of beams and columns.o wall bearing Structures

The vertical members of both systems are mainly subjected to compression forces withthe requirement to have sufficient cross section to resist buckling. The instability underlateral forces is a main issue for both systems.

A main principle of seismic-resistant design is to ensure collapse prevention; therefore itis essential to design lateral-load resisting systems with lateral stability. NBCC-2010 andS16-09 seismic design provisions for lateral load resistance are based on the capacitydesign procedure. In this design procedure, certain structural components are designedto act as structural fuses (sacrificial elements). Specifically designed and detailed, thesecomponents are to fail and exhibit inelastic response dissipating energy during a designlevel earthquake. The locations of these components are engineered such that the gravityload-carrying capacity of the whole system is not impaired due to the damage in thesecomponents. The rest of the systems structural components are then proportioned tobehave elastically.


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Building codes largely adopt the R-factor design procedure . In this procedure, elasticseismic forces are reduced by factors Rd and Ro to obtain design forces. This procedurehas matured into the capacity design procedure. The R-factor procedure can beillustrated by using a typical lateral load-deformation model. If we have a structuredesigned to behave elastically when subjected to an earthquake, the lateral load-deformation relationship would be linear and the structure would have a strength valuecorresponding to the elastic base shear ratio Ce caused by the earthquake, where Ce is aratio of base shear force (V) caused by the earthquake to the weight of structure (W).

W

VCe

if it were elastic.

However, due to the uncertainties in determining the degree of severity of earthquakesand for obvious economical reasons, it is unrealistic to design a structure to respondelastically during a major earthquake. Thus, the code permits the reduction of the designbase shear value to a lower value than the elastic base shear. The design base shear ratiodefined by the code can be expressed as:

od

ed RR

CC


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Two levels of reduction are inferred from this equation through the

reduction factors dR and oR :

dR is a ductility-related force reduction factor that reflects the capability of astructure to dissipate energy through inelastic behavior.

oR is an overstrength-related force reduction factor that reflects the dependableportion of reserve strength in the structure.

Both of these factors form the essence of Canadian seismic design philosophy andhave numerically assigned values in [Table 4.1.8.9] of NBCC-2010.

9.4.2 Seismic Lateral Force Resisting Systems

The three most common systems used for seismic lateral force resistance are:

Structural Shear Walls Braced Frames Moment-Resisting Frames

- no penetrations - triangular penetrations - rectangular penetrations resist lateral forces asvertical cantilevers withrigid connection to thefoundation

resist lateral forces ascantilevered vertical trusses(braced bays).

resist lateral forcesthrough rigid connectivitybetween beams andcolumns (rigid frames).

One of the three lateral systems should be present in each orthogonal direction of thestructure.

od

ed RR

CC


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9.5 Seismic Forces estimation based on NBCC-2010

9.5.1 Hazard and Design SpectraThe procedure for estimating seismic-induced forces on buildings presented by theNBCC-2010 is based on seismic hazard analysis for different locations in Canada. Asillustrated on the 2010 Seismic Hazard Map of Canada, each Canadian location has acertain degree of relative hazard. This is reflected in the quantification of seismic forces.When designing a structure to resist earthquakes, the design engineer should check thelocation of the structure and the corresponding degree of hazard.


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Hazard maps are further expressed in terms of spectral response accelerations Sa(T):

The above spectral accelerations are for periods of < 0.2, 0.5, 1.0 and 2.0 seconds>,respectively at a probability of 2% in 50 years, and for firm ground conditions (NBCCsoil class C reference soil). Spectral acceleration contours are in gs (gravitationalacceleration).

Note that there are two spectral response accelerations in NBCC-2010:

Sa(T) 5% damped spectral response acceleration (shown above),( and as defined in NBCC-2010, Article 4.1.8.4, sentence 1)

S(T) design spectral response acceleration,( as defined in NBCC-2010, Article 4.1.8.4, sentence 7, and determined from

Sa(T) shown above).It is a common error for un-experienced engineers to fail to recognize this distinction.Therefore, in this class, a subscripted Sda(T) will be used in lieu of S(T) for clarity.


