基于拓扑优化的钢筋混凝土复杂受力构件配筋设计
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摘要
为了得到适用于复杂受力构件的配筋设计,研究其最优拓扑钢筋布置,将遗传演化结构优化应用于钢筋分离式模型得到的最优拓扑钢筋,提出一种新的复杂受力构件配筋设计方法。首先,通过分解、连接、归并设计等简化措施对拓扑解中的钢筋进行简化设计,得到施工可操作性大幅提高的初步配筋图,再进行局部补强以满足现行规范的构造要求,得到最终配筋设计图。运用提出的方法对5种不同类型的复杂受力构件进行了配筋设计,并在双侧开孔深梁的算例中,与弹性应力法及经验法进行钢筋利用率、力学性能等比较。研究结果表明:钢筋分离模型遗传演化结构优化可以直观地构造出钢筋混凝土复杂受力构件的钢筋布置方案,但该方案的施工可操作性不高,且其忽视构造要求,导致弹塑性内力重分布后安全保障缺失;简化设计结果能直观地得出钢筋具体布置情况,钢筋简化明确、布置规整;斜向钢筋较大幅度地被简化,施工可操作性增强,并添加必要的满足规范要求的构造钢筋,配筋设计结果更趋完善;双侧开孔深梁的算例中,按照简化设计方法对最优拓扑钢筋进行简化设计,增加7.74%的钢筋用量后得到初步配筋图,添加26.19%的构造钢筋用量后可以得到简化设计方法设计的最终配筋图,与弹性应力设计法和经验设计方法相比,最终配筋图分别节省了16.24%和35.35%以上的用钢量;经大量不同类型的复杂受力构件算例证实,该新方法不仅有着良好的普遍性、稳定性与可行性,且与当前设计方法相比,有着较高的经济性,能够为复杂受力构件的配筋设计提供参考。
In order to obtain a suitable reinforcement design for complex-stressed members, the optimal topological reinforcement layout of it was studied. The optimal topological reinforcement was obtained by applying the separated-elements model genetic evolutionary structural optimization(GESO) to the reinforced-concrete separating model. A new method for the reinforcement layout of complex-stressed members was proposed. Firstly, through simplified measures such as reinforcement decomposition, connection, and merging design, the reinforcement in the topological solution was simplified and designed, and the preliminary reinforcement layout drawing scheme that was substantially improved in terms of operability was obtained. Next, some local regions were reinforced to fulfill the construction requirements of the current code, and the final design of the reinforcement layout was completed. This method was applied to the reinforcement design of five different types of complex-stressed members. The utilization ratios of reinforcement and mechanical properties were compared with those of the elastic stress method and empirical method,in the case of a deep beam with two small openings in each side. The results show that the separated-elements model GESO can intuitively construct the reinforcement layout of reinforced concrete complex-stressed members, but the operability of construction of the scheme is lower,and the structural requirements is ignored, which leads to the lack of safety guarantee after the redistribution of elastic-plastic internal forces. The simplified design results can intuitively get the concrete layout of reinforcing bars, and the simplified design of reinforcement is clear and regular arrangement.The diagonal reinforcement is greatly simplified, the operability of the construction is enhanced, the necessary structural reinforcements that meet specification requirements are added, and the design results of the reinforcement tends to be more perfect. In the case of a deep beam with two small openings in each side, the optimal topological reinforcement is simplified according to the simplified design method. After adding 7.74% of the reinforcement amount, the preliminary reinforcement drawing is obtained. After adding 26.19% of the structural reinforcement amount, the final reinforcement drawing of the simplified design method is obtained. Compared with the elastic stress design and empirical design methods, the final reinforcement drawing reduces steel consumption by 16.24% and 35.35%, respectively. It is proven that the new method with different types of members under complex stress states not only has favorable universality, stability, and feasibility, but is also more cost-effective, compared with the current design method, and can serve as a reference for the reinforcement design of complex-stressed members. 1 tab, 18 figs, 29 refs.
