Beams neutral surface

Observe that this is a geometric property, not to be confused with the modulus of the material, which is a material property. I, c, Z, and the cross-sectional areas of some common cross-sections are given in Fig. 3-1, and the mechanical engineering handbooks provide many more. The maximum stress and defection equations for some common beamloading and support geometries are given in Fig. 3-2. Note that for the T- and U-shaped sections in Fig. 3-1 the distance from the neutral surface is not the same for the top and bottom of the beam. It may occasionally be desirable to determine the maximum stress on the other nonneutral surface, particularly if it is in tension. For this reason, Z is provided for these two sections. 

There are several methods in use for producing these clusters. Particle bombardment or laser vaporization of a graphite surface leads to direct formation of ions that can be detected by mass spectrometry. These are normally of relatively small size (n<30). By laser vaporization of graphite into a molecular beam neutral... 

To overcome this problem, we have modified a commercial ion gun to generate a diffuse fast-atom beam [116, 117]. The ion beam neutralizer shown in Figure 7 consists of a multi-hole metal plate through which the primary ions pass. The ions are neutralized by the ion/surface interactions that occur as the beam passes through the metal aperatures and by charge-exchange reactions that occur within the gun assembly. A repeller grid is used to remove the residual ions from the neutralized beam. 

Except for the alkali beams, where surface ionization can be used, the weak beam is difficult to detect. Cohen et al.51 succeeded in detecting Ba and A1 beams with a specially designed electron bombardment detector. In spite of these problems sputtering is for many substances, like light metal atoms and any other material of high melting point, the only way to produce a fast neutral beam. 

Many applications of ion beams in surface analysis use a rastered ion beam to insure uniform erosion. The fraction of the ion beam that is neutral atoms is not affected by the potentials applied to the deflection plates of an ion gun and result in distortion in the erosion rate over the analysis area of the sample. Unfortunately, it is difficult to measure the composition of an ion beam to detect the presence of impurity ions, doubly charged or neutral species in most experimental situations. 

In these composites, the layers are bonded together. A sandwich panel beam is symmetrical if the skins have equal thickness, and are made of the same material. The neutral surface is at the mid-thickness, so the analysis of Appendix C can be used. Figure 4.6 shows the stress variation through a sandwich beam, calculated using Eq. (C.4) separately for the skins with high Young s modulus E, and the core with low modulus Eq. 

Figure 13.6 shows the relative efficiency of different beam cross sections. Each has the same cross-sectional area and the neutral surface is horizontal. The I beam, of height equal to twice its width, is given a second moment of... 

Figure C. I Geometry of a bent beam, showing a fibre , a distance y above the neutral surface.

For beams of symmetrical cross section (Fig. C.2), the neutral surface is at the mid-depth. However, for asymmetric cross sections (Section 13.3.2), the neutral surface goes through the centroid of the cross section. For symmetrical cross section beams, the maximum and minimum strains, at the top and bottom surfaces, respectively, are given by... 

The neutral surface is that horizontal section between the concave and convex surfaces of a loaded beam, where there is no change in the... 

The maximum stress occurs at the surface of the beam farthest from the neutral surface, as given by the following equation ... 

Figure 4.8 Beam of thickness h bent to radius of curvature R. The beam will have a (neutral) surface that has undergone no strain.

Consider the cantilever beam shown in Fig. 4.9 in which it can be shown that M=F L-x) and Vis constant along the beam length. Using Eqs. (4.7) and (4.8) for a beam of rectangular cross-section, one finds the shear stresses are parabolic, being zero at the free surfaces of the beam and rising to a maximum of ZFUbh at the neutral surface. 

Structures are often designed to give maximum stiffness for minimiun weight. For beams, the cross-sectional shape is often modified to meet this goal. For example, material near the neutral surface is relatively unstressed and is not really needed . This leads to the use of I-beams, in which the central area is reduced to a thin web. This shape change allows the second moment of area to... 

As indicated in Chapter 3, in simple beam-bending theory a number of assumptions must be made, namely that 1) the beam is initially straight, unstressed, and synunetrical 2) its proportional limit is not exceeded 3) Young s modulus for the material is the same in both tension and compression and 4) all deflections are small, so that planar cross-sections remain planar before and after bending. The maximum stress occurs at the surface of the beam farthest from the neutral surface, as given by the following equation (see Fig. 5-8) [2]. 

The neutral surface is that horizontal section between the concave and convex surfaces of a loaded beam, where there is no change in the length of the fibers and no tensile or compressive stresses acting upon them. The neutral axis is the trace of the neutral surface on any cross section of a beam. The elastic curve of a beam is the curve formed by the intersection of the neutral surface with the side of the beam, it being assumed that the longitudinal stresses on the fibers are within the elastic limit. 

Neutralization (electrical) The removal of an electrical charge by the addition of charges of the opposite sign. Example Surface charge neutralization. See also Beam neutralization. 

These equations indicate that the energy of the scattered ions is sensitive to the mass of the scattering atom s in the surface. By scanning the energy of the scattered ions, one obtains a kind of mass spectrometric analysis of the surface composition. Figure VIII-12 shows an example of such a spectrum. Neutral, that is, molecular, as well as ion beams may be used, although for the former a velocity selector is now needed to define ,. ... 

The intensity of SS /. from an element in the solid angle AD is proportional to the initial beam intensity 7q, the concentration of the scattering element N., the neutralization probability P-, the differential scattering cross section da(0)/dD, the shadowing coefficient. (a, 5j ) and the blocking coefficient(a,5 ) for the th component on the surface ... 

In TOF-SARS [9], a low-keV, monoenergetic, mass-selected, pulsed noble gas ion beam is focused onto a sample surface. The velocity distributions of scattered and recoiled particles are measured by standard TOF methods. A chaimel electron multiplier is used to detect fast (>800 eV) neutrals and ions. This type of detector has a small acceptance solid angle. A fixed angle is used between the pulsed ion beam and detector directions with respect to the sample as shown in figure Bl.23.4. The sample has to be rotated to measure ion scattering... 

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