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Using the Sa(T) information from seismic hazard maps which are expressed in terms ofdamped spectral response acceleration, the engineer can develop the design responsespectrum for any locality in Canada. The design spectral acceleration (expressed as afraction of gravitational acceleration), for a period T, is defined as Sda(T) and is given as:

Sda(T) = Fa Sa(0.2) for T 0.2 seconds,= Fv Sa(0.5) or Fa Sa(0.2), whichever is smaller for T=0.5 sec,= Fv Sa(1.0) for T=1.0 sec,= Fv Sa(2.0) for T=2.0 sec,= Fv Sa(2.0) for T 4.0 sec.

where: T period (seconds); linear interpolation may be used for intermediate values,Sa(T) the damped spectral response acceleration from seismic hazard maps,Fa and Fv acceleration- and velocity-based site coefficients, respectively.

Fa and Fv values are given in the NBCC-2010 and depend on the type of site condition(rock, or dense soil, or soft soil,.. etc). Sample design spectra for different localities areillustrated in the following figure.

S a(T

) :

T :


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9.5.2 Base Shear Force Estimation

For structures with geometrical and structural regularity, NBCC-2010 Article 4.1.8.11permits using an Equivalent Static Force procedure for estimating the design base shearforce.More rigorous dynamic analysis is required for structures with geometrical and/orstructural irregularities, which are beyond the scope of the present chapter.

For regular structures, Article 4.1.8.11 defines the minimum base shear force as:

WRR

IMTSV

od

Eva )(

WRR

IMTSV

od

Evada )(

where,V is the base shear force;Ta is the fundamental period of vibration of the structure;S(Ta) Sda(Ta) is the design spectral acceleration corresponding to the fundamental

period Ta;Mv is a factor which accounts for higher mode effects;IE is a factor which accounts for the degree of importance of the structure;

dR and oR are the ductility-, and overstrength- related force reduction factors,respectively; and

W is the weight of the structure.

The previous formula can be viewed as:

WFactorsductionReForce

tCoefficienShearBaseElasticV

similar to Section 9.4.1.

This approach can only be used for structures satisfying the conditions of Article 4.1.8.7.


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9.5.3 Distribution of Forces (along the height of the building).

NBCC-2010 establishes the vertical distribution of the total base shear force at differentfloor levels based on the relationship:

n

1iii

xxtx

hW

hW)FV(F

where:VT07.0F at but does not to exceed V25.0

and,Fx = the force at floor number xiV = the total base shear as defined in Section 9.5.2Ft = force portion concentrated at the top of the building in addition to the above

distribution,Wx = the weight of floor xihx = the height of floor xi from the foundation level,

and,

n

1iiihW = summation of (floor weight) x (height) for all the floors in the building, and

n =number of floors.


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9.6 Design of Ductile Moment-Resisting Frames based on S16-09

Clause 27 of S16-09 presents both proportioning and detailing requirements whichprovide acceptable inelastic response of steel structures under seismic actions. The mainobjectives of Clause 27 code provisions are:

a) avoid unstable sidesway mechanisms for structures exhibiting inelastic behavior, andb) ensure ductile flexural behavior in yielding regions of the steel frame.

In other words, S16-09 code provisions for seismic design provide the guidelines tocorrectly define the locations of yielding regions (fuses, plastic hinges) as well as thecriteria for detailing the steel frames to ensure a safe failure of these regions under theeffect of a major earthquake. This section highlights some of the principles presented byS16-09 for the design and detailing of Ductile Moment-Resisting Frames.

