![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/data1.png\")
<\/figure> ![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/data2.png\")
<\/figure> \u7531\u4e0a\u56fe\u53ef\u77e5\uff0c\u7d20\u6df7\u51dd\u571f\u8bd5\u4ef6\u5728\u7eb5\u5411\u538b\u5e94\u53d8\u8fbe\u5230 0.003\u65f6\u8fbe\u5230\u5cf0\u503c\u5f3a\u5ea6\uff0c\u7136\u540e\u5f3a\u5ea6\u8fc5\u901f\u9000\u5316\uff0c\u5e76\u6700\u7ec8\u51fa\u73b0\u659c\u622a\u9762\u526a\u574f\u5bfc\u81f4\u67f1\u5931\u6548\uff0c\u8fd9\u662f\u4e00\u79cd\u8106\u6027\u7834\u574f\u6a21\u5f0f\u3002\u800c\u6211\u4eec\u6240\u671f\u671b\u7684\u5ef6\u6027\u7834\u574f\u6a21\u5f0f\u662f\uff0c\u5f53\u7eb5\u5411\u5e94\u53d8\u8fbe\u5230 0.003 \u65f6\uff0c\u7b8d\u7b4b\u51fa\u73b0\u5c48\u670d\uff0c\u800c\u5f53\u7eb5\u5411\u5e94\u53d8\u8fbe\u52300.004\u65f6\uff0c\u4fdd\u62a4\u5c42\u6df7\u51dd\u571f\u5265\u843d\uff0c\u7136\u540e\u5f3a\u5ea6\u51fa\u73b0\u7f13\u6162\u9000\u5316\u3002\u968f\u7740\u7eb5\u5411\u5e94\u53d8\u7684\u9010\u6e10\u589e\u52a0\uff0cA\u67f1\u548cB\u67f1\u5728\u635f\u5931\u4e86\u90e8\u5206\u5f3a\u5ea6\u540e\u53c8\u51fa\u73b0\u4e86\u5f3a\u5316\uff0c\u7136\u540e\u518d\u7f13\u6162\u5730\u9000\u5316\uff0c\u800cC\u67f1\u5219\u662f\u76f4\u7ebf\u9000\u5316\u3002\u5f53B\u67f1\u73af\u5411\u7b8d\u7b4b\u5c48\u670d\uff0c\u7eb5\u7b4b\u51fa\u73b0\u5c48\u66f2\uff0c\u90e8\u5206\u89d2\u90e8\u5f2f\u94a9\u88ab\u62c9\u76f4\uff0cB\u67f1\u51fa\u73b0\u5931\u6548\u3002<\/p>\n
\u5bf9\u6bd4\u7d20\u6df7\u51dd\u571f\u67f1\uff0c\u7b8d\u7b4b\u5bf9\u6838\u5fc3\u533a\u6df7\u51dd\u571f\u8d77\u5230\u4e86\u5f88\u597d\u7684\u7ea6\u675f\u4f5c\u7528\uff0c\u5176\u589e\u5f3a\u4e86\u6838\u5fc3\u533a\u6df7\u51dd\u571f\u7684\u53d8\u5f62\u80fd\u529b\u3002\u4ec5\u914d\u7f6e\u6709\u5916\u5708\u7b8d\u7b4b\u7684C\u67f1\uff0c\u5176\u53d8\u5f62\u80fd\u529b\u5f97\u5230\u4e86\u6539\u5584\uff0c\u4f46\u4e0d\u5982A\u67f1\u548cB\u67f1\uff0c\u914d\u6709\u4ea4\u53c9\u6216\u91cd\u53e0\u7684\u7b8d\u7b4b\u53ef\u4ee5\u589e\u5f3a\u7ea6\u675f\u6df7\u51dd\u571f\u7684\u5f3a\u5ea6\u3002<\/strong><\/p>\n \u9664\u4e86\u94a2\u7b4b\u6df7\u51dd\u571f\u67f1\u4e4b\u5916\uff0c\u526a\u529b\u5899\u7684\u8fb9\u7f18\u6784\u4ef6\u6216\u7aef\u67f1\u4e5f\u662f\u914d\u7f6e\u6709\u95ed\u5408\u7684\u7b8d\u7b4b\uff0c\u800c\u7ec4\u5408\u7ed3\u6784\u6784\u4ef6\u53ca\u94a2\u7ba1\u6df7\u51dd\u571f\u4f5c\u7528\uff0c\u578b\u94a2\u5bf9\u5176\u6240\u5305\u88f9\u7684\u6df7\u51dd\u571f\u4e5f\u662f\u6709\u8f83\u5927\u7684\u7ea6\u675f\u4f5c\u7528\uff0c\u5f53\u7136\u8fd9\u91cc\u4e3b\u8981\u8bf4\u7684\u5e38\u89c4\u94a2\u7b4b\u6df7\u51dd\u571f\u6784\u4ef6\u3002\u8bf4\u8d77\u526a\u529b\u5899\u8fb9\u7f18\u6784\u4ef6\u7684\u91cd\u8981\u6027\uff0c\u5f97\u8bf4\u8bf42010\u5e74\u7684\u667a\u5229\u526a\u529b\u5899\u7ed3\u6784\u9707\u5bb3\u3002\u667a\u5229\u4f7f\u7528\u7684\u5730\u9707\u8bbe\u8ba1\u65b9\u6cd5\u4e0e\u6211\u4eec\u76f8\u4f3c\uff0c\u90fd\u662f\u91c7\u7528\u7684\u53cd\u5e94\u8c31\u6cd5\u3002\u9488\u5bf91985\u5e743\u67083\u65e5\u53d1\u751f\u5728\u5357\u7f8e\u6d32\u548c\u7eb3\u65af\u5361\u677f\u5757\u4ea4\u754c\u4fef\u51b2\u5e26\u76847.8\u7ea7\u5730\u9707\uff0c1996\u5e74\u667a\u5229\u7684\u8bbe\u8ba1\u8c31\u8fdb\u884c\u4e86\u4fee\u8ba2\u3002\u94a2\u7b4b\u6df7\u51dd\u571f\u526a\u529b\u5899\u5efa\u7b51\u7684\u8bbe\u8ba1\u8981\u6c42\u4e5f\u8fdb\u884c\u4e86\u66f4\u65b0\uff0c\u53c2\u8003\u4e86ACI318-95\uff0c\u4f46\u4e5f\u6709\u4e2a\u89c4\u5b9a\u4f8b\u5916\u7684\uff0c\u5c31\u662f\u5899\u8fb9\u7f18\u6784\u4ef6\u7684\u7ea6\u675f\u6df7\u51dd\u571f\u53ca\u7ea6\u675f\u94a2\u7b4b\u5c48\u66f2\u7684\u52a0\u5bc6\u7b8d\u7b4b\u88ab\u53d6\u6d88\u3002<\/p>\n 