[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-108180-arch_structure-9":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-108180-801-0102-009","architect","108180",108,"建築結構",9,null,"承上題，試求該鋼斷面之斷面模數約為多少 mm3？",{"A":14,"B":15,"C":16,"D":17},"1.01×106","5.61×106","8.46×106","12.35×106",[19],"A","single",[],"本題考點：斷面模數 S = I \u002F c，c 為形心軸到斷面最外緣纖維的距離；承上題沿用同一 I 型斷面的強軸慣性矩。\n【正解理由】斷面模數用來把彎矩換算成最外緣的彎曲應力（σ = M \u002F S），定義是慣性矩除以形心到最外緣的距離。前題的 I 型斷面由兩塊寬 200 mm、厚 22 mm 的翼板與一塊高 200 mm、厚 22 mm 的腹板組成，全深 244 mm，上下對稱，形心到上、下緣的距離相同，都是全深的一半 122 mm。強軸慣性矩逐塊相加約 123446400 mm⁴，除以 122 mm 得約 1011856 mm³，即約 1.01×10⁶ mm³，與選項 (A) 相符，故選 A。\n【逐項排除】\n(A) 1.01×10⁶ mm³：強軸慣性矩除以形心到最外緣距離 122 mm，得約 1.01×10⁶ mm³，正確。\n(B) 5.61×10⁶ mm³：比正確值大了好幾倍，若用正確的強軸慣性矩除以半深，不可能得到這個值；斷面模數應為約 1.01×10⁶ mm³。\n(C) 8.46×10⁶ mm³：同樣遠大於正確值，與慣性矩除以 122 mm 的結果對不上；正確應為約 1.01×10⁶ mm³。\n(D) 12.35×10⁶ mm³：有效數字雖與前題的慣性矩相同，但斷面模數是慣性矩除以形心到外緣距離，單位為 mm³，數值應為約 1.01×10⁶ mm³，此選項遠大於正確值。\n【演算步驟】\n斷面全深 h = 200 mm + 22 mm + 22 mm = 244 mm。\n形心到最外緣距離 c = h \u002F 2 = 244 mm \u002F 2 = 122 mm。\n翼板形心到斷面形心距離 d = 200 mm \u002F 2 + 22 mm \u002F 2 = 111 mm。\n強軸慣性矩 Ix = 22 mm × (200 mm)³ \u002F 12 + 2 × [200 mm × (22 mm)³ \u002F 12 + 200 mm × 22 mm × (111 mm)²] ≈ 123446400 mm⁴。\n斷面模數 S = Ix \u002F c = 123446400 mm⁴ \u002F 122 mm ≈ 1011856 mm³ ≈ 1.01×10⁶ mm³。\n【記憶點】斷面模數 = 慣性矩 ÷ 形心到最外緣距離；對稱斷面的 c 取全深的一半，單位從 mm⁴ 降成 mm³。",615,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},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":31,"session":7,"stem":32},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":34,"session":7,"stem":35},8,"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…",{"number":37,"session":7,"stem":38},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":40,"session":7,"stem":41},11,"下列四個工程圖中的敘述，何者正確？",{"number":43,"session":7,"stem":44},12,"關於建築物耐震設計之敘述，下列何者錯誤？",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","某等跨距構架活載重 w 全部負載、間隔負載如圖(a)、圖(b)所示，若活載重大於靜載…",{"number":10,"session":50,"stem":51},"113190","依「建築物耐震設計規範」，下列有關地震加速度反應譜之敘述何者正確？",{"number":10,"session":53,"stem":54},"112190","一個微小的矩型六面體受到純剪力作用，下列敘述何者正確？",{"number":10,"session":56,"stem":57},"111180","有一長度為 L，直徑為 d 之圓桿，彈性模數為 E，波松比（Poisson’s ra…",{"number":10,"session":59,"stem":60},"110180","下圖結構的穩定與可定性質為何？ L L L L",1791863208287]