9.6.1 Strong-Column/Weak-Beam principleClause 27.2.1.1 promotes a multi-storey side-sway mechanism dominated by hinging ofbeams rather than columns. The requirement of the formation of hinges (fuse locations) atbeam ends and at column bases only is termed strong-column/weak-beam design. This isintended to avoid the formation of weak-storey (single-storey) mechanisms in whichhinging occurs at the top and bottom ends of a single storey leading to overall instability.

weak-column / strong-beam strong-column / weak-beam concept

To achieve strong-column/weak-beam design, S16-09 requires that the sum of columnflexural strength at each joint exceeds the sum of beam flexural strengths as specified byClause 27.2.3.2.


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9.6.2 Beam-to-Column Connections

S16-09 provisions require that a beam-to-column connection is capable of transferring themoment and shear forces developed in the beam to the column. Clause 27.2.5.1 requiresthat the connections should be capable of deforming in order that the frames can achievespecified drift levels. This is further discussed in Annex J where reference is made topre-qualified connection configurations that have been tested for the ability to providesatisfactory performance. Some of these configurations are illustrated below:

Reduced beam section connection

Bolted flange plate connection Bolted bracket connections


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9.6.3 Detailing for Ductile BehaviorThe higher the level of ductility of the lateral load resisting system, the more it isexpected to undergo significant inelastic behavior. Thus, S16-09 sets detailing provisionsto ensure ductile behavior which include:

Protected Zones:Clause 27.2.8 requires the designation of regions subject to inelastic deformations.Clause 27.1.9 sets the requirements for protected zones where structural and otherattachments that can alter the desired behavior of these zones should be prohibited.Protected zones should be indicated on structural design documents and shop details.

Compact Sections (Class 2):To ensure reliable inelastic deformation, S16-09requires width-to-thickness b/t ratios of compressionelements to be limited such as to avoid local buckling(Class 1 or 2).

Column splices:Since column splices are critical to the overall performance of moment-resisting frames,it is essential to ensure the reliability of the splice. In most cases a complete jointpenetration grove weld is required for column splices.

New and innovative concepts:The University of Toronto hasdeveloped a yielding bracesystem (YBS) shown inthe attached photograph byMichael Gray. Details ofthis scorpion YBS systemare given in CISCs No 41,Fall 2011 publication ofADVANTAGE STEEL.

Video Demonstrations:Full-scale test: http://www.youtube.com/watch?v=TAXpwimvbjANon-linear finite element model: http://www.youtube.com/watch?v=Lsb5gdtnb30


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n

iii

xxtx

hW

hWFVF

1

)(

9.7 Seismic Example: . EQUIVALENT STATIC FORCE PROCEDURE .

required: - vertical distribution of lateral seismic-induced forces due to groundshaking only according to ESFP (EQUIVALENT STATIC FORCE PROCEDURE)using the equivalent lateral seismic force

base shear equation:Article 4.1.8.11, sentence 6)

given: 9-storey office building has an SFRS (SEISMIC FORCE RESISTING SYSTEM)consisting of a steel ductile moment-resisting seismic frame as illustrated above,

- located in Victoria, BC- rock soil condition equivalent to site soil class B

solution steps:

Note: all the information required to solve this problem is provided by NBCC2010 inSubsection 4.1.8 and its Articles 4.1.8.__ and its sentences 4.1.8.__ )

also, as stated in Articles 4.1.8.4 the 5% damped SRA data provided for the problem isbased on Class C reference ground conditions for the locale in question.

designer input required to solve the problem: go to . in NBCC-2010Ta fundamental period of lateral vibrationof building in the direction of analysis. Article 4.1.8.11, sentence 3)Spectral Response Accelerations SRA:

Sa(T) 5% damped SRA

Sda(T) design SRA Sda(Ta) design SRA at T=Ta

Article 4.1.8.4, sentence 1) ,or, seismic hazard maps, or COMMENTARY J (Table J-2)______________________________________________

Article 4.1.8.4, sentence 7)

6

5

4

3

2

1

9

8

79

x 36

00 =

324

00 =

h n

h n

8000 Storey Weight (kN), Wi

1800

1900

1870

1870

1870

2080

1500

1800

1800

Level, i8000


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Overview of Steps:

