NBCC 05 Professor Saatcioglu

Structural Design For Earthquake Structural Design For Earthquake Loads as per NBCCLoads as per NBCC--20052005

Murat Saatcioglu PhD,P.Eng.Professor and University Research ChairDepartment of Civil EngineeringThe University of OttawaOttawa, ON

Seismic Response

-400-300-200-100

0100200300400

0 1 2 3 4 5 6 7 8 9

Time (sec)

Acce

lera

tion

(cm

/s2 )

Earthquake forces are different than gravity and wind loads. They are internally generated inertia forces caused by the acceleration of ground motion and the building mass.

Performance CriterionBuildings will be designed to maintain their structural integrity and ensure life-safety in the event of a strong earthquake, even though they may be damaged substantially beyond repair.

Buildings will be designed to survive a medium seismic event with some repairable damage.

Buildings will be designed to survive a low level seismic event without damage.

Post-disaster buildings are expected to remain operational after a strong earthquake.

General Design RequirementsThe structures shall have a clearly defined Seismic Force Resisting Systems (SFRS) which will be designed for 100% of the earthquake loads and their effects.

All structural framing systems not part of SFRS must be designed to behave either elastically or with sufficient ductility to maintain their gravity load carrying capacities during the earthquake (as they go for the ride).

Non-structural elements shall be either isolated or integrated.

Provides maximum spectral acceleration for a 5% damped SDOF system of selected periods, Sa(T)

Spectral values derived for a uniform probability of exceedance, 2% in 50 years

Uniform Hazard Spectra reflects differences in spectral shapes in different regions.

Earthquake Hazard (UHS)

Uniform Hazard Spectra (UHS)

For T ≤ 0.2 sec S(T) = Fa Sa(0.2)

S(T) = Fv Sa(0.5) or

For T = 0.5 sec S(T) = Fa Sa(0.2) . whichever is smaller

For T = 1.0 sec S(T) = Fv Sa(1.0)

For T = 2.0 sec S(T) = Fv Sa(2.0)

For T ≥ 4.0 sec S(T) = Fv Sa(2.0)/2

Design Spectral Values

Table 4.1.8.4.A.Site Classification for Seismic Site Response

Forming Part of Sentences 4.1.8.4.(2) and (3)

Average Properties in Top 30 m as per Appendix A

Site Class

Soil Profile Name

Soil Shear Wave Average Velocity, V s

(m/s)

Standard Penetration

Resistance, N 60

Soil Undrained Shear Strength, su

A Hard Rock V s > 1500 Not applicable Not applicable B Rock 760 < V s .1500 Not applicable Not applicable C Very Dense Soil

and Soft Rock 360 < V s < 760 N 60 > 50 su > 100kPa

D Stiff Soil 180 < V s < 360 15 < N 60 < 50 50 < su < 100kPa

E Soft Soil V s <180 N 60 < 15 su < 50kPa E Any profile with more than 3 m of soil with the following

characteristics: • Plastic index PI > 20 • Moisture content w >= 40%, and • Undrained shear strength su < 25 kPa

F (1) Others Site Specific Evaluation Required

Notes to Table 4.1.8.4.A (1) Other soils include: a) Liquefiable soils, quick and highly sensitive clays, collapsible weakly cemented soils, and other soils susceptible to failure or collapse under seismic loading. b) Peat and/or highly organic clays greater than 3 m in thickness. c) Highly plastic clays (PI > 75) with thickness greater than 8 m. d) Soft to medium stiff clays with thickness greater than 30 m.

Values of Fa as a Function of Site Class and T = 0.2 s Spectral Acceleration.

Values of Fa Site Class Sa(0.2)≤

0.25 Sa(0.2) =

0.50 Sa(0.2) =

0.75 Sa(0.2) =1.00

Sa(0.2) = 1.25

A 0.7 0.7 0.8 0.8 0.8 B 0.8 0.8 0.9 1.0 1.0 C 1.0 1.0 1.0 1.0 1.0 D 1.3 1.2 1.1 1.1 1.0 E 2.1 1.4 1.1 0.9 0.9 F Site specific investigation required

Acceleration-Based Site Coefficients

Values of Fv as a Function of Site Class and T = 1.0 s Spectral Acceleration.

