Structural Design For Earthquake Loads as per NBCC-2005 Murat Saatcioglu PhD,P.Eng. Professor and University Research Chair Department of Civil Engineering The University of Ottawa Ottawa, ON
Seismic Response 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. 400 2
)
300
s / 200 m c ( 100 n o 0 it a-100 r e l e c-200 c A-300
-400
0123456789 Time (sec)
Performance Criterion
Buildings 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 Requirements
The 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.
Earthquake Hazard (UHS)
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.
Uniform Hazard Spectra (UHS)
Design Spectral Values 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
Table 4.1.8.4.A. Site Classification for Seismic Site Response Forming Part of Sentences 4.1.8.4.(2) and (3)
Site Class
Average Properties in Top 30 m as per Appendix A Soil Profile Name Soil Shear Wave Average Velocity, V (m/s)
A B C D E E
F
Hard Rock Rock
Very Dense Soil and Soft Rock Stiff Soil Soft Soil
(1)
Others
V s > 1500 760 < V s .1500 360 < V s < 760
s
Standard Penetration Resistance, N
Soil Undrained Shear Strength, 60
Not applicable Not applicable
N 60 > 50
Not applicable Not applicable su > 100kPa
50 < su < 100kPa 15 < N 60 < 50 180 < V s < 360 su < 50kPa V s <180 N 60 < 15 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 s u < 25 kPa 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 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.
soils
susceptible to
Acceleration-Based Site Coefficients Values of Fa as a Function of Site Class and T = 0.2 s Spectral Acceleration. Site Class A B C D E F
Sa(0.2) 0.25 0.7 0.8 1.0 1.3 2.1
Sa(0.2) = 0.50 0.7 0.8 1.0 1.2
Values of Fa Sa(0.2) = 0.75 0.8 0.9 1.0 1.1
Sa(0.2) =1.00 0.8 1.0 1.0 1.1
1.4 1.1 0.9 Site specific investigation required
Sa(0.2) = 1.25 0.8 1.0 1.0 1.0 0.9
Velocity-Based Site Coefficients Values of Fv as a Function of Site Class and T = 1.0 s Spectral Acceleration. Site Class A B C D E F
Sa(1.0) < 0.1 0.5 0.6 1.0 1.4 2.1
Sa(1.0) = 0.2 0.5 0.7 1.0 1.3
Values of Fv Sa(1.0) = 0.3 0.5 0.7 1.0 1.2
Sa(1.0) =0.4 0.6 0.8 1.0 1.1
2.0 1.9 1.7 Site specific investigation required
Sa(1.0) > 0.5 0.6 0.8 1.0 1.1 1.7
Importance Factor Ie = 0.8
L o w o c c u pa n c y
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
A ll o t h e r b u ild in g s
Design Spectral Values as Adjusted for Building Importance Modification Factor for Building Importance
Ie Fa Sa(T)
Modification Factor for Site Soil Conditions
5% Damped Spectral Acceleration for Reference Soil Conditions
Method of Analysis
Dynamic Analysis (Preferred Method)
• Elastic Spectral Analysis • Elastic Time History Analysis • Inelastic Time History Analysis
Equivalent Static Force Procedure
Equivalent Static Force Procedure May be used for:
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
Modes of Vibration
3-Storey Frame
Mode 1
M od e 2
Mode 3
Equivalent Static Force Procedure Ft
Although seismic action is dynamic in nature, building codes often recommend “Equivalent Static Load Analysis”
V
for simplicity, based on first mode response, as modified empirically for higher mode effects.
