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| 1 | +<TMU|<tuple|1.1.0|2026.2.5>> |
| 2 | + |
| 3 | +<style|<tuple|generic|chinese|table-captions-above|number-europe|preview-ref>> |
| 4 | + |
| 5 | +<\body> |
| 6 | + 本讲义围绕钢结构轴心受力构件展开,涵盖轴心受拉与受压构件的核心知识点,包含<strong|知识框架脑图>、<strong|核心知识点讲解>、<strong|典型例题解析>三部分,贴合钢结构设计原理课程教学要求,兼顾理论推导与工程应用,可用于课堂授课、课后复习及设计参考。 |
| 7 | + |
| 8 | + <\enumerate> |
| 9 | + <item><strong|定义>:仅承受通过截面形心轴线的轴向力,分<strong|轴心拉杆>(受拉)和<strong|轴心压杆>(受压)。 |
| 10 | + |
| 11 | + <item><strong|截面分类> |
| 12 | + |
| 13 | + <\itemize> |
| 14 | + <item>实腹式:整体连通,含热轧型钢(圆管 / 角钢 / H 型钢等)、组合截面(型钢 / 钢板拼接)、冷弯型钢(轻钢结构专用);型钢截面分<strong|强轴(<math|x> 轴,惯性矩大)<strong|和>弱轴(<math|y> 轴,惯性矩小)>。 |
| 15 | + |
| 16 | + <item>格构式:由肢件 + 缀件组成,常用双肢;实轴(<math|y> 轴)过肢件腹板,虚轴(<math|x> 轴)过缀件,易实现两主轴等稳定性,适用于大轴压荷载。 |
| 17 | + </itemize> |
| 18 | + |
| 19 | + <item><strong|选型原则>:满足强度 / 刚度 / 稳定的前提下,用料经济、制作简便、便于连接,优先<strong|宽肢薄壁>截面(提高抗弯刚度和稳定)。 |
| 20 | + </enumerate> |
| 21 | + |
| 22 | + <math|<tabular|<tformat|<table|<row|<cell|I<rsub|x>>|<cell|=<frac|1|12>\<times\>19\<times\><around|(|17.2+2\<times\>1.6|)><rsup|3>-<frac|1|12>\<times\><around|(|19-1|)>\<times\>17.2<rsup|3>>>|<row|<cell|>|<cell|=<frac|1|12>\<times\>19\<times\><around|(|17.2+3.2|)><rsup|3>-<frac|1|12>\<times\>18\<times\>17.2<rsup|3>>>|<row|<cell|>|<cell|=<frac|1|12>\<times\>19\<times\>20.4<rsup|3>-<frac|1|12>\<times\>18\<times\>17.2<rsup|3>>>|<row|<cell|>|<cell|=<frac|1|12>\<times\>19\<times\>8489.664-<frac|1|12>\<times\>18\<times\>5088.448>>|<row|<cell|>|<cell|=<frac|161303.616|12>-<frac|91592.064|12>>>|<row|<cell|>|<cell|=<frac|13441.97-7632.67|12>>>|<row|<cell|>|<cell|=5809.3*c*m<rsup|4>*<space|1em><around|(|<text|保留1位小数,约>5809*c*m<rsup|4>|)>>>>>>> |
| 23 | + |
| 24 | + \; |
| 25 | + |
| 26 | + <math|<tabular|<tformat|<cwith|1|4|4|4|cell-halign|c>|<cwith|1|4|4|4|cell-rborder|1ln>|<cwith|1|4|5|5|cell-halign|c>|<cwith|1|4|5|5|cell-rborder|1ln>|<cwith|1|4|6|6|cell-halign|c>|<cwith|1|4|6|6|cell-rborder|1ln>|<cwith|1|1|1|6|cell-tborder|1ln>|<cwith|1|1|1|6|cell-bborder|1ln>|<cwith|2|2|1|6|cell-bborder|1ln>|<cwith|3|3|1|6|cell-bborder|1ln>|<cwith|4|4|1|6|cell-bborder|1ln>|<cwith|1|4|1|3|cell-tborder|1ln>|<cwith|1|4|1|3|cell-bborder|1ln>|<cwith|1|4|1|3|cell-lborder|1ln>|<cwith|1|4|1|3|cell-rborder|1ln>|<cwith|1|4|4|4|cell-lborder|1ln>|<cwith|1|4|1|6|font|Noto CJK SC>|<cwith|4|4|6|6|font-base-size|8>|<table|<row|<cell|序号>|<cell|截面形式>|<cell|图例>|<cell|<text|当 >\<lambda\><rsub|y>\<geqslant\>\<lambda\><rsub|z><text|时>>|<cell|<text|当 >\<lambda\><rsub|y>\<less\>\<lambda\><rsub|z><text|时>>|<cell|<text|式中的 >\<lambda\><rsub|z>>>|<row|<cell|1>|<cell|等边双角钢>|<cell|图4-7a>|<cell|\<lambda\><rsub|y z> =\<lambda\><rsub|y>*<around*|[|1+0.16<around*|(|<frac|\<lambda\><rsub|z>|\<lambda\><rsub|y>>|)><rsup|2>|]>>|<cell|\<lambda\><rsub|y z>=\<lambda\><rsub|z>*<around*|[|1+0.16<around*|(|<frac|\<lambda\><rsub|y>|\<lambda\><rsub|z>>|)><rsup|2>|]>>|<cell|\<lambda\><rsub|z>=3.9*<frac|b|t>>>|<row|<cell|2>|<cell|长肢相拼的不等边双角钢>|<cell|图4-7b>|<cell|\<lambda\><rsub|y