2010\u5e74\u667a\u5229\u5730\u9707\u4e2d\uff0c\u94a2\u7b4b\u6df7\u51dd\u571f\u526a\u529b\u5899\u5efa\u7b51\uff08\u5899\u7387\u5927\u6982\u4e3a3%\u5de6\u53f3\uff0c\u4e00\u5b57\u578b\u3001L\u578b\u5899\u6216T\u578b\u5899\u7ec4\u5408\u5f62\u6210\uff09\u4e3b\u8981\u635f\u574f\u4e3b\u8981\u51fa\u73b0\u5728\u5730\u9762\u6216\u63a5\u8fd1\u5730\u9762\u7684\u90e8\u4f4d\uff0c\u53ef\u4ee5\u770b\u5230\u6df7\u51dd\u571f\u7684\u7834\u788e\u548c\u5265\u843d\u4ee5\u53ca\u7ad6\u5411\u94a2\u7b4b\u7684\u5c48\u66f2\u3002\u50cf\u8fd9\u79cd\u8d2f\u7a7f\u6574\u4e2a\u526a\u529b\u5899\u6216\u8005\u96c6\u4e2d\u57281~3\u500d\u5899\u539a\u7684\u9ad8\u5ea6\u7684\u635f\u4f24\uff0c\u663e\u7136\u662f\u56e0\u4e3a\u5782\u76f4\u94a2\u7b4b\u5c48\u66f2\u5bfc\u81f4\u7684\u3002<\/p>\n \u9707\u5bb3\u4e2d\u53d1\u73b0\u5899\u4f53\u8fb9\u7f18\u6784\u4ef6\u7684\u7b8d\u7b4b\u95f4\u8ddd\u504f\u5927\uff0c\u8fb9\u7f18\u7b8d\u7b4b\u548c\u6c34\u5e73\u5206\u5e03\u7b4b\u95f4\u8ddd\u5747\u4e3a200mm\u3002\u7531\u4e8e\u8fd9\u4e9b\u526a\u529b\u5899\u5747\u8f83\u8584\uff0c\u4e3a150mm~200mm\u539a\u5ea6\uff0c\u800c\u4fdd\u62a4\u5c4220mm\uff0c\u5265\u843d\u5219\u4f1a\u5bfc\u81f4\u5899\u4f53\u7684\u6709\u6548\u539a\u5ea6\u51cf\u5c0f10%-27%\u3002\u800c\u4e00\u65e6\u4fdd\u62a4\u5c42\u5265\u843d\uff0c\u5219\u526a\u529b\u5899\u8fb9\u7f18\u6784\u4ef6\u7684\u76f4\u94a9\u7b8d\u7b4b\u88ab\u62c9\u76f4\u540e\u5931\u53bb\u7ea6\u675f\u4f5c\u7528\uff0c\u8fd9\u6837\u7ad6\u5411\u94a2\u7b4b\u5931\u53bb\u7ea6\u675f\u540e\u5c31\u4f1a\u53d1\u751f\u5c48\u66f2\u3002<\/p>\n \u5f53\u7136\u6709\u4e9b\u4e5f\u662f\u7531\u4e8e\u8f74\u5411\u538b\u529b\u8f83\u5927\u5bfc\u81f4\u5899\u4f53\u51fa\u73b0\u6574\u4f53\u5c48\u66f2\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u4e5f\u5c31\u662f\u5899\u4f53\u7684\u6574\u4f53\u5931\u7a33\u3002\u8fd9\u79cd\u5931\u7a33\uff0c\u52a0\u5f3a\u7b8d\u7b4b\u914d\u7f6e\u4e0d\u80fd\u89e3\u51b3\u95ee\u9898\uff0c\u6700\u597d\u662f\u52a0\u539a\u5899\u4f53\u3002\u8fd9\u79cd\u4e0e\u4e0a\u9762\u7684\u60c5\u51b5\u6709\u6240\u4e0d\u540c\u3002<\/p>\n \u770b\u6765\u7b8d\u7b4b\u7684\u7ea6\u675f\u6548\u5e94\u5f88\u91cd\u8981\uff0c\u90a3\u4e48\u975e\u7ebf\u6027\u8ba1\u7b97\u65f6\uff0c\u5982\u4f55\u8003\u8651\u7ea6\u675f\u6df7\u51dd\u571f\u672c\u6784\u663e\u5f97\u5c24\u4e3a\u91cd\u8981\uff0c\u800c\u5176\u4e2d\u4ee5Mander\u7ea6\u675f\u6df7\u51dd\u571f\u672c\u6784\u6700\u4e3a\u6d41\u884c\u3002<\/p>\n \u8bf4\u5230\u8fd9\uff0c\u8fd8\u771f\u4e0d\u77e5\u9053Mander\u672c\u6784\u662f\u5982\u4f55\u6d41\u884c\u8d77\u6765\u7684\uff0c\u4f46\u5927\u6982\u662f\u56e0\u4e3a\u4ed6\u7684\u8bba\u6587\u88ab\u5927\u91cf\u5b66\u8005\u5f15\u7528\uff0c\u800c\u5de5\u7a0b\u4e2d\u5e38\u7528\u7684\u622a\u9762\u5206\u6790\u8f6f\u4ef6XTRACT\u5185\u7f6e\u7684\u7ea6\u675f\u6750\u6599\u672c\u6784\u4e5f\u662f\u9ed8\u8ba4\u91c7\u7528Mander\u672c\u6784\u3002\u4e00\u4f4d\u83f2\u5f8b\u5bbe\u7684\u670b\u53cb\u4e5f\u8bf4\uff0c\u4ed6\u66f4\u503e\u5411\u4e8e\u4f7f\u7528Mander\u672c\u6784\u8fdb\u884c\u975e\u7ebf\u6027\u5206\u6790\u3002Mander\u90a3\u7bc7\u975e\u5e38\u6709\u540d\u7684\u8bba\u6587\u8be6\u7ec6\u4ecb\u7ecd\u4e86Mander\u672c\u6784\u66f2\u7ebf\uff0c\u89c1\u4e0b\u56fe\u3002<\/p>\n \u5f0f\u4e2d\uff0c \u5f0f\u4e2d\uff0c \u5f0f\u4e2d\uff0c \u5176\u4e2d\uff0c Mander\u672c\u6784<\/strong>\u5f15\u5165\u4e86\u6709\u6548\u7ea6\u675f\u5e94\u529b<\/strong>\u548c\u6709\u6548\u7ea6\u675f\u7cfb\u6570<\/strong>\u8fd9\u4e24\u4e2a\u6982\u5ff5\u3002\u6ce8\u610f\u6b64\u5904\u7684\u5f3a\u5ea6\u5747\u6307\u7f8e\u89c4\u7684\u6df7\u51dd\u571f\u5706\u67f1\u4f53\u5f3a\u5ea6\u3002\u5bf9\u4e8e\u77e9\u5f62\u622a\u9762\u9700\u8981\u67e5\u8868\u786e\u5b9a\u6709\u6548\u7ea6\u675f\u7cfb\u6570\u3002<\/p>\n G.A. Chang \u6539\u8fdb\u4e86Mander\u672c\u6784\uff0c\u4f7f\u5f97Mander\u672c\u6784\u7684\u6709\u6548\u7ea6\u675f\u7cfb\u6570<\/strong> \u5bf9\u4e8e\u5706\u5f62\u622a\u9762<\/strong>\u6309\u4e0b\u9762\u516c\u5f0f\u53ef\u4ee5\u6c42\u5f97\uff1a<\/p>\n \u6838\u5fc3\u533a\u6df7\u51dd\u571f\u9762\u79ef \u5f0f\u4e2d\uff0c \u5f0f\u4e2d\uff0c\u4f53\u79ef\u914d\u7b4b\u7387 \u77e9\u5f62\u622a\u9762<\/strong>\u7684\u6709\u6548\u7ea6\u675f\u7cfb\u6570\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u7ecf\u9a8c\u516c\u5f0f\u6c42\u5f97\uff0c\u800c\u4e0d\u9700\u8981\u67e5\u8868\u3002<\/p>\n \u6700\u7ec8\u53ef\u4ee5\u5f97\u5230\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/p>\n \u5176\u4e2d\uff0c \u7528\u4e0a\u9762\u516c\u5f0f\u53ef\u4ee5\u753b\u51faMander\u8bba\u6587\u4e2d\u6240\u7528\u7684\u56fe\u8868\u5982\u4e0b\u3002<\/p>\n \u5347\u7ea7\u6253\u602a\u79bb\u4e0d\u5f00\u5404\u79cd\u88c5\u5907\uff0c\u590d\u6742\u7ed3\u6784\u5206\u6790\u79bb\u4e0d\u5f00\u5404\u79cd\u5b9e\u7528\u5c0f\u5de5\u5177\uff0cXTRACT\u7edd\u5bf9\u7b97\u662f\u622a\u9762\u9a8c\u7b97\u4e2d\u7684\u6743\u5a01\u4e0e\u4f7c\u4f7c\u8005\u3002\u56de\u5230<\/p>\n \u901a\u8fc7\u8ba1\u7b97\u5f97\u5230\u7ea6\u675f\u6df7\u51dd\u571f\u5f3a\u5ea6\u63d0\u9ad8\u4e861.46\u500d\uff0c\u66f4\u91cd\u8981\u7684\u662f\u5ef6\u6027\u4e5f\u6709\u8f83\u5927\u63d0\u9ad8\u3002<\/p>\n \u6700\u540e\u6839\u636e\u4ee5\u4e0a\u7684\u622a\u9762\u53ef\u4ee5\u6c42\u5f97\u67f1PM\u66f2\u7ebf\u5982\u4e0b\u3002<\/p>\n \u6709\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u7528XTRACT\u518d\u9a8c\u7b97\u4e0b\u5f00\u59cb\u8bd5\u9a8c\u7684\u7ed3\u679c\uff0c\u8bd5\u8bd5XTRACT\u4e0d\u540c\u7b8d\u7b4b\u7ea6\u675f\u5f62\u5f0f\u5bf9\u7ea6\u675f\u6df7\u51dd\u571f\u5f3a\u5ea6\u7684\u5f71\u54cd\u3002<\/p>\n In 1985, Moehle<\/strong> and Cavanagh<\/strong> conducted a comparative test between plain concrete columns and reinforced concrete columns with different stirrup configurations. All test columns were square (305 mm \u00d7 305 mm) with a length of 914 mm, using the same batch of concrete and steel materials. The test results are shown in the figures below.<\/p>\n From the figure above, it is evident that the plain concrete specimen reached its peak strength when the longitudinal compressive strain reached 0.003, followed by rapid strength degradation and eventual diagonal shear failure\u2014a brittle failure mode. In contrast, the desired ductile failure mode involves stirrup yielding at a longitudinal strain of 0.003, spalling of the concrete cover at 0.004, and gradual strength degradation. As longitudinal strain increased, columns A and B exhibited post-degradation strengthening before slow degradation, while column C degraded linearly. Column B failed when transverse stirrups yielded, longitudinal bars buckled, and corner hooks were straightened.