Paper presented to Joint Technical Sessions Between
Recent Code Developments for Earthquake Resistance
By Alfrico D. Adams F.I.Struct.E, FJIE
The more mature among us engineers would have grown with the SEAOC Code, the Recommended Lateral Force Requirement of the Structural Engineers Association of California. The design philosophy of the SEAOC Code was that the buildings designed to the code should:-
(a) Resist Minor Earthquakes without damage
(b) Resist Moderate Earthquakes without structural damage, but with some non-structural damage
(c) Resist Major Earthquakes without collapse, but with some structural and non-structural damage
This philosophy has served us for at least three decades, but more and more it has become evident that rational means must be introduced to distinguish the treatment of special buildings from conventional buildings and ensure different levels of performance for different buildings based on characteristics such as their use and occupancy, the economic costs of the contents of the buildings and the need for some essential buildings to come unscathed through extreme events.
2.0 Scope of this Presentation
This presentation lists some of the developments in earthquake resistant design procedure, aimed at refining the procedure and at selecting values and methods of design which are consistent with the
(a) earthquake risk to be experienced
(b) the building performance desired for the particular level of earthquake chosen
It also gives an introduction to the procedure now being proposed by the International Building Code (USA).
3.0 Development of Our Current Methods
Quite early in the development of earthquake resistant design technology it became evident that conventional buildings could not resist the forces from the predicted major earthquakes if their structural frames were to remain in the elastic range.
Any attempt to ensure totally elastic behaviour would result in prohibitive costs of construction. The next step was therefore to accept inelastic behaviour and by appropriate selection of materials and detailing practices, to encourage well-conditioned behaviour, beyond the elastic range.
Fig. 3.1 and 3.2 show the relationship between lateral shear and deformation which illustrates the range of damage control.
The early codes (e.g., SEAOC 1959) expressed the lateral force for design as V=KCW.K varied from 0.67 to 1.33 and depended on the type of structural system It reflected among other things, the redundancies in the building systems and the ductility of the element of the system. C was related to the natural period of the structure and was inversely proportional to it.
Later introductions were:-
Z - A zone factor which allowed for varying
seismicities, suitable for locations other than
S - A soil factor to allow for the thickness and or firmness of the supporting soil. Later this was incorporated in to the C factor.
I - An importance factor which introduced higher design forces for buildings which housed critical post-disaster facilities, or housed large numbers of persons.
Rw - A Response Modification Factor which represented damping, ductility and observed performance in earthquakes. This replaced the K-factor.
These developments culminated in the expression; V = ZIC.W. in the 1980’s
and this form with minor variations appeared in the SEAOC, UBC and CUBiC Codes of that decade.
4.0 Other Research and Development Efforts
all these developments research was pursued by the Applied Technology Council,
4.1 Applied Technology Council
The ATC3-06 which was parallel with the other codes, but somewhat more advanced used the expression:
V = CSW
Where CS = 1.2 AvS where Av represented mapped acceleration
4.2 National Earthquake Hazard Reduction Program
This American research program introduced the concept of Building Performance Levels.
In working to develop guidelines for Seismic rehabilitation, it was recognised that some owners might desire to have better building performance than that implied by the traditional SEAOC methods, i.e. that buildings would:
· Survive moderate earthquakes with only minor repairable damage to the structure.
· Survive major earthquakes by ensuring life safety, but sustaining damage which may be beyond repair.
Furthermore, the recognition that non-structural damage often represented an even greater economic loss than structural damage, urged them to introduce performance levels which included non-structural considerations.
The following are definitions of the various Building Performance Levels; Structural Performance Levels, Non-structural Performance Levels and the Basic Safety Objective.
4.2.1 Building Performance Levels
1. Operational Level
2. Immediate Occupancy Level
3. Life Safety Level
4. Collapse Prevention
Building Performance comprises structural & non-structural performance levels.
Determination of SDS
The 5% damped design spectral response acceleration at short periods SDS is determined from:
SDS = 2/3 SMS
SMS = Maximum Considered Earthquake Spectral response acceleration for short period as determined in Section 1615.1.2
Note: similarly SD1 = 2/3 SM1, where
SM1 = Max. Considered earthquake spectral response acceleration for 1 second period.
From 1615.1.2 SMS = Fa SS
Where Fa = Site Coefficient from site classes definition table 1615.1.1 and table 1615.1.2-1.
