研究目的：以钢筋混凝土单筋矩形截面梁的造价为目标函数,截面高度和配筋率作为自变量，以挠度作 为控制条件，建立约束条件,可得非线性优化数学模型,并利用Matlab优化工具箱通过编程进行求解。在考 虑钢筋代换相关规定的基础上，给出矩形截面梁等强度代换、等挠度代换及等裂缝宽度代换的实用计算方法，并分析不同情况下起控制作用的因素,从而使钢筋代换计算过程简捷且结果可靠。
研究结论:大截面尺寸受弯构件采用考虑正截面承载力及挠度控制的方法进行优化设计,避免了因盲目 加大截面尺寸和配筋量而造成浪费;运用Matlab软件能简便、快捷地实现单筋矩形截面梁正截面优化设计， 从而得到截面高度及配筋率的初始值，再考虑梁的自重及尺寸模数要求稍作调整即可确定最终设计结果;对 于矩形截面梁,在其常用配筋率pe [0.6% ,1.6% ]范围内，根据本文给出的钢筋代换原则及具体计算方法， 能简便地得到满足截面承载力、挠度控制及裂缝宽度验算要求的代换结果。算例表明,该优化设计方法经济 效益显著,可推广应用于工程实际。
Research purposes: Optimal non-linear mathematical mode is established by taking cross - sectional area of gravity retaining wall as object function and then taking the requirement of ground bearing capacity and stability check as constraint condition. Based on Matlab toolbox, the optimum result is obtained. This method avoids trial calculation process and appropriate cross 一 section is available. Based on considering relative principles of reinforcement replacement, some practical methods for calculating reinforcement replacement of rectangular section flexural members with equal strength, equal deflection and equal crack width are presented，and the key factors in different conditions are analysed. The process of replacing reinforcement becomes shortcut and the results are reliable with this method.
Research conclusions ： For large - sized sectional bended members, the optimum design can be made with the method of controlling cross - section bearing capacity and deflection control to avoid the waste caused by blindly increase of the size and amount of reinforcing bars for the cross-section. With using Matlab, the optimum design of rectangular cross section beam with single reinforcing bar can be easily made, and from it the primary values of the section height and ratio of reinforcement can be obtained and the final design result can be obtained after the slight modification is done in consideration of the requirements of beam, weight and its size, module. For the rectangular cross section beam，its common ratio of reinforcement is within 0. 6% and 1. 6%. With using the substitution principle of reinforcing bar and concrete computing method described in this paper, the substitution outcomes can be easily obtained, which meet the checking calculation requirements of section bearing capacity, deflection control and crack width. The calculation example shows this optimum design method can make perfect economic benefits and is worth wide using.
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