<\/p>\n Compared to plain concrete columns, stirrups provide significant confinement to the core concrete, enhancing its deformation capacity. Columns with only outer stirrups (e.g., column C) show improved ductility but not as effectively as configurations with cross or overlapping stirrups, which further enhance confined concrete strength.<\/strong><\/p>\n In addition to concrete columns, shear wall boundary elements or end columns also use closed stirrups. Composite structures and concrete-filled steel tubes similarly exhibit confinement effects. However, this discussion focuses on conventional reinforced concrete members. The importance of shear wall boundary elements became evident during the 2010 Chile earthquake. Chilean seismic design methods, similar to ours, use response spectrum analysis. After the 1985 M7.8 earthquake, Chile revised its seismic code (ACI318-95), but an exception removed requirements for confined boundary elements and stirrup\u52a0\u5bc6 for buckling prevention.<\/p>\n During the 2010 Chile earthquake, concrete shear walls (wall ratio ~3%) suffered severe damage at ground levels or near the base, including concrete crushing, spalling, and longitudinal bar buckling. Such damage, spanning the entire wall or concentrated over 1\u20133 times the wall thickness, was caused by vertical bar buckling.<\/p>\n Investigations revealed that stirrup spacing in wall boundary elements was excessive (200 mm for both stirrups and horizontal reinforcement). For thin walls (150\u2013200 mm thick) with 20 mm concrete cover, spalling reduced effective thickness by 10\u201327%. Once the cover spalled, straight-hook stirrups lost confinement, leading to longitudinal bar buckling.<\/p>\n Some failures were due to high axial compression causing global wall buckling (Figure 5), which cannot be resolved by adding stirrups\u2014thicker walls are required.<\/p>\n The importance of stirrup confinement highlights the need to model confined concrete behavior accurately in nonlinear analysis. The Mander model<\/strong> is the most widely used for this purpose.<\/p>\n The popularity of the Mander model likely stems from its extensive citation in literature and its default adoption in section analysis software like XTRACT. A colleague from the Philippines noted his preference for Mander\u2019s model in nonlinear analysis. Mander\u2019s seminal paper introduced the constitutive curve (Figure 6):<\/p>\n \u00a0 <\/span> \u00a0 <\/span> where \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> Here, \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> where \u00a0 <\/span> \u00a0 <\/span> The Mander model introduces effective confining stress<\/strong> and effective confinement coefficient<\/strong> concepts. Strength refers to US-standard cylinder strength. For rectangular sections, the confinement coefficient requires lookup tables.