Values of Fv Site Class Sa(1.0) <

0.1 Sa(1.0) =

0.2 Sa(1.0) =

0.3 Sa(1.0)

=0.4 Sa(1.0) >

0.5 A 0.5 0.5 0.5 0.6 0.6 B 0.6 0.7 0.7 0.8 0.8 C 1.0 1.0 1.0 1.0 1.0 D 1.4 1.3 1.2 1.1 1.1 E 2.1 2.0 1.9 1.7 1.7 F Site specific investigation required

Velocity-Based Site Coefficients

Ie = 0.8 Low occupancy

Ie = 1.3 Buildings used as post disaster shelters, such as, schools and community centres, and manufacturing facilities containing toxic, explosive or hazardous substances

Ie = 1.5 Buildings used for post-disaster recovery, such as, hospitals, telephone exchanges, generating stations, fire and police stations, water and sewage treatment facilities

Ie = 1.0 All other buildings

Importance Factor

Design Spectral Values as Adjusted for Building

Importance

Ie Fa Sa(T)5% Damped Spectral Acceleration for Reference Soil ConditionsModification Factor

for Site Soil Conditions

Modification Factor for Building Importance

Method of Analysis

Dynamic Analysis (Preferred Method)

• Elastic Spectral Analysis

• Elastic Time History Analysis

• Inelastic Time History Analysis

Equivalent Static Force Procedure

Structures located in zones of low seismicity, Ie Fa Sa(0.2) < 0.35, or

Regular structures that are less than 60 m in height and have Ta < 2 s, where Ta is the fundamental period, or

Irregular structures that are less than 20 m in height, have Ta < 0.5 s and are not torsionally sensitive

Equivalent Static Force ProcedureMay be used for:

3-Storey Frame Mode 1 Mode 2 Mode 3

Modes of Vibration

Ft

V

Equivalent Static Force Procedure

Although seismic action is dynamic in nature, building codes often recommend “Equivalent Static Load Analysis”for simplicity, based on first mode response, as modified empirically for higher mode effects.

Ve

Ve /Rd Ro

Ve /Rd

Δ

W: Weight of the structure contributing to inertia forces (D+0.25L+06LS)

Ta: Fundamental PeriodMv: Higher mode factorIE: Importance FactorRd: Ductility related force

modification factorRo: Oversterngth related force

modification factor

od

Eva

RRWI)MS(TV =

Equivalent Static Force

od

E

RRWS(2.0)IV ≥

For Rd ≥ 1.5, V need not exceed:

Because of uncertainties associated with UHS values for Ta > 2.0 sec, V is not reduced beyond the value at S(2.0)

od

E

RRWS(0.2)I

32V ≤

Cut-off Values

Fundamental Period (Ta) For Steel Moment Frames: Ta = 0.085 (hn)3/4

For Concrete Moment Frames: Ta = 0.075 (hn)3/4

For other Moment Frames: Ta = 0.1 N

For Braced Frames: Ta = 0.025 (hn)

For Shear Wall Buildings: Ta = 0.05 (hn)3/4

R/C MRF Buildings

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0

Height hn, m

Perio

d T,

sec

T= 0.075 (hn)3/4

Measured Versus NBCC-05 (Ta)

R/C Shear Wall Buildings

0.00

0.50

1.00

1.50

2.00

2.50

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

Height, hn (m)

Perio

d, T

(sec

)

T = 0.05 hn3/4


R/C Shear Wall Buildings

T = 0.09 hn / D1/2

0

0.5

1

1.5

2

2.5

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

H / D1/2

Perio

d, T

(sec

)


Fundamental Period (Ta)

The use of more accurate methods of mechanics is permitted by NBCC – 2005 (Ex: Rayleigh’s Method)

provided the values do not exceed 1.5 times those obtained by the empirical expressions

The above limit can be justified because of:

