ENGR 482 Lecture 11

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Risk

All codes protect public from "unacceptable risk"

What is acceptable?

Definiion

Exposure to:

• chance of injury, damage, or loss
• a hazardous or dangerous chance

Involves

1. Probability that something will happen
2. Consequences of the event

Note: Risk and safety are conceptual inverses

From mathematics:

Risk = (sum of) probability × consequence

Example: Bridge Collapse

Bridge fonudation dephts are often governed by the depth of scour, which is related to the size of the fluod, defined in terms of its probability:

• A 100-year flood has a 0.01 chance of accurring in any given year
• A 500 year flood is a flood which has a 0.002 chance of occurring in any given year

Consider bridge designed for a 500-year flood

• If the collapse occurs during rush hour (1/24 probability), 10 lives will likely be lost.
• If the collapse occurse any other time (23/24 probablitiy), suppose only 1 life will likely be lost.

Total risk would be sum of probabilities:

• risk of death during rush hour = (2 × 10⁻³)(1/24)(10) = 833 × 10⁻⁶
• risk of death in any other time = (2 × 10⁻³)(23/24)(10) = 1917 × 10⁻⁶
• total risk = risk of death occurring in rush hour + risk of death in any other time = 2750 × 10⁻⁶

Example: Nuclear Meltdown

Control rods and emergency cooling pump prevent reactor meltdown

Event tree:

|-- fails (p1)
|   |-- fails (p2)
|   `-- available (1-p2)
`-- available (1-p1)
    |-- fails (p2)
    `-- available (1-p2)

First level is control rod, second level is cooling pump, and chances of any outcome happening is product of all probabilities involved (e.g. $p_{1}(1-p_{2})$ would be the probability that the control rods fail, but the pump works.

In Theer Mile Island:

• feedwater pumps failed
• pressure relief valve opened, but became stuck open
• Signals failed to show valve was stuck.

Notes

• Not all risks can be antiicipated (human error, terrorist attacks)
• All work involves risk
• Innovation in design generally increases risk (Tacoma Narrows bridge)

Exacerbation of Risk

• Tight coupling: if one system fails, other systems will fail quickly if they are tightly coupled.
• Processes or systems interact in unanticipated ways:
  • Accelerator sticks on Toyota and crash occurs
  • Electric cars present danger due to lack of engine noise
  • Columbia foam strike admits hot plasma to wing's inner structure
• Normalizing deviance is an acceptance of a level of risk as normal (allows greater risks to be accepted more readily

Safety: Reducing Risk

• Develop inherently low-risk designs (e.g. using gravity for lowering control rods)
• Incorporate redundancy (multiple sensors in control systems: if one doesn't match, then it's usually a red flag)
• Design failure modes that give warning before catastrophic failure
• Design for appropriate factor of safety (FS)
• Design gradual failure

Factors of Safety

$FS={\frac {\mbox{failure load (capacity)}}{\mbox{design load (demand)}}}$

Jet liner risk is mitigated by very close control of

• applied loads
• construction quality
• variations in material properties
• manufacturing variability
• maintenance

Example: Elevator Engineer

Full load weigs 6450 lbs.

Elevator supported by 4 cables so individual tension is 1/4 total load.

Tension (demand) = weight × 1.35 / 4 = 2176 lbs

Use specified factor of safety = 6.5

Choose 1/2-in. cable that has 11.8 ton capacity gives safety factor

$FS={\frac {11.8ton\cdot 2000lb/ton}{2176lb}}=10.8>6.5$