Re: Beams
Ashlie Hagenson
A beam is a structural element that primarily resists loads applied laterally to the beam's axis (an element designed to carry primarily axial load would be a strut or column). Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beams, that in turn induce internal stresses, strains and deflections of the beam. Beams are characterized by their manner of support, profile (shape of cross-section), equilibrium conditions, length, and their material.
Beams are traditionally descriptions of building or civil engineering structural elements, where the beams are horizontal and carry vertical loads. However, any structure may contain beams, for instance automobile frames, aircraft components, machine frames, and other mechanical or structural systems. In these structures, any structural element, in any orientation, that primarily resists loads applied laterally to the element's axis would be a beam element.
Historically beams were squared timbers but are also metal, stone, or combinations of wood and metal[1] such as a flitch beam. Beams primarily carry vertical gravitational forces. They are also used to carry horizontal loads (e.g., loads due to an earthquake or wind or in tension to resist rafter thrust as a tie beam or (usually) compression as a collar beam). The loads carried by a beam are transferred to columns, walls, or girders, which then transfer the force to adjacent structural compression members and eventually to the ground. In light frame construction, joists may rest on beams.
Internally, beams subjected to loads that do not induce torsion or axial loading experience compressive, tensile and shear stresses as a result of the loads applied to them. Typically, under gravity loads, the original length of the beam is slightly reduced to enclose a smaller radius arc at the top of the beam, resulting in compression, while the same original beam length at the bottom of the beam is slightly stretched to enclose a larger radius arc, and so is under tension. Modes of deformation where the top face of the beam is in compression, as under a vertical load, are known as sagging modes and where the top is in tension, for example over a support, is known as hogging. The same original length of the middle of the beam, generally halfway between the top and bottom, is the same as the radial arc of bending, and so it is under neither compression nor tension, and defines the neutral axis (dotted line in the beam figure). Above the supports, the beam is exposed to shear stress. There are some reinforced concrete beams in which the concrete is entirely in compression with tensile forces taken by steel tendons. These beams are known as prestressed concrete beams, and are fabricated to produce a compression more than the expected tension under loading conditions. High strength steel tendons are stretched while the beam is cast over them. Then, when the concrete has cured, the tendons are slowly released and the beam is immediately under eccentric axial loads. This eccentric loading creates an internal moment, and, in turn, increases the moment carrying capacity of the beam. They are commonly used on highway bridges.
Most beams in reinforced concrete buildings have rectangular cross sections, but a more efficient cross section for a beam is an I or H section which is typically seen in steel construction. Because of the parallel axis theorem and the fact that most of the material is away from the neutral axis, the second moment of area of the beam increases, which in turn increases the stiffness.
A thin walled beam is a very useful type of beam (structure). The cross section of thin walled beams is made up from thin panels connected among themselves to create closed or open cross sections of a beam (structure). Typical closed sections include round, square, and rectangular tubes. Open sections include I-beams, T-beams, L-beams, and so on. Thin walled beams exist because their bending stiffness per unit cross sectional area is much higher than that for solid cross sections such a rod or bar. In this way, stiff beams can be achieved with minimum weight. Thin walled beams are particularly useful when the material is a composite laminate. Pioneer work on composite laminate thin walled beams was done by Librescu.
Several studies have shown that removal of the flattening filter from the treatment head of a clinical accelerator increases the dose rate and changes the lateral profile in radiation therapy with photons. However, the multileaf collimator (MLC) used to shape the field was not taken into consideration in these studies. We therefore investigated the effect of the MLC on flattened and unflattened beams. To do this, we performed measurements on a Varian Clinac 21EX and MCNPX Monte Carlo simulations to analyze the physical properties of the photon beam. We compared lateral profiles, depth dose curves, MLC leakages, and total scatter factors for two energies (6 and 18 MV) of MLC-shaped fields and jaw-shaped fields. Our study showed that flattening filter-free beams shaped by a MLC differ from the jaw-shaped beams. Similar differences were also observed for flattened beams. Although both collimating methods produced identical depth dose curves, the penumbra size and the MLC leakage were reduced in the softer, unflattened beam and the total scatter factors showed a smaller field size dependence.