• Uncertainties associated with the participation ofnon-structural elements

• Possible inaccuracies in analytical modelling

• Differences between design and as-built conditions

For frame structures:

6.0 m6.0 m6.0 m6.0 m6.0 m

30 .0 m

6.0 m

Effect of Participating Infill Masonry Walls

3 @ 6 m = 18 m 3 @ 6 m = 18 m 3 @ 6 m = 18 m


0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Wall-to-floor area ratio (%)

Perio

d, T

(sec

)

5-storey building10-storey building15 storey buildingNBCC (5 storeys)

NBCC (10 storeys)NBCC (15 storeys)



The use of more accurate methods of mechanics is permitted by NBCC – 2005 (Ex: Rayleigh’s Method)

provided the values do not exceed 2.0 times those obtained by the empirical expressions .

For braced frames and shear-wall structures:

The above can be justified because of:• Improved accuracy of analytical models for braced

frames and shear walls, which dominate the structural response

• Improved correlation of computed and measuredperiod values

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0 2.5Computed Period (sec)

Mea

sure

d Pe

riod

(sec

)

Shear Wall Buildings


Rd – Ductility Related Force Modification Factor

1.0 ≤ Rd ≤ 5.0

Established by tests, non-linear analysis of structural systems and field assessment of actual structural behaviour.

Indicates the ability of structure to undergo deformations beyond yielding without a significant loss of strength, while dissipating energy under hysteretic loading

Park and Paulay (1975) and Paulay and Priestley (1992) found that Rd ≤ 5 in multi-degree-of-freedom structures.

Because of the field observations after the 1985 Mexico City E.Q., the Mexico Code (1987) reduced “Q” factor (Rd) from 6.0 to 4.0.

2001 draft of Eurocode 8 (ECS 1998) recommends a “q” factor (Rd) to vary between 1.0 and 5.0



In order for the structure to have sufficient ductility and energy absorption capacity, consistent with the Rd used in design, the structure must conform to:

• Relevant CSA Standard

• The Capacity Design requirements

Building with Lateral Deformability Building that suffered failure

due to lack of deformability

Ro – Overstrength Related Force Modification Factor

Structures, particularly the more ductile ones can

have considerable reserve strength not explicitly

considered in NBCC - 1995

Old Codes have attempted to calibrate seismic

design force levels to historical levels deemed

appropriate (i.e., U factor)

Ro – Overstrength Related Force Modification Factor

NBCC – 2005 Explicitly accounts for overstrength in structures

Only dependable or minimum overstrength is considered

Ro = Rsize ⋅ Rφ ⋅ Ryield ⋅ Rsh ⋅ Rmech

Rsize – OverstrengthRelated to Member Size

Standard member sizes used in practice result in overstrength, i.e., restricted sizes of steel shapes, plates, re-bars, timber and masonry elements.

Practical design considerations often lead to conservative rounding of elements, such as spacing of connectors and reinforcing elements.

Rsize = 1.05 for R/C structures 1.05 to 1.10 for structural steel

1.05 to 1.15 for timber and masonry

Rφ – Overstrength Related to Material Resistance (φ) Factors

It is appropriate to use nominal resistances when designing for an extremely rare event, such as an earthquake with a return period of 2500 years.

Rφ = 1/φφ Rφ

R/C and RM 0.85 1.18

Structural Steel 0.90 1.11

Timber 0.70 1.43

URM 1.00 1.00

Ryield – Overstrength Related to Actual Yield Strength

Ryield reflects the ratio of actual steel yield strength to

specified design yield strength.

Ryield = 1.05 for re-bars (Mirza and MacGregor 1979)

1.10 for structural steel (Schmidt and Bartlett 2002)

1.00 for timber

Rsh – Overstrength Related to Strain Hardening of Steel

Rsh reflects the effect of steel strain hardening in post-yield region. Therefore, it depends on the degree of

inelasticity expected (Rd).