SS = Mapped spectral acceleration for short period
Typical values Site Class Definition
Stiff Soil Profile SPTN 15≤N≤50 – Site Class Definition
Then for SS = 0.5 or Interpolating for SS = 0.4
Fa = 1.4
SS = The mapped spectral acceleration for short periods as determined in Section 1615.1
4.2.2 Basic Safety Objective
This is met when a building can satisfy two criteria:-
1. The Life Safety Building Performance Level, i.e. Structural and Non-Structural Life Safety Performance Levels, for Basic Safety Earthquake 1.
2. The Collapse Prevention Performance Level, which only pertains to Structural Performance, assuming the stronger shaking from the less frequent Basic Safety Earthquake 2.
Figure 4.2.1 shows the hierarchy of Building Performance Levels.
illustrates the Rehabilitation Objectives and the relative costs of the
objectives contemplated by NEHRP in their attempt to develop systematic
guidelines for seismic rehabilitation of buildings in the
4.2.3 Rationalising the Terms used in NEHRP Guidelines for Seismic Rehabilitation
NEHRP – National Earthquake Hazard Reduction Programme
One phase of NEHRP was aimed at Seismic Rehabilitation of Existing Buildings. For this, a range of Rehabilitation objectives are listed:
- Operational Performance Level – Non-Structural facilities useable after event (e.g. elevator, escalator etc)
- Immediate Occupancy Level – say for E/q 50% Probability of exceedance in 50 years.
- Life Safety Level of Performance – 10% Probability of exceedance in 50 years
The Basic Safety Earthquake 1 – BSE1 is the 10% probability of exceedance in 50 years earthquake. This is equivalent to the Design earthquake spectral response acceleration parameters for short and long period earthquake.
BSE2 is the maximum credible earthquake (mapped MCE response).
BSE1 can either be 10% probability of exceedance, 50 year ground shaking or 2/3 of BSE2, whichever is smaller.
BSE2 can be taken as 150% of BSE1.
4.3 Seismic Design by IBC 2000
4.3.1 Design Accelerations
Select Site Class A-F
When insufficient data is available Site Class can be considered to be D i.e. assuming unconfined shear strength ≤ 1000 pst.
SMS = Maximum considered short period (0.2 sec.) spectral acceleration.
SM1 = Maximum considered long period (1 sec.) spectral acceleration.
The mapped values are:
SS = Mapped spectral response acceleration for short period (0.2 sec).
S1 = Mapped spectral response acceleration for long period (1.0 sec).
The above sets of values are linked by a coefficients Fa and Fv derived from the site class and mapped acceleration.
Fa applies to the short period values.
Hence the maximum considered spectral accelerations are:
SMS = Fa SS
SM1 = Fv S1
TABLE 184.108.40.206 - TYPICAL SITE CLASS DEFINITIONS
SITE CLASS S1
SOIL PROFILE NAME
SHEAR WAVE VEL. or SHEAR STRENGTH
Very Dense Soil Soft Rock
Stiff Soil Profile
Refer to IBC
4.3.2. Design Spectral Response Acceleration Parameters
220.127.116.11 SDS and SD1
These are based on 5% damping.
SDS = 5% damped design spectral acceleration at short periods
SD1 = 5% damped design spectral acceleration at 1 second period
SDS = 2/3 SMS – where SMS = maximum considered E/q spectral response – short period.
SD1 = 2/3 SM1 – where SM1 = maximum considered E/q spectral response acceleration for 1 second period.
18.104.22.168 General Procedure Response Spectrum - Sa
The design spectral acceleration is Sa
1. For period less than To
the formula Sa is 0.6 SDS T + 0.45SDS
To is taken = 0.2 SD1/SDS
2. For periods between To and Ts
Sa = SDS, where Ts = SD1/SDS
3. For period greater than Ts
Sa = SD1/T
Where T = Fundamental period (in seconds) of the structure.
Fig. 22.214.171.124 illustrates these relationships.
4.3.3 Seismic Design Category
Buildings are classified into Seismic Use Groups I to III varying with the importance of the structure (see table 126.96.36.199), Table 188.8.131.52 gives Seismic Design Category from A-D depending on the Use Group and the design acceleration SDS or SD1.
4.3.4. Design Requirements
Seismic Category A
For Seismic Category A, a nominal Minimum Lateral Force of
Fx = 0.01wx is assigned.
Certain irregularities are ignored for one and two storey buildings for Category A and also for B&C.
4.3.5 Seismic Category B&C
The equivalent lateral force procedure V = CSW is permitted in Seismic Category B&C for reinforced concrete buildings 2-storey and over.
For 3-storey light frame buildings or for one and two storey building in
Use Group 1 Simplified Method (V = 1.2SDS W) is permitted.
