CE470(2012) Chapter9(Filled in Notes)

8/13/2019 CE470(2012) Chapter9(Filled in Notes)

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CE470 (2012 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 Ro

27.2 Type D(ductile) moment-resisting frames 5.0 1.5

27.3 Type MD(moderately ductile) moment-resisting frames MRFs 3.5 1.5

27.4 Type LD(limited-ductility) moment-resisting frames 2.0 1.3

27.5 ype MD(moderately ductile)concentrically-braced frames 3.0 1.3

27.6 ype LD(limited-ductility) concentrically-braced frames Braced 2.0 1.3

27.7 ype D(ductile) eccentrically-braced frames Frames 4.0 1.527.8 ype D(ductile) buckling-restrained braced frames 4.0 1.2

27.9 Type D(ductile) plate walls 5.0 1.6

27.10 Type LD(limited-ductility) plate walls 2.0 1.5

27.11 Conventional construction 1.5 1.3

27.12 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 (2012)

Reference publications:

FEMA (2000) Recommended seismic design criteria for new steel moment frame

buildings, 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 practicing

engineers," 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 definitions

Earthquake Engineeringdeals with applying civil engineering design principles to

reduce life and economic losses due to earthquakes, (i.e. to mitigate seismic risk).

Seismic riskcan be defined as the probability of losses occurring due to earthquakes

within the lifetime of a structure. The two main components of seismic risk are:

a) Seismic hazard : This component of risk is determined by nature and cannotbe

reduced. There are several damaging effects due to earthquakes including: ground

shaking, landslides, surface ruptures and liquefaction. The level of seismic hazard

can vary from having frequent low intensity earthquakes to having rare severe

earthquakes.

b) Structural vulnerability : This component depends on the structural

configuration and properties and thus can be reduced by proper seismic design ofstructures. Steel structures have several inherent characteristics that are

advantageous for seismic design. At the top of the list is the high ductility of steel

compared to other construction materials. Ductility is the ability of the structure to

deform past yielding without significant strength deterioration. However, to make

use of the advantages of steel as a construction material for seismic design, the

design engineer has to be familiar with the code design and construction

provisions. In essence, code provisions are set to avoid different sources of

structural 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 Earthquakes

There are several causes for earthquakes: Some are caused by volcanoes which may be atriggering factor for earthquakes, or there can be induced seismicity resulting from

underground explosions. However, a cause which is believed to be the main reason for

most 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 of

several 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 pressures

involved, cause potential sliding and slipping movements to generate friction forces large

enough to lock-up surfaces in contact. Instead of sliding past each other, rock in a plate

boundary area absorbs greater and greater compression and shear strains until it suddenly

ruptures. At rupture, the accumulated energy (strain energy) within the strained rock mass

releases in a sudden manner with a violent jarring motion. This is an earthquake.

Most earthquakes are caused by movement between tectonic plates: 70% around the

perimeter 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 the

earth fractures is an earthquake fault.

The point in the fault surface area

considered the centre of energy release is

termed the focus, its projection up to the

earths surface defines the epicenter.

The distancebetween thefocus and the

epicenter is known as the focal depth.






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When the fault ruptures, seismic wavesemanate in all directions from the focus. The two

types of underground waves which are generated by the 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, significantly

amplify shaking and also modify the frequency content of seismic waves by filtering out

higher 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 quantitativemeasure of earthquake severity commonly

measured by the Richter scale(1935). Each earthquake is assigned only one magnitude

value. This is determined by seismologists from seismograph records. The Richter scale

is 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 scale

represents a ten-fold (101) increase in amplitude and a 30-fold increase in

discharged energy.(10

3)






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On the other hand, earthquake intensity is a qualitativedescription of the earthquake

severity. Accordingly, earthquake intensity varies according to the location where

shaking is felt. Factors affecting earthquake intensity at a certain location includes:

earthquake magnitude, epicentral distance and soil conditions. The most recognized

intensity scale for earthquakes is the Modified Mercalli Intensity Scalesummarized in

the 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 or

items overturned.

VI Felt by all. Some fallen plaster or damaged chimneys. Some heavy

furniture moved.

VII Negligible damage in well designed and constructed buildings through to

considerable damage in construction of poor quality. Some chimneys

broken.

VIII Depending on the quality of design and construction, damages ranges

from slight through to partial collapse. Chimneys, monuments and walls

fall.

IX Well designed structures damaged and permanently racked. Partial

collapses and buildings shifted off their foundations.

