SECTION 6 EQUIVALENT STATIC ANALYSIS
6.4 SPECTRAL SHAPE FACTOR (C h (T))
The spectral shape factor (Ch(T)) shall be as given in Table 6.4 (illustrated in Figure 6.4) for the appropriate site sub-soil class defined in Section 4.
TABLE 6.4
SPECTRAL SHAPE FACTOR (Ch(T))
Site sub-soil class
* Values in brackets correspond to values of spectral shape factor for the modal response spectrum and the numerical integration time history methods and for use in the method of calculation of forces on parts and components (see Section 8)
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Soil Ae Soil Be Soil Ce Soil De Soil Ee
PERIOD IN SECONDS (T) SPECTRAL ORDINATES (Ch(T))
FIGURE 6.4 NORMALIZED RESPONSE SPECTRA FOR SITE SUB-SOIL CLASS 6.5 DETERMINATION OF STRUCTURAL DUCTILITY (µ) AND STRUCTURAL PERFORMANCE FACTOR (Sp)
The ductility of the structure (μ) and the structural performance factor (Sp) shall be determined either—
(a) in accordance with the appropriate material standard where the data is provided; or (b) as given in Table 6.5(A) or 6.5(B) for the structure type and material where the data
is not provided,
except that, for a specific structure, it shall be permissible to determine μ and Sp by using a non-linear static pushover analysis.
NOTES:
1 Where the design is carried out using other than recognized Australian material design Standards, then the values given in the last row for each material type in Table 6.5A should be used.
2 Where the design is carried out in accordance with NZS 1170.5, µ and Sp should be determined as set out therein.
A lower μ value that is specified in this Clause or the relevant material standard may be used. In all cases, the structure shall be detailed to achieve the level of ductility assumed in the design, in accordance with the applicable material design Standard.
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TABLE 6.5(A)
STRUCTURAL DUCTILITY FACTOR (µ) AND STRUCTURAL PERFORMANCE FACTOR (Sp)—BASIC STRUCTURES
Structural
system Description µ Sp Sp/µ µ/Sp
Steel structures
Special moment-resisting frames (fully ductile)* 4 0.67 0.17 6 Intermediate moment-resisting frames (moderately ductile) 3 0.67 0.22 4.5 Ordinary moment-resisting frames (limited ductile) 2 0.77 0.38 2.6 Moderately ductile concentrically braced frames 3 0.67 0.22 4.5 Limited ductile concentrically braced frames 2 0.77 0.38 2.6 Fully ductile eccentrically braced frames* 4 0.67 0.17 6 Other steel structures not defined above 2 0.77 0.38 2.6 Concrete structures
Special moment-resisting frames (fully ductile)* 4 0.67 0.17 6 Intermediate moment-resisting frames (moderately ductile) 3 0.67 0.22 4.5
Ordinary moment-resisting frames 2 0.77 0.38 2.6
Ductile coupled walls (fully ductile)* 4 0.67 0.17 6
Ductile partially coupled walls* 4 0.67 0.17 6
Ductile shear walls 3 0.67 0.22 4.5
Limited ductile shear walls 2 0.77 0.38 2.6
Ordinary moment-resisting frames in combination with a limited
ductile shear walls 2 0.77 0.38 2.6
Other concrete structures not listed above 2 0.77 0.38 2.6 Timber structures
Shear walls 3 0.67 0.22 4.5
Braced frames (with ductile connections) 2 0.77 0.38 2.6
Moment-resisting frames 2 0.77 0.38 2.6
Other wood or gypsum based seismic-force-resisting systems not
listed above 2 0.77 0.38 2.6
Masonry structures
Close-spaced reinforced masonry† 2 0.77 0.38 2.6
Wide-spaced reinforced masonry† 1.5 0.77 0.5 2
Unreinforced masonry† 1.25 0.77 0.62 1.6
Other masonry structures not complying with AS 3700 1.00 0.77 0.77 1.3
* The design of structures with µ > 3 is outside the scope of this Standard (see Clause 2.2)
† These values are taken from AS 3700
TABLE 6.5(B)
STRUCTURAL DUCTILITY FACTOR (µ) AND STRUCTURAL PERFORMANCE FACTOR (Sp)—SPECIFIC STRUCTURE TYPES
Type of structure µ Sp µ/Sp Sp/µ
Tanks, vessels or pressurized spheres on braced or unbraced legs 2 1 2 0.5 Cast-in-place concrete silos and chimneys having walls continuous to
the foundation 3 1 3 0.33
Distributed mass cantilever structures, such as stacks, chimneys, silos
and skirt-supported vertical vessels 3 1 3 0.33
Trussed towers (freestanding or guyed), guyed stacks and chimneys 3 1 3 0.33
Inverted pendulum-type structures 2 1 2 0.5
Cooling towers 3 1 3 0.33
Bins and hoppers on braced or unbraced legs 3 1 3 0.33
Storage racking 3 1 3 0.33
Signs and billboards 3 1 3 0.33
Amusement structures and monuments 2 1 2 0.5
All other self-supporting structures not otherwise covered 3 1 3 0.33
6.6 TORSIONAL EFFECTS
For each required direction of earthquake action, the earthquake actions, as determined in Clause 6.3, shall be applied at the position calculated as ±0.1b from the nominal centre of mass, where b is the plan dimension of the structure at right angles to the direction of the action.
