Document Design and Performance of Beam Theory - Assignment Example

? Beam Theory A Beam is any structural element that can withstand a load majorly through resisting bending. The forceof bending is induce into the beam material due to external span, loads, own weight and any other external reactions to the loads is referred to as bending moment. Traditionally, beams are descriptions of elements of civil engineering or building structures, however, smaller structures like automobile frames, truck, machine frames or structural or mechanical systems has structures of the beam designed and analyzed is the same fashion. Beams are often characterized by their profile, material and length. Contemporarily, beams are made of reinforced concrete, steel, cased fluid, wood or composites in a typical construction. Some of the most common beams include wide flange beam and I-beam. These are used commonly in building steel frames and bridges. Other types of beams include pipe, C-channel, angle and hollow structural section1. This paper therefore seeks to discuss the beam theory, its document design, performance and constraints involved. Statement of problem Due to the need of a comprehensive explanation of the physics of beams as well as the intense space charge an explanation of the accelerator systems requiring adequate intensity in which mutual interaction of particles in the beam cannot be neglected, this paper is important as it is aimed to give a discussion of all these elements involved in the beam theory. There is also a need to provide a wider overview of beam dynamics. The paper will put emphasis on the analytical and theoretical methods that describe the transport and acceleration of beams. There is also a need to cover aspects of experimental and numerical methods in order to bring familiarity with the basic methods used to understand the longitudinal and transverse evolution of beams. This may enable an intense foundation in designing a practical architecture. Often beams are described in the way of their support. This support restricts rotational and/ or lateral movements in order to satisfy the conditions of stability and to limit deformations to some extent of allowance. In addition, there is need to understand how a simple beam is supported by a roller in one end and a pin in the other. One may also need to understand how a cantilever beam is established. It is the interest of this paper to also explain how an overhanging beam is formed from a support of two points with one or both ends stretched beyond supports. Beams primarily support vertical loads2. Compared to their span in the diagrams in engineering, they have a small cross section. Document design Beams are vital class of the structural elements. The major function of constructing structures is to enable support of the space that encloses the elements such as roofs, floors and walls. Beams are often horizontal to support such elements. The behavior of any structure of a building can get complicated; however, sub structures such as horizontal elements that are associated with roofs and floors, and vertical structures identified with the walls can be identified. The horizontal elements include space frames; trusses, beams and slabs, and the vertical elements include walls, columns and lift cores3. The external bonding of reinforced strips of fiber plastic and reinforced concrete beams are broadly accepted as an effective and efficient method for upgrading and strengthening members. A growth in the exponential research has been observed due to the attention paid to the strengthening area of structures through reinforced strips of fiber plastic. The objective of the study is to enhance mechanical performance of the reinforced concrete. In order to prove the results of the research, the method of the finite element will be used to analyze the principal of inter-laminar, distribution of the normal stress and shear along the reinforced strips of fiber plastic and concrete4. Performance requirement The performance requirement of beams and engineering structures are more ambitious. There is a growing need to analyze computation of probabilities and uncertainties. Based on poor accuracy of computation of small to median sizes of Monte Carlo simulation sample techniques in estimation of the failure probability of the structures of engineering, the methodology of the number theoretical net is proposed to reduce the effort of computation. There is a provision of the comparison between the Monte Carlo and the number theoretical net in the estimation of the failure. Constraints In the beam theory, constraints are classified as pinned or fixed depending on the rotational stiffness of freestanding portion is greater or less than the rotational stiffness of the support. For intermediate rotational stiffness values of support, the conditions of the boundary must account for the rotational stiffness of constraint. The constraints only exist on one side of the beam in most of the applications, specifically in nano-mechanics and micro-electromechanical systems. It may therefore appear in such cases at first that similar conditions hold on the stiffness of the constraint. However, even if the beam is bonded perfectly on one side of a completely constraining rigid surface, the appropriate model for the conditions of the boundary of the beam is still responsible for the deformation of the beam in the bonded region5. The application of a modified beam theory that is responsible for extensional deformation, bending and shear in the bonded region, is necessary for modeling this behavior. For examples in bridge, cantilever, and guided structures that are subjected to either residual stresses or transverse loads. Assumptions The structural analysis of the beam is founded on a continuum assumption rather than making considerations of the composition of the molecular material. The assumption made is that this material is that of a homogeneous continuum. It is also assumed that the material agrees with the assumption of the continuum even if different materials are mixed up in a composite structure. Another assumption made is in relation to the theory of the type of the structural members. These are related to the deformation of kinematics and material behavior. For example in Euler-Bernoulli beam theory, assumptions are made that the material remains linearly elastic as in Hooke’s law and the sections of the plane are perpendicular and plane to the neutral axis when bending. A diagram showing a bending Source: benging.png Bibliography Timoshenko, S. History of strength of materials. New York: McGraw-Hill, 1953. Truesdell, C. The rational mechanics of flexible or elastic bodies 1638-1788, Venditioni Exponunt Orell Fussli Turici, 1960. McKenzie, William. Examples in Structural Analysis, London: Taylor & Francis, 2006. Gere, J. M. and Timoshenko, S. P. Mechanics of Materials, Boston: PWS Publishing Company, 1997. Reddy, J. N. Nonlinear finite element analysis, Oxford: Oxford University Press, 2007. Read More