Chapter V First Part

Chapter V Determination of the seismic action by Equivalent Static Force Method
DETERMINATION OF THE SEISMIC ACTION

BY THE EQUIVALENT STATIC FORCE METHOD
5.1 Structural seismic response of a structure

5.2 Structural seismic analysis
5.3 Code's seismic procedures
5.4 The Concept of the Equivalent Static Force Method
5.5 Seismic analyses to RPA99
5.6 Equivalent static method to RPA99 version 2003
5.7 Justification for safety to RPA99 version 2003
5.8 Lateral Forces Method to EC8
Earthquake Engineering Courses 2sd Year Master Structures 2023 / 2024 By Abderrahim Labed 84
5.1 Structural seismic response of a structure

The seismic action is characterised by its acceleration, velocity and displacement
imposed to the base of the structure vary with the duration of the motion. It is thus clear that
the seismic action has dynamic properties that interact with those of the stricken building.
Indeed, due to ground vibrations, deformations occur in the structure, which in turn generate
restoring forces (due to the structure’s stiffness), damping forces (due to internal friction,
external dissipation and essentially by the damage of the dissipative zones) and inertial forces
(due to the mass of the structure).
Dynamic loading can be defined as any loading which varies with time, and seismic
loading is a complex variant of this. The way in which a structure responds to a given dynamic
excitation depends on many factors including the nature of the excitation and the dynamic
characteristics of the structure, i.e. on the manner in which it stores and dissipates vibrational
energy. In addition, seismic excitation may be described in terms of displacement, velocity, or
acceleration varying with time. When this excitation is applied to the base of a structure it
produces.
The response of steel structures, including multi-storeyed buildings, to loading is
influenced by two non-linear effects, the non-linearity concerning material behaviour and the
geometric non-linearity. The assessment of the seismic response of buildings should provide
load distributions and displacements resulting from design seismic action. In particular, the
analysis should evaluate seismic demand in terms of strength and ductility within each
structural element, taking part in the absorption of seismic forces.
5.2 Structural seismic analysis

5.2.1 General
The analysis of a structural system, as an essential step in the design of a structure to
resist earthquakes, is required to determine the structural response to the applied loadings or
ground excitation in terms of internal forces and moments, stresses strains, deformations. For
seismic context, the performance evaluation, a structural analysis of the mathematical model
of the structure is required to determine force and displacement demands in various
components of the structure. This can be also done by setting up appropriate numerical models
implanted in computer codes. Using finite element methods (FEM) in order to represent the
structure and perform the analysis at the design stage, through global model in a 3D (three
dimensional) or 2D (two dimensional). Several analysis methods, both elastic and inelastic, are
available to predict the seismic performance of the structures. Generally speaking, a structural
analysis procedure requires:
• A model of the structure,
• A method of analysis for forming and solving the governing equations. In fact,
it does exist a range of methods from a plastic analysis to a sophisticated nonlinear, dynamic
analysis of a detailed structural model that can be used, depending on the purpose of the
analysis in the design process.
5.2.2 Analysis methods for structures
• Linear and nonlinear analyses
An important decision in a structural analysis is to assume whether the relationship
between forces and displacements is linear or nonlinear. Although the seismic design for
buildings is currently based on elastic analysis, nonlinear structural analysis has become
increasingly important in the investigation of structural response to earthquakes.
Nonlinear structural analysis, but the existing method used for calculating the nonlinear
behaviour of civil engineering structures is often by changing the structural member stiffness.
Linear analysis for static and dynamic loads has been used in structural design for decades.
Nonlinear analysis methods in civil engineering is not a new topic and are widely used, because
emerging performance-based guidelines require representation of nonlinear behaviour. There
are two major sources of nonlinear behaviour of a structure or an element of structure. The first
is a nonlinear relationship between force and deformation resulting from material behaviour
such as ductile yielding, stiffness and strength degradation or brittle fracture. The second type
of nonlinear behaviour is caused by the inclusion of large displacements in the compatibility
and equilibrium relationships.
In succinct manner, the main characteristics of the various methods are recalled.
• Linear analysis (LA)
Displacements and strains are small so that material behaviour is elastic and analysis
may be performed on the basis of the initial, un-deformed geometry of the structure. This
analysis is also called elastic analysis according to 1storder theory. Design is made separately
by application of code-prescribed formulas.
• Linear buckling analysis (LBA)