Rsh = 1.10 to 1.25 for R/C structures 1.05 to 1.30 for structural steel

1.05 for timber1.00 for reinforced masonry

Rmech – Overstrength Caused by Continuity and Redundancy

Rmech accounts for the additional resistance that can be developed before a collapse mechanism forms in the structure.

Rmech increases with the degree of indeterminacy and redundancy. It can be high in R/C structures where continuity is more prevalent as opposed to steel structures where pin-ended members are common.

cf cf

bf bf

1

1

Elastic Behaviour

Beam Yielding

1

2

by by

2

Beams and Columns @ Capacity

bu bu

3

cu cu

1

2

3

Rmech – Overstrength Caused by Continuity and Redundancy

A value of 1.0 or a value close to 1.0 may be used as a conservative estimate for Rmech

Rmech

Ductile Plate Walls 1.10

Ductile R/C MRF 1.05

Ductile Coupled Walls 1.05

Ductile Partial Coupled Walls 1.05

Rmech = 1.00 Except for;

R/C Structures Rd RoDuctile moment-resisting frames 4.0 1.7Moderately ductile moment-resisting frames

2.5 1.4

Ductile coupled walls 4.0 1.7Ductile partially coupled walls 3.5 1.7Ductile shear walls 3.5 1.6Moderately ductile shear walls 2.0 1.4Conventional construction

•Moment-resisting frames•Shear walls

1.51.5

1.31.3

Other concrete SFRS(s) not listed above

1.0 1.0

Distribution of Base Shear

( )

3.6T for 0.25VF3.6T0.7for V0.07TF0.7T for 0F

FVhW

hWF

at

aat

at

tii

iii

≥=<<=≤=

−=∑

Overturning Moments

Overturning MomentsFirst mode distribution gives the highest overturning moments. The equivalent force approach is based on first mode behaviour.

Moments become smaller when higher mode effects are considered. Therefore, the adjustment factor J is applied to the base overturning moment to account for higher mode effects.

∑=

−=n

1ixiixx )h(hFJM ( ) nx

n

xx

nxx

h.hhh

JJJ

h.h.J

60for 1

60for 01

<−+=

≥=

Torsional Effects

Torsional EffectsTorsion will be considered when:

Torsional moments are introduced by the eccentricity between the centres of mass and resistance.

Torsional moments are generated due to accidental eccentricities.

Torsional sensitivity is established by computing Bx for each level x when equivalent static forces are acting at ± 0.10 Dnx from the centre of mass.

Bx = δmax / δave

Torsional Effects

Torsional EffectsFor buildings with B ≤ 1.7; apply torsional

moments about a vertical axis at each level computed for each of the following two loading cases:

i. Tx = Fx (ex + 0.10 Dnx)

ii. Tx = Fx (ex - 0.10 Dnx)

For buildings with B > 1.7 in cases where IEFaSa(0.2) ≥ 0.35 by Dynamic Analysis

1 Vertical stiffness irregularity2 Weight (mass) irregularity3 Vertical geometric irregularity4 In-plane discontinuity5 Out-of-plane offsets6 Discontinuity in capacity (weak storey)7 Torsional sensitivity8 Non-orthogonal systems

Structural Irregularities

Irregularity trigger

When:

IE·Fa·Sa(0.2) ≥ 0.35

+ any one of the 8 irregularity types,

the special design provisions for irregular structures apply. However, post disaster buildings should never have irregularity type 6 (weak storey)

Types of Irregularities1. Vertical Stiffness

Lateral stiffness of the SFRS in a storey:< 70% of that in any adjacent storey, or < 80% of the average stiffness of the 3

storeys above or below.

Types of Irregularities

2. Weight (Mass)

weight of a storey > 150% of weight of an adjacent storey.(a roof lighter than a floor below is excluded)


3. Vertical Geometric

horizontal dimension of the SFRS in a storey > 130% of that in any adjacent storey.(one-storey penthouse excluded)

Types of Irregularities4. In-Plane Discontinuity

in-plane offset of an element of the SFRS,orreduction in lateral stiffness of an element in the storey below.


5. Out-of-Plane Offsetsdiscontinuity of lateral force path

e.g., out-of-plane offsetsof the elements of the SFRS.