X Some well-built wooden structures destroyed along with most masonry

and 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 V ulner ability PBEE Quantification Response SpectrumEQ. Eng. Hazard

Minor

Severe

Performance Based EarthquakeEngineering

9.2.4 Philosophy of Seismic-Resistant Design

Given the uncertainties in determining the degree of severity of earthquakes and for

obvious economical reasons, it is unrealistic to design a structure to respond elastically

during a major earthquake. Thus, the philosophy of seismic design for major earthquakes

is collapse prevention rather than damage prevention.

For less severe earthquakes, lower

levels of damage are accepted. As

the importance of the structure

increases, the criteria of accepted

performance are more stringent as

shown in the next figures taken from

SEAOC.

Operational Immediate

occupancy

Life safety Structural

stability

Fully

operational

Operational Life safety Near

Collapse

Frequent

(Low Intensity)

Occasional

Rare

Very rare

(Severe

intensity)

Performance leve

Seismichazardle

vels

Vision 2000 (SEAOC 1995)

Risk Vulnerability PBEE Quantification Response SpectrumEQ. Eng. Hazard

Performance Objectives

H

a

z

a

r

d

L

e

ve

l

Se

i

s

m

i

c

H

a

z

ar

d

L

e

v

e

l

s






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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 its

mass according to Newtons second law of motion. Thus, as the weight of an object

increases, the inertia force increases for a given level of acceleration. Buildings with

heavier-weight structural materials are subjected to higher levels of seismic-induced

forces than lighter ones. It is therefore advisable to use lighter weight construction in

seismic 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 structure

would undertake when subjected to an initial dynamic stimulus and then left to oscillate

freely. The lowest frequency has the largest natural time period of vibration and is called

the 1stmode or fundamental mode of the structure. Depending on the structural and

geometrical configuration of the structure, there may be other periods corresponding to

higher-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 and

medium-rise buildings.

(c) Damping:

Damping is a resistance to free vibration and defines the energy-dissipation mechanism

which steadily diminishes the amplitude of vibration. Damping in structures is mainly

caused by internal friction within building elements. The type of construction material

affects the degree of damping. There are many forms of damping. Viscous damping is

velocity dependent. Currently, the most popular form is proportional damping (mass

and stiffness dependent); it is also known as: Rayleigh, classical, orthogonal or

modal 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 or

displacement) of buildings to an earthquake. Design codes use this response spectrum to

develop design spectra.






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9.4 Lateral Load Resisting Systems

9.4.1 Lateral Load Resistance

The two main types of gravity load resisting systems are:

oskeleton type structures: consisting of beams and columns.

o wall bearing Structures

The vertical members of both systems are mainly subjected to compression forces with

the requirement to have sufficient cross section to resist buckling. The instability under

lateral forces is a main issue for both systems.

A main principle of seismic-resistant design is to ensure collapse prevention; therefore it

is essential to design lateral-load resisting systems with lateral stability. NBCC-2010and

S16-09seismic design provisions for lateral load resistance are based on the capacity

design procedure. In this design procedure, certain structural components are designed

to act as structural fuses (sacrificial elements). Specifically designed and detailed, these

components are to fail and exhibit inelastic response dissipating energy during a design

level 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 these

components. The rest of the systems structural components are then proportioned to

behave elastically.






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Two levels of reduction are inferred from this equation through the

reduction factors dR and oR :

dR is a ductility-relatedforce reduction factor that reflects the capability of a

structure to dissipate energy through inelastic behavior.

oR is an overstrength-relatedforce reduction factor that reflects the dependable

portion of reserve strength in the structure.

Both of these factors form the essence of Canadian seismic design philosophy and

have 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 force as

vertical cantilevers with

rigid connection to the

foundation

resist lateral forces as a

cantilevered vertical trusses

(braced bays).

resist lateral forces

through rigid connectivity

between beams and

columns (rigid frames).

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

structure.

od

ed

RR

CC =






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9.5 Seismic Forces estimation based on NBCC-2010

9.5.1 Hazard and Design Spectra

The procedure for estimating seismic-induced forces on buildings presented by the

NBCC-2010is based on seismic hazard analysis for different locations in Canada. As

illustrated on the 2010Seismic Hazard Map of Canada, each Canadian location has a

certain 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 the

location of the structure and the corresponding degree of hazard.