Equivalent Static Force V=
S(Ta )M v I E W R dR o
Ve
W: Weight of the structure contributing to inertia forces (D+0.25L+06LS) Ta: Fundamental Period Mv: Higher mode factor I E: I m p o r t a n c e F a c t o r
Ve /Rd Ve /Rd Ro
R : Ductility related force d modification factor Ro: Oversterngth related fo modification factor
Cut-off Values
Because of uncertainties associated with UHS values for Ta > 2.0 sec, V is not reduced beyond the value at S(2.0)
V≥
S(2.0)I E W R dR o
For Rd ≥ 1.5, V need not exceed:
V≤
2 S(0.2)I E W 3
R dR o
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
Measured Versus NBCC-05 (Ta) R/C MRF Buildings 3.5 3.0 c e s , T d o i r e P
2.5 2.0 3/4
T= 0.075 (h n )
1.5 1.0 0.5 0.0 0.0
10.0
20.0
30.0
40.0
50.0
Height h n, m
60.0
70.0
80.0
90.0
1
Measured Versus NBCC-05 (Ta) R/C Shear Wall Buildings 2.50 2.00 ) c e s ( T , d o i r e P
1.50 T = 0.05 h n
3/4
1.00 0.50 0.00 0.00
10.00
20.00
30.00
40.00
Height, hn (m)
50.00
60.00
7
Measured Versus NBCC-95 (Ta) R/C Shear Wall Buildings 2.5
2 ) c e s ( T , d o i r e P
1.5
1
T = 0.09 h n / D
1/2
0.5
0 0.0
2.0
4.0
6.0
8.0
H /D
1/2
10.0
12.0
14
Fundamental Period (Ta) For frame structures: 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 of non-structural elements • Possible inaccuracies in analytical modelling • Differences between design and as-built conditions
Effect of Participating Infill Masonry Walls 30.0 m 6.0 m
6.0 m
6.0 m
6.0 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
Effect of Participating Infill Masonry Walls 6 5-storey building 10-storey building
5
15 storey building NBCC (5 storeys)
4 )
NBCC (1 0 st oreys )
c e s (
NBCC (1 5 st oreys )
T , d o i r e P
3 2
1 0 0
0.1
0.2
0.3
0.4
Wall-to- floor area ratio (%)
0.5
0.6
Fundamental Period (Ta) For braced frames and shear-wall structures: 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 . 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 measured period values
Fundamental Period (Ta) 2.5
Shear Wall Buildings
ce) 2.0 s( d o ir 1.5 e P erd 1.0 u aes M 0.5 0.0 0.0
0.5
1.0 1.5 Computed Period (sec)
2.0
2.5
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
Rd – Ductility Related Force Modification Factor
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 (R d) from 6.0 to 4.0.
2001 draft of Eurocode 8 (ECS 1998) recommends a “q” factor (R d) to vary between 1.0 and 5.0
Rd – Ductility Related Force Modification Factor 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 structures
Only dependable or mi nimum overstrength is considered
Ro = Rsize R
Ryield Rsh Rmech
Rsize – Overstrength Related 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
R – Overstrength Related to Material Resistance ( ) 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.
R = 1/ R R/CandRM StructuralSteel
0 .85 0.90
1.18 1 .11
Ti m b er
0.70
1.43
UR M
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 f or re-bars (Mirza and M acGregor 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 postyield 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 timber 1.00 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.
Elastic Behaviour
1
bf
bf
cf
cf
1
Beam Yielding
2 1
by
by
2
Beams and Columns @ Capacity
3 2 1
bu
bu
cu
cu
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 = 1.00
Except for; Rmech
Ductile Plate Walls DuctileR/CMRF D u c t ile C o u p le d W a lls
1.10 1.05 1.05
Ductile Partial Coupled Walls 1.05
R/C Structures
Rd
Ro
Ductile moment-resisting frames
4.0
1.7
Moderately ductile momentresisting frames
2.5
1.4
Ductile coupled walls
4.0
1 .7
Ductile partially coupled walls
3.5
1.7
Ductile shear walls
3.5
1.6
Moderately ductile shear walls
2.0
1.4
Conventional construction Moment-resisting frames Shear walls
1.5 1.5
1.3 1.3
Other concrete SFRS(s) not listed above
1.0
1.0
•
•
Distribution of Base Shear
Wi h i
F = i
∑ Wi h i
V−F
(
t
)
Ft = 0
for
Ta ≤ 0.7
Ft = 0.07Ta V Ft = 0.25V
for 0.7 < Ta < 3.6 for Ta ≥ 3.6
Overturning Moments
Overturning Moments First
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
M x = J x ∑ Fi (h i − h x ) i =1
Jx Jx
= 1 .0 = J + (1 − J )
hx hn
for
hx
≥ 0 .6
for
hx
< 0.
Torsional Effects
Torsional Effects
Torsion will be considered when:
Torsional moments are in troduced 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 D nx from the centre of mass. Bx =
max
/
ave
Torsional Effects
Torsional Effects
For 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 D nx)
For buildings with B > 1.7 in cases where IEFaSa(0.2) ≥ 0.35 by Dynamic Analysis
Structural Irregularities 1 Vertical stiffness irregularity 2 W e ig h t ( m a s s ) i r r e g u la r it y 3 Vertical geometric irregularity 4 I n - p la n e d is c o n t in u i t y 5 O u t -o f-p l a n e o ff s e t s 6 Discontinuity in capacity (weak storey) 7 T o r s io n a l s e n s i t iv it y 8 N o n - o r th o g o n a l s y s t e m s
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 Irregularities 1. 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)
Types of Irregularities 3.
Vertical Geometric horizontal dimension of the SFRS in a storey > 130% of that in any adjacent storey. (one-storey penthouse excluded)
Types of Irregularities 4. In-Plane Discontinuity
in-plane offset of an element of the SFRS, or
reduction in lateral stiffness of an element in the storey below.
Types of Irregularities 5. Out-of-Plane Offsets discontinuity of lateral force path e.g., out-of-plane offsets of the elements of the SFRS.
