[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-108180-arch_structure-33":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-108180-801-0102-033","architect","108180",108,"建築結構",33,null,"如圖所示之 C 型斷面，對通過其形心之 X 軸轉動時，斷面慣性矩（Moment of inertia）I 之大小為下列何者？",{"A":14,"B":15,"C":16,"D":17},"6.667×107 mm4","3.936×107 mm4","2.731×107 mm4","1.344×107 mm4",[19],"B","single",[22],"\u002Fimages\u002Farch-108180-801-0102-033.png","本題考點：組合斷面的慣性矩。C 型斷面對稱於 X 軸，可用「外框矩形減去缺口矩形」的負面積法，以矩形對形心軸慣性矩 I = b × h × h × h \u002F 12 直接相減求得。\n【正解理由】依題圖，C 型斷面外框寬 100 mm、總高 100 mm + 100 mm = 200 mm；右側開口的缺口寬 80 mm、高 80 mm + 80 mm = 160 mm，因此腹板厚與上下翼板厚都是 100 − 80 = 20 mm。上下兩半各為 100 mm 與 80 mm，斷面對 X 軸上下對稱，形心就在 X 軸上，外框矩形與缺口矩形的形心也都在 X 軸上，相減時不需要平行軸修正。外框矩形 I1 = 100 × 200 × 200 × 200 \u002F 12 = 66666666.67 mm⁴；缺口矩形 I2 = 80 × 160 × 160 × 160 \u002F 12 = 27306666.67 mm⁴；C 型斷面 I = I1 − I2 = 39360000 mm⁴，即 3.936×10⁷ mm⁴，故選 B。\n【逐項排除】\n(A) 6.667×10⁷ mm⁴ 不符。這是外框 100 mm × 200 mm 實心矩形的慣性矩 66666666.67 mm⁴，沒有扣除右側缺口；C 型斷面中間是空的，要再減去 80 mm × 160 mm 缺口的慣性矩，才是 3.936×10⁷ mm⁴。\n(B) 3.936×10⁷ mm⁴ 符合。外框慣性矩減去缺口慣性矩，66666666.67 − 27306666.67 = 39360000 mm⁴。\n(C) 2.731×10⁷ mm⁴ 不符。這是缺口 80 mm × 160 mm 矩形本身的慣性矩 27306666.67 mm⁴，是要被扣掉的部分，不是 C 型斷面的慣性矩；正確值是外框減去它之後的 3.936×10⁷ mm⁴。\n(D) 1.344×10⁷ mm⁴ 不符。此值小於正確值 3.936×10⁷ mm⁴，與外框減缺口的結果不一致，不是本斷面對 X 軸的慣性矩。\n【演算步驟】\n① 尺寸：外框高 h1 = 100 mm + 100 mm = 200 mm，寬 b1 = 100 mm；缺口高 h2 = 80 mm + 80 mm = 160 mm，寬 b2 = 80 mm；壁厚 = 100 mm − 80 mm = 20 mm。\n② 外框矩形：I1 = b1 × h1 × h1 × h1 \u002F 12 = 100 mm × 200 mm × 200 mm × 200 mm \u002F 12 = 66666666.67 mm⁴。\n③ 缺口矩形：I2 = b2 × h2 × h2 × h2 \u002F 12 = 80 mm × 160 mm × 160 mm × 160 mm \u002F 12 = 27306666.67 mm⁴。\n④ C 型斷面：I = I1 − I2 = 66666666.67 mm⁴ − 27306666.67 mm⁴ = 39360000 mm⁴ = 3.936×10⁷ mm⁴。\n【記憶點】對稱軸上的開口斷面，用「大矩形減小矩形」最快；兩塊形心都在同一軸上時，直接相減，不必平行軸修正。",640,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},30,"如圖所示之 ABCD 為一均質之預鑄混凝土構件，長度為 6 m，寬度為 4 m，重量…",{"number":32,"session":7,"stem":33},31,"關於鋼筋混凝土結構之韌性設計，下列敘述何者正確？",{"number":35,"session":7,"stem":36},32,"關於鋼筋混凝土結構之構材性能，下列何者錯誤？",{"number":38,"session":7,"stem":39},34,"根據建築技術規則，下列何者應計入靜載重？",{"number":41,"session":7,"stem":42},35,"圖示具斜拉索 BC 之懸臂梁 AB 構造，當載重通過矩形梁之斷面形心，則何者不是固定…",{"number":44,"session":7,"stem":45},36,"關於折板結構之敘述，下列何者正確？",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","下圖為一偏心斜撐構架（Eccentrically Braced Frame）之示意圖…",{"number":10,"session":51,"stem":52},"113190","下列鋼結構斜撐構架中，地震時何種耐震性能最差？圖(a) 圖(b) 圖(c) 圖(d)",{"number":10,"session":54,"stem":55},"112190","關於鋼梁桿件的鋼板「局部挫屈」，下列敘述何者錯誤？",{"number":10,"session":57,"stem":58},"111180","關於矩形斷面鋼筋混凝土簡支梁的設計與分析，下列敘述何者錯誤？",{"number":10,"session":60,"stem":61},"110180","有一簡支梁承受均布載重如圖所示，若梁自重不計，下列何者所得之最大正彎矩值與此梁相同？",1791863208489]