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Using the Sa(T)information from seismic hazard maps which are expressed in terms of

damped spectral response acceleration, the engineer can develop the design response

spectrum for any locality in Canada. The design spectral acceleration (expressed as a

fraction of gravitational acceleration), for a period T,is defined as Sda(T)and is given as:

Sda(T) = Fa Sa(0.2)for T0.2 seconds,

= Fv Sa(0.5)or FaSa(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 T4.0 sec.

where: Tperiod (seconds) linear interpolation may be used for intermediate values,

Sa(T) the damped spectral response acceleration from seismic hazard maps,

Faand Fvacceleration- and velocity-based site coefficients, respectively.

Faand Fvvalues are given in the NBCC-2010and 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.






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9.5.2 Base Shear Force Estimation

For structures with geometrical and structural regularity, NBCC-2010Article 4.1.8.11

permits using an Equivalent Static Forceprocedure for estimating the design base shear

force.

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,

Vis the base shear force;

Tais the fundamental period of vibration of the structure;

S(Ta)Sda(Ta) is the design spectral acceleration corresponding to the fundamental

period Ta;

Mvis a factor which accounts for higher mode effects;

IEis 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

Wis 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-2010establishes the vertical distribution of the total base shear force at different

floor levels based on the relationship:

=

=n

1i

ii

xxtx

hW

hW)FV(F

where:

VT07.0F at = but does not to exceed V25.0

and,

Fx=

the force at floor number xi

V = the total base shear as defined in Section 9.5.2

Ft = force portion concentrated at the top of the building in addition to the above

distribution,

Wx = the weight of floor xi

hx = the height of floor xifrom the foundation level,

and,

=

n

1i

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

n=number offloors.






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

Clause 27of S16-09present both proportioning and detailing requirements which provide

acceptable inelastic response of steel structures under seismic actions. The main

objectives of Clause 27code provisions are:

a) avoid unstable sidesway mechanisms for structures exhibiting inelastic behavior.

b) ensure ductile flexural behavior in yielding regions of the steel frame.

In other words, S16-09code provisions for seismic design provide the guidelines to

correctly defining the locations of yielding regions (fuses, plastic hinges) as well as the

criteria for detailing the steel frames to ensure a safe failure of these regions under the

effect of a major earthquake level. This section highlights some of the principles

presented by S16-09for the design and detailing of Ductile Moment-Resisting Frames.

9.6.1 Strong-Column/Weak-Beam principle

Clause 27.2.1.1promotes a multi-storey side-sway mechanism dominated by hinging of

beams rather than columns. The requirement of the formation of hinges (fuse locations) at

beam ends and at column bases only is termed strong-column/weak-beam design. This is

intended to avoid the formation of weak-storey (single-storey) mechanisms in which

hinging 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, S16-09requires that the sum of columns

flexural strengths at each joint exceed the sum of beam flexural strengths as specified by

Clause 27.2.3.2.






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9.6.2 Beam-to-Column Connections

S16-09provisions require that a beam-to-column connection is capable of transferring the

moment and shear forces developed in the beam to the column. Clause 27.2.5.1requires

that the connections should be capable of deforming in order that the frames can achieve

specified drift levels. This is further discussed inAnnex Jwhere reference is made to

pre-qualified connection configurations that have been tested for the ability to provide

satisfactory 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 Behavior

The higher the level of ductility of the lateral load resisting system, the more it is

expected to undergo significant inelastic behavior. Thus, S16-09sets detailing provisions

to ensure ductile behavior which include:

Protected Zones:

Clause 27.2.8requires the designation of regions subject to inelastic deformations.

Clause 27.1.9sets the requirements for protected zones where structural and other

attachments 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/tratiosof

compression elements to be limited such as to avoid local buckling (Class 1or 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 joint

penetration grove weld is required for column splices.

New and innovative concepts:The University of Toronto has

developed a yielding brace

system (YBS) shown in

the attached photograph by

Michael Gray. Details of

this scorpion YBS system

are given in CISCs No 41,

Fall 2011 publication of

ADVANTAGE STEEL.