This analysis provides buckling eigenvalues and buckling modes under the assumption
of small displacements, elastic material behaviour and no imperfections. It is a useful tool to
explore to what extend geometric effects influence the structural behaviour and to provide
deformed structural shapes that may be used as geometrical imperfections.
• Materially non-linear analysis (MNA)
Displacements are small but strains are large. Analysis may be performed on the basis
of the initial, un-deformed geometry of the structure but the effects of nonelastic irreversible
strains must be taken into account. This analysis is also called 1st order plastic analysis. For
frame structures it is further distinguished into rigid plastic analysis, plastic hinge analysis or
plastic zone analysis as illustrated in Table 3.1 It may be used for design as long as geometric
effects and imperfections can be ignored.
Table 5.1 Non-linear moment-curvature diagrams of cross-sections for beam elements
(Vayas et al 2019).
5.3 Code's seismic procedures

According to several international seismic codes, including US and European ones, the
following analysis options for the design of buildings and for the evaluation of their seismic
performance can be used:
• Linear static analysis: equivalent static analysis (termed the ‘lateral force’
method of analysis in EN 1998-1)
• Modal response spectrum analysis (also termed in practice ‘linear dynamic’
analysis. Do not to be confused with linear time-history analysis.
• Non-linear static analysis, commonly known as Pushover Analysis, not included
yet in RPA99 version 2003
• non-linear dynamic analysis or time-history or response-history analysis, not
included in RPA99. Linear time-history analysis is not explicitly mentioned as an alternative
to linear modal response spectrum analysis.
Unlike US and Algerian codes, which consider the linear static analysis as the reference
method for the seismic design of buildings, Eurocode 8 gives this status to the modal response
spectrum method.
The linear methods of analysis use the design response spectrum, which is essentially
the elastic response spectrum with 5% damping divided by the behaviour factor R (q in EC8).
Internal forces due to the seismic action are taken to be equal to those estimated from the
linear analysis; however, and consistent with the equal displacement rule and the concept and
use of the behaviour factor R or q, displacements due to the seismic action are taken as equal
to those derived from the linear analysis, multiplied by the behaviour factor R or q. In contrast,
when a non-linear analysis method is used, both internal forces and displacements due to the
seismic action are taken to be equal to those derived from the non-linear analysis. The use of a
linear method of analysis does not imply that the seismic response will be linear elastic; it is
simply a device for the simplification of practical design within the framework of force-based
seismic design with the elastic spectrum divided by the behaviour factor.
The problem of selecting an analysis method, of course, depends largely upon whether
the materials are intended to be elastic or inelastic during the design earthquake. The usual
methods of analysis for these two states are set out and well summarized.
5.4 The Concept of the Equivalent Static Force Method