Top FloorsBottom Floors

Types of Irregularities6. Discontinuity in Capacity - Weak Storey

storey shear strength less thanthat in the storey above.(Storey shear strength = total of all elements of the SFRS in the direction considered)


7. Torsional sensitivity

if the ratio B > 1.7.

B = δmax / δavg

δ calculated for static loads applied at ± 0.10 Dn

Plan

Types of Irregularities8. Non-orthogonal systems

SFRS not oriented along a set of orthogonal axes.

Plan

Irregular SFRS

Stiffness of non-structural components

shall not be included to make an irregular

SFRS regular.

Irregular SFRS

For sites with IE·Fa·Sa(0.2) ≥ 0.35 dynamic analysis is required if h ≥ 20 m, T ≥ 0.5 s or Type 7 (Torsion) irregularity.

For fundamental period equal to or greater than 1.0 s and IEFvSa(1.0) > 0.25, walls forming parts of SFRS shall be continuous from ground to top levels and shall not have irregularity types 4 (in-plane discont.), 5 (out-of-plane offsets)

Irregular SFRSIrregularity type 6 (weak storey) not permitted except if IEFaSa(0.2) < 0.2 and the design base shear = RdRoV.

Post-disaster buildings shall not have any irregularity of:

types 1 (vert. stiffness), 3 (vert. geom.), 4 (in-plane discont.), 5 (out-of-plane offsets) or 7 (torsion) if IEFaSa(0.2) > 0.35;

type 6 (weak storey).

2005 NBCC IEFaSa(0.2)

2005 NBCC

-400-300-200-100

0100200300400

0 1 2 3 4 5 6 7 8 9

Time (sec)

Acce

lera

tion

(cm

/s2 )

m a + c v + k u = m ag

Dynamic Analysis for Dynamic Analysis for Seismic DesignSeismic Design

3-Storey Frame Mode 1 Mode 2 Mode 3

Modes of Vibration

Dynamic Analysis

Linear (Elastic) Dynamic Analysis

Modal Response Spectrum Analysis

Numerical Integration Time History Analysis

Non-linear (Inelastic) Dynamic Analysis

Numerical Integration Time History Analysis

0.0

0.2

0.4

0.6

0.8

1.0

0 0.5 1 1.5 2Period, T

Spec

tral

Acc

eler

atio

n, S

a(T

)

0 100 200 300

Time, t

If site-specific record is available

Otherwise use site-specific design response spectra (UHS)

SPECTRAL ANALYSIS

Spec

tral

acc

eler

atio

n, S

a(T

)

Modal Spectrum Analysis1. Determine periods (Ti) and mode shapes (φi)

2. Determine the design spectral acceleration value for

each mode S(Ti) from the UHS values specified in

NBCC-2005

3. Compute modal participation factor (γi) for each

mode under consideration

∑=

n

1j

2ji,j

i

φmγ

∑−=

n

1jji,jφm

Modal Spectrum Analysis

4. Compute elastic modal forces and displacements at each floor level

jiiji,ji, )mS(TγφF = )S(T4πT

γφδ i2

2i

iji,ji, =

5. Find elastic modal storey shears (Vi,x) and base shear (Vi).

∑=

=n

xjji,xi, FV ∑

=

=n

1jji,i FV


6. Combine the effects of each mode by usingan appropriate modal combination rule (likeSRSS Method).

∑=

=m

ixix FF

1

2, ∑

=

=m

ixix VV

1

2,

∑=

=m

iie VV

1

2 ∑=

=m

ixix

1

2,δδ


7. Determine the design base shear Vd

Edo

ed I

RRVV =

8. If Vd < 0.8 V (by Eq. Static Load) Then Vd = 0.8V, except for irregularstructures requiring dynamic analysis in which case Vd is taken as the larger ofVd and 100% of V

Example – Modal SuperpositionA 5-storey ductile moment resisting concrete frame is to

be designed for a Vancouver condominium. The soil

condition can be classified as soft rock (Class C) as per

NBCC-2005.