In order to obtain a suitable reinforcement design for complex-stressed members, the optimal topological reinforcement layout of it was studied. The optimal topological reinforcement was obtained by applying the separated-elements model genetic evolutionary structural optimization(GESO) to the reinforced-concrete separating model. A new method for the reinforcement layout of complex-stressed members was proposed. Firstly, through simplified measures such as reinforcement decomposition, connection, and merging design, the reinforcement in the topological solution was simplified and designed, and the preliminary reinforcement layout drawing scheme that was substantially improved in terms of operability was obtained. Next, some local regions were reinforced to fulfill the construction requirements of the current code, and the final design of the reinforcement layout was completed. This method was applied to the reinforcement design of five different types of complex-stressed members. The utilization ratios of reinforcement and mechanical properties were compared with those of the elastic stress method and empirical method,in the case of a deep beam with two small openings in each side. The results show that the separated-elements model GESO can intuitively construct the reinforcement layout of reinforced concrete complex-stressed members, but the operability of construction of the scheme is lower,and the structural requirements is ignored, which leads to the lack of safety guarantee after the redistribution of elastic-plastic internal forces. The simplified design results can intuitively get the concrete layout of reinforcing bars, and the simplified design of reinforcement is clear and regular arrangement.The diagonal reinforcement is greatly simplified, the operability of the construction is enhanced, the necessary structural reinforcements that meet specification requirements are added, and the design results of the reinforcement tends to be more perfect. In the case of a deep beam with two small openings in each side, the optimal topological reinforcement is simplified according to the simplified design method. After adding 7.74% of the reinforcement amount, the preliminary reinforcement drawing is obtained. After adding 26.19% of the structural reinforcement amount, the final reinforcement drawing of the simplified design method is obtained. Compared with the elastic stress design and empirical design methods, the final reinforcement drawing reduces steel consumption by 16.24% and 35.35%, respectively. It is proven that the new method with different types of members under complex stress states not only has favorable universality, stability, and feasibility, but is also more cost-effective, compared with the current design method, and can serve as a reference for the reinforcement design of complex-stressed members. 1 tab, 18 figs, 29 refs.
引文
[1] ACI 318—14,Building code requirements for structural concrete and commentary[S].
[2] GB 50010—2010,混凝土结构设计规范[S].GB 50010—2010,Code for design of concrete structures[S].
[3] 徐栋,徐方圆.深梁的非线性网格抗弯配筋设计方法[J].土木工程学报,2014,47(8):56-62.XU Dong,XU Fang-yuan.Non-linear grid model method for flexural reinforcement design of deep beams[J].China Civil Engineering Journal,2014,47(8):56-62.
[4] NAJAFIAN H A,VOLLUM R L.Design of planar reinforced concrete D regions with nonlinear finite element analysis[J].Engineering Structures,2013,51(2):211-225.
[5] NAJAFIAN H A,VOLLUM R L.Automated nonlinear design of reinforced concrete D regions[J].Structural Engineering & Mechanics,2013,46(1):91-110.
[6] 谭子希,刘霞,易伟建.钢筋混凝土开孔深梁有限元分析与设计研究[J].计算力学学报,2016,33(3):313-320.TAN Zi-xi,LIU Xia,YI Wei-jian.Finite element analysis of RC deep beams with openings and researching of the design method[J].Chinese Journal of Computational Mechanics,2016,33(3):313-320.
[7] ASHOUR A F,RISHI G.Tests of reinforced concrete continuous deep beams with web openings[J].Structural Journal,2000,97(3):418-426.
[8] 傅学怡,曲家新,孙璨.复杂截面剪力墙配筋研究[J].土木工程学报,2009,42(12):43-50.FU Xue-yi,QU Jia-xin,SUN Can.Reinforcement design of shear walls with complex cross sections[J].China Civil Engineering Journal,2009,42(12):43-50.
