# Reliability based design

• “Japan’s bus services are very reliable”
• “Zen’s water supply is not reliable”

What is reliability (technical terms)?

• How is it measured
• Why are the reasons for a system to be not reliable?

Civil Engineering Systems

• Transportation (Road systems, Railways, Air traffic)
• Water (Water supply networks, Waste water networks)

Structural (Buildings, Bridges, Dams, Fly-overs)

Each system is calculated in a different way, but there is a widespread philosophy.

How to Design?

 Requirement Provision Demand Capacity/Supply Load Resistance x million liter/day of x million liter/day of water for IITB water for IITB residents Residents

General Design Philosophy

Capacity has to be more than required

C ? D

For instance: Give at least x million liter/day of water to colony residents

How much more than the demand?

• In theory, just more
• But, designers provide a lot more
• Why?->Due to uncertainty

Uncertainty

We are not sure about the standards of the parameters which we use in design provisions Sources/reasons of uncertainty:

• Errors/faults/discrepancies in calculation(for demand) or manufacturing (for capacity)
• Approximations/idealizations/pressumptions in modeling
• Inherent uncertainty — “Aleatory”
• No knowledge — “Epistemic”

Measurement and Manufacturing Errors

• Potency of concrete is not same at each part of a column or a beam in a building system
• the depth of a steel girder is not accurately same (and not as given) at each section (Faults in estimating demand/capacity?)
• Mass of concrete is not similar each part of a column or a beam in a structure system (Fault in estimating demand/capacity?)
• Wheels of an aircraft hit the runway at varying speeds for diverse flights

Moral of the story:

Reiterate a measurement/estimate/experiment numerous times and we do not get accurately the similar outcome everytime.

IDEALIZATIONS IN MODELING

• Each real system is accessed via its “model”
• Idealizations/generalities are used in attaining this model
• For instance, (modeling live load on a classroom floor)
• Live loads are from temporary “occupants”; like people, portable furnishers, etc.
• We presume live load to be consistent on a classroom (unit?)
• [We also pressume the floor concrete to be “uniform” (that is, having same characteristics, such as potency, throughout)]
• As a result our investigation outcomes are unlike from the real situation

Example: (modeling friction in water systems)

• Friction between water and inner surface of a pipeline diminishes flow
• We presume a constant friction factor for a pipe material
• But in real, the amount of friction alters if you have joints, bends and valves in a pipe
• If we need to deem these effects, the investigation processes will be very complex
• On the other hand, we have to remember that there is distinction between the actions of model and the real system

Epistemic and Aleatory Uncertainties

Epistemic

• Because of lack of understanding
• Having no knowledge of how a system really functions
• These reservations can be diminished over time (better knowledge, more examinations)
• Aleatory
• Because of reacquired variability of the parameter
• Volatility in estimating a future event
• These doubts can be diminished as well, with more observations

The reasons for Earthquakes

• Buildings have to be designed to endure earthquake effects
• Earthquakes that a buildings are going to endure during its life-span are not predictable
• We cannot predict when, how big (magnitude), how damaging (intensity)
• This is because of the unpredictability intrinsic in the physical characteristics of earthquakes

How do earthquakes occur?

Plate tectonics

Elastic rebound Theory

AD = Fault line (along which one side of earth slides with respect to the other)

A = Focus of the earthquake (where the slip occurs and energy is released)

C = Epicenter of the earthquake (point on earth surface directly above the focus)

B = Site (location for the structure)

Earthquake wave’s travel from A to B (body waves) and C to B (surface waves)

Earthquake waves travel from epicenter to the site (site= where the structure is located)
The shock-wave characteristics are altered by the medium it is traveling

• The earthquake force that is coming to the base of a building is also dependent by the soil below
• We have to know precisely these processes by which the ground motion is affected
• Any kind of lack of knowledge in these regards will lead to:Epistemic uncertainty

Consequences of Uncertainty

• Analysis results are not accurately precise (that is, not uniform as in real life)
• Assessment of demand and capacity parameters is defective
• We may not really assure the C ? D equation
• Nonetheless, we will not know this
• Solution: apply a factor of safety (F)

C ? FD or C/F ? D

• This factor takes care of the unforeseen errors due to uncertainty

If C ? 2.5D, then even in real situation, it should be C ? D

Reliability based design

 Deterministic Reliability-Based safe Not 100% safe No doubts reservations are properly accounted for Factor of safety is dependent on judgment Factors are premeditated from ambiguities Simple, but claims are not practical More systematic in all aspects, but complicated

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