Recent progress in the plastic methods of structural analysis

The techniques described in Part I of this paper for the calculation of plastic failure loads under proportional loading are further exemplified by indicating solutions for a rectangular building frame, a Vierendeel girder, and a shed-type portal frame. A method for estimating deflections of a frame just as the collapse load is attained is then described, with some indications as to its reliability. More general conditions of loading than proportional loading are next discussed, and generalized load and failure concepts are defined. The theorems and techniques for determining critical shakedown loads under variable, repeated loading are then described and illustrated. The relation of the elastic-plastic shakedown analysis to the much simpler analysis for failure under single load applications is discussed.     

The electron mechanics of induction acceleration

The radial and axial motions of electrons in the betatron are described by means of a potential function of forces. Previously reported conditions of equilibrium, stability and damping of oscillations are derived for the region of parabolic variation of the potential. Extension of the analysis to, non-parabolic regions gives an account of the injection in conventional instruments in better agreement with experiment, particularly in regard to higher voltages of injection.Space charge limitations are discussed with the help of the Laplacian of the potential of forces.By means of an additional radial electric field electrons can be introduced as in the magnetron, without any asymmetry inherent in the conventional betatron circumferential injector. The analysis of the conditions of equilibrium and stability, greatly facilitated in this case by the notion of potential, shows that no substantial improvement in space charge limitations can be expected and that the required variations between the flux linking the electron orbits and the magnetic and electric fields at the orbits are difficult to realize on account of their complexity and narrow tolerances. The X-ray output of a small experimental double yoke instrument was measured by a phototube multiplier viewing an irradiated fluorescent screen and gave evidence of multiple group electron capture.     

Secondary electron emission from oxide-coated cathodes

The secondary electron emission from alkaline-earth oxide-coated cathodes has been investigated under both continuous and pulsed bombardment. Various factors affecting the yield, such as dependence upon primary voltage, collecting voltage, temperature, time, and angle of incidence, are noted, and the present state of the theory is discussed.Experiments have been performed with three types of apparatus. Yield vs. Energy data reveal values of δ of 4–7 at room temperature, with a more or less flat maximum at approximately 1,000 volts primary energy.The yield increases with temperature in an exponential manner, and plots of log Δδ (i.e. δ_K° ? δ_300°K) vs. 1/T give straight lines. Values of Q₁ between 0.9 – 1.5 eV. are generally indicated, and from extrapolation of these curves, yields exceeding 100 at 850° C. are deduced. The secondary emission depends upon the degree of activation, and increases with enhancement of the thermionic emission characteristics. Short-time effects such as growth or decay of secondary current after the onset of primary bombardment or persistence after the cessation of bombardment have not been observed, and values of yield obtained by pulsed methods are in accord with those obtained under D.C. conditions. Tail phenomena reported by J. B. Johnson and interpreted as “enhanced thermionic emission” from oxidecoated cathodes become manifest only under experimental conditions characterized by certain space-charge effects, and have been effectively simulated by bombarding a tantalum target adjacent to an electron-emitting tungsten filament. Various measurements of the energy distribution of secondary electrons as a function of primary voltage and temperature have been obtained. It was observed that the average energy of the secondary electrons decreases with temperature at a rate which more than compensates for the increase in the number of secondaries emitted per incident primary. The mechanism of the observed dependence of yield upon temperature is not well understood. Various alternative explanations are discussed and, in the light of the present state of our knowledge, regarded as untenable.