Step 1: Estimate fundamental period, Ta [Clause 4.1.8.11.(3)]

Step 2: Spectral Response Accelerations (SRA), Sa(T)[NBCC 2010 Commentary J, Table J-2], or[NBCC Division B, Appendix C, Table C-2]

Step 3: Design Spectral Response Acceleration, Sda(T)o Site Class [Table 4.1.8.4.A.]o Fa [Table 4.1.8.4.B.]o Fv [Table 4.1.8.4.C.]o Calculate and graph Sda(T) using Sa(T), Fa, Fvo Find Sda(Ta) from graph or interpolationo Find Sda(0.2) and check if 0.12

[i.e. whether seismic design necessary]

Step 4: Base Shear Design Force, V [Clause 4.1.8.11.(2)]o IE [Table 4.1.8.5]o Mv [Table 4.1.8.11]o Rd , Ro [Table 4.1.8.9]

Step 5: Check Minimum and Maximum Limits of Base Shearo Vmin [Clause 4.1.8.11.(2)(b)]o Vmax [Clause 4.1.8.11.(2)(c)]

Step 6: Vertical Distribution of Horizontal Forces [Clause 4.1.8.11.(6)]

n

1iii

xxtx

hW

hW)FV(F


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STEP 1: estimate of fundamental period, Ta :

The response spectrum adopted by the Code is based on estimating a value of thefundamental period of vibration of the structure. NBCC-2010 provides a number ofempirical formulas for different structural systems to estimate the fundamental period:

Article 4.1.8.11 (sentence 3):

3) The fundamental lateral period, Ta in the direction under consideration, shall bedetermined as:

a) for moment-resisting frames that resist 100% of the required lateral forces and wherethe frame is not enclosed by or adjoined by more rigid elements that would tend toprevent the frame from resisting lateral forces, and where hn is in metres:i) 0.085 (hn)

3/4 for steel moment framesii) 0.075 (hn)

3/4 for concrete moment frames, oriii) 0.1 N for other moment frames,

b) 0.025 hn for braced frames where hn is in metres,c) 0.05 (hn)

3/4 for shear wall and other structures where hn is in metres, ord) other established methods of mechanics using a structural model that complies with

the requirements of sentence 4.1.8.3.(8), except that:i) for moment-resisting frames, Ta shall not be taken greater than 1.5 times that

determined in Clause (a),ii) for braced frames, Ta shall not be taken greater than 2.0 times that determined in

Clause (b),iii) for shear wall structures, Ta shall not be taken greater than 2.0 times that

determined in Clause (c),iv) for other structures, Ta shall not be taken greater than that determined in Clause (c),

andv) for the purpose of calculating the deflections, the period without the upper limit

specified in Subclauses (d)(i) to (d)(iv) may be used, except that for walls, coupledwalls and wall-frame systems, Ta shall not exceed 4.0 sec, and for moment-resisting frames, braced frames and other systems, Ta shall not exceed 2.0 sec.

The upper limits (above) are imposed on the periods of structures (Ta) because of concernthat structural modeling does not include non-structural stiffening elements, therebyresulting in values of Ta which are too high results in calculated seismic design forceswhich will be too low.

Calculations: hn = 9 x 3.6 metres = 32.4 metres from Article 4.1.8.11 (above), Ta= 0.085(32.4)3/4=1.15 seconds

the structure meets the criteria of Article 4.1.8.7, sentence 1), case (b) and, thereforequalifies for analysis by ESFP method (equivalent static force procedure).