There are two commonly used methods for specifying seismic design forces:
1. Equivalent Static Force Method
2. Dynamic Analysis
5.4.1 Definition
The equivalent lateral force for an earthquake is a unique concept used in earthquake
engineering. ESFM is a simplified method used to analyse the behaviour of structures under
seismic loading conditions. The concept is attractive because it converts a dynamic analysis
into partly dynamic and partly static analyses for finding the maximum displacement (or
stresses) induced in the structure due to earthquake excitation. The equivalent lateral force for
an earthquake is deﬁned as a set of lateral static forces which will produce the same peak
response of the structure as that obtained by the dynamic analysis of the structure under the
same earthquake. This equivalence is restricted only to a single mode of vibration of the
structure, that is, there a set of lateral force exist for each mode of vibration.
5.4.2 Applicability conditions
The lateral force method, is the easiest structural analysis method preferred and used
by structural engineers to assess the structural response because of the familiarity with the basic
calculation approaches used in structural mechanics, allowing also for hand computation for
simple and low-redundant structural schemes. As it is well-known, this method can be applied
only to structures whose dynamic response is basically dominated by the fundamental mode of
vibration. This type of analysis cannot be applied in case of complex structures that are not
vertically regular because of the non-uniform stiffness, strength or mass distribution.
In fact, the structural seismic analysis commonly adopted for calculating the seismic-
induced effects on structures are the lateral force method and modal response spectrum
analysis, because of their computational ease and their high efficiency. It should be noted that
in both methods of analysis an elastic structural response is assumed and the seismic actions
are combined with gravitational loads by the use of d'Alambert's principle of superposition of
effects.
5.4.3 Procedure
In the equivalent static force method, the inertial forces are specified as static forces
using empirical formulas. The empirical formulas do not explicitly account for the "dynamic
characteristics" of the particular structure being designed or analysed.
The formulas were, however, developed to adequately represent the dynamic behaviour
of what are called "regular" structures, which have a reasonably uniform distribution of mass
and stiffness. For such structures, the equivalent static force method is most often adequate.
The formulas were, however, developed to adequately represent the dynamic behaviour of
what are called "regular" structures, which have a reasonably uniform distribution of mass and
stiffness. For such structures, the equivalent static force method is most often adequate.
Furthermore, concentrated lateral forces tend to be larger at higher elevations in a structure.
Thus, the greatest lateral displacements and the largest lateral forces often occur at the top
level of a structure (particularly for tall buildings). These effects are modelled in equivalent
static lateral force procedures of the RPA99, EC8, IBC and UBC by placing a force at each
storey level in a structure.
It involves calculating the equivalent static force that would produce the same
maximum response as the dynamic loads that the structure is expected to experience during an
earthquake. This method assumes that the seismic load can be approximated by a single static
force that acts on the structure along a particular direction. The equivalent static force is then
used to determine the design forces and moments on the structure.
Furthermore, concentrated lateral forces tend to be larger at higher elevations in a
structure. Thus, the greatest lateral displacements and the largest lateral forces often occur at
the top level of a structure (particularly for tall buildings). These effects are modelled in
equivalent static lateral force procedures of the IBC and UBC by placing a force at each story
level in a structure.
The equivalent (static) lateral force for an earthquake is obtained by carrying out a
modal analysis of structures, and then a static analysis of the structure with equivalent (static)
lateral force in each mode of vibration is performed to obtain the desired responses. The entire
procedure is known as the response spectrum method of analysis and is developed using the
following steps.
1. A modal analysis of the structure is carried out to obtain the mode shapes,
frequencies, and mode participation factors for the structure.
2. An equivalent static load is derived to get the same response as the maximum
response obtained in each mode vibration, using the acceleration response spectrum of the
earthquake.
3. The maximum modal responses are combined to find the total maximum response of
the structure.
5.4.4 Comparison between EFM and RSA
On the other hand, RSA is a more advanced method used to analyse the behaviour of
structures under seismic loading conditions. It involves calculating the response of the structure
to a range of ground motions, which are represented by a response spectrum. RSA provides a
more detailed analysis of the behaviour of the structure, which can help engineers to design
safer and more efficient structures.
One of the main differences between ESM and RSA is the level of accuracy they
provide. ESM is a simplified method that assumes the seismic load can be approximated by a
single static force. This method is less accurate than RSA, which takes into account the dynamic
nature of the seismic load and its effect on the behaviour of the structure.
In terms of computational requirements, ESM is typically faster and less
computationally intensive than RSA. ESM involves the calculation of a single static force,
while RSA involves the calculation of the response of the structure to a range of ground
motions. This makes RSA more time-consuming and computationally expensive than ESM.
5.5 Seismic analyses to RPA99