[9] CARDENAS A E,HANSON J M,CORLEY W G,et al.Design provisions for shear walls[J].ACI Journal,1973,70(3):221-230.
[10] 刘立渠,王娟娟,韩继云,等.钢筋混凝土简支深梁静力性能试验研究及拉压杆模型分析[J].建筑结构学报,2013,34(10):137-143.LIU Li-qu,WANG Juan-juan,HAN Ji-yun,et al.Research on strut-and-tie model based on tests of simply supported reinforced concrete deep beams[J].Journal of Building Structures,2013,34(10):137-143.
[11] 叶列平,孟杰,王宇航.拉-压杆模型在钢筋混凝土深梁设计中的应用[J].建筑科学与工程学报,2009,26(2):81-86.YE Lie-ping,MENG Jie,WANG Yu-hang.Application of strut-and-tie model in design of reinforced concrete deep beams[J].Journal of Architecture and Civil Engineering,2009,26(2):81-86.
[12] SCHLAICH J,SCHAFER K.Design and detailing of structural concrete using strut-and-tie models[J].Structural Engineer,1991,69(6):113-125.
[13] PARRA-MONTESINOS G J.Strut-and-tie models for deep beam design[J].Concrete International,2008,30(12):41-46.
[14] CHETCHOTISAK P,TEERAWONG J,YINDEESUK S,et al.New strut-and-tie-models for shear strength prediction and design of RC deep beams[J].Computers & Concrete,2014,14(1):19-40.
[15] BRUGGI M.Generating strut-and-tie patterns for reinforced concrete structures using topology optimization[J].Computers & Structures,2009,87(23/24):1483-1495.
[16] KWAK H G,NOH S H.Determination of strut-and-tie models using evolutionary structural optimization[J].Engineering Structures,2006,28(10):1440-1449.
[17] XIE Y M,STEVEN G P.A simple evolutionary procedure for structural optimization[J].Computers & Structures,1993,49(5):885-896.
[18] HARDJASAPUTRA H.Evolutionary structural optimization as tool in finding strut-and-tie-models for designing reinforced concrete deep beam[J].Procedia Engineering,2015,125:995-1000.
[19] QUERIN O M,STEVEN G P,XIE Y M.Evolutionary structural optimisation (ESO) using a bidirectional algorithm[J].Engineering Computations,1998,15(8):1031-1048.
[20] LIANG Q Q,XIE Y M,STEVEN G P.Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure[J].ACI Structural Journal,2000,97(2):322-332.
[21] ALMEIDA V S,SIMONETTI H L,NETO L O.Comparative analysis of strut-and-tie models using smooth evolutionary structural optimization[J].Engineering Structures,2013,56(6):1665-1675.
[22] LIU X,YI W J,LI Q S,et al.Genetic evolutionary structural optimization[J].Journal of Constructional Steel Research,2008,64:305-311.
[23] 刘霞,易伟建.优化方法建立钢筋混凝土梁压杆-拉杆模型[J].工程力学,2013,30(9):151-157.LIU Xia,YI Wei-jian.Construction of strut-and-tie model for reinforced concrete beams by optimal method[J].Engineering Mechanics,2013,30(9):151-157.
[24] 刘霞,张鹄志,易伟建,等.钢筋混凝土开洞深梁拉压杆模型方法与经验方法试验对比研究[J].建筑结构学报,2013,34(7):139-147.LIU Xia,ZHANG Hu-zhi,YI Wei-jian,et al.Testing comparison between strut-and-tie model method and empirical method for RC deep beams with openings[J].Journal of Building Structures,2013,34(7):139-147.
[25] 张鹄志,刘霞,易伟建,等.复杂应力构件多荷载工况下的配筋优化[J].湖南大学学报:自然科学版,2014,41(9):42-47.ZHANG Hu-zhi,LIU Xia,YI Wei-jian,et al.Reinforcement layout optimization of members under complex stress states and multiple loading cases[J].Journal of Hunan University:Natural Sciences,2014,41(9):42-47.