Bottom Floors
Top Floors
Types of Irregularities 6. Discontinuity in Capacity - Weak Storey storey shear strength less than that in the storey above. (Sto rey shea r s tr engt h = tot al o f all ele ment s o f t he SFRS in th e di rectio n c ons id ered)
Types of Irregularities 7. Torsional sensitivity if the ratio B > 1.7. B=
max
/
avg
calculated for static loads applied at 0.10 Dn
Plan
Types of Irregularities 8. Non-orthogonal systems SFRS not oriented along a set of orthogonal axes.
Plan
Irregular SFRS
Stif fne ss o f no n-str uct ura l co mpon ents shall no t b e in cl ude d t o m ake an i rr egul ar 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 SFRS
Irregularity type 6 (weak storey) not permitted except if I F S (0.2) < 0.2 and the design base shear = R R V. E a
a
d
o
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
Dynamic Analysis for Seismic Design m a + c v + k u = m ag 400 2
)
300
s / 200 m c ( 100 n 0 io t a r -100 e l e c-200 c A-300
-400
0123456789 Time (sec)
Modes of Vibration
3-Storey Frame
Mode 1
M od e 2
Mode 3
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
) T ( a
0
100
200
300
S , n o it a r e l e c c a l a r t c e p S
Time, t
1.0
If site-specific record is available Otherwise use site-specific design response spectra (UHS)
SPECTRAL ANALYSIS
) T ( a
S , n o i tr a e l e c c A l a r t c e p S
0.8 0.6 0.4 0.2 0.0 0
0.5
1
Period, T
1.5
2
Modal Spectrum Analysis 1. Determine periods (T i) and mode shapes ( i) 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 (γ ) for each i
n
∑ m jφ i, j
mode under consideration γi =
j−1 n
∑ m jφ i, j j=1
2
Modal Spectrum Analysis 4. Compute elastic modal forces and displacements at each floor level
Fi, j
φ i, j γ i S(Ti )m j
δ i, j
φ i, j γ i
Ti
2
4π
2
S(Ti )
5. Find elastic modal storey shears (Vi,x) and base shear (Vi). n
Vi, x = ∑ Fi, j j= x
n
Vi = ∑ Fi, j j=1
Modal Spectrum Analysis 6. Combine the effects of each mode by using an appropriate modal combination rule (like SRSS Method). m
Fx
=
∑
Fi , x
2
m
Vx =
i =1
∑ i =1
i x
i =1
m
m
Ve =
∑V ,
2
Vi
2
δx =
∑ i =1
δ i,x
2
Modal Spectrum Analysis 7. Determine the design base shear Vd
Vd =
Ve R oR d
IE
8. 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
Example – Modal Superposition A 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
Example – Modal Superposition Fi, j Floor
T 1 = 1 . 56 s 1=1.25
φ i, j γ i S(Ti )m j T 2=0.56 s 2=0.39
T 3=0.34 s 3=0.21
3
Fx
=
Fi
∑ i =1
S 1 = 0 . 24 g
S2=0.59g
S3=0.77g
5
1765
-1 2 4 7
726
228 0
4
1623
-3 8 6
-5 1 8
174 7
3 2
1347 964
7 64 1399
-8 7 2 270
177 7 172 0
1
503
1067
949
151 4
6202
1597
555
642 8
5
∑ Fi, j j=1
x
,
Example – Modal Superposition
Ve = 6428 kN
Vd =
Ve R oR d
IE =
6428 (4.0)(1.7)
(1.0) = 945 kN
Linear Time History Analysis Employed 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 V = d
Ve R oR d
I E
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 Analysis Involves 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 Analysis When 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 Analysis The 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 modelling assumptions. 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
Structural Modelling
Structural Modelling
Structural Modelling
Member Modelling
⎧1/12 Span length (simle beams) ⎪1/10 Span length (cont. beams) ⎪ Lo ≤ ⎨ 12 t
⎪⎩1/2 clear distance to next we
Member Modelling
m
h
L
Member Modelling Mi
Mj l l
l
1
2
Flexural Springs
i
j Elastic Beam Element with EI and GA
Hysteretic Behaviour (Steel Structure
Hysteretic Models for Steel Elements in Flexure
R/C Member in Flexure n y
cr
Bilinear Idealization n
n
y
u
Formation of a Plastic Hinge
Hysteretic Behaviour (R/C Structure Drift (%) -6
-4
-2
0
2
4
6
400
)m . N200 k ( M 0 ,t n e o-200 M = F l + PΔ m M -400 -120 -80 -40 0 40 80 Displacement, (mm)
120
Stiffness Degrading Models for R/C
ByClough(1966)
B yT a k e d a( 19 7 0
Strength Degradation in R/C
Strength decay
Stiffness Degradation and Pinching in R/C
Anchorage Slip
s s h
y
e
f
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)
Hysteretic Modelling In spite of all the complications of hysteretic behaviour of structural elements and subassemblages, it is possible to select reasonably simple hysteretic models for inelastic seismic analysis of structures….
Thank You…
Questions and Comments ?