<\/p>\n G.A. Chang improved the Mander model by deriving formulas for the effective confinement coefficient<\/strong> For circular sections<\/strong>:<\/p>\n \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> Core area \u00a0 <\/span> \u00a0 <\/span> Volume stirrup ratio For rectangular sections<\/strong>, the confinement coefficient \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> \u00a0 <\/span> Final equation:<\/p>\n \u00a0 <\/span> \u00a0 <\/span> XTRACT is a leading tool for section analysis. As shown in the example below:<\/p>\n XTRACT calculated a 1.46x increase in confined concrete strength and significantly improved ductility:<\/p>\n The resulting PM interaction curve is shown below:<\/p>\n Readers are encouraged to re-analyze the initial experiment using XTRACT to compare the effects of different stirrup configurations on confined concrete strength:<\/p>\n \u5f80\u671f\u6587\u7ae0<\/strong><\/p>\n #\u53c2\u6570\u5316\u5efa\u6a21#<\/strong><\/p>\n #\u8be6\u89e3Grasshopper\u4e2d\u7684C#\u811a\u672c\u7535\u6c60\u8be6\u89e3[\u9644\u6e90\u7801]<\/a><\/p>\n #\u5982\u4f55\u5f00\u53d1Grasshopper\u63d2\u4ef6[\u9644\u6e90\u7801]<\/a><\/p>\n #Rhino.Python\u811a\u672c\u5efa\u6a21\u5b66\u4e60\u7b14\u8bb0\u30101\u3011<\/a><\/p>\n #\u7ed3\u6784\u7f16\u7a0b#<\/strong><\/p>\n #OpenSEES\u81ea\u52a8\u524d\u540e\u5904\u7406\u7a0b\u5e8fAutoOS<\/a><\/p>\n #\u8d85\u9650\u62a5\u544a\u81ea\u52a8\u751f\u6210\u5e73\u53f02022\u7248\u672c\u4e4b\u5c0f\u9707\u6a21\u5757\u6f14\u793a<\/a><\/p>\n #\u4e00\u8d77\u73a9\u73a9\u7ed3\u6784\u8bbe\u8ba1\u8f6f\u4ef6API<\/a><\/p>\n #ETABS\u5899\u80a2\u7f16\u53f7\u63d2\u4ef6\u53ca\u6f14\u793a<\/a><\/p>\n #Abaqus\u6a21\u62df\u526a\u529b\u5899\u6ede\u56de\u66f2\u7ebf\u3010python\u6e90\u7801\u3011<\/a><\/p>\n #\u6709\u5173\u9009\u6ce2\u7684\u82e5\u5e72\u6280\u672f\u5410\u69fd<\/a><\/p>\n #\u81ea\u52a8\u9009\u6ce2\u7a0b\u5e8fAutoWave\u66f4\u65b0<\/a><\/p>\n #PKPM5.\u8f6cETABS201X\u63a5\u53e3\u7a0b\u5e8f[Free]<\/a><\/p>\n #YJK\u6a21\u578b\u8f6cETABS201X\u81ea\u7f16\u63a5\u53e3\u4ecb\u7ecd<\/a><\/p>\n #\u7ed3\u6784\u8f6f\u4ef6\u5173\u4e8e\u6881\u67f1\u521a\u57df\u7684\u8003\u8651<\/a><\/p>\n #AutoWave\u81ea\u52a8\u9009\u6ce2\u53ca\u4eba\u5de5\u6ce2\u751f\u6210\u5de5\u5177\u64cd\u4f5c\u6f14\u793a<\/a><\/p>\n #\u7ed3\u6784\u5206\u6790\u8bbe\u8ba1\u6709\u54ea\u4e9b\u5de5\u4f5c\u53ef\u4ee5\u8ba9Python\u5e72\uff1f<\/a><\/p>\n #\u4e00\u540d\u7ed3\u6784\u5de5\u7a0b\u5e08\u5b66\u4e60Python\u7684\u5fc3\u8def\u5386\u7a0b<\/a><\/p>\n #Python\u4eceYJK\u6570\u636e\u5e93\u8bfb\u53d6\u8377\u8f7d\u5de5\u51b5\u4fe1\u606f<\/a><\/p>\n #\u5efa\u7b51\u5927\u5e08#<\/strong><\/p>\n #[\u5efa\u7b51\u5927\u5e08]\uff081\uff09\u8c9d\u807f\u9298\u7684\u5149\u5f71\u50b3\u5947<\/a><\/p>\n #[\u5efa\u7b51\u5927\u5e08]\uff082\uff09\u52d2\u00b7\u67ef\u5e03\u897f\u8036\u7684\u73b0\u4ee3\u4e3b\u4e49<\/a><\/p>\n #[\u5efa\u7b51\u5927\u5e08]\uff083\uff09\u5965\u65af\u5361\u6885\u5c3c\u8036\u7684\u5efa\u7b51\u66f2\u7ebf\u4e0e\u5973\u4eba<\/a><\/p>\n #[\u5efa\u7b51\u5927\u5e08](4)\u624e\u54c8\u00b7\u54c8\u8fea\u5fb7\u7528\u66f2\u7ebf\u6f14\u7ece\u4f20\u5947<\/a><\/p>\n #\u7ed3\u6784\u5927\u5e08#<\/strong><\/p>\n #\u9ad8\u5c42\u5efa\u7b51\u8bbe\u8ba1-\u4ee5\u7ed3\u6784\u4e3a\u5efa\u7b51[\u4e0a] bySOM\u5927\u795e\u9a6c\u514b*\u590f\u51ef\u661f<\/a><\/p>\n #\u9ad8\u5c42\u5efa\u7b51\u8bbe\u8ba1-\u4ee5\u7ed3\u6784\u4e3a\u5efa\u7b51[\u4e2d] bySOM\u5927\u795e\u9a6c\u514b*\u590f\u51ef\u661f<\/a><\/p>\n #\u9ad8\u5c42\u5efa\u7b51\u8bbe\u8ba1-\u4ee5\u7ed3\u6784\u4e3a\u5efa\u7b51[\u4e0b] bySOM\u5927\u795e\u9a6c\u514b*\u590f\u51ef\u661f<\/a><\/p>\n #\u6297\u9707\u6027\u80fd\u8bbe\u8ba1\u5927\u795eGraham.H.Powell\u8bb2\u5ea7\u7b2c1\u8282-\u4e0a<\/a><\/p>\n #\u6297\u9707\u6027\u80fd\u8bbe\u8ba1\u5927\u795eGraham.H.Powell\u8bb2\u5ea7\u7b2c1\u8282-\u4e0b<\/a><\/p>\n #\u8d85\u9ad8\u5c42\u5efa\u7b51\u6297\u9707\u6027\u80fd\u8bbe\u8ba1by\u4f2f\u514b\u5229\u6559\u6388Jack Moehle<\/a><\/p>\n #\u7ed3\u6784\u8bbe\u8ba1#<\/strong><\/p>\n #\u300a\u6df1\u5733\u9ad8\u89c4\u300b\u975e\u5b98\u65b9\u8ba8\u8bba[\u4e00]<\/a><\/p>\n![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/DAMAGE1.png\")