5.5.1 Used methods
The seismic loads calculation can be performed according to three methods:
- the equivalent static method
- the modal response spectrum analysis method
- the time history dynamic analysis method
5.5.2 Required conditions for the application of the equivalent static method (ESM)
The equivalent static method can be used in the following conditions:
a) For the building or a block of building must comply with the conditions of
regularity in plan and in elevation prescribed in the chapter III, paragraph 3.5 with a height
to most equal to 65m in zones I and IIa and to 30m in zone IIb and III.
b) For the building or a block of building which presents an irregular configuration but
satisfying, in addition to the conditions of height expressed in a), the following complementary
conditions:
Zone I: all groups
Zone II: using group 3 using group 2, if the height is lower or equal to 7 stories or
23m.using group 1B, if the height is lower or equal to 5 stories or 17m. using group 1A, if the
height is lower or equal to 3 stories or 10m.
Zone III: using groups 3 and 2, if the height is lower or equal to 5 stories or 17m.
using group 1B, if the height is lower or equal to 3 stories or 10m. using group 1A, if the
height is lower or equal to 2 stories or 08m

.
5.6 Equivalent static method to RPA99 version 2003
5.6.1 principles
The dynamic real loads developed in the construction are replaced by a system of
nominal static loads with the effects of which are considered equivalent to those of the seismic
action.
The soil motion can be in any direction in the horizontal plan. The equivalent horizontal
seismic loads will be considered successively applied in two successive orthogonal directions
chosen by the designer. In general, these two directions are the principal axes of the horizontal
plan of the structure. However, the loads and deformations for a given element obtained
from the static analysis methods for recommended design loads are lower than those that
would be observed on the structure under effects of a major earthquake for which the loads
have been specified. This excess of loads is balanced by the ductile behaviour that is provided
by detailing of the element. It is why the use of this method cannot be dissociated from the
rigorous application of the detailing requirements being able to give to the structure:
- a sufficient ductility
- a capacity to dissipate the vibration energy transmitted to the structure by
major earthquakes.
5.6.2 Modelling
a) The building model to be used in each of the two directions for analysis is plane, with
masses concentrated at the gravity centre of the floor and only one degree of freedom by floor
in horizontal translation is considered.
b) The lateral stiffness of supporting elements of the bracing system is calculated from
non-cracked sections for reinforced concrete structures or masonry structures.
c) Only the fundamental vibration mode of the structure is considered in the calculation
of the total seismic load.
5.6.3 Total seismic load

The total seismic load V, applied to the basement of the structure, must be calculated
successively in two orthogonal and horizontal directions, according to the following formula:
A. D. Q
V= W
R
V: base shear force associated with ground motion at the base of the structure.
• Base Shear to UBC 97
Base shear is an estimate of the maximum expected lateral force that will occur due to seismic
ground motion at the base of a structure. Calculations of base shear (V) depend on:
• soil conditions at the site
• proximity to potential sources of seismic activity (such as geological
faults)
• probability of significant seismic ground motion

• the level of ductility and overstrength associated with various structural
configurations and the total weight of the structure
• the fundamental (natural) period of vibration of the structure when
subjected to dynamic loading
- A: zone acceleration coefficient, given in table 5.1, according to the seismic zone
and the using group of the building.
Table 5.2 Coefficient of zone acceleration

Zone
Group I IIa IIb III
1A 0,15 0,25 0,30 0,40
1B 0,12 0,20 0,25 0,30
2 0,10 0,15 0,20 0,25
3 0,07 0,10 0,14 0,18
- D: average dynamic amplification factor, depending on the site category, on the

damping correction factor (η) and on the fundamental period of the structure (T). The
factor D is given in flowchart forms in figure 4.1 for a damping coefficient ξ = 5%.
2.5 0  T  T2

 2
D = 2.5(T2 T )3 T2  T  3.0s
 2 5
2.5(T2 3.0)3 (3.0 T )3 T  3.0s
T2: characteristic period, associated to the category of the site and given in the table
4.7
η: is the damping correction factor given by the following formula:
 = 7 (2 +  )  0.7
where ζ (%) is the critical damping ratio depending on constitutive material,
structure type and importance of infills.
When ζ=5%, with η =1.
Tableau 5.3 Values of ξ (%)

