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The continuum topology optimization theory in the practical engineering application 1.Abstract :To study the application of continuum structural topology optimization methods to real engineering structures an optimization method for an optimal topology design of multistory steel frame bracing systems is presented On a sensitivity analysis an element removal criterion for continuum structures with stress and multi-displacement constraints under multiple lateral loading conditions is proposed. A concept of mean thickness of a design domain is provided to ensure the reasonableness of optimal results In the proposed optimization method the optimal design of an unbraced steel frame without displacement constraints is performed firstly, and then the optimal topology of a bracing system for the multistory steel frame considering displacement constraints is obtained by using evolutionary structural optimization and the given removal criterion, and finally the optima layout of the bracing system is interpreted as bracing members. An example of 3-bay 12-story plane steel frame shows that it is effective for the given optimization method in the optimal design of bracing systems for multistory steel frames.
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2. 1Reinforced Concrete34148
Plain concrete is formed from a hardened mixture of cement, water, fine aggregate, coarse aggregate (crushed stone or gravel), air, and often other admixtures. The plastic mix is placed and consolidated in the formwork, then cured to facilitate the acceleration of the chemical hydration reaction lf the cement/water mix, resulting in hardened concrete. The finished product has high compressive strength, and low resistance to tension, such that its tensile strength is approximately one tenth lf its compressive strength. Consequently, tensile and shear reinforcement in the tensile regions of sections has to be provided to compensate for the weak tension regions in the reinforced concrete element. It is this deviation in the composition of a reinforces concrete section from the homogeneity of standard wood or steel sections that requires a modified approach to the basic principles of structural design. The two components of the heterogeneous reinforced concrete section are to be so arranged and proportioned that optimal use is made of the materials involved. This is possible because concrete can easily be given any desired shape by placing and compacting the wet mixture of the constituent ingredients are properly proportioned, the finished product becomes strong, durable, and, in combination with the reinforcing bars, adaptable for use as main members of any structural system. The techniques necessary for placing concrete depend on the type of member to be cast: that is, whether it is a column, a bean, a wall, a slab, a foundation. a mass columns, or an extension of previously placed and hardened concrete. For beams, columns, and walls, the forms should be well oiled after cleaning them, and the reinforcement should be cleared of rust and other harmful materials. In foundations, the earth should be compacted and thoroughly moistened to about 6 in. in depth to avoid absorption of the moisture present in the wet concrete. Concrete should always be placed in horizontal layers which are compacted by means of high frequency power-driven vibrators of either the immersion or external type, as the case requires, unless it is placed by pumping. It must be kept in mind, however, that over vibration can be harmful since it could cause segregation of the aggregate and bleeding of the concrete. Hydration of the cement takes place in the presence of moisture at temperatures above 50°F. It is necessary to maintain such a condition in order that the chemical hydration reaction can take place. If drying is too rapid, surface cracking takes place. This would result in reduction of concrete strength due to cracking as well as the failure to attain full chemical hydration. It is clear that a large number of parameters have to be dealt with in proportioning a reinforced concrete element, such as geometrical width, depth, area of reinforcement, steel strain, concrete strain, steel stress, and so on. Consequently, trial and adjustment is necessary in the choice of concrete sections, with assumptions based on conditions at site, availability of the constituent materials, particular demands of the owners, architectural and headroom requirements, the applicable codes, and environmental reinforced concrete is often a site-constructed composite, in contrast to the standard mill-fabricated beam and column sections in steel structures. A trial section has to be chosen for each critical location in a structural system. The trial section has to be analyzed to determine if its nominal resisting strength is adequate to carry the applied factored load. Since more than one trial is often necessary to arrive at the required section, the first design input step generates into a series of trial-and-adjustment analyses. The trial-and –adjustment procedures for the choice of a concrete section lead to the convergence of analysis and design. Hence every design is an analysis once a trial section is chosen. The availability of handbooks, charts, and personal computers and programs supports this approach as a more efficient, compact, and speedy instructional method compared with the traditional approach of treating the analysis of reinforced concrete separately from pure design.