<\/figure>
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/rebardamage.png\")
<\/figure>
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/damage2.png\")
<\/figure>
2 Mander\u672c\u6784<\/h4>\n
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/mander1.png\")
<\/figure>
![\"f_{c}=\frac{f_{c c}^{\prime} x r}{r-1+x^{r}}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-c9d39f7dd20b184b13f0cc7bda3a70e3_l3.png\" "\\"Rendered")
\uff081\uff09<\/p>\n![\"f_{c c}^{\prime}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-36eb16295e45e59acd9214c7f49c3d0b_l3.png\" "\\"Rendered")
\u662f\u7ea6\u675f\u6df7\u51dd\u571f\u5cf0\u503c\u5f3a\u5ea6\uff0c\u662fMander\u672c\u6784\u6a21\u578b\u7684\u5173\u952e\u3002<\/p>\n![\"f_{c c}^{\prime}=f_{c o}^{\prime}+k_{1}f_{l}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-5376de6275457358d2768e19fc889acd_l3.png\" "\\"Rendered")
\uff082\uff09<\/p>\n![\"x=\frac{\varepsilon_{c c}}{\varepsilon_c}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-a8e0602e8910a27e697fa13a627e8a69_l3.png\" "\\"Rendered")
\uff083\uff09<\/p>\n![\"\varepsilon_{c c}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-a7f6a9be870fc1589f1c4beb29848e7f_l3.png\" "\\"Rendered")
\u662f\u5cf0\u503c\u5f3a\u5ea6\u5bf9\u5e94\u7684\u6df7\u51dd\u571f\u538b\u5e94\u53d8\u3002<\/p>\n![\"\varepsilon_{c c}=\varepsilon_{c o}\left[1+5\left(\frac{f_{c c}^{\prime}}{f_{c o}^{\prime}}-1\right)\right]\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-289f5bf76dc4e284d941c91a6c583fdb_l3.png\" "\\"Rendered")
\uff084\uff09 <\/p>\n![\"f_{c o}^{\prime}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-8370dac2c2c2951a9f464412df8c506a_l3.png\" "\\"Rendered")
\u548c![\"\varepsilon_{c o}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-26d4f2aaac6d1f65bceede9f90e3c714_l3.png\" "\\"Rendered")
\u5206\u522b\u662f\u975e\u7ea6\u675f\u6df7\u51dd\u571f\u7684\u5cf0\u503c\u5f3a\u5ea6\u548c\u5176\u5bf9\u5e94\u538b\u5e94\u53d8\uff0c\u4e00\u822c\u53d60.002\u3002<\/p>\n![\"r=\frac{E_{c}}{E_{c}-E_{\mathrm{sec}}}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-974e765ff2977c9f49a4c8ab78083b14_l3.png\" "\\"Rendered")
\uff085\uff09<\/p>\n![\"E_{c}=5,000 \sqrt{f_{c o}^{\prime}} \mathrm{MPa}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-840065fdd79421399c8eb7fbf529a3f5_l3.png\" "\\"Rendered")
\u3002<\/p>\n![\"E_{s e c}=\frac{f_{c c}^{\prime}}{\varepsilon_{c c}}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-65806307cba392460c7ca56aaa0ac148_l3.png\" "\\"Rendered")
\uff086\uff09<\/p>\n![](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2022\/04\/Mander2.png\")
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/jili.png\")
<\/figure>
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/arch.png\")
<\/figure>
![\"k_e\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-ca91533967c245ea07e11acbd78e3b4a_l3.png\" "\\"Rendered")