[26] ZHANG H,LIU X,YI W.Reinforcement layout optimisation of RC D-regions[J].Advances in Structural Engineering,2014,17(7):979-992.
[27] ZHANG H,LIU X,YI W J,et al.Performance comparison of shear walls with openings designed using elastic stress and genetic evolutionary structural optimization methods[J].Structural Engineering and Mechanics,2018,65(3):303-314.
[28] 张望喜,黄星,刘霞.遗传递增演化算法配筋优化设计[J].计算力学学报,2017,34(3):303-311.ZHANG Wang-xi,HUANG Xing,LIU Xia.Reinforcement layout optimization design using the genetic adding evolutionary structural optimization[J].Chinese Journal of Computational Mechanics,2017,34(3):303-311.
[29] 张鹄志.钢筋混凝土复杂应力构件的配筋优化研究[D].长沙:湖南大学,2014.ZHANG Hu-zhi.The research on reinforcement optimization of reinforced concrete member under complex stress state[D].Changsha:Hunan University,2014.
[2] GB 50010—2010,混凝土结构设计规范[S].GB 50010—2010,Code for design of concrete structures[S].
[3] 徐栋,徐方圆.深梁的非线性网格抗弯配筋设计方法[J].土木工程学报,2014,47(8):56-62.XU Dong,XU Fang-yuan.Non-linear grid model method for flexural reinforcement design of deep beams[J].China Civil Engineering Journal,2014,47(8):56-62.
[4] NAJAFIAN H A,VOLLUM R L.Design of planar reinforced concrete D regions with nonlinear finite element analysis[J].Engineering Structures,2013,51(2):211-225.
[5] NAJAFIAN H A,VOLLUM R L.Automated nonlinear design of reinforced concrete D regions[J].Structural Engineering & Mechanics,2013,46(1):91-110.
[6] 谭子希,刘霞,易伟建.钢筋混凝土开孔深梁有限元分析与设计研究[J].计算力学学报,2016,33(3):313-320.TAN Zi-xi,LIU Xia,YI Wei-jian.Finite element analysis of RC deep beams with openings and researching of the design method[J].Chinese Journal of Computational Mechanics,2016,33(3):313-320.
[7] ASHOUR A F,RISHI G.Tests of reinforced concrete continuous deep beams with web openings[J].Structural Journal,2000,97(3):418-426.
[8] 傅学怡,曲家新,孙璨.复杂截面剪力墙配筋研究[J].土木工程学报,2009,42(12):43-50.FU Xue-yi,QU Jia-xin,SUN Can.Reinforcement design of shear walls with complex cross sections[J].China Civil Engineering Journal,2009,42(12):43-50.
[9] CARDENAS A E,HANSON J M,CORLEY W G,et al.Design provisions for shear walls[J].ACI Journal,1973,70(3):221-230.
[10] 刘立渠,王娟娟,韩继云,等.钢筋混凝土简支深梁静力性能试验研究及拉压杆模型分析[J].建筑结构学报,2013,34(10):137-143.LIU Li-qu,WANG Juan-juan,HAN Ji-yun,et al.Research on strut-and-tie model based on tests of simply supported reinforced concrete deep beams[J].Journal of Building Structures,2013,34(10):137-143.
[11] 叶列平,孟杰,王宇航.拉-压杆模型在钢筋混凝土深梁设计中的应用[J].建筑科学与工程学报,2009,26(2):81-86.YE Lie-ping,MENG Jie,WANG Yu-hang.Application of strut-and-tie model in design of reinforced concrete deep beams[J].Journal of Architecture and Civil Engineering,2009,26(2):81-86.
[12] SCHLAICH J,SCHAFER K.Design and detailing of structural concrete using strut-and-tie models[J].Structural Engineer,1991,69(6):113-125.