Frames Shear walls or walls
Infill Reinforced metal reinforced
concrete concrete/masonry
light 6 4
10
heavy 7 5
- R: global behaviour coefficient of the structure, given in table 5.4 according to

the lateral force resisting system.
In case of different lateral force resisting systems in the two considered directions, the
smallest value of R must be used.
- Q: Quality factor
The quality factor of the structure depends on:
- the redundancy and the geometry of the constituent elements.
- the regularity in plan and in elevation.
- the quality of the control of construction.
The value of Q is determined by the formula:
5
Q = 1 +  Pq
1
is the penalty to be applied depending on whether the criteria of quality q “is

satisfied or not”. Its value is given in table 4.4
• Criteria of quality “q” to verify are:
1. minimal conditions on bracing plans.

- frames system: every plan of frames must include at all floors, at least three (03) bays and
the ratio of two adjacent spans must not exceed 1.5. The frame bay can be constituted of
shear walls.
shear walls system: every plan of shear-walls must include at all floors, at least one (01)
pier having a ratio “storey height on width” less or equal to 0.67 or two (02) piers having a
ratio “story height on width” less or equal to 1. These piers must rise on all the height of the
floor and must not have any opening or perforation that can reduce significantly their strength
or their stiffness.
2. redundancy in plan
Every story should have, in plan, at least, four (04) plans of frames and/or shear walls
in the considered direction.
These bracing plans should be arranged as much as possible symmetrically with a ratio
between maximal and minimal values of spacing less than 1.5.
3. regularity in plan
The structure is classified regular in plan. (cf. 3.5 1a)
4. regularity in elevation
The structure is classified regular in elevation. (cf. 3.5 1b)
5. control of material quality

Systematic tests on used materials must be achieved by the enterprise.
6. control of the quality of construction
A control mission to follow-up the works on yard is contractually foreseen.

This mission must include a supervision of tests done on materials.
Table 5.4 Values of behaviour factor R
Cat Description of lat. Force res. systems (see chapter III § 3.4) Value of R
A Reinforced concrete
1a Moment resistant frames without stiff masonry infill 5

Moment resistant frames with stiff masonry infill
1b 3,5
Bearing shear walls
2 central core 3,5
3 Mixed moment resistant frames/shear walls with interaction 3,5
4a Frames braced by shear walls 5
4b Vertical cantilever with distributed masses 4
5 Inverted pendulum 2
6 2
B Steel
7 Ductile moment resistant frames 6
8 Ordinary moment resistant frames 4
9a Structure braced by X triangulated elements 4
9b Structure braced by V triangulated elements 3
10a Mixed moment resisting frames/ X triangulated braces 5
Mixed moment resisting frames/ V triangulated braces
10b 4
Vertical cantilever frames
11 2
C Masonry
12 Bearing tied masonry 2,5
D Other systems
13 Steel structure braced by diaphragm
2
14 Steel structure braced by reinforced concrete core
3
15 Steel structure braced by reinforced concrete shear walls
3,5
16 Steel structure with mixed bracing including a reinforced concrete
core and steel braces or frames in façade
Systems including transparencies (soft stories)

4
17
Table 5.5 values of the penalties Pq 2
Pq
Criteria Q Observed unobserved
1. Minimal conditions on bracing lines 0 0,05

2. Redundancy in plan 0 0,05
3. Regularity in plan 0 0,05
4. Regularity in elevation 0 0,05
5. Control of material quality 0 0,05
6. Control of construction quality 0 0,10
- W: total weight
n
W=  Wi
i =1 And Wi= WGi +  WQi
W is equal to the sum of the load calculated at each storey
- WGi: weight due to the dead loads and loads of the eventual fixed equipment attached
to the structure.
- WQi: live loads
- β: weighting coefficient, depending on the nature and the duration of the live load,
given in table 5.5.
Table 5.6 Weighting coefficient
Type of building β
Case
1 Residential use building, offices and assimilated 0,20
2 Buildings receiving the public temporarily:

