[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-108180-arch_structure-8":3},{"question":4,"neighbors":26,"sameNumber":45,"prev":34,"next":37},{"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":22,"withheld":11,"deepChars":23,"freq":24,"indexable":25},"arch-108180-801-0102-008","architect","108180",108,"建築結構",8,null,"由三塊寬度 b=200 mm，厚度 t=22 mm 之鋼板組成 I 型鋼斷面，則該鋼斷面之強軸慣性矩約為多少 mm4？",{"A":14,"B":15,"C":16,"D":17},"1.01×107","5.61×107","8.46×107","12.35×107",[19],"D","single",[],"本題考點：組合斷面的強軸慣性矩，用平行軸定理把翼板與腹板對同一條形心軸的慣性矩逐塊相加（I = Σ(I₀ + A·d²)）。\n【正解理由】三塊寬 200 mm、厚 22 mm 的鋼板組成 I 型斷面：兩塊水平放置當上、下翼板，一塊垂直夾在兩翼板之間當腹板，腹板高即為板寬 200 mm，斷面全深是腹板高加上兩塊翼板厚。斷面上下對稱，形心落在全深中點。強軸是平行翼板、通過形心的水平軸；翼板離這條軸最遠，面積乘上距離平方的移軸項是慣性矩的主力，腹板只貢獻自身的矩形慣性矩。把腹板自身慣性矩、兩塊翼板的自身慣性矩與移軸項相加，得到約 12.35×10⁷ mm⁴，與選項 (D) 相符，故選 D。\n【逐項排除】\n(A) 1.01×10⁷ mm⁴：比正確值小了將近一個數量級，連兩塊翼板移軸項的總和都遠遠不到，不可能是三塊鋼板組合後的強軸慣性矩；正確值應為約 12.35×10⁷ mm⁴。\n(B) 5.61×10⁷ mm⁴：數量級雖然對了，但數值明顯低於正確值，表示翼板對強軸的貢獻被大幅低估；強軸慣性矩應把兩塊翼板的移軸項完整算入，結果約為 12.35×10⁷ mm⁴。\n(C) 8.46×10⁷ mm⁴：仍低於正確值，與逐塊相加的結果對不上；只要翼板形心到斷面形心的距離取腹板半高加翼板半厚，並把兩塊翼板都算進去，結果應為約 12.35×10⁷ mm⁴。\n(D) 12.35×10⁷ mm⁴：腹板自身慣性矩加上兩塊翼板的自身慣性矩與移軸項，合計約 123446400 mm⁴，即約 12.35×10⁷ mm⁴，正確。\n【演算步驟】\n斷面全深 h = 200 mm + 22 mm + 22 mm = 244 mm，形心在 h \u002F 2 處。\n腹板（寬 22 mm、高 200 mm，形心與斷面形心重合）：I腹 = t·b³ \u002F 12 = 22 mm × (200 mm)³ \u002F 12 ≈ 14666667 mm⁴。\n單塊翼板自身形心慣性矩：I₀ = b·t³ \u002F 12 = 200 mm × (22 mm)³ \u002F 12 ≈ 177467 mm⁴。\n單塊翼板面積：A = 200 mm × 22 mm = 4400 mm²。\n翼板形心到斷面形心距離：d = 200 mm \u002F 2 + 22 mm \u002F 2 = 111 mm。\n單塊翼板移軸項：A·d² = 4400 mm² × (111 mm)² = 54212400 mm⁴。\n強軸慣性矩：Ix = I腹 + 2 × (I₀ + A·d²) = 14666667 mm⁴ + 2 × (177467 mm⁴ + 54212400 mm⁴) ≈ 123446400 mm⁴ ≈ 12.35×10⁷ mm⁴。\n【記憶點】I 型斷面強軸慣性矩看翼板：自身慣性矩很小，A·d² 移軸項才是主力，d 要量到翼板形心。",702,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},5,"如圖所示為梁（OAB）與桁架（BCDE）之複合結構，OA、AB、BC、CD 及 CE…",{"number":31,"session":7,"stem":32},6,"圖中為一平面纜索系統的部分簡圖，其中 B 為支壓材，A、C 為連接纜索。A 索拉力為…",{"number":34,"session":7,"stem":35},7,"一圓球薄殼屋頂結構，頂部因採光需求而部分挖空，試問自重作用下頂部與底部的環形圈梁主要…",{"number":37,"session":7,"stem":38},9,"承上題，試求該鋼斷面之斷面模數約為多少 mm3？",{"number":40,"session":7,"stem":41},10,"非公眾使用之建築物，若樓地板面積為 120 m2，單位面積之靜載重為 420 kg\u002F…",{"number":43,"session":7,"stem":44},11,"下列四個工程圖中的敘述，何者正確？",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","有關高層建築結構系統與設計，下列敘述何者錯誤？①高層建築於設計風力下之層間位移角，不…",{"number":10,"session":50,"stem":51},"113190","關於設計載重組合，下列敘述何者正確？",{"number":10,"session":53,"stem":54},"112190","一結構如圖所示，上部為一個短柱，底部為兩個面積較小的長柱支撐，中間塗黑部分為剛體，當…",{"number":10,"session":56,"stem":57},"111180","有關一般混凝土材料的敘述，下列何者正確？",{"number":10,"session":59,"stem":60},"110180","下列何者與土壤液化潛能之判定並無直接關係？",1791863208281]