A fatigue design procedure is proposed for the structural elements subjected to a stress process, modeled as stationary wide-band gaussian. This procedure, restricted to high cycle fatigue design, uses available constant amplitude material fatigue data and a modified, probability based, Palmgren-Miner (PM) rule. Statistical uncertainty in fatigue behavior and nonstatistical uncertainty in the PM rule are implicitly accounted for by treating the PM index at failure as a random variable. The rain flow method of counting stress cycles is used. The fatigue design algorithm requires only that the RMS and irregularity factor of the stress process be specified in addition to the constant amplitude S-N curve for the material.

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For dominant forced convection with significant gas property variation, even in low Mach number flow through a circular tube, apparently the only published profile data available to guide (or test) the development of predictive turbulence models are K. R. Perkins' measurements of mean temperature structure [Perkins, 19751. The work here takes the next step: the frrst mean velocity distributions for this situation are presented.In order to dissect the anatomy of the viscous layer in gaseous, turbulent, tubie flow with strong heating, it has been probed via thermal anemometry coupled with diagnostic application of simple computational thermal fluid dynamics. Experiments for air flowing upward in a vertical circular tube were conducted for heating rates causing significant property variation. An unheated entry of fifty diameters preceeded the heating.Two entry Reynolds numbers of approximately 6000 and 4000 were employed, concentrating on three heating rates, q+ = q"w/Gcp,inTin = 0.0018, 0.00135 and 0.0045, to give conditions considered to be "turbulent," "subturbulent" and "laminarizing," respectively. Exit Reynolds numbers were above 3000 in all cases.Examination emphasizes the wall region which would conventionally be expected to contain the viscous layer, 0 < y+ < -30, if the flow were unheated. In the flow called "turbulent", after being disturbed in the first few diarneters by the heating (and its accompanying variation of viscosity, density and thermal conductivity), profiles representing the turbulence quantities --l/y, E /v, -p UV /'cw and -pc+ 5 /qtvw --appear to recover to approximately selfpreserving conditions. In the other two runs with higher heating rates, the turbulence quantities decrease after the immediate thermal entrance until they are small relative to molecular effects. m DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use wouid not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, rnanufacturer, or otherwise does not necessarily constitute or imply its endorsement, m mmendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors ~XPT~SSUI herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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