- “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 |