4.3.6 Plan and Vertical Structural Irregularities
These are classified and the building assigned to various more stringent design categories e.g. D, E &F depending on the nature and extent of the irregularity.
Included for some of these categories is a requirement for dynamic model analysis. In addition, certain types of construction are not permitted in these more stringent categories.
4.3.7 Seismic Design Procedure – In Accordance with IBC 2000
Say building exceeds two storeys and is of Reinforced Concrete construction.
Refer to Section 1617-IBC 2000
EARTHQUAKE LOADS – Minimum Design Lateral Force and Related Effects
The loads computed here are for use in the Load Combinations set out in Section 1605.
e.g. Strength Design: 1.2D + 1.0E + (f1L or f2S) or 0.9D + (1.0E or 1.3W)
L = Live Load
S = Snow Load
f1 = 0.5 exception for certain cases
fz = 0.2 for most roofs
It should be noted: It seems obvious that the earthquake loads computed are ultimate loads, unlike the values previously computed for SEAOC and CUBiC.
To Compute Seismic Load Effect ‘E’
E = ρ QE + 0.2SDSD
This is where seismic and gravity loads are additive, where:
E = combined effect of horizontal and vertical earthquake loads.
Ρ = a reliability factor based on system redundancy (Note: For Seismic category A-C, ρ = 1.0)
QE = The effect of horizontal seismic forces.
SDS = The design spectral response acceleration at short periods obtained from Section 1615.1.3 or Section 16184.108.40.206 of IBC
D = The effect of dead load
Where the effects of gravity and seismic load counteract each other plus changes to minus.
(For light framed structures up to 3 stories and for other types up to 2- stories in Seismic Use Group 1). The SIMPLIFIED ANALYSIS PROCEDURE 1616.6.1 is allowed as indicated in 1617.5 of IBC
i.e. V = 1.2 SDS W
SDS = The design elastic response acceleration for short period as determined in accordance with: 220.127.116.11 herein
R – Response Modification Coefficient
W – Effective Seismic Weight
V – Seismic Base Shear
(Note: the above appears to include Group 1 for all Seismic Categories.)
For Other Structures in Seismic Category B or C
The analysis procedures are to be in accordance with Section 1617.4 of IBC where:
V = CSW
CS = The seismic response coefficient determined in accordance with 1618.104.22.168 i.e. SDS = 2/3 DMS
R = Response Modification Factor
I = The Occupancy Importance factor determined in accordance with 1616.2
CS need not exceed SD1; SD1 = design spectral acceleration at 1 second period.
Nor be less than CS = 0.444 SD
(Note: There are other rules for Categories E & F)
Fundamental Period Ta = CThn3/4
CT = Building Period Coefficient
= 0.035 for moment resisting frames of steel resisting 100% of the required seismic force.
(Note: Metric coefficient is 0.085)
= 0.030 for moment resisting frames of reinforced concrete resisting 100% of the required seismic force.
(Note: Metric coefficient is 0.073)
= 0.030 for eccentrically braced steel frames
= 0.020 for all other building systems.
(Note: Metric coefficient is 0.049)
hn = The height (ft or m) above the base to the highest level.
Alternatively for up to 12 stories and minimum storey heights = 10ft (3m)
T = 0.1N, where N = number of stories.
(a) Consider RC Frame Building 5-storeys.
Choose Life Safety Performance level for this Example.
Consider Mapped Accelerations
Say, Short Period Acceleration SS = 0.75
Say, Long Period Acceleration S1 = 0.3
(b) Select Site Class from SPT N value between 15 & 50
Say Site Class C
Then Fa = 1.1
Fv = 1.5
(c) Max considered earthquake accelerations
SMS = Fax SS = 1.1 x 0.75 = 0.825
SM1 = Fv S1 = 1.5 x 0.3 = 0.45
(d) Design Spectral Response Acceleration 5% Damped
SDS = 2/3 SMS = 2/3 x 0.825 = 0.55
SD1 = 2/3 SM1 = 2/3 x 0.45 = 0.3
(e) Choose Seismic Design Category
Assume Seismic Use Group 1
- For Short Period
If SDS between 0.33g and 0.5g therefore Seismic Category C
- For 1 Second Period
SD1 exceeds 0.2g therefore Seismic Category D
Hence Category D controls as the more severe of the two.
The Seismic Category determines:
(1) What irregularities, if any, must considered
(2) What analysis procedure must be used
For Seismic Category D
The requirements would be:-
1. Plan structural irregularities and vertical structural irregularities would all need to be allowed for.
2. The Equivalent Lateral Force procedure must be used for design
V = CSW where CS = SDS/(R/I)
Upper and lower limitations of CS are set.