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STEP 2: Spectral Response Accelerations (SRA):

This is the crucial step in seismic analysis and is based on the hazard classification givenby NBCC. The value of Sa(T) 5% damped spectral response acceleration will depend onthe period of the structure and the location of the building. It can be obtained using themaps included earlier in this chapter or, in this case, from NBCC-2010 COMMENTARY J(Table J-2). A comprehensive set of data can be found in NBCC-2010, Division B,Appendix C, Table C-2. The value of Sa(T) is always based on reference soil that isclass C. Some of the data from this table is:

CitySa(T): 5% damped SRA seismic data

Sa(0.2) Sa(0.5) Sa(1.0) Sa(2.0) PGA

Victoria 1.2 0.82 0.38 0.18 0.61Vancouver 0.94 0.64 0.38 0.17 0.46Calgary 0.15 0.084 0.041 0.023 0.088Edmonton 0.095 0.057 0.026 0.008 0.036Saskatoon 0.095 0.057 0.026 0.008 0.036Regina 0.10 0.057 0.026 0.008 0.040Winnipeg 0.095 0.057 0.026 0.008 0.036

Table Row Lookup

Legend:

Interpolation

WARNING!

Sa(0.2) is NOT the same as S(0.2)Sda(0.2)

Article 4.1.8.1, sentence 1 states that you do not need todesign for subsection 4.1.8 Earthquake Load and Effects

if S(0.2)Sda(0.2) 0.12 NOT if Sa(0.2) 0.12.

Do not get them confused!For design, use S(T)Sda(T)


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STEP 3: Sda(T) design Spectral Response Acceleration:

Need values for Fa and Fv: and the Table below Article 4.1.8.4, sentence 7).

Sda(T) = Fa Sa(0.2) for T 0.2 sec.= Fv Sa(0.5) or Fa Sa(0.2), whichever is smaller for T=0.5 sec.= Fv Sa(1.0) for T=1.0 sec.= Fv Sa(2.0) for T=2.0 sec.= Fv Sa(2.0)/2 for T 4.0 sec.

Fa acceleration-based site soil coefficient; it is based on the short-periodamplification factor of Sa(0.2) and it is required for non-Class C soils.

NEHRPFv velocity-based site soil coefficient; it is based on the long-period

amplification factor of Sa(1.0) and it is needed for non-Class C soils.

The site soil conditions are given as class B , the reference soil is class C, need to use Tables 4.1.8.4 A, B & C to get the site coefficients Fa and Fv

(for educational purposes, copies of these tables are reproducedbelow and the following page):

referencesoil C


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From Step 2, Table J-2, for Victoria, BC: Sa(0.2) = 1.2 FaSa(1.0) = 0.38 Fv

Find Fa and Fv by interpolation

examplesite soil

examplesite soil

To obtain seismic design parameters for site soil class B, use the above values ofFa and Fv from NBCC Tables B and C.

Table B has Fa at Sa(0.2) (short period vibrations), while Table C has Fv at Sa(1.0) (long period vibrations),

At class C sites, all values of Fa and Fv are unity (=1.0) because this is the referencesoil class on which the seismic hazard maps are based, but our example is class B.

Fa and Fv are used in calculations that need to be done on the Sa(T) values provided byNBCC-2010 (Appendix C) to get S(T) Sda(T) values for Victoria, BC class B soilsas shown on the following page:

Example: Since Sa(0.2) = 1.2, interpolating between 1.00 and 1.25 gives Fa = 1.0[1.0 and 1.0]

Example: Since Sa(1.0) = 0.38, interpolating between 0.3 and 0.4 gives Fv = 0.78[0.7 and 0.8]

Fa is based on Sa(0.2)

Fv is based on Sa(1.0)


CE470 (2013 S16-09) IX - 27

DescriptionResponse Spectra (accelerations), g

T= 0.2 sec T= 0.5 sec T= 1.0 sec T= 2.0 sec T 4.0 sec

Sa(T)

5% dampedseismic responsespectrum (SRA)

[NBCC-2010Appendix C]

data from SeismicHazard Maps(class C soils)

Sa(0.2)=1.2 Sa(0.5)=0.82 Sa(1.0)=0.38 Sa(2.0)=0.18 [PGA=0.61]

S(T)

Sda(T)

designseismic responsespectrum (SRA)

[calculations forclass B soils]

