Measures of Reliablity

1. ANALISA KEHANDALAN INFRASTRUKTUR
LINGKUNGAN
RELIABILITY ANALYSIS OF ENVIRONMENTAL
INFRASTRUCTURES
Anik Sarminingsih
Email :aniksarminingsih@lecturer.undip.ac.id
Measures of Reliability
Week – 5

2. Safety factor and Reliability
 Analisis Faktor Keamanan dan Reliability, untuk
mengevaluasi probabilitas kegagalan struktural dengan
menentukan apakah batas keamanan terlampaui.
 analisis keandalan tidak terbatas pada perhitungan
probabilitas kegagalan
 Evaluasi statistik baik sifat, seperti fungsi distribusi
probabilitas dan interval kepercayaan respon
struktural, memainkan peran penting dalam analisis
keandalan.

3. Structural Reliability Assessment
(Penilaian Keandalan Struktur)
 Jika struktur (atau bagian dari struktur) melebihi batas
tertentu, elemen struktur (atau bagian dari struktur)
tidak dapat melakukan seperti yang diperlukan, maka
batas tertentu disebut batas-keadaan (boundary state).
 Struktur ini akan dianggap tidak dapat diandalkan jika
probabilitas kegagalan batas-keadaan (boundary state)
struktur melebihi nilai yang diminta

4. Batas-keadaan (boundary state)
Batas keadaan dapat dibagi menjadi dua kategori:
1. Batasan Ultimate yang terkait dengan runtuhnya
struktural dari sebagian atau seluruh struktur.
Contoh yang paling umum batasan ultimate adalah korosi,
kelelahan, kerusakan, kebakaran, mekanisme plastik,
keruntuhan progresif, fraktur, dll.
Beberapa batasan harus memiliki probabilitas yang
sangat rendah dari kejadian, sebab dapat menyebabkan
risiko hilangnya nyawa dan kerugian keuangan yang
banyak
2. Batasan Pelayanan terkait dengan gangguan penggunaan
normal dari struktur……………….continued

5. Batas-keadaan (boundary state)
Batas keadaan dapat dibagi menjadi dua kategori:
2. Batasan Pelayanan terkait dengan gangguan
penggunaan normal dari struktur.
Contoh : batasan pelayanan adalah lendutan yang
berlebihan, getaran yang berlebihan, drainase,
kebocoran, kerusakan lokal, dll.
Karena bahaya yang kurang dari pada dalam kasus
batasan ultimate, probabilitas yang lebih tinggi dari
kejadian mungkin ditoleransi dalam batasan ini.
Namun, orang tidak dapat menggunakan struktur yang
menghasilkan terlalu banyak lendutan, getaran, dll

6. BASIC CONCEPTS
 Uncertainties
 pekerjaan konstruksi adalah sistem teknis yang rumit menderita
sejumlah ketidakpastian yang signifikan di semua tahap
pelaksanaan dan penggunaan.
The following types of uncertainties can usually be identified:
– natural randomness of actions, material properties and
geometric data;
– statistical uncertainties due to limited available data;
– uncertainties of theoretical models owing to the simplification of
actual conditions;
– vagueness due to inaccurate definitions of performance
requirements;
– gross errors in design, execution and operation of the structure;
– lack of knowledge of the behaviour of new materials in real
conditions.
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7. BASIC CONCEPTS
 Definition of reliability
 In Eurocode no definition is offered and it is noted that
reliability covers only the load-bearing capacity,
serviceability as well as the durability of a structure.
 In the Fundamental requirements that “a structure shall be
designed and executed in such a way that it will, during its
intended life with appropriate degrees of reliability and in
an economic way:
– remain fit for the use for which it is required; and
– sustain all actions and influences likely to occur during
execution and use.”
 A different level of reliability for load-bearing capacity and
for serviceability may be accepted
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8. BASIC CONCEPTS
 Definition of reliability
 The probability of failure pf and the reliability index  are
related to failure consequences.
The above definition of reliability includes four important
elements:
 given (performance) requirements – the definition of
structural failure;
 time period – the assessment of the required service-life
T;
 reliability level – the assessment of the probability of
failure pf ; and
 conditions of use – limiting input uncertainties.
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9. The are three basic design methods and to indicate the
explicit measures that might affect the probability factors of
failure and structural reliability
The first universally-accepted design method for civil
structures is the method of permissible stresses. It is based
on the condition :
9
Historical development of design
methods
where the coefficient k is assessed with regard to uncertainties in the
determination of local load effect max and of resistance per and
therefore may ensure with an appropriate level of security the reliability
of the structure.