The recent prediction and subsequent creation of electron vortex beams in a number of laboratories occurred after almost 20 years had elapsed since the recognition of the physical significance and potential for applications of the orbital angular momentum carried by optical vortex beams. A rapid growth in interest in electron vortex beams followed, with swift theoretical and experimental developments. Much of the rapid progress can be attributed in part to the clear similarities between electron optics and photonics arising from the functional equivalence between the Helmholtz equations governing the free-space propagation of optical beams and the time-independent Schrödinger equation governing freely propagating electron vortex beams. There are, however, key differences in the properties of the two kinds of vortex beams. This review is primarily concerned with the electron type, with specific emphasis on the distinguishing vortex features: notably the spin, electric charge, current and magnetic moment, the spatial distribution, and the associated electric and magnetic fields. The physical consequences and potential applications of such properties are pointed out and analyzed, including nanoparticle manipulation and the mechanisms of orbital angular momentum transfer in the electron vortex interaction with matter.
Computer-simulated fine structure of the diffraction of truncated Bessel beams (FT-TBB): the first row is for intensity and the second row for the corresponding phase distribution. From left to right, for the FT-TBB vortex beams with l=1 but with different radial modes (p=0, 1, and 2). Adapted from [234].
Comparison of the theory and the simulation of the nonzero order approximate Bessel-type electron vortex beam. The topological order of the beams is denoted by n, which is identical to the l defined in this review. Adapted from [101].
Vortex probes at focus of the condenser lens of a JEOL 2200FS aberration-corrected tranmission electron microscope operating at 200 kV. The central spot is the image of the nonvortex beam, while the other spots are images of the diffracted vortex beams produced by a forked diffractive hologram with a binary pattern similar to that given in Fig. 12. Sizes of the first and second vortex cores at FWHM are 3.4 and 2.6 nm, respectively. Because of the incoherent effect, the intensity dip is only partially visible for the second-order vortex beam.
Four snapshots of Au nanoparticles rotated by second-order vortex beams selected from a video at 1.2 s intervals. The center dark core surrounded by the bright ring of the first-order vortex beams is partially visible at the bottom right corner. The angles of lattice fringes correspond to 99.5, 99.0, 87.0, and 84.5, respectively. The insets show the corresponding fast Fourier transform.
Dude, this post was super helpful!! I had a weird transition in my one family room and was trying to figure out how to bridge this odd ceiling gap and this trick worked out great! Since the ceiling was all white I just went with using white PVC beams to create my box so it matched the color easily and also is even lighter than wood. The metal straps also was a great idea as well since there was a gap in between the box and the walls on each side. Thanks for posting!!
Most radiation therapy machines use photon beams. Photons are also used in x-rays, but x-rays use lower doses. Photon beams can reach tumors deep in the body. As they travel through the body, photon beams scatter little bits of radiation along their path. These beams do not stop once they reach the tumor but go into normal tissue past it.
Protons are particles with a positive charge. Like photon beams, proton beams can also reach tumors deep in the body. However, proton beams do not scatter radiation on their path through the body and they stop once they reach the tumor. Doctors think that proton beams might reduce the amount of normal tissue that is exposed to radiation. Clinical trials are underway to compare radiation therapy using proton beams with that using photons beams. Some cancer centers are using proton beams in radiation therapy, but the high cost and size of the machines are limiting their use.
Every athlete who steps on a balance beam expects a solid, comfortable feel under their feet and Tumbl Trak does not disappoint. We craft our balance beams with wood cores and perfectly dense foam, cushioning every turn, leap, jump, tumbling pass and seemingly boosting confidence from the beam up.
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