This ±0.1b eccentricity shall be applied in the same direction at all levels and orientated to produce the most adverse torsion moment for the 100% and 30% loads.
6.7 DRIFT DETERMINATION AND P-DELTA EFFECTS 6.7.1 General
Storey drifts, member forces and moments due to P-delta effects shall be determined in accordance with Clauses 6.7.2 and 6.7.3.
6.7.2 Storey drift determination
Storey drifts shall be assessed for the two major axes of a structure considering horizontal earthquake forces acting independently, but not simultaneously, in each direction. The design storey drift (dst) shall be calculated as the difference of the deflections (di) at the top and bottom of the storey under consideration.
The design deflections (di) shall be determined from the following equations:
di = dieμ/Sp . . . 6.7(1)
where
die = deflection at the ith level determined by an elastic analysis, carried out using the horizontal equivalent static earthquake forces (Fi) specified in Clause 6.3, applied to the structure in accordance with Clause 6.6
Where applicable, the design storey drift (dst) shall be increased to allow for the P-delta effects as given in Clause 6.7.3.
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6.7.3 P-delta effects 6.7.3.1 Stability coefficient
For the inter-storey stability coefficient (θ) calculated for each level, design for P-delta effects shall be as follows:
(a) For θ ≤ 0.1, P-delta effects need not be considered.
(b) For θ > 0.2, the structure is potentially unstable and shall be re-designed.
(c) For 0.1 < θ ≤ 0.2, P-delta effects shall be calculated as given in Clause 6.7.3.2,
∑
=∑
= ⎟⎟⎠
⎞
⎜⎜
⎝
= n ⎛
i j
n i
j j
si j
st W / h F
d μ
θ . . . 6.7(2)
where
i = level of the structure under consideration
hsi = inter-storey height of level i, measured from centre-line to centre-line of the floors
6.7.3.2 Calculating P-delta effects
Values of the horizontal earthquake shear forces and moments, the resulting member forces and moments, and the storey drifts that include the P-delta effects shall be determined by—
(a) scaling the equivalent static forces and deflections by the factor (0.9/(1 – θ)), which is greater than or equal to 1; or
(b) using a second-order analysis.
S E C T I O N 7 D Y N A M I C A N A L Y S I S 7.1 GENERAL
Dynamic analysis, when used, shall be carried out in accordance with this Section. The analysis shall be based on an appropriate ground-motion representation in accordance with Clause 7.2. The mathematical model used shall be in accordance with Clause 7.3.
The analysis procedure may be either a modal-response-spectrum analysis in accordance with Clause 7.4 or a time-history analysis in accordance with Clause 7.2(c).
Drift and P-delta effects shall be determined in accordance with Clause 7.5.
7.2 EARTHQUAKE ACTIONS
The earthquake ground motion shall be accounted for by using one of the following:
(a) Horizontal design response spectrum (Cd(T)), including the site hazard spectrum and the effects of the structural response as follows:
Cd(T) = C(T)Sp/μ . . . 7.2(1)
= kpZCh(T)Sp/μ . . . 7.2(2)
where values are as given in Section 6, except that—
T = period of vibration appropriate to the mode of vibration of the structure being considered
(b) Site-specific design response spectra developed for the specific site, which shall be based on analyses that consider the soil profile and apply a bedrock ground motion compatible with the rock spectra given in Clause 6.4.