10. The second widely-accepted method of structural design is
the method of global safety factor. It is based on the
condition:
10
Historical development of design
methods
according to which the calculated safety factor s must be greater than
its specified value so.
The aggregate quantities of structural resistance Xresist and action
effect Xact

11. At present, the most advanced operational method of
structural design is the partial factor format (often
inaccurately denoted as the limit states method). This
method ie based on the conditionn:
11
Historical development of design
methods
where the action effect Ed and the structural resistance Rd are
assessed according to the design values of basic quantities
describing the action Fd, material properties fd, dimensions ad
and model uncertainties d.

12. • Probabilistic design methods are based on the condition
that the probability of failure pf does not exceed a specified
target value pt during the service life of a structure T
12
Historical development of design
methods
It is usually possible to assess the probability of failure pf using a
computational structural model, defined through basic quantities
X [X1, X2, ... , Xn] for actions, mechanical properties and
geometrical data.
The limit state of a structure is defined by the limit state function
(the performance function) g(X) for which, according to the
definition, in case of a favourable (safe) state of the structure the
limit state function is positive; it holds that
pf ≤ pt
g(X) ≥ 0

13. • the unfavourable state (failure) of the structure occurs when
the limit state function is negative, i.e. when g(X) < 0
• For most ultimate limit states and serviceability limit states
the probability of failure can be expressed by the equation
pf = P{g(X) < 0}
• In many cases the problem may be transformed to a time-
independent one, for example by considering a minimum of
the function g(X) over the time period T.
13
Historical development of design
methods

14. 14
Limit states
Definisi yang tajam dan tidak jelas dari keadaan batas
In order to simplify the design procedure two fundamentally different types of
limit states are generally recognised:
(a) ultimate limit states; and
(b) serviceability limit states.

15. 15
Ultimate limit states
• Its associated with collapse and other similar forms of
structural failure and directly concern the safety of the
structure and the safety of people
• The following list provides the most typical ultimate limit
states that may require consideration in the design:
(a) loss of equilibrium of the structure or any part of it,
considered as a rigid body;
(b) failure of the structure or part of it due to rupture, fatigue
or excessive deformation;
(c) instability of the structure or one of its parts;
(d) transformation of the structure or part of it into a
mechanism; and
(e) sudden change of the structural system to a new
system.

16. 16
Serviceability limit states
• The serviceability limit states are associated with conditions of
normal use
• In particular they concern the functioning of the structure or
structural members, the comfort of people and appearance of the
construction works
• Taking into account the time-dependency of load effects it is useful
to distinguish two types of serviceability limit states which are:
(a) Irreversible serviceability limit states which are those limit states
that remain permanently exceeded even when the actions
which caused the infringement are removed (for example a
permanent local damage, permanent unacceptable
deformations);
(b) Reversible serviceability limit states which are those limit states
that will not be exceeded when the actions that caused the
infringement are removed (for example cracks of prestressed
components, temporary deflections, excessive vibration).

17. 17
Serviceability limit states

18. 18
Reliability differentiation
• The purpose of reliability differentiation establishes
reliability classes RC (also called consequence classes (CCs)).
• Three classes are defined in accordance with consequences
of failure or malfunction of the structure as follows:
Reliability Class, RC3
High consequence for loss of human life, or economic, social or
environmental consequences very great
Reliability Class, RC2
Medium consequence for loss of human life, economic, social or
environmental consequences considerable
Reliability Class, RC1
Low consequences for loss of human life, and economic, social or
environmental consequences small or negligible

19. 19
Reliability differentiation
Reliability classes and recommended minimum
values for reliability index 

20. THANK YOU!