Victoria, BC soils

Sda(0.2)=1.2 Sda(0.2)=0.640 Sda(0.2)=0.296 Sda(0.2)=0.140 Sda(0.2)=0.070

=Fa Sa(0.2)=(1.0)(1.2)= 1.2

lesser of:=Fv Sa(0.5)

or

Fa Sa(0.2),= (0.78)(0.82)or (1.0)(1.2)= 0.640

=Fv Sa(1.0)=(0.78)(0.38)= 0.296

=Fv Sa(2.0)=(0.78)(0.18)= 0.140

=Fv Sa(2.0)/2=(1.0)(1.2)/2= 0.070

To get the overall picture, the above Sa(T) and S(T) Sda(T) should be presented ongraphs as shown below. This is the design response spectrum for the project and is usedrepeatedly for static as well as dynamic analyses of different structures on the project.

1.2

0.640

0.296

0.140 0.070 0.070

1.2

0.82

0.38

0.18

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Spec

tral

Res

pons

e Ac

cele

ratio

ns (g

's)

T, Time Period (seconds)

Victoria: Class C reference soilsNBCC-2010 Appendix C

Sa(T)5% damping SRA

Victoria: Class B soilsS(T) Sda(T)

design SRA

Ta= 1.15 sec Sda(Ta) = Sda(1.15 sec)= 0.273

Interpolate for Ta=1.15Sda(1.15) = 0.273

Sda(1.0) Sda(2.0)

0.296

0.140

0.273

Sda(1.15)


CE470 (2013 S16-09) IX - 28

SRA summary for Victoria, BC example:

site soil class B

Ta=1.15 sec,

Fa=1.0 at Sa(0.2), Fv=0.78 at Sa(1.0),

Sda(Ta) Fa Sa(0.2) for T 0.2 .Fv Sa(0.5) Lesser of .Fa Sa(0.2) for T = 0.5.Fv Sa(1.0) for T = 1.0 . = 0.273, as interpolated from graphs for Ta=1.15Fv Sa(2.0) for T = 2.0 .Fv Sa(2.0)/2 for T = 4.0.

Now must check whether or not the structure needs to be designed for seismic.

According to Article 4.1.8.1, sentence 1), if S(0.2) Sda(0.2) 0.12, thenyou do not need to design for Subsection 4.1.8 Earthquake Load and Effects

For this example, since S(0.2) Sda(0.2)= 1.2 > 0.12, thenyou shall design for Subsection 4.1.8 Earthquake Load and Effect

WARNING!

Sa(0.2) is NOT the same as S(0.2)Sda(0.2)

Article 4.1.8.1, sentence 1 states that you do not need todesign for subsection 4.1.8 Earthquake Load and Effects

if S(0.2)Sda(0.2) 0.12 NOT if Sa(0.2) 0.12.

Do not get them confused!For design, use S(T)Sda(T)


CE470 (2013 S16-09) IX - 29

STEP 4: Base Shear Design Force: ( remember, in these notes: S(Ta) Sda(Ta) )


WRR

IMTSV

od

Evada )(

Need more Tables to get IE and Mv but these are simple-to-read values as follows:

from Table 4.1.8.5, normal importance IE =1.0 from Table 4.1.8.11, higher-modes for ductile MRFs (moment-resisting frames)

with Sa(0.2)/Sa(2.0)=1.2/0.18= 6.7 Mv =1.0

Rd & Ro :

from Table 4.1.8.9, for ductile MRFs (moment-resisting frames)with IE Fa Sa(0.2)=(1.0)(1.0)(1.2)= 1.2 , read Rd =5.0, Ro =1.5

Note: a high ductility rating like Rd =5.0 will require ductile detailing and design.