(c) Ground-motion time histories chosen for the specific site, which shall be representative of actual earthquake motions. Response spectra from these time histories, either individually or in combination, shall approximate the site design spectrum conforming to Item (a) or (b). A dynamic analysis of a structure by the time-history method involves calculating the response of a structure at each increment of time when the base is subjected to a specific ground-motion time-history. The analysis should be based on well-established principles of mechanics using ground-motion records compatible with the site-specific design response spectra.
Where design includes consideration of vertical earthquake actions, both upwards and downwards directions shall be considered and the vertical design response spectrum shall be as follows:
Cvd(T) = Cv(Tv)Sp . . . 7.2(3)
= 0.5C(Tv)Sp
= 0.5kpZCh(Tv)Sp where
Cv(Tv) = elastic site hazard spectrum for vertical loading for the vertical period of vibration
7.3 MATHEMATICAL MODEL
A mathematical model of the physical structure shall represent the spatial distribution of the mass and stiffness of the structure to an extent that is adequate for the calculation of the significant features of its dynamic response.
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7.4 MODAL ANALYSIS 7.4.1 General
A dynamic analysis of a structure by the modal response spectrum method shall use the peak response of all modes having a significant contribution to the total structural response as specified in Clause 7.4.2. Peak modal responses shall be calculated using the ordinates of the appropriate response spectrum curve specified in Clause 7.2(a) or 7.2(b) that corresponds to the modal periods. Maximum modal contributions shall be combined in accordance with Clause 7.4.3.
7.4.2 Number of modes
In two-dimensional analysis, sufficient modes shall be included in the analysis to ensure that at least 90% of the mass of the structure is participating for the direction under consideration.
In three-dimensional analysis, where structures are modelled so that modes that are not those of the seismic-force-resisting system are considered, then all modes not part of the seismic-force-resisting system shall be ignored. Further, all modes with periods less than 5% of the fundamental natural period of the structure (<0.05T1) may be ignored.
7.4.3 Combining modes
The peak member forces, displacements, horizontal earthquake shear forces and base reactions for each mode shall be combined by a recognized method.
When modal periods are closely spaced, modal interaction effects shall be considered.
7.4.4 Torsion
7.4.4.1 Three-dimensional dynamic analysis
Three-dimensional dynamic analysis shall take account of torsional effects, including accidental torsional effects as described in Clause 6.6. Where three-dimensional models are used for analysis, the effects of accidental torsion shall be accounted for, either by appropriate adjustments in the model, such as adjustment of mass locations, or by equivalent static procedures, as described in Clause 6.6.
7.4.4.2 Two-dimensional dynamic analysis with static analysis for torsion
For static analysis for torsional effects, applied torsion at each level shall use either the actions calculated by the equivalent static method or the combined storey earthquake forces found in a two-dimensional modal response spectrum analysis for translation. The eccentricity used shall be as required in Clause 6.6. Action effects arising from torsion shall be combined with the translational action effects by direct summation, with signs chosen to produce the most adverse combined effects in the resisting members.
7.5 DRIFT DETERMINATION AND P-DELTA EFFECTS
Storey drifts, member forces and moments due to P-delta effects shall be calculated in accordance with Clause 6.7, using the deflections, forces and moments calculated from the dynamic analysis.
S E C T I O N 8 D E S I G N O F P A R T S A N D C O M P O N E N T S
8.1 GENERAL REQUIREMENTS 8.1.1 General
Non-structural parts and components and their fastenings, as listed in Clause 8.1.4, shall be designed for horizontal and vertical earthquake forces as defined in Clauses 8.1.2 and 8.1.3.
Base isolation may be used to reduce the forces on a component. Where flexible mounting devices (such as spring mountings) are used, they shall be fitted with restraining devices to limit the horizontal and vertical motions, to inhibit the development of resonance in the flexible mounting system, and to prevent overturning.
8.1.2 Earthquake actions
Design of parts and components shall be carried out for earthquake actions by one of the following methods:
(a) Using established principles of structural dynamics.
(b) Using the general method given in Clause 8.2.
(c) Using the forces determined by the simplified method given in Clause 8.3.
8.1.3 Forces on components
The horizontal earthquake force on any component shall be applied at the centre of gravity of the component and shall be assumed to act in any horizontal direction. Vertical earthquake forces on mechanical and electrical components shall be taken as 50% of the horizontal earthquake force.
