[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-107180-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-107180-801-0102-026","architect","107180",107,"建築結構",26,null,"如圖所示之懸臂柱構件頂端承受軸壓力 N 與側力 V，構件斷面寬與深分別為 B 與 D。若忽略自重，當軸壓應力可剛好抵銷柱底最大撓曲拉應力，使斷面完全受壓時，N 與 V 之比值為何？",{