[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-109180-arch_structure-26":3},{"question":4,"neighbors":27,"sameNumber":46,"prev":35,"next":38},{"id":5,"classKey":6,"session":7,"year":8,"subject":9,"number":10,"groupStem":11,"ownStem":12,"stem":12,"options":13,"answer":18,"answerKind":20,"answerS":11,"answerNote":11,"images":21,"explanation":23,"withheld":11,"deepChars":24,"freq":25,"indexable":26},"arch-109180-801-0102-026","architect","109180",109,"建築結構",26,null,"如圖示之均質矩形斷面，對於形心水平軸 x 之面積慣性矩記為 Ixx，而對於矩形底邊水平軸 X 之面積慣性矩記為 JXX，則 JXX\u002FIxx =？",{"A":14,"B":15,"C":16,"D":17},"3","4","6","8",[19],"B","single",[22],"\u002Fimages\u002Farch-109180-801-0102-026.png","本題考點：矩形斷面的面積慣性矩與平行軸定理。先寫出對形心軸 x 的慣性矩 Ixx，再用平行軸定理把軸移到底邊 X，求兩者的比值。\n【正解理由】依題圖，矩形寬 b、高 h，形心水平軸 x 位於斷面高度中央，底邊軸 X 與 x 平行、位於斷面最下緣，兩軸距離 d 等於 h 的一半。矩形對形心軸的慣性矩為 Ixx = bh³\u002F12。平行軸定理規定：對任一平行軸的慣性矩，等於對形心軸的慣性矩加上「面積 × 兩軸距離的平方」。面積 A = b × h，距離的平方 d × d = h × h \u002F 4，所以移軸項 A × d × d = bh³\u002F4，換成十二分之幾就是 3bh³\u002F12。於是 JXX = bh³\u002F12 + 3bh³\u002F12 = 4bh³\u002F12 = bh³\u002F3。比值 JXX\u002FIxx = (bh³\u002F3) ÷ (bh³\u002F12) = 12 ÷ 3 = 4，b 與 h 全部約掉，結果與斷面尺寸無關。故選 B。\n【逐項排除】\n(A) 錯。3 是移軸項 A × d × d 與 Ixx 的比值，也就是只算了「面積 × 距離平方」這一項、漏加形心軸本身的 Ixx。平行軸定理是兩項相加，補上 Ixx 後比值才是 4。\n(B) 正確。JXX = Ixx + A × d × d = bh³\u002F12 + bh³\u002F4 = bh³\u002F3，與 Ixx = bh³\u002F12 相除得 4。\n(C) 錯。6 比正確比值 4 大。依平行軸定理，JXX 只由形心軸慣性矩 bh³\u002F12 與移軸項 bh³\u002F4 兩項組成，移軸距離取形心到底邊的距離，即 h 的一半；照此相加得 bh³\u002F3，比值應為 4。\n(D) 錯。8 比正確比值 4 大一倍。矩形對底邊的慣性矩是 bh³\u002F3，對形心軸是 bh³\u002F12，兩者相除只能得到 4；改成 4 才對。\n【演算步驟】\n① 形心軸慣性矩：Ixx = b × h³ \u002F 12。\n② 兩軸距離：d 為 h 的一半，所以 d × d = h × h \u002F 4。\n③ 平行軸定理：JXX = Ixx + A × d × d = bh³\u002F12 + (b × h) × (h × h \u002F 4) = bh³\u002F12 + bh³\u002F4。\n④ 通分：bh³\u002F4 = 3bh³\u002F12（因 12 ÷ 4 = 3），故 JXX = bh³\u002F12 + 3bh³\u002F12 = 4bh³\u002F12 = bh³\u002F3。\n⑤ 比值：JXX\u002FIxx = (bh³\u002F3) ÷ (bh³\u002F12) = 12 ÷ 3 = 4。\n【記憶點】矩形對形心軸是 bh³\u002F12、對底邊是 bh³\u002F3，兩者相差 4 倍；平行軸定理只能「從形心軸出發」加上面積乘距離平方。",641,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},23,"相較於磚造建築物，鋼骨建築物一般較有利於耐震，下列何者最有可能為其原因？",{"number":32,"session":7,"stem":33},24,"如圖示，AC 及 BC 均為曲梁，A、B 為鉸支承，C 為鉸接，下列有關支承反力敘述…",{"number":35,"session":7,"stem":36},25,"若一懸臂梁為實心圓桿，下列何者受力情況，桿件斷面不會產生剪應力？",{"number":38,"session":7,"stem":39},27,"下列何者不屬於形抗結構？",{"number":41,"session":7,"stem":42},28,"下列何者最不適合視為等向性（isotropic）材料？",{"number":44,"session":7,"stem":45},29,"均質材料之柏松比（poisson ratio）定義為構件受拉伸或壓縮力時，其橫向應變…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","下列何者載重分布，使懸臂梁固定端彎矩最大？ 2w 2w w 0 0 L L L (a…",{"number":10,"session":51,"stem":52},"113190","如圖所示之構架承受側力 P，兩柱分別高 L 及 2 L，柱頂皆為鉸接（pin），兩柱…",{"number":10,"session":54,"stem":55},"112190","下圖中之圖(i)所示為一單跨抗彎矩構架（moment-resisting frame…",{"number":10,"session":57,"stem":58},"111180","試分析下圖桁架結構，下列選項何者正確（T 為張力，C 為壓力）？ 10 m 10 m…",{"number":10,"session":60,"stem":61},"110180","一簡支梁跨距為 5 m，分別受到以下兩種載重形式：（A）跨距中央受到集中載重 10 …",1791863206349]