Mechanical connectors from the following shall be designed for 1.5 times the design force for the supported element:
(a) Curtain walls.
(b) External walls.
(c) Walls enclosing stairs, stair shafts, lifts and required exit paths.
8.1.4 Parts and components
The following parts and components and their connections shall be designed in accordance with this Section:
(a) Architectural components:
(i) Walls that are not part of the seismic-force-resisting system.
(ii) Appendages, including parapets, gables, verandas, awnings, canopies, chimneys, roofing components (tiles, metal panels) containers and miscellaneous components.
(iii) Connections (fasteners) for wall attachments, curtain walls, exterior non-loadbearing walls.
(iv) Partitions.
(v) Floors (including access floor systems, where the weight of the floor system shall be determined in accordance with Clause 6.2.2).
(vi) Ceilings.
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(vii) Architectural equipment including storage racks and library shelves with a height over 2.0 m.
(b) Mechanical and electrical components:
(i) Smoke control systems.
(ii) Emergency electrical systems (including battery racks).
(iii) Fire and smoke detection systems.
(iv) Fire suppression systems (including sprinklers).
(v) Life safety system components.
(vi) Boilers, furnaces, incinerators, water heaters, and other equipment using combustible energy sources or high-temperature energy sources, chimneys, flues, smokestacks, vents and pressure vessels.
(vii) Communication systems (such as cable systems motor control devices, switchgear, transformers, and unit substations).
(viii) Reciprocating or rotating equipment.
(ix) Utility and service interfaces.
(x) Anchorage of lift machinery and controllers.
(xi) Lift and hoist components including structural frames providing support for guide rail brackets, guide rails and brackets, car and counterweight members.
(xii) Escalators.
(xiii) Machinery (manufacturing and process).
(xiv) Lighting fixtures.
(xv) Electrical panel boards and dimmers.
(xvi) Conveyor systems (non-personnel).
(xvii) Ducts and piping distribution systems.
(xviii) Supports for ducts and piping distribution systems, except supports in the following situations:
(A) In structures classified as being in EDC I.
(B) For gas piping less than 25 mm inside diameter.
(C) For piping in boiler and mechanical rooms less than 32 mm inside diameter.
(D) For all other piping less than 64 mm inside diameter.
(E) For all electrical conduit less than 64 mm inside diameter.
(F) For all rectangular air-handling ducts less than 0.4 m2 in cross-sectional area.
(G) For all round air-handling ducts less than 700 mm in diameter.
(H) For all ducts and piping suspended by individual hangers 300 mm or less in length from the top of the pipe to the bottom of the support for the hanger.
(c) All other components similar to those listed in Items (a) and (b).
8.2 METHOD USING DESIGN ACCELERATIONS
Architectural, mechanical and electrical components and their fixings shall be designed for earthquake actions from the accelerations determined using the design methods given in Sections 6 and 7, as appropriate for the particular structure in which the component or fixing is incorporated.
The forces generated on the part or component in the specific structure being considered are given as follows, based on the principles given in this Standard for design of the structure:
Fc = afloor[Icac/Rc]Wc≤ 0.5Wc . . . 8.2(1)
where
afloor = effective floor acceleration at the level where the component is situated,
calculated from the earthquake actions determined for the structure using Sections 5, 6 and 7 divided by the seismic weight, but not less than kpZCh(0), where the values of Ch(0) are the bracketed values given in Table 6.1
NOTE: The fundamental natural period of vibration of a completed structure may be determined by measurement.
Ic = component importance factor, taken as:
= 1.5 for components critical for life safety, which includes parts and components required to function immediately following an earthquake, those critical to containment of hazardous materials, storage racks in public areas and all parts and components in importance level 4 structures
= 1.0 for all other components ac = component amplification factor
= 2.5 for flexible spring-type mounting systems for mechanical equipment (unless detailed dynamic analysis is used to justify lower values)
= 1.0 for all other mounting systems Rc = component ductility factor
= 1.0 for rigid components with non-ductile or brittle materials or connections
= 2.5 for all other components and parts
Wc = seismic weight of the component, in kilonewtons
For objects mounted on the ground, the acceleration should be taken as follows:
afloor = kpZCh(0) . . . 8.2(2)
where
Ch(0) = bracketed value of the spectral shape factor for the period of zero seconds, as given in Clause 6.4
8.3 SIMPLE METHOD
Non-structural parts or components and their attachments shall be designed to resist the horizontal earthquake force determined as follows and applied to the component at its centre of mass in combination with the gravity load of the element:
Fc = [kpZCh(0)]ax[Icac/Rc]Wc but > 0.05Wc . . . 8.3 where Ic, ac, Rc, Wc are as given in Clause 8.2; and
kp = probability factor (see Section 3) Z = hazard factor (see Section 3)
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ax = height amplification factor at height hx at which the component is attached, given as follows:
= (1 + kchx)
kc = 2/hn for hn≥ 12 m
= 0.17 for hn < 12 m
hx = height at which the component is attached above the structural base of the structure, in metres
hn = total height of the structure above the structural base, in metres
APPENDIX A
DOMESTIC STRUCTURES (HOUSING) (Normative)
A1 GENERAL
For the purposes of this Appendix, a domestic structure (housing) is a single dwelling or one or more attached dwellings complying with Class 1a or 1b, as defined in the Building Code of Australia (as shown in Figure A1).