[13] PARRA-MONTESINOS G J.Strut-and-tie models for deep beam design[J].Concrete International,2008,30(12):41-46.
[14] CHETCHOTISAK P,TEERAWONG J,YINDEESUK S,et al.New strut-and-tie-models for shear strength prediction and design of RC deep beams[J].Computers & Concrete,2014,14(1):19-40.
[15] BRUGGI M.Generating strut-and-tie patterns for reinforced concrete structures using topology optimization[J].Computers & Structures,2009,87(23/24):1483-1495.
[16] KWAK H G,NOH S H.Determination of strut-and-tie models using evolutionary structural optimization[J].Engineering Structures,2006,28(10):1440-1449.
[17] XIE Y M,STEVEN G P.A simple evolutionary procedure for structural optimization[J].Computers & Structures,1993,49(5):885-896.
[18] HARDJASAPUTRA H.Evolutionary structural optimization as tool in finding strut-and-tie-models for designing reinforced concrete deep beam[J].Procedia Engineering,2015,125:995-1000.
[19] QUERIN O M,STEVEN G P,XIE Y M.Evolutionary structural optimisation (ESO) using a bidirectional algorithm[J].Engineering Computations,1998,15(8):1031-1048.
[20] LIANG Q Q,XIE Y M,STEVEN G P.Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure[J].ACI Structural Journal,2000,97(2):322-332.
[21] ALMEIDA V S,SIMONETTI H L,NETO L O.Comparative analysis of strut-and-tie models using smooth evolutionary structural optimization[J].Engineering Structures,2013,56(6):1665-1675.
[22] LIU X,YI W J,LI Q S,et al.Genetic evolutionary structural optimization[J].Journal of Constructional Steel Research,2008,64:305-311.
[23] 刘霞,易伟建.优化方法建立钢筋混凝土梁压杆-拉杆模型[J].工程力学,2013,30(9):151-157.LIU Xia,YI Wei-jian.Construction of strut-and-tie model for reinforced concrete beams by optimal method[J].Engineering Mechanics,2013,30(9):151-157.
[24] 刘霞,张鹄志,易伟建,等.钢筋混凝土开洞深梁拉压杆模型方法与经验方法试验对比研究[J].建筑结构学报,2013,34(7):139-147.LIU Xia,ZHANG Hu-zhi,YI Wei-jian,et al.Testing comparison between strut-and-tie model method and empirical method for RC deep beams with openings[J].Journal of Building Structures,2013,34(7):139-147.
[25] 张鹄志,刘霞,易伟建,等.复杂应力构件多荷载工况下的配筋优化[J].湖南大学学报:自然科学版,2014,41(9):42-47.ZHANG Hu-zhi,LIU Xia,YI Wei-jian,et al.Reinforcement layout optimization of members under complex stress states and multiple loading cases[J].Journal of Hunan University:Natural Sciences,2014,41(9):42-47.
[26] ZHANG H,LIU X,YI W.Reinforcement layout optimisation of RC D-regions[J].Advances in Structural Engineering,2014,17(7):979-992.
[27] ZHANG H,LIU X,YI W J,et al.Performance comparison of shear walls with openings designed using elastic stress and genetic evolutionary structural optimization methods[J].Structural Engineering and Mechanics,2018,65(3):303-314.
[28] 张望喜,黄星,刘霞.遗传递增演化算法配筋优化设计[J].计算力学学报,2017,34(3):303-311.ZHANG Wang-xi,HUANG Xing,LIU Xia.Reinforcement layout optimization design using the genetic adding evolutionary structural optimization[J].Chinese Journal of Computational Mechanics,2017,34(3):303-311.
[29] 张鹄志.钢筋混凝土复杂应力构件的配筋优化研究[D].长沙:湖南大学,2014.ZHANG Hu-zhi.The research on reinforcement optimization of reinforced concrete member under complex stress state[D].Changsha:Hunan University,2014.