ENGR 482 Lecture 12

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Test next week

Risk, Safety, and Liability Cont'd

Allowable (or Working) Stress Design Philosophy

Limits stress to a certain "allowable" value

Weaknesses / design difficulties:

• Different loadings have different uncertainties
• Differetn failure modes have different risks
• resistence of some modes may be affected by construction/maintenance quality

Therefore different FS may be appropriate for different loadings and failure modes

Load Factor Design Philosophy:

• Expected loads multiplied by Load factors

Dead Loads (DL) vs. Live loads (LL):

• Dead loads are constant and always present
• Live Loads are changing and dynamic

Higher load factors placed on live load because of uncertainty

Failed to parse (unknown function "\cdto"): {\displaystyle F_{LL} \cdto M_{LL} + F_{DL} \cdot M_{DL} \le \Phi \, M_{ult} \,\!}

• $F_{LL}=2.2$ and $F_{DL}=1.3$ are load factors for live and dead loads (respectively)
• $\Phi$ is strength reduction factor (usually 90%) stating how much of claimed strength (how much builders say it will hold) will be trusted.

Probablistic Design Philosophy (LRFD) Example:

Bridges should be designed to withstand vessel collisions

Categorize types and number (N) of vessels (per year on average) that would cross beneath bridge. For each vessel, calculate probability of aberrancy (PA), geometric probability of collision by an aberrant vessel (PG), and probability of bridge collapse due to collision (PC)

$AF=\sum N\cdot PA\cdot PG\cdot PC$

Resulting AF is the Annual frequency of collapse

Acceptable risks are

• $AF<10^{-3}$ for "regular" bridges (that can afford to collapse)
• $AF<10^{-4}$ for "critical" bridges (that must remain operational even in event of collision)

Example

Portable cylinder of compressed air.

Calculated hoop stress:

$\sigma _{H}={\frac {pr}{t}}$

Specify steel with minimum yield strength of 36 ksi, and design for allowable stress of 20 ksi.

Design pressure is 120 psi, which will cause allowable stress of 20 ksi in the 12 inch diameter steel tank if wall thickness is 0.0375 in.

Increases wall thickness by 0.060 inches to allow for corrosion

FS of new tank is 5.04

FS of corroded tank (0.045 inch wall thickness) is 2.16

Cost-Benefit Analisys

One example of utilitarian approach Commonly used by risk experts Final result usually in currency units ($) Significant Problem: estimate value of human life

Estimating Value of Human Life

• Purchasing decisions involving safety: how much more are people willing to pay for a safer product? (but what if customer does not have the money?)
• Extra pay for risky jobs
• Future earnings of the individual

Ford Pinto Case

• Ford Introduced Pinto in early 1970's
• Competition with Japanese cars
• Goal: weight < 2000 lbs and cost < $2000
• Designed in 25 months (typical was 43 months)

Gas tank was not well-protected, and rear-end collision could damage tank

During 20 mph crash tests, tank or filler pipe ruptured in 11/12 impacts

Fixing problem would require moving tank ($11 / car) or adding a rubber bladder ($5 / car)

Cost-benefit approach indicated to sell cars unmodified:

• Costs: $11/vehicle × $12.5M vehicles = $137 M
• Benefits: (sum = $49.5M)
  • Deaths prevented: $200K × 180
  • Burn injuries prevented: $67K × 180
  • Auto burn damage prevented: $700 × 2100

First liability lawsuit from Pinto crash was $128M:

• Burn deaths are very painful
• There are a few things you don't do to people, and burning them alive is one of them.
• Burning to death in an otherwise nonfatal accident is unacceptable
• Risk not known by public
• Jury prefers respect for persons approach

Layman's Approach to Risk: Respect for Persons

• Is risk distributed equitably?
• Are those assuming risk compensated?
• Is risk voluntary?
• Does person assuming risk understand it?
• Does person know about risk?

In this approach, risk is often overestimated (esp. if risk is of human origin)

Acceptable risk may then be defined

• freely assumed with informed consent
• equitably distributed
• properly compensated

Capabilities Approach: New Method

Quantifying harm and benefit is difficult

Capabilities are what human beings can do or become