z>=\<lambda\><rsub|y>*<around*|[|1+0.25<around*|(|<frac|\<lambda\><rsub|z>|\<lambda\><rsub|y>>|)><rsup|2>|]>>|<cell|\<lambda\><rsub|y z>=\<lambda\><rsub|z>*<around*|[|1+0.25<around*|(|<frac|\<lambda\><rsub|y>|\<lambda\><rsub|z>>|)><rsup|2>|]>>|<cell|\<lambda\><rsub|z>=5.1*<frac|b<rsub|2>|t>>>|<row|<cell|3>|<cell|短肢相拼的不等边双角钢>|<cell|图4-7c>|<cell|\<lambda\><rsub|y z>=\<lambda\><rsub|y>*<around*|[|1+0.06<around*|(|<frac|\<lambda\><rsub|z>|\<lambda\><rsub|y>>|)><rsup|2>|]>>|<cell|\<lambda\><rsub|y z>=\<lambda\><rsub|z>*<around*|[|1+0.06<around*|(|<frac|\<lambda\><rsub|y>|\<lambda\><rsub|z>>|)><rsup|2>|]>>|<cell|\<lambda\><rsub|z>=3.7*<frac|b<rsub|1>|t>>>>>>> |
| 27 | + |
| 28 | + \; |
| 29 | + |
| 30 | + <math|A=2\<times\>250\<times\>12+250\<times\>8=8000*<space|0.17em>m*m<rsup|2>>,\ |
| 31 | + |
| 32 | + <math|A<rsub|n>=8000-100\<times\>8=7200*<with|math-font-family|rm|m m><rsup|2>>,\ |
| 33 | + |
| 34 | + <math|I<rsub|x><space|0.17em>=<space|0.17em><tfrac|1|12><around*|[|b*<around*|(|h+2*t|)><rsup|3>-<around*|(|b-t<rsub|w>|)>*<space|0.17em>h<rsub|w><rsup|3>|]>=<frac|1|12>*<around*|[|250\<times\>274<rsup|3>-242\<times\>250<rsup|3>|]>=11345\<times\>10<rsup|4>*m*m<rsup|4>>, |
| 35 | + |
| 36 | + <\equation*> |
| 37 | + I<rsub|y>=2\<times\><frac|1|12>*t*b<rsup|3>+<frac|1|12>*h<rsub|w>*t<rsub|w><rsup|3>=2\<times\><frac|1|12>\<times\>12\<times\>250<rsup|3>+<frac|1|12>\<times\>250\<times\>8<rsup|3>=3126\<times\>10<rsup|4>*m*m<rsup|4>, |
| 38 | + </equation*> |
| 39 | + |
| 40 | + <equation*|(教材忽略了腹板对惯性矩的影响,得到结果非常接近I<rsub|y>=2\<times\><frac|1|12>t<with|mode|text| >b<rsup|3>=3125\<times\>10<rsup|4>mm)> |
| 41 | + |
| 42 | + <\equation*> |
| 43 | + i<rsub|x>=<sqrt|<frac|I<rsub|x>|A>>=11.91<text|cm>,<space|1em>i<rsub|y>=<sqrt|<frac|I<rsub|y>|A>>=6.25<text|cm>. |
| 44 | + </equation*> |
| 45 | + |
| 46 | + 工字钢,翼缘为焰切边,则查表E-1,为b类截面, |
| 47 | + |
| 48 | + <surround|| |<math|<\aligned> |
| 49 | + <tformat|<cwith|1|-1|1|1|cell-hmode|exact>|<cwith|1|-1|2|2|cell-hmode|exact>|<cwith|1|-1|1|1|cell-width|160515tmpt>|<cwith|1|-1|2|2|cell-width|292740tmpt>|<table|<row|<cell|\<varepsilon\><rsub|k>>|<cell|=<sqrt|<frac|235|f<rsub|y>>>=<sqrt|<frac|235|355>>=0.8136,>>|<row|<cell|\<lambda\><rsub|0>>|<cell|=<frac|\<lambda\><rsub|m a x>|\<varepsilon\><rsub|k>>=<frac|50.4|0.8136>\<approx\>62,查表E-4,\<varphi\>=0.796,>>|<row|<cell|<frac|N|\<varphi\>*A>>|<cell|=<frac|2000\<times\>10<rsup|3>|0.796\<times\>8000>\<approx\>314*N/m*m<rsup|2>,>>|<row|<cell|<frac|314-305|305>\<times\>100%>|<cell|=2.95%\<less\>5%,<space|1em>满*足.(实际规范不允许有任何偏差)>>>> |
| 50 | + </aligned>>> |
| 51 | +</body> |
| 52 | + |
| 53 | +<\initial> |
| 54 | + <\collection> |
| 55 | + <associate|page-screen-margin|false> |
| 56 | + <associate|stem-doc-id|63992928-5153-4E50-878E-3D6F738EE6C0> |
| 57 | + </collection> |
| 58 | +</initial> |
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