\u53ef\u4ee5\u7531\u516c\u5f0f\u6c42\u5f97\u3002\u7b8d\u7b4b\u7684\u7ea6\u675f\u4f5c\u7528\u5e76\u4e0d\u662f\u5747\u5300\u65bd\u52a0\u5230\u6838\u5fc3\u533a\u6df7\u51dd\u571f\u4e0a\u7684\uff0c\u800c\u662f\u4ea7\u751f\u4e86\u62f1\u6548\u5e94\uff0c\u4f7f\u5f97\u6838\u5fc3\u533a\u5916\u56f4\u90e8\u5206\u538b\u5e94\u529b\u8f83\u5c0f\uff0c\u800c\u4e2d\u95f4\u533a\u57df\u8f83\u5927\u3002<\/p>\n![\"f_{l}=\frac{1}{2}k_{e}\rho_{s}{f_{s}}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-b6fcf7c5fbb2c07ce4120397708754e5_l3.png\" "\\"Rendered")
\n![\"k_{e}=\frac{A_{e}}{A_{c c}}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-e89889785455005046d9aee8f8ca0541_l3.png\" "\\"Rendered")
\n![\"A_{e}=\frac{\pi d_{s}^{2}}{4}\left(1-0.5 \frac{s^{\prime}}{d_{s}}\right)^{k}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-d69f5ef3c84344ab57b34f16eaf4e293_l3.png\" "\\"Rendered")
\n![\"A_{c c}=\left(1-\rho_{c c}\right) \frac{\pi d_{s}^{2}}{4}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-ea21e18de195d6090598f0aafc0a6d74_l3.png\" "\\"Rendered")
<\/p>\n![\"f_{l}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-c1d3afdbbed3553af088d1746118475a_l3.png\" "\\"Rendered")
\u4e3a\u6709\u6548\u4fa7\u5411\u7ea6\u675f\u5e94\u529b\u3002<\/p>\n![\"f_{l}=\frac{\rho_{s} f_{s}}{2} \frac{\left(1-0.5 \frac{s^{\prime}}{d_{s}}\right)^{k}}{1-\rho_{c c}}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-4dbce7ecbc7de398ef1d3af882ad0727_l3.png\" "\\"Rendered")
\n![\"\rho_{s}=\frac{4 A_{s h}}{s d_{s}}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-8df02c2bf78e496c55de55a0db7fee34_l3.png\" "\\"Rendered")
,\u7eb5\u7b4b\u4f53\u79ef\u914d\u7b4b\u7387![\"\rho_{c c}=\frac{A_{s t}}{\pi d_{s}^{2}}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-3a1654bfea97b187b6e4a502c3d27f03_l3.png\" "\\"Rendered")
\u3002<\/p>\n![\"K=\frac{f_{c c}^{\prime}}{f_{c}^{\prime}}=1+A \bar{x}\left(0.1+\frac{0.9}{1+B \bar{x}}\right)\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-5f7de45375d1d2d4d395d132d8f61f5f_l3.png\" "\\"Rendered")
\n![\"\bar{x}=\frac{f_{l 1}^{\prime}+f_{l 2}^{\prime}}{2 f_{c}^{\prime}}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-bd73cd341472401b2c57f97dfa4c5efc_l3.png\" "\\"Rendered")
\n![\"r=\frac{f_{l 1}^{\prime}}{f_{l 2}^{\prime}} \quad f_{l 2}^{\prime} \geq f_{l 1}^{\prime}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-84a71581715acd37dd21fbcea2ef1364_l3.png\" "\\"Rendered")
\n![\"A=6.8886-(0.6069+17.275 r) e^{-4.989 r}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-0c694bdc3c0aeed6571dbc8b4b1f1c64_l3.png\" "\\"Rendered")
\n![\"B=\frac{4.5}{\frac{5}{A}\left(0.9849-0.6306 e^{-3.8939 r}\right)-0.1}-5\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-236321f532e3e828315c9b00548cf882_l3.png\" "\\"Rendered")
\n![\"K=\frac{f_{c c}^{\prime}}{f_{c o}^{\prime}}=1+k_{1} \bar{x}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-581d7953dfcaa4b2a5d55f6bf9b6b265_l3.png\" "\\"Rendered")
\n![\"k_{1}=A\left(0.1+\frac{0.9}{1+B \bar{x}}\right)\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-724f098318360698d543a638dfc03e78_l3.png\" "\\"Rendered")
.<\/p>\n![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/manderkk.png\")
<\/figure>
3 \u5728XTRACT\u4e2d\u7684\u5e94\u7528<\/h4>\n
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/xtractzz.png\")