T1 = 1.56 sec; T2 = 0.54 sec; T3 = 0.34 sec

Storey mass; m = 600,000 kg

Total column stiffness; k=120 x 106 N/mm

Rd = 4.0; Ro = 1.7; Ie = 1.0

Example – Modal Superposition

T1=1.56 s T2=0.56 s T3=0.34 sFloor

2 964 1399 270 17201 503 1067 949 1514

γ1=1.25 γ2=0.39 γ3=0.21

S1=0.24g S2=0.59g S3=0.77g

5 1765 -1247 726 2280

4 1623 -386 -518 1747

3 1347 764 -872 1777

6202 1597 555 6428

∑=

=3

1

2,

ixix FF

jiiji,ji, )mS(TγφF =

∑=

5

1jji,F


Ve = 6428 kN

kN945)0.1((4.0)(1.7)

6428IRR

VV Edo

ed ===


Linear Time History AnalysisEmployed when the entire time history of elastic response is required during the ground motion of

interest

Time history analysis should be conducted for an

ensemble of ground motion records that represent

magnitudes, fault distances and source mechanisms

that are consistent with those of the design

earthquakes used to generate design response spectra

Linear Time History Analysis

Edo

ed I

RRVV =

If Vd < 0.8 V (by Eq. Static Load)

Then Vd = 0.8V, except for irregular

structures requiring dynamic analysis

in which case Vd is taken as the larger of

Vd and 100% of V

Inelastic Time History AnalysisInvolves the computation of dynamic response at each

time increment with due considerations given to the

inelasticity in members

Nonlinear analysis allows for flexural yielding (or

other inelastic actions) and accounts for subsequent

changes in strength and stiffness. This is done by

incorporating

“Hysteretic Models”

Inelastic Time History AnalysisWhen non-linear time history analysis is used to justify a

structural design, a special study is required, consisting

of a complete design review by a qualified independent

engineering team. The review is to include ground

motion time histories and the entire design of the

building with emphasis placed on the design of lateral

force resisting system and all the supporting analyses

Inelastic Time History AnalysisThe results of non-linear time history analysis directly

account for reductions in elastic forces due to inelasticity. The structural overstrength can also be

accounted for directly through appropriate modellingassumptions. The analysis results need not therefore be modified by Rd and Ro. The importance factor IE can be

accounted for either by scaling up the design ground motion histories or by reducing the acceptable

deflection and ductility capacities

Structural Modelling

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

≤

webnexttodistanceclear1/2t12

beams)(cont.lengthSpan1/10beams)(simlelengthSpan1/12

Lo

Member Modelling

m

h

L

Member Modelling

i jFlexural Springs

Elastic Beam Element with EIand GA

Mi Mj

l 1 l 2

l

Member Modelling

Hysteretic Behaviour (Steel Structures)

Hysteretic Models for Steel Elements in Flexure

y

cr

n

R/C Member in Flexure

n

n

y u

Bilinear Idealization

Formation of a Plastic Hinge

-120 -80 -40 0 40 80 120-400

-200

0

200

400

Mom

ent,

M (

kN.m

)-6 -4 -2 0 2 4 6

Drift (%)

Δ

M = F + P Δ l

Displacement, (mm)

Hysteretic Behaviour (R/C Structures)

By Clough (1966) By Takeda (1970)

Stiffness Degrading Models for R/C

Strength decay

Strength Degradation in R/C

Stiffness Degradation and Pinching in R/C

ssh

y

e f

Anchorage Slip

Anchorage Slip Model for R/C By Alsiwat & Saatcioglu (1992)

Effect of Variable Axial Force on R/C

Axial Force – Flexure Interaction Model By Saatcioglu, Derecho and Corley (1983)

In spite of all the complications of hysteretic behaviour of structural elements and sub-

assemblages, it is possible to select reasonably simple hysteretic models for inelastic seismic

analysis of structures….

Hysteretic Modelling

Thank You…

Questions and Comments ?

NBCC 05 Professor Saatcioglu

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