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Typically, a program will vary the test option for different components depending on type of structure, material or method of construction, weight criticality, perceived test difficulty, program schedule, and planned quantity of flight articles.

We should proof test (option 2) each flight article if strength is significantly affected by workmanship or process variations. The test conditions should apply the critical stresses in all load directions possible during the mission. Proof tests should also include the effects of predicted temperature changes during the mission, which can be significant in certain types of structures. Proof testing is the only viable option for advanced composite structures and bonded joints, unless we can become confident that our processes are controlled well enough to keep strength variations low. We also proof test all pressure vessels.

If strength is relatively insensitive to workmanship, such as for most mechanically fastened metals, we can choose any of the four test options. When building many articles, we can save money by testing just one (option 3), but this option carries a weight penalty because of its high factors of safety. Alternatively, we can build a dedicated qualification article and use the lower factors of safety that go with the "Ultimate Test" (option 1). With this approach, we have three additional benefits:

1. We can shorten the flight-article development schedule by conducting the test program in parallel.

2. We can use the test article as a pathfinder for launch-site operations.

3. The impact of test failure is not as severe.

We must weigh these advantages against the cost of building the test article, for which we must use the same processes as for the flight structure.

Option 4 ("No Test") can be risky, and we must use it with caution. The space industry has no design codes, such as for many commercial structures, and relies heavily on testing to verify structural integrity. Without a test, a critical analysis error or oversight could lead to a mission-ending structural failure, even with high factors of safety. However, with caution, we can confidently use this option for relatively simple structures. The "no test" option may be most cost effective for structures designed for stiffness rather than strength.

To provide confidence the structure will survive multiple loading cycles, we also perform fatigue analysis. Fatigue is a much greater concern for aircraft than for most primary structures in a spacecraft because launch is of such short duration. But if stresses are high enough, it does not take many cycles for a material to fatigue, and launch is not the only event that can cause fatigue damage. Ground testing and transportation can significantly degrade service life. Structures sensitive to high-frequency vibrations or on-orbit thermal cycling are particularly susceptible to fatigue.

All materials have internal defects, most of which are microscopic. The number, sizes, and locations of these defects all contribute to high variability in fatigue life between specimens of the same material. In a fatigue analysis, we compare the number of cycles at the limit stress level with the test-determined average number of cycles at which failure occurs. We account for variability in a material's fatigue life by multiplying the predicted number of load cycles over the mission life by a scatter factor of four [Rolfe and Barsom, 1977].

To account for the possibility of a large pre-existing flaw in a critical location of a structural part, we can establish a fracture control program. This includes inspections of raw materials and fabricated parts for defects, special handling procedures for critical parts, and fracture-mechanics safe-life analysis. This analysis, which is a semi-empirical method of predicting crack growth and part life, is more conservative than fatigue analysis because we assume an initial crack exists at the location of peak stress. We set the size of the assumed initial crack equal to the minimum our inspection methods can reliably detect. MIL-HDBK-5G provides fatigue and fracture mechanics data for most metals.

11.6£ Preliminary Sizing of Structural Members

To size the structural members of a spacecraft, we consider stiffness, strength, and weight We will rarely find a design in the first iteration that is acceptable for all three. Before the design is final, we will perform many iterations that also consider fatigue life, cost, and changes in subsystem requirements.

Stiffness—Flexibility is a measure of how much a structure deflects under unit load. Stiffness is a measure of force required to cause a unit displacement. (For a single-degree-of-freedom system, stiffness is the inverse of flexibility.) A structure's mode shapes and natural frequencies of vibration depend on its stiffness and mass properties. We discussed typical considerations for stiffness in Sec. 11.6.1.

