Determination of hypocentral parameters of local earthquakes using weighting factor based on take-off angle

In flaw evaluation criteria, the secondary stresses (displacement controlled) may have different design limits than primary stresses (load-controlled stress components). The design limits are based on elastic stress analysis. Traditionally the elastic design stresses are used in the flaw evaluation procedures. But realistically a flaw in the piping system can cause non-linear behavior due to the plasticity at the crack plane as well as in the adjacent uncracked-piping material. A Secondary Stress Weighting Factor (SSWF) was established which is the ratio of elastic-plastic moment to the elastic moment calculated through an elastic stress analysis. As long as the remote uncracked pipe stresses are below yield, the SSWF is 1.0, and if the uncracked pipe plastic stresses are above the yield stress, the SSWF reaches a limit which is called the Plastic Reduction Factor (PRF). Four-point-bend tests were conducted on pipes with varying circumferential surface-crack lengths and depths. The moment-rotation plots obtained from various pipe tests were used in the determination of PRF. A lower-bound limiting PRF can be calculated from a tensile test, but pipe systems are not uniformly loaded like a tensile specimen. The actual PRF value for a cracked pipe was shown to have a lower bound, which occurs when the test section of interest is at a uniform stress (such as the center region in a four-point pipe bend tests). When multiple plastic hinges develop in a pipe system (a “balanced system” by ASME Section III NB-3650 design rules), this gives a greater reduction to the elastically calculated stresses since there is more plasticity. It was found that the plastic reduction is less when most parts of the pipe system remains elastic, or if the crack is located in the high strength/ lower toughness pipe or welds, or if the pipe size is large enough that elastic-plastic conditions occur even for a higher toughness material. Interestingly, it was shown that the same system with different loading directions could exhibit different actual PRF values if the change in the loading direction changes how much of the pipe system experiences plastic stresses. For smaller cracks, where the bending moments are high, the actual PRF is controlled by plasticity of the uncracked pipe, which is much larger than the plasticity that occurs locally at the crack. However, for large cracks where the bending moments are lower (closer to design conditions), the plasticity at the crack is equally important to the smaller amount of plasticity in the uncracked pipe for the actual PRF. Hence the plasticity of both the uncracked pipe and at the cracked sections is important to include in the determination of actual PRF values.

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Determination of relevant “average” properties for tubular filler materials used in composites

Journal of Polymer Engineering ◽

10.1515/polyeng.2011.075 ◽

2011 ◽

Vol 31 (4) ◽

Author(s):

Patrick M. Piccione

Keyword(s):

Carbon Nanotubes ◽

Average Diameter ◽

Weighting Factor ◽

Filler Materials ◽

Cross Sectional ◽

The Third ◽

Materials Used ◽

Third Moment ◽

Calculation Procedures

Abstract To obtain the best estimate of the average diameter and number of walls of tubular objects such as carbon nanotubes, which are used as filler materials in composites, both inner and outer diameters must be taken into consideration. The appropriate weighting factor is calculated from the cross-sectional circular shell area. In the case of cylindrical objects, the formulae simplify considerably and the average diameter and wall thickness are the third moment of their distribution function. Two examples illustrate the numerical effects of these calculation procedures.

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The use of a high-speed digital computer for the direct determination of crystal structures. I

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1955.0025 ◽

1955 ◽

Vol 227 (1171) ◽

pp. 486-500 ◽

Cited By ~ 14

Keyword(s):

Crystal Structure ◽

Fourier Series ◽

Crystal Structures ◽

Digital Computer ◽

High Speed ◽

Electronic Computer ◽

Direct Determination ◽

Direct Methods ◽

Weighting Factor

A method is described whereby an electronic computer, the EDSAC, may be used to select a set, or sets, of signs for the coefficients F (h) of a Fourier series, such that the Fourier series, satisfies a certain condition. This condition is expressed as X ≡ Ʃ h Ʃ h ' P (h,h') S (h) S (h') S (h+h')≽ X 0 , where S (h) denotes the sign of F (h) and P (h, h') is a weighting factor related to the probability that S (h) S (h') = S (h+h'). In certain circumstances the determination of a crystal structure which is beyond the range of other direct methods is possible by this procedure.

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Local seismic monitoring—Fairview Peak Area, Nevada

Bulletin of the Seismological Society of America ◽

10.1785/bssa0570061279 ◽

1967 ◽

Vol 57 (6) ◽

pp. 1279-1298

Author(s):

W. H. Westphal ◽

A. L. Lange

Keyword(s):

Active Faults ◽

Seismic Monitoring ◽

Focal Points ◽

Local Earthquakes ◽

West Central

Abstract Four portable seismographs were used in January-February and April to August 1965 to record local earthquakes in the Fairview Peak Area of west-central Nevada. During these recording periods, which totalled 129 days, over 1300 local shocks were recorded of which 224 were large enough for determination of focal points. These hypocenters defined the active faults of the region and provided a means for mapping the probable extent of these faults at depth.

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