Total Weight of Structure: = Wi=16490 kNBase Shear: V=0.273 x 1.0 x 1.0 x 16490 kN / (5.0 x 1.5)

= 600 kN 3.6% W


CE470 (2013 S16-09) IX - 30

STEP 5: Check Minimum and Maximum Limits of Base Shear:

to safeguard against long period repetitive sway vibrations where ductility demandmight not be uniform along the height of the frame:Vmin: Article 4.1.8.11, sentence 2) case (b)

WRR

IMSV

od

Evda )0.2(min

Vmin(Class C)=(0.18)(1.0)(1.0)W/ (1.5x5.0) = 0.024W= 0.024 x 16490 kN= 396 kNVmin(Class B) will be less yet (0.140) and Vmin does not govern.

for short period vibrations the ESFP method overestimates the magnitude of baseshear and, for SFRS systems with Rd 1.5, an experience-based factor of is usedto place an upper bound on the value of V , see COMMENTARY J (page J-49).

Vmax: Article 4.1.8.11, sentence 2) case (c)

WRR

ISV

od

Eda )2.0(32

max for SFRS systems with Rd 1.5 and not on class F soils.

class C soil Vmax =()(1.2)(1.0)W/7.5=0.1067W=0.1067x16490 kN= 1759 kNclass B soil Vmax same as class C

Vcalculated governs, use V= 600 kN.


CE470 (2013 S16-09) IX - 31

STEP 6: Vertical distribution of horizontal forces:


n

1iii

xxtx

hW

hW)FV(F

where:Ft= 0.07 Ta V but not to exceed 0.25V

Ft= 0.07(1.15)V= 0.081V= 48.3 kN(VFt)= 600.0 48.3=551.7 kN

Level hx[metres]Wx[kN]

Wxhx[kN.m] Wxhx / Wihi

Fx[kN]

9 32.4 1500 48600 0.1693639 141.748 28.8 1800 51840 0.1806549 99.677 25.2 1800 45360 0.158073 87.216 21.6 1800 38880 0.1354912 74.755 18 1900 34200 0.119182 65.754 14.4 1870 26928 0.0938402 51.773 10.8 1870 20196 0.0703801 38.832 7.2 1870 13464 0.0469201 25.891 3.6 2080 7488 0.0260946 14.40

16490 [kN] 286956 [kN.m] 1.000000 600.0 [kN]

[end of ESFP example problem.]


CE470 (2013 S16-09) IX - 32

9.8 Seismic Analyses summaryStructural seismic analyses is a world of its own. Structural design analysts mayencounter any of the following procedures indicated below. National and internationalcodes are trending away from ESFPs (equivalent static frame procedures).

SEISMIC ANALYSIS / DESIGN TOOLS Linear Static:

o Building code formulae for calculating base shears similar to ESFP.

(NBCC-2010 Article 4.1.8.11 , see example problem 9.7 class notes).

Linear Dynamic by Modal Response Spectrum Analysis (Article 4.1.8.12):

o response spectrum analysis requires a response-spectrum curve

consisting of digitized points of pseudo-spectral accelerations vs. time

periods in a given direction for the structure (Commentary J, Note 32)o response spectrum seeks maximum response rather than a full time

history analysis. It is based on modal superposition and eigenvectors or

Ritz vectors.

Non-Linear Static: Pushover Analysis

o performance-based analysis,

o the structure is pushed to failure with an increasing load up to expected

level of performance,

o progression of plastic hinges are monitored until complete collapse

mechanism is formed.

Time History Analyses (THAs) (NBCC-2010 Article 4.1.8.12):- used at fault locations and whenever historic data is available,

o can be linear, or non-linear (geometric and/or material).

o can be modal superposition (MTHA) or direct-integration .

o can be transient or periodic.

Although more sophisticated seismic analyses are a daunting task, they are becoming therequirement of codes. Software such as SAP2000 and related tutorials, webinars andtraining sessions are available to assist structural seismic engineers.__________________________________________[end of Chapter IX Seismic Loads]

prepared (2010) by: M.M. Safar, Ph.D. (McMaster), P.Eng. edited (2012) by: A. Mir, M.Eng. (UBC), P.Eng. edited (2013) by: J.M. Kulyk, EIT reviewed by: M.M. Hrabok, Ph.D. (Alberta), P.Eng.


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