We can estimate the primary frequencies of a stowed spacecraft by representing it with an equivalent beam, which simulates mass properties and core stiffness, then using simple beam-frequency equations provided in Sec. 11.6.6. As the design evolves, we construct a finite element model (a mathematical representation of the structure) to obtain more accurate predictions of mode shapes and frequencies. For a given mode of vibration, most finite element software can identify the locations in a structure that have the most strain energy, which is the energy absorbed when a structure deforms under load. Reinforcing the areas with high strain energy is the most efficient way to stiffen a structure.

A structural assembly is usually more flexible than predicted by a math model because of local flexibility in mechanical attachments. Thus, even if our model demonstrates the design is adequate, we may find out during testing that the structure doesn't meet stiffness requirements. It usually doesn't cost much in weight to stiffen a joint—the key is being aware of stiffness in the design of attachments. We should also not cut a stiffness requirement too close before verifying it by test.

Strength—We can use various methods to predict distributions of internal loads, depending on the structure's complexity and the scope of our analysis. Free-body diagrams show applied load, which in preliminary design equals weight multiplied by load factor at the center of gravity, and the reactions necessary for static equilibrium. With these diagrams, we can easily determine member loads in a statically determinate structure, which has just one solution for member loads that satisfies equilibrium. Finite element analysis is the most efficient method of predicting loads in a statically indeterminate structure, which has redundant load paths.

To have adequate strength, the structure must not rupture, collapse, or deform such that its function is impaired. Primary structural members made of ductile materials seldom rupture in tension for two reasons: (1) Most structures are statically indeterminate, and ductile materials will stretch enough prior to failure for loads to redistribute. (2) Tension is an easy mode of failure to assess for a member of constant cross-section and is seldom overlooked. Instead, tension members fail most often at their attachments: fittings, welds, fasteners, and adhesives.

Stability is a structure's resistance to collapsing under compression. Compressive failures are the most sudden and catastrophic, and they are often the hardest to predict. An overall instability failure of a column is called buckling. This is the kind of failure we would expect if we pushed on the ends of a long, slender rod. The load at which a column buckles decreases with the square of its length. Crippling is a compression failure that starts with local buckling of thin-walled flanges or webs in a member's cross-section.

We often design panels in skin-stringer structures to buckle under compressive loads, with shear being transferred by diagonal tension. This is a common practice for weight-critical structures and is not catastrophic if we design the rivets, stringers, and frame members properly. Diagonal tension will induce lateral loads in edge members that cause compression and bending, as discussed in Bruhn [1973].

We also must check that structural elements do not yield, or take on permanent deformations that can jeopardize the mission. Yielding is a characteristic of all structural materials except those that are perfectly brittle (no ductility). Other deformations can be detrimental as well, such as shifting in mechanical joints, so we must assess them as well.

When assessing rupture and collapse, we use design ultimate loads, which are limit loads multiplied by the ultimate factor of safety. We use the yield factor of safety to assess permanent deformations. The onset of compressive yielding will often be followed by collapse because of reduced stiffness, so we should ensure there will be no compressive yielding at design ultimate loads.

Weight—Designers of flight structures quickly develop an instinct for meeting requirements with the lightest structure. Throughout preliminary design, the configuration and loads will change, and we will have to increase the sizes of many structural elements. We will also find elements that are unnecessarily heavy, but we won't always change the design. As the design becomes more detailed, weight optimization becomes increasingly difficult and complicates production.

At each design iteration, we compare a component's weight with its allocation. Once the allocation has been met, we focus our attention on other issues. The test design will seldom be the lightest design—it will be the one that is optimal for the system, considering performance, reliability, and cost

### 11.6.6 Structural Mechanics and Analysis

A part made from a solid material will change shape as force is exerted on it Mechanics of materials is the term used to describe how materials respond to applied forces and other environments. The most basic term in mechanics of materials is stress, <7, which is the load, P, in a member, divided by its cross-sectional area, A, (Fig. 11-27).

Area A

Typical units for stress are N/m2 and lb/In2 or psi.

Strain, e, is a dimension]ess measure of deformation for a given load. In Fig. 11-27 the bar's length, L, is increased by AL in response to the axial load, P.

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