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Stress and Strain

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MIT - 16.20

Fall, 2002

Unit 2 Loads and Design Considerations

Readings: Rivello (Ch. 1) Cutler book (at leisure) G 7.1

Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering Systems

Paul A. Lagace © 2001

MIT - 16.20

Fall, 2002

Sources of Stresses and Strains
Depends on type of structure Aircraft Launch Vehicles Space Structures

General

Other Considerations

Paul A. Lagace © 2001

Unit 2 - p. 2

MIT - 16.20

Fall, 2002

Can generally divide these into: • Normal operational effects (regular use) • Environmental effects (internal stresses, material property degradation) • Isolated effects (lightning, impact) In a (large company) • “Design” group does general management • “Loads” group determines operating conditions • This is passed on to “stress” group that analyzes stresses and deformations • “Materials” group provides material ultimates, etc. ⇒ Need to understand each part NOTE: New approach in companies: IPT (Integrated Product Teams) DBT (Design Build Teams) - people from each branch including manufacturing and marketing ⇒ even more important to understand various factors
Paul A. Lagace © 2001

Unit 2 - p. 3

MIT - 16.20

Fall, 2002

Factors, Margins, etc.
Two important definitions for static considerations Limit Load/Stress/Condition: Maximum load/stress/condition where structure shows no permanent deformation. Ultimate Load/Stress/Condition: Maximum load/stress/condition where structure does not “fail.” Definition is key; often defined as “break” (i.e., carry no more load) Operationally, the limit load is the maximum load the structure is expected to see The ultimate load provides a “factor of safety” for unknowns Ultimate Factor of Safety (U.F.S.) = Ultimate Load Limit Load This is a design value
Paul A. Lagace © 2001

Unit 2 - p. 4

MIT - 16.20

Fall, 2002

F.O.S. is also a “Factor of Ignorance” This accounts for probability & statistics (also in material allowances) U.F.S. = 1.5 for Aircraft 1.25 for Spacecraft (unmanned) Design is usually conservative and an additional “Margin of Safety” (M.O.S.) is used/results Limit MOS = Tested Limit X - Limit X Limit X Ultimate MOS = Tested Ultimate X - Ultimate X Ultimate X An MOS is an experimental reality.
Paul A. Lagace © 2001

Unit 2 - p. 5

MIT - 16.20

Fall, 2002

Try to minimize M.O.S. - Too conservative ⇒ too heavy - Not conservative enough ⇒ plane falls out of sky (things have flown with negative M.O.S.) So, begin with “operational envelope”, the way the structure will be used • Aircraft --> v-n diagram • Spacecraft, etc. Then add special conditions (gusts, etc.) Also need to account for • Environmental effects - change in material properties - causes stresses and strains • Special conditions - Lightning - Impact - etc.

Paul A. Lagace © 2001

Unit 2 - p. 6

MIT - 16.20

Fall, 2002

• Fatigue (cyclic loading) - Effect on material properties - Damage growth

Example
A fighter aircraft has a gross take-off weight of 30,000 lbs. In a test of one wing, the wing fails at a total loading of 243,000 lbs. What is the margin of safety? Definition of M.O.S. = Tested Ultimate - Ultimate Ultimate We know: Tested Ultimate = 243,000 lbs. (for one wing) How do we get the Design Ultimate? Design Ultimate = Design Limit x Factor of Safety For aircraft, F.O.S. = 1.5
Paul A. Lagace © 2001

Unit 2 - p. 7

MIT - 16.20

Fall, 2002

How do we get the Design Limit? Use the v-n diagram From U.E., max n for fighter = 9 = limit n (Note: n for level flight = 1 ⇒ loading for level flight = weight) ⇒ Design Limit = nlimit x weight = 9 x 30,000 lbs. = 270,000 lbs. But, each wing carries 1/2 of this Design limit load for one wing = 135,000 lbs. ⇒ Design ultimate load for one wing = 202,500 lbs. Finally, M.O.S. = 243,000 lbs. - 202,500 lbs. 202,500 lbs. = 40,500 lbs. = 202,500 lbs.

0.2 = M.O.S

+ 20% margin

Paul A. Lagace © 2001

Unit 2 - p. 8

MIT - 16.20

Fall, 2002

What is “failure”?
It depends on use…. ….may be deflection based (CTE example) ….may be fracture ….may be buckling . . . Overall, you must consider: Static Stresses - Fracture - Yielding - Buckling Deflections - Clearances - Flutter - Vibration - Tolerances (e.g., C. T. E.)
Paul A. Lagace © 2001

Unit 2 - p. 9

MIT - 16.20

Fall, 2002

Life Damage accumulation “Fatigue”

For aircraft, design guidelines provided by FAA F.A.R.’s (Federal Aviation Regulations) Part 23 Aircraft Under 14,000 lbs. Part 25 Aircraft Above 14,000 lbs. Part 27 Part 29 Helicopter

USAF guidelines (e.g., Damage Tolerance Regulations)

Paul A. Lagace © 2001

Unit 2 - p. 10…...

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