Domestic structures (housing) exceeding 8.5 m in height (see Figure A1), shall be designed in accordance with Section 2 for Importance Level 2 structures, using the annual probability of exceedance specified for housing.
TABLE A1
DESIGN OF DOMESTIC STRUCTURES OF HEIGHT LESS THAN OR EQUAL TO 8.5 METRES
Hazard at the kpZ
Provision for lateral
resistance Material type Specific deemed
to satisfy limits Design required As per the relevant
Standard
As per the relevant Standard
None provided Use Paragraph A2 or design as for importance level 2 (see Section 2)
≤0.11 Housing designed and detailed for lateral wind forces in accordance with AS 1684, AS 3600, AS 3700, AS 4100, AS/NZS 1664, AS 1720.1 or NASH Standard Part 1—2005
Other materials ∗ None provided Use Paragraph A2 or design as for importance level 2 (see Section 2)
>0.11 Housing designed and detailed for lateral wind forces in accordance with AS 1684, AS 3600, AS 3700, AS 4100, AS/NZS 1664, AS 1720.1 or NASH Standard Part 1—2005
As per the relevant Standard
As per the relevant Standard
∗ This includes any other materials that are not covered by accepted design Standards such as random stone masonry or hay bale construction
A2 DESIGN AND DETAILING
Domestic structures required to be designed in accordance with this Paragraph shall comply with the following requirements:
(a) Where the racking forces calculated in this item are greater than those calculated for wind action, lateral bracing shall be provided in both orthogonal directions, distributed into at least two walls in each orthogonal direction with a maximum spacing between walls of 9 m to resist the following forces:
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(i) For masonry veneer, reinforced masonry, timber, steel and concrete structures—
Fr = 1.4 kp Z W . . . A2(1)
(ii) For unreinforced masonry and other structures—
Fr = 2.3 kp Z W . . . A2(2)
where
Fr = horizontal design racking earthquake force applied in each orthogonal direction on the part or component, in kilonewtons
W = sum of the seismic weight of the building (G + 0.3Q) at the level where bracing is to be determined and above this level (see Figure 1.5(A)) kp = probability factor appropriate for the limit state under consideration Z = earthquake hazard factor, which is equivalent to an acceleration
coefficient with an annual probability of exceedance of 1/500 (i.e., a 10% probability of exceedance in 50 years)
(b) Walls shall be tied to other walls that they abut and shall be anchored to the roof and all floors that provide horizontal in-plane and perpendicular to the plane of the wall support for the wall, with an anchorage capable of resisting 0.5 kN/m. Walls shall be checked for stability under out-of-plane lateral loads of Z times the weight of the wall.
(c) Non-ductile components, such as unreinforced masonry gable ends, chimneys and parapets shall be restrained to resist a minimum force of 0.1Wc, where Wc is the weight of the component. Masonry veneer walls tied to framing in accordance with AS 3700 are deemed to comply with this Item (c).
NOTE: See AS 3700 for detailing requirements for masonry structures.
FIGURE A1 SECTION GEOMETRY
BIBLIOGRAPHY AS
4678 Earth retaining structures NZS
1170 Structural design actions
1170.5 Part 5: Earthquake actions—New Zealand
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NOTES
NOTES
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Committees of experts from industry, governments, consumers and other relevant sectors prepare Australian Standards. The requirements or recommendations contained in published Standards are a consensus of the views of representative interests and also take account of comments received from other sources. They reflect the latest