Rectangular beams

Stiffness For an isotropic material with a modulus of elasticity E, the bending stiffness factor (El) of a rectangular beam b wide and h deep stiffness is ... 

Both the pulsed and cw lasers were used for photodissociation of gaseous ions produced by laser desorption. The cw laser had a maximum output power of 50 watts at 10.61 micrometers and a beam diameter of 6 mm. The pulsed laser produced 2.6 joules in a pulse of 1 microsecond duration at 10.61 micrometers and had a 2 x 3 cm rectangular beam shape. Modifications of the FTICR vacuum chamber that facilitate ion irradiation have been reported previously (13). 

Rectangular beam of width b To simple supports Single concentrated load P at 3 PL PL3 6 dy... 

Rectangular beam of width b Two simple supports Two equal loads P/2 at 1/3 PL 23 PL3 108 dy... 

Rectangular beam of width b Fixed cantilever Single concentrated load at 6 PL APL 3 dy... 

For a rectangular beam of thickness d, the polar moment of inertia is given by... 

Thus, the deflection of a rectangular beam under force F, for small (Hookean) deformations has the following form ... 

Typically, a rectangnlar electron beam is used, with a size of 1 mm by 10 mm. This rectangular beam hits the anticathode, which, as a result, emits another beam of X-rays. The surface of the anode irradiated by the electron beam constitutes the actual focal spot, also referred to as the thermal focal spot, not to be confused with the apparent focal spot, which depends in which we see the angle of the X-ray beam. The diagram in Figure 2.4 makes it possible to visualize this effect. 

The ratio of stress to strain for a solid rectangular beam for third-point load is equal to (see Eq. (7.29))... 

The stiffness of a rectangular beam of any given material is proportional to its breadth, and to the cube of its depth, find the stiffest beam that... 

Standard methods use rectangular beam test pieces. The geometry of the beam is chosen to make shear stresses and flexure across the width unimportant. For three-point loading a span-to-depth ratio of 16 is generally satisfactory but does vary with the material characteristics. The quite different situation of deliberately introducing shear forces to measure interlaminar strength was discussed in Section 5. 

In four-point bending, the stress for a rectangular beam and for a circular rod become respectively... 

In 1871, French mathematician and engineer Barre de Saint-Venant (1797-1886) wrote a paper on elasto-plastic analysis of partly plastic problems, such as the twisting of rods, bending of rectangular beams and pressurizing of hollow cylinders. Sain-Venant considered the following assumptions ... 

For a rectangular beam, b(y) is a constant (=6) and the integral in Eq. (4.5) can be solved to give I=bhVl2. It is useful to note that Young s modulus can be determined from Eq. (4.5) provided a technique is available to measure the radius of curvature (e.g., by optical interference or with a profilometer). 

It is also possible to determine the lowest resonant frequency of a rectangular beam statically loaded by a mass M in three-point bending. The tensile modulus is then given by ... 

Which fraction of H atoms in the i S /2 ground state that can be excited by a Doppler-free two-photon transition into the 2 5 i/2 state in a collimated H atomic beam with T = 10 m/s, when a laser with 7 = 10 W/cm and a rectangular beam cross section of 1 x 1 mm crosses the atomic beam perpendicularly and the absorption probability is P// = (ao 7) /(y hv) where ao = 10" cm and y is the linewidth. 

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