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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 the

fundamental period of vibration of the structure. NBCC-2010provides a number of

empirical formulas for different structural systems to estimate the fundamental period:

Article 4.1.8.11 (sentence 3):

3) The fundamental lateral period, Tain the direction under consideration, shall be

determined as:

a) for moment-resisting frames that resist 100% of the required lateral forces and where

the frame is not enclosed by or adjoined by more rigid elements that would tend to

prevent the frame from resisting lateral forces, and where hnis in metres:

i) 0.085 (hn)3/4

for steel moment frames

ii) 0.075 (hn)3/4

for concrete moment frames, or

iii) 0.1 N for other moment frames,

b) 0.025 hnfor braced frames where hnis in metres,c) 0.05 (hn)

3/4 for shear wall and other structures where hnis in metres, or

d) 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, Tashall not be taken greater than 1.5 times that

determined in Clause (a),

ii) for braced frames, Tashall not be taken greater than 2.0 times that determined in

Clause (b),

iii) for shear wall structures, Tashall not be taken greater than 2.0 times that

determined in Clause (c),

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

and

v) 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, coupled

walls and wall-frame systems, Tashall not exceed 4.0 sec, and for moment-

resisting frames, braced frames and other systems, Tashall not exceed 2.0 sec.

- the upper limits (above) are imposed on the periods of structures (Ta) because of

concern that structural modeling does not include non-structural stiffening elements,

thereby resulting in values of Tawhich are too high

results in calculated seismicdesign forces which will be too low.

calculations:

Hn= 9 x3.6 metres=32.4 metres

fromArticle 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, therefore

qualifies for analysis by ESFPmethod (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 given

by NBCC. The value of Sa(T)5% damped spectral response acceleration will depend on

the period of the structure and the location of the building. It can be obtained using the

maps included earlier in this chapter or, in this case, from NBCC-2010 COMMENTARY J

(TableJ-2). The reference soil is always class C. Some of the data from this table is:

CitySa(T): 5% damped SRAseismic data

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

Victoria 1.2 0.82 0.38 0.18 0.61

Vancouver 0.94 0.64 0.38 0.17 0.46

Calgary 0.15 0.084 0.041 0.023 0.088

Edmonton

Saskatoon

Regina 0.10 0.057 0.026 0.008 0.040

Winnipeg 0.095 0.057 0.026 0.008 0.036

Since the period of our structure is t=1.15second, we interpolate between the values of

Sa(1.0)and Sa(2.0)for Victoria, BC and could

get spectral response acceleration at t=1.15sec, as

Sa(1.15sec)= 0.35 (units are fractions of g), but

there is a better way using the complete spectrum.

- also, Sa(0.2)= 1.2 > 0.12,according to

Article 4.1.8.1, sentence 1)need to design for

Subsection 4.1.8 Earthquake Load andEffects

____________________________________

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

- need values for Faand Fv: and the Tablebelow Article4.1.8.4, sentence 7).

Sda(T) = Fa Sa(0.2)for T0.2 sec.

= Fv Sa(0.5) or FaSa(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 T4.0 sec.

Faacceleration-based site soil coefficient; it is based on the short-period

amplification factor of Sa(0.2) and it is required for non-Class C soils.NEHRP

Fvvelocity-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.

Sa(1.0) Sa(2.0)

0.38

0.19

0.35

Sa(1.15)

0.18






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CE470 (2012 S16-09) IX - 24

- the site soil conditions are given as class B , the reference soil is class C,

need to useTables4.1.8.4A,B &C to get the site coefficients Faand Fv

(for educational purposes, copies ofthese tables are reproduced below):

reference

soil C

example

site soil

example

site soil

example: Sa(1.0)=0.38Fv= 0.78






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To obtain seismic design parameters for site soil class B, use the above values of

Faand Fv from NBCCTables B and C.

TableB has Faat Sa(0.2)(short period vibrations), while

Table C has Fvat Sa(1.0)(long period vibrations),

At class C sites, all values of Faand Fvare unity (=1.0) because this is the reference

soil class on which the seismic hazard maps are based but our example is class B.Calculations need to be done on the Sa( )values provided by NBCC-2010(Appendix C)

to get S( )Sda( )for Victoria B soils as indicated below:city:

Victoria, B.C.Response Spectra (accelerations)

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

NBCC-2010Appendix C

Sa(T): 5% damped

SRA(response

spectrum) datafrom Seismic

Hazard Maps

(class C soils)

Sa(0.2)=1.2

Sa(0.5)=0.82Sa(1.0)=0.38

Sa(2.0)=0.18

PGA=0.61

- design response

spectrumcalculations for

class B

Victoria soils

S(T)Sda(T)

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

= 1.2

lesser of:

Fv Sa(0.5)and

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

To get the overall picture, the above Sa(T) and S(T)Sda(T) should be presented on

graphs as shown below. This is the design response spectrum for the project and is used

repeatedly for static as well as dynamic analyses of structures on the project.

