Stress reduction factor

In equation (15.20) the parameter A is termed the stress reduction factor and is given by ... 

A recent analysis by Kastritseas etal. (2004c) suggested that in both cases the magnitude of the thermal shock-induced stresses was overestimated as the anisotropic character of the materials was not taken into account. If material anisotropy is accounted for, then both (15.36) and (15.37) cannot predict A Tc accurately even for the largest possible value of the thermal shock-induced stresses (corresponding to a maximum value of the stress reduction factor, A = 0.66). To explain the discrepancy, it was proposed that the interfacial properties may be affected by the shock due to the biaxial nature of the induced stress field, which dictates that a tensile thermal stress component that acts perpendicular to the fibre-matrix interface is present for the duration of the shock. 

Temperature can ultimately be viewed as a thermal stress — one that causes an increase in failure rate (and life if applicable). But how severe a stress really is, must naturally be judged relative to the ratings of the device. For example, most semiconductors are rated for a maximum junction temperature of 150°C. Therefore, keeping the junction no higher than 105°C in a given application represents a stress reduction factor, or alternately — a temperature derating factor equal to 105/150 = 70%. 

Figure 9.12 Stress reduction factor as a function of non-dimensional time for various values of Biot s modulus, /3.

The very rapid cooling rates needed to define dt values do not occur often and, thus, a second TSR parameter 2ft is sometimes used. This approach introduces the other important material parameter, thermal conductivity. For slow cooling rates, it is found that the stress reduction factor is 0.31 jS and is, thus, inversely dependent on thermal conductivity. If this condition is introduced, 2ft is defined... 

F Exceptionally high inflow or pressure continuing without decay 6. Stress reduction factor... 

The stress reduction factor, SRF, which accounts for the loading on a tunnel caused either by loosening loads in the case of clay-bearing rock masses, or unfavourable stress-strength ratios in the case of massive rock. Squeezing and swelling also are taken account of in the SRF. 

Code Case 2286 assumes that shells are axisym-metric, that for unstiffened vessels the shells are the same thickness, and that for stiffened cylinders and cones the thickness between stiffeners is uniform. Additionally, capacity reduction factors (or knockdown factors) are provided for general use, but are incorporated in the allowable stress equations. Stress reduction factors (FS) must be found for each direction of loading so that the values of FS are determined independently for both the longitudinal and circumferential directions. The stress reduction factors cover elastic and inelastic buckling, and plastic collapse behavior for elements in compression. 

Popelar developed two reduction equations, one for temperature-reduction factors and a second for stress-reduction factors. Popelar s work provides the following shift functions ... 

Analysis of Table II shows discrepancies in the hardness and stress behavior of a-C(N) H films. Although all the works reported a clear stress reduction upon nitrogen incorporation, the hardness sometimes is quoted as almost constant, or on the other hand clearly decreasing. In addition to the possible effect of different deposition methods and conditions, it can be easily seen that the differences in hardness testing methods are the major source for discrepancies. Constant hardness behavior is only reported with the use microindentation methods, like Vickers and Knoop microhardness. On the other hand, the use of low-load nanoindentation methods always led to a nitrogen-induced decrease in hardness. This is basically the consequence of two factors. The first one is the higher penetration... 

The weld joint strength reduction factor is the ratio of the nominal stress to cause failure of the weld joint to that of the base material for the same duration. In the absence of more applicable data (e.g., creep testing), the factor shall be taken as 1.0 at temperatures equal or colder than 510°C (950°F), and 0.5 at 815°C (1,500°F) for all materials. The strength reduction factor shall be linearly interpolated for intermediate temperatures. The designer is responsible for determining weld joint strength reduction factors for temperatures warmer than 815°C (1,500°F). 

Creep testing of weld joints to determine weld joint strength reduction factors should be full thickness crossweld specimens with test durations of at least 1 000 h. Full thickness tests shall be used unless the designer otherwise considers effects such as stress redistribution across the weld. 

The allowable stress for occasional loads of short duration, such as surge, extreme wind, or earthquake, may be taken as the strength reduction factor times 90% of the yield strength at temperature times Mj for materials with ductile behavior. This yield strength shall be as listed in ASME BPV Code Section II, Part D, Table Y-l (ensure materials are suitable for hydrogen service see API 941), or determined in accordance with para. 

IP-2.2.7(d). The strength reduction factor represents the reduction in yield strength with long-term exposure of the material to elevated temperatures and, in the absence of more applicable data, shall be taken as 1.0 for austenitic stainless steel and 0.8 for other materials. For castings, the basic allowable stress shall be multiplied by the casting quality factor, Ec. Where the allowable stress value exceeds two-thirds of yield strength at temperature, the allowable stress value must be reduced as specified in para. IP-2.2.7(c). Wind and earthquake forces need not be considered as acting concurrently. At temperatures warmer than 427°C (800°F), use 1.33... 

Sf = product SEWMj [of the stress value, S the appropriate quality factor, E, from Tables IX-2 or IX-3A weld joint strength reduction factor per para. IP-2.2.10(e) and the performance factor, Mj(see Mandatory Appendix IX)] for flange or pipe material see para. IP-2.2.7(c). 

Output includes node displacements, member end forces and support reactions A three-dimensional model would produce more accurate results hut a two-dimensional analysis normally is sufficient for this type of structure. Members will be subjected to loads from both long and short walls. The member capacity used in the mode or the allowable deformation must be limited to account for the fact that the members will be subjected to simultaneous bi-axial loading. A typical capacity reduction factor is 25%. This factor reflects the fact that peak stresses from each direction rarely occur at the same time. 

Tees Tees may be cast, forged, or hot- or cold-formed from plate or pipe. Tees are typically stocked with both header (run) ends of the same size. In general, run ends of different sizes are not typically stocked or specified however, occasionally run ends of different sizes are specified in threaded or socket-welded sizes. Branch connections may be full size or reducing sizes. Branch reductions two sizes smaller than the header are routinely stocked, and it is not typically difficult to purchase reducing tees with branches as small as those listed in ASME B16.9 (i.e., approximately one-half the header size). Economics, stress intensification factors, and nondestructive examination requirements typically dictate the branch connection type. 

Longitudinal stresses Sl- The sum of longitudinal stresses Sl in any component in a piping system, due to sustained loads such as pressure and weight, shall not exceed the product S W, where is the basic allowable stress at maximum metal temperature expected during the displacement cycle under analysis, and W is the weld joint strength reduction factor. 

FIG. 10-168 Stress range reduction factor,/ Reproduced from ASME B31.3-2004 with permission of the publisher, the American Society of Mechanical Engineers, New York.)... 

Sc = basic allowable stress for the material at minimum (cold) metal temperature Sh = basic allowable stress for the material at maximum (hot) metal temperature / = stress-range reduction factor for cyclic conditions for the total number of full temperature cycles over the expected life / = 1.0 for 7000 cycles or less. 

Thus, the magnitude of the reduction in the applied stress intensity factor, Kt, due to the cohesive zone is... 

Stress relaxation between manufacture and testing. Between manufacturing and testing, relaxation of the residual stress will occur as a result of the viscoelastic properties of the matrix, which controls the behaviour of the 90° layer. Measurements to determine the relaxation of the ply-to-ply residual stress of the carbon-polyetherimide lay-up, with the highest level of residual stresses of the laminates tested ([904c/04c]s), have been presented previously [5]. It shows that the level of residual stress follows a power law with time. For the purpose of this study, it was chosen to perform the bending experiments 240 hours after fabrication, as the level of residual stress remains more or less constant. The level of residual stress as calculated in (1) is then altered by a reduction factor,/,. The relaxed residual stress. 

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