- Rooms of exhibition, of sport, places of cult, meeting rooms with
stand up places 0,30
- classrooms, restaurants, dormitories, meeting rooms with sitting
seats
0,40
Warehouses, hangars
3 Archives, libraries, tanks and assimilated buildings 0,50
4 Other buildings no aimed above 1,00
5 0,60
Estimation of the fundamental period of the structure
The time period of a structure may exactly be calculated by performing free vibration
analysis of the structure, which involves lengthy calculations. Following empirical methods
are also available to reasonably guess the fundamental time period of a structure:
1. The value of the fundamental period (T) of the structure can be estimated from
empirical formulae or can be calculated by numerical or analytic methods.
2. The empirical formula recommended is the following:
3
T = CTh N 4
hN: height measured in meters from the basis of the structure to the top of the last level
(N). CT: coefficient, function of the lateral force resisting system and of the type of infill. It is
given by the following table.
Table 5.7 Values of the coefficient CT
Case n° Resisting System CT

Reinforced Concrete Moment Resisting Frames without infilled
1 0.075
masonry
2 Steel Moment Resisting Frames without infilled masonry 0.085
Steel or Reinforced Concrete Moment Resisting Frames with infilled
3 0.050
masonry
4 Partially or totally RC Shear walls, Braced Frames and Masonry Walls 0.050
3
N.B. Method A of UBC: T = CTh N 4
•
where
h = height of the roof above the base in meters, not including the height of parapets.
Ct = 0.085 for steel moment resisting frames = 0.073 for reinforced concrete moment
resisting frames and t eccentric braced steel frames = 0.050 +for all other buildings.
In cases n° 3 and 4, the following formula can be used also:
T = 0.09 hN/D0.5
Where D is the dimension of the building measured at its basis in the direction
of calculation.
In this case the smaller value between the values given by the formulae 4.6 and 4.7 is considered.
3. The value of T can be calculated using the Rayleigh formula or a
simplified version of this formula:
n 
) / g  f  )
n
T = 2  Wi  i
 i i
i i
fi: horizontal forces system, distributed according to formulae of V

distribution following the vertical line.
δi: horizontal displacements due to fi forces calculated following a linear elastic model
of the structure that takes into account all elements which contribute to its rigidity.
Method B To UBC
δi = static elastic deflection at level “i” due to the forces applied at all levels, increasing
in a linear way with height. The value of deflection must be with respect to the base in mm.
= to
ki = shear stiffness of columns under floor “i”
fi = lateral force at level “i”, N
wi= dead load located at level “i”, N
g= acceleration due to gravity = 9810 mm/sec.
b) Simplified version of Rayleigh formula:

δN: horizontal displacement at to the top of the building, measured in meters, due to the
vertical dead loads applied horizontally.
T = 2 N
4. The Values of T, calculated using Rayleigh formulae or numerical methods must not
exceed those estimated by appropriate empirical formulae of more than 30%.
Distribution of the global seismic force in the building height