T= 1.15 secSda(1.15 sec)= 0.273

Class B soilVictoria, B.C.






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CE470 (2012 S16-09) IX - 26

SRAsummary for Victoria example:

site soil classBTa=1.15 sec, and Sa(1.15)=0.35 (interpolated, but not required if using graphs above),

Fa=1.0 at Sa(0.2),

Fv=0.78 at Sa(1.0),

Sda(Ta)FvSa(Ta) =0.273 as interpolated from graphs, or 0.78 x 0.35= 0.273

!!"






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CE470 (2012 S16-09) IX - 27

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

Article4.1.8.11, sentence 2)

WRR

IMTSV

od

Evada )(=

- need more Tablesto getIEandMvbut these are simple-to-read values as follows:

from Table4.1.8.5, normal importanceIE=1.0

from Table4.1.8.11, 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 Table4.1.8.9, for ductile MRFs(moment-resisting frames)

withIEFa Sa(0.2)=(1.0)(1.0)(1.2)= 1.2 , readRd=5.0, Ro=1.5

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

Total Weight of Structure: = Wi=16490 kN

Base Shear: V=0.273 x 1.0 x 1.0 x 16490 kN/(5.0 x 1.5)= 600 kN3.6% W

_________________________________________

step 5:check Minimum and Maximum Limits of Base Shear:

to safeguard against long period repetitive sway vibrations where ductility

demand might not be uniform along the height of the frame:

Vmin: Article4.1.8.11, sentence 2) case (b)

WRR

IMSV

od

Ev)0.2(min=

Vmin(Class C)=(0.18)(1.0)(1.0)W/ (1.5x5.0) = 0.024W= 0.024 x 16490 kN= 396 kN

Class B soil will be less yet (0.140) and Vmindoes not govern.

for short period vibrations the ESFPmethod overestimates the magnitude of base

shear and, for SFRSsystems with Rd1.5,an experience-based factor of is used

to place an upper bound on the value of V , see COMMENTARYJ(page J-49).

Vmax: Article4.1.8.11, sentence 2) case (c)

WRR

IS

Vod

E)2.0(3

2

max= for SFRSsystems with Rd1.5 and not on class F soils.

class C soilVmax=()(1.2)(1.0)W/7.5=0.1067W=0.1067x16490 kN= 1759 kN

class B soilVmaxsame as class C

Vcalculated governs, use V=600 kN.__________________________________________________






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CE470 (2012 S16-09) IX - 28

step 6:Vertical distribution of horizontal forces:

Article4.1.8.11, sentence 6)

=

= n

1i

ii

xxtx

hW

hW

)FV(F

where:

Ft= 0.07TaV but not to exceed 0.25V

Ft= 0.07(1.15)V= 0.081V= 48.3 kN

(VFt)= 600.048.3=551.7 kN

Level hx[metres] Wx[kN] Wxhx[kN.m] Wxhx/Wihi Fx [kN]

9 32.4 1500 48600 0.1693639 141.74

8 28.8 1800 51840 0.1806549 99.67

7 25.2 1800 45360 0.158073 87.21

6 21.6 1800 38880 0.1354912 74.75

5 18 1900 34200 0.119182 65.75

4 14.4 1870 26928 0.0938402 51.77

3 10.8 1870 20196 0.0703801 38.83

2 7.2 1870 13464 0.0469201 25.89

1 3.6 2080 7488 0.0260946 14.40

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

[end of ESFPexample problem.]






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9.8 Seismic Analyses summary

Structural seismic analyses is a world of its own. The structural design analysts may

encounter any of the following procedures indicated below. National and international

codes are trending away from ESFPs (equivalent static frame procedures).

SEISMIC ANALYSIS / DESIGN TOOLS Linear Static:

oBuilding code formulae for calculating base shears similar to ESFP.

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

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

oresponse 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)

oresponse 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

operformance-based analysis,

othe structure is pushed to failure with an increasing load up to expected

level of performance,

oprogression 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,

ocan be linear, or non-linear (geometric and/or material).ocan be modal superposition (MTHA) or direct-integration .

ocan be transient or periodic.

Although more sophisticated seismic analyses are a daunting task, they are becoming the

requirement of codes. Software such as SAP2000and related tutorials, webinars and

training sessions are available to assist structural seismic engineers.





CE470(2012) Chapter9(Filled in Notes)

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