Fi„ = Allowable Tensile Ultimate Stress, the highest unl-axlal tensile stress a material can sustain before rupturing.

/rty= Allowable Compressive Yield Stress, the compressive stress that causes a permanent deformation ol

0.2% at the specimen's length. E = Young's Modulus, a.ka. Modulus of Elasticity, the ratio of stress to strain (length change divided by original length) In the linear elastic range (see Sec. 11.6.6). e = Elongation, a measure of ductmy, equal to the percentage change In length caused by plastic deformation prior to rupture, a = Coefficient ot Thermal Expansion, a measure of strain per degree temperature change. Values shown for a are at room temperature.

p = Density

Fi„ = Allowable Tensile Ultimate Stress, the highest unl-axlal tensile stress a material can sustain before rupturing.

/rty= Allowable Compressive Yield Stress, the compressive stress that causes a permanent deformation ol

0.2% at the specimen's length. E = Young's Modulus, a.ka. Modulus of Elasticity, the ratio of stress to strain (length change divided by original length) In the linear elastic range (see Sec. 11.6.6). e = Elongation, a measure of ductmy, equal to the percentage change In length caused by plastic deformation prior to rupture, a = Coefficient ot Thermal Expansion, a measure of strain per degree temperature change. Values shown for a are at room temperature.

develop fastener strength, we must provide adequate fitting thicknesses, fastener spacing, and edge distances. The torque value for installing a tension fastener must provide a preload that will maintain stiffness and preclude fatigue, which is a failure resulting from cracks that form and grow because of cyclic loading. A locking feature, typically a deformed thread in the nut or insert, will prevent a threaded fastener from backing out when the structure vibrates. Many similar guidelines help us design a dependable structural joint.

To develop a structure light enough for flight, and to keep spacecraft affordable, we must accept some risk of failure. Material strengths vary because of random, undetectable flaws and process variations, and loads depend on unpredictable environments. Random variables affect the adequacy of most structures, such as a dam whose load depends on how much it rains; but for space missions, we must accept a higher probability of failure than for most other types of structures. Launch loads are affected by many different random variables, such as acoustics, engine vibrations, air turbulence, and gusts, and we seldom have enough data to confidently model the probability distributions of these variables.

Because of loads uncertainty, we cannot accurately quantify the structural reliability of a spacecraft We can approximate it, however, and we can develop design criteria that will provide acceptable reliability. Let us work backwards from a subsystem-level reliability to understand how conservative our design approach should be for an individual structural part.

If we select a goal for structural reliability of 99% (we probably should aim higher), which means there is a 1% chance of a mission-ending structural failure, we must design each structural element to much higher reliability. If the structure has 1,000 parts whose failure would jeopardize the mission, and if their chances of failure are independent, each must have 99.999% reliability (0.999991000 = 0.99, from probability theory). This explains why design criteria may appear so conservative. To achieve appropriate reliability, many programs use the following ground rules:

• Use a design-allowable strength for the selected material that we expect 99% of all specimens will equal or exceed.

• From available environmental data, derive a design limit load equal to the mean value plus three standard deviations. This means there will be 99.87% probability that the limit load will not be exceeded during the mission, assuming the load variability has a Gaussian distribution. Because data will be limited, we can only approximate the true probability level of the design load; but "3-sigma" remains the goal. (Some programs aim for 99% probability instead of 3d.)

• Multiply the design limit load by a factor of safety, then show that the stress level at this load does not exceed the corresponding allowable strength.

• Test the structure to verify design integrity and/or workmanship, to correlate analytical models, and to protect against human errors.

Table 11-53 summarizes the criteria used to design space structures.

Space programs use different factors of safety, but most recognize the need to balance the factors with the type of structure and scope of testing. Factors of safety are highest for pressure vessels and for structures we will not test For most other structures, a contractor will be able to choose from several test options. Table 11-54 shows the test options for an unmanned launch. If personnel safety is at risk, as for a Shuttle launch or during ground handling, we use higher factors.

TABLE 11-53. Terms and Criteria Used in Strength Analysis. We design space structures to meet specified or selected criteria for preventing yield and ultimate failures. A yield failure is one in which the structure suffers permanent deformation that degrades the mission; ultimate failure is rupture or collapse. Two factors of safety—one for yield and one for ultimate—typically apply to a structural assembly, and depend on the selected test option (Table 11-54). For each structural member, the allowable load, the design load, and the margin of safety each have two values, one for yield and one for ultimate.

TABLE 11-53. Terms and Criteria Used in Strength Analysis. We design space structures to meet specified or selected criteria for preventing yield and ultimate failures. A yield failure is one in which the structure suffers permanent deformation that degrades the mission; ultimate failure is rupture or collapse. Two factors of safety—one for yield and one for ultimate—typically apply to a structural assembly, and depend on the selected test option (Table 11-54). For each structural member, the allowable load, the design load, and the margin of safety each have two values, one for yield and one for ultimate.

Term |
Definition |

Load Factor |
A multiple of weight on Earth, representing the force of inertia that resists acceleration. The load factor applies in the direction opposite that of the acceleration. For example, an object under an acceleration of 5 g, where g Is the gravitational acceleration, has a load factor of -5; if that object weighs 500 N (a mass of 51 kg), the force it exerts on its support structure is-2,500 N. |

Limit Load (or design limit load) |
The maximum load expected during the mission or for a given event, at a specified or selected statistical probability (typically 99% for expendable launch vehicles and 99.87% for launches with humans aboard). The load can be acceleration, load factor, force, or moment |

Allowable Load or Stress |
The highest load or stress a structure or material can withstand without failure, based on statistical probability (usually 99%; I.e., only 1% chance the actual strength is less than the allowable). |

Factor of Safety, FS |
A factor applied to the limit load to obtain the design load for the purpose of decreasing the chance of failure. |

Design Load Limit load multiplied by the yield or ultimate factor of safety; this value must be no greater than the corresponding allowable load. | |

Design Stress Predicted stress caused by the design load; this value must not exceed the corresponding allowable stress. | |

Margin of Safety, MS A measure of reserve strength: | |

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