The global seismic force V at the base of the building should be distributed following
the height of the structure according to the following formulae:
V = Fi + Σ Fi
The concentrated force Ft at the top of the structure allows to take into account the
influence of the high vibration modes of the structure. It is determined by the formula: Ft =
0.07 TV Where T is the fundamental period of the structure (in second). The value of Ft
should not exceed 0,25 V and should be taken equal to 0 when T is smaller or equal to 0.7
seconds
The differential part of V, i.e., (V - Ft) should be distributed following the height
of the structure following the formula:
(V − Ft )Whi
Fi = n
W h j j
j =1
N.B to UBC97
A concentrated force Ft that shall be applied to the top of the structure as part of the base
shear shall be determined from the following formula:
Ft = 0.07 TV < 0.25 V for T>0.7 seconds
And
Ft = 0.0 for T<0.7
So,
V = Fi + Σ Fi
(V − Ft )Whi
Fi = n
W h j j
j =1
Horizontal distribution of the seismic forces
n
The shear force at the level k: Vk = Ft +  Fi
i =k
In the case of structures containing rigid floors in their plan, is distributed to vertical
elements of the resisting system proportionally to their relative stiffness.
Torsion Effect
The increasing of the shear force provoked by the horizontal torsion due to the
eccentricity between the centre of gravity and the centre of rigidity should be taken into
account. The negative shear forces due to the horizontal torsion should be neglected.
For all structures having rigid floors or diaphragms in their plan, it is supposed that at
each level and in each direction, the global horizontal force has an eccentricity in comparison
with the torsion centre equals to the greater of the two values:
-5% of the greatest dimension of the building at this level (this eccentricity
should be considered on either side of the centre of torsion)
-Theoretical eccentricity given by the schemes.
5.7 Justification for safety to RPA99 version 2003

5.7.1 General
The safety objectives of the structure subjected to the effects of seismic action
are deemed to be achieved if the following criteria relating to resistance, ductility,
overall balance, stability of the foundations, seismic joints, deformations and shape
stability (P-* effect) are satisfied simultaneously.
5.7.2 Combinations of actions
The seismic action is considered as an accidental action in the sense of the Limit States
calculation philosophy.
The combinations of actions to consider for determining the design stresses
and deformations are:
• G + Q +E (5-1)
• 0.8 G * E (5-2)
For Columns in free-standing frames, the combination (5-1) is replaced by the

following combination:
• G + Q + 1.2 E (5.3)
G: permanent loads
Q: live actions
E: action of the earthquake represented by its horizontal components
Although no mention was made of the effects of vertical acceleration due to
earthquakes, these effects are included as follows:
The combination (5-1) includes the entire operating load as well as the seismic
load. Because this operating load is quite improbable, a large part of it (around 40 to
60%) may actually represent the effect of vertical accelerations of earthquakes.
The combination (5-2) accounts for the reduction in vertical load that will
occur due to the effects of vertical acceleration
In the previous combinations, it is necessary to take into account the
reversibility of seismic loads
For the columns, the combination G+P+1.2 E in (5-3) aims to provide them with
better resistance to the effects of overturning moments due to major seismic
movements.

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Chapter V Determination of the seismic action by Equivalent Static Force Method

DETERMINATION OF THE SEISMIC ACTION

5.1 Structural seismic response of a structure

5.1 Structural seismic response of a structure

5.2 Structural seismic analysis

• Linear buckling analysis (LBA)

5.3 Code's seismic procedures

5.4 The Concept of the Equivalent Static Force Method

5.5 Seismic analyses to RPA99

height is lower or equal to 2 stories or 08m

5.6.3 Total seismic load

• probability of significant seismic ground motion

Table 5.2 Coefficient of zone acceleration

- D: average dynamic amplification factor, depending on the site category, on the

When ζ=5%, with η =1.

Tableau 5.3 Values of ξ (%)

- R: global behaviour coefficient of the structure, given in table 5.4 according to

is the penalty to be applied depending on whether the criteria of quality q “is

• Criteria of quality “q” to verify are:

1. minimal conditions on bracing plans.

5. control of material quality

6. control of the quality of construction

A control mission to follow-up the works on yard is contractually foreseen.

Table 5.4 Values of behaviour factor R

1a Moment resistant frames without stiff masonry infill 5

Systems including transparencies (soft stories)

1. Minimal conditions on bracing lines 0 0,05

1 Residential use building, offices and assimilated 0,20

2 Buildings receiving the public temporarily:

Case n° Resisting System CT

fi: horizontal forces system, distributed according to formulae of V

b) Simplified version of Rayleigh formula:

Distribution of the global seismic force in the building height

Horizontal distribution of the seismic forces

5.7 Justification for safety to RPA99 version 2003

For Columns in free-standing frames, the combination (5-1) is replaced by the

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