<\/figure>
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/xtrrr.png\")
<\/figure>
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/mander5.png\")
<\/figure>
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/PM1.png\")
<\/figure>
4 \u7ed3\u8bed<\/h4>\n
![\"\"](\"http:\/\/www.structurevspoem.com\/wp-content\/uploads\/2025\/05\/xtr5.png\")
<\/figure>
1 An Experiment<\/h4>\n
<\/figure>
<\/figure>
<\/figure>
<\/figure>
<\/figure>
\n2 Mander Constitutive Model<\/h4>\n
![\"\\[f_{c}=\\frac{f_{c](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-fb501dc8dc7f4b6f6b51b2ebc9ebea9c_l3.png\" "\\"Rendered")
<\/p>\n is the confined concrete peak strength, critical to the model:<\/p>\n![\"\\[f_{c](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-2c56af718f0cae7024d31a6cc0e4f416_l3.png\" "\\"Rendered")
<\/p>\n![\"\\[x=\\frac{\\varepsilon_{c](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-20668b7a529bc205b64bc007fe8afac9_l3.png\" "\\"Rendered")
<\/p>\n is the strain at peak strength:<\/p>\n![\"\\[\\varepsilon_{c](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-d31a7d17a6636317b13ded12b70ba06a_l3.png\" "\\"Rendered")
<\/p>\n and are the unconfined concrete peak strength and corresponding strain (typically 0.002). <\/p>\n![\"\\[r=\\frac{E_{c}}{E_{c}-E_{\\mathrm{sec}}}](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-dc1864877b34a186894d18b2b39b954d_l3.png\" "\\"Rendered")
<\/p>\n![\"E_{c}=5,000 \sqrt{f_{c o}^{\prime}} \, \text{MPa}\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-b6673aa51863798c9ca5700b599850b4_l3.png\" "\\"Rendered")
, and <\/p>\n![\"\\[E_{\\mathrm{sec}}=\\frac{f_{c](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-bc0237ef7180f04cfae367189e6d4c4b_l3.png\" "\\"Rendered")
<\/p>\n
<\/figure>
<\/figure>
. Stirrups do not uniformly confine concrete; arching effects create higher stress in the core center than the periphery.<\/p>\n![\"\\[f_{l}=\\frac{1}{2}k_{e}\\rho_{s}{f_{s}},](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-abce630ba87f6736504c9bc914feddc8_l3.png\" "\\"Rendered")
<\/p>\n![\"\\[A_{e}=\\frac{\\pi](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-b6e17df4bbf09ddcdbdbcc5182acf7db_l3.png\" "\\"Rendered")
<\/p>\n, where:<\/p>\n![\"\\[f_{l}=\\frac{\\rho_{s}](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-5de5a6e68fae8d916cb783602b79bd09_l3.png\" "\\"Rendered")
<\/p>\n, longitudinal ratio .<\/p>\n![\"K\"](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-7fb8d8d37cb2b48aee9e97aee7728d8f_l3.png\" "\\"Rendered")
uses empirical formulas without lookup tables:<\/p>\n![\"\\[K=\\frac{f_{c](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-15b5c2422c07cc008d9d1770888c17b7_l3.png\" "\\"Rendered")
<\/p>\n![\"\\[r=\\frac{f_{l](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-592d785d94e0fd07f278b84e3e87cadc_l3.png\" "\\"Rendered")
<\/p>\n![\"\\[A=6.8886-(0.6069+17.275](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-f857ce299d44d204c2fb42a4d139646d_l3.png\" "\\"Rendered")
<\/p>\n![\"\\[K=\\frac{f_{c](\"http:\/\/www.structurevspoem.com\/wp-content\/ql-cache\/quicklatex.com-a6d888feb892ae7bb5e7e18ddc32a1f5_l3.png\" "\\"Rendered")
<\/p>\n<\/figure>
\n3 Application in XTRACT<\/h4>\n
<\/figure>
<\/figure>
<\/figure>
<\/figure>
\n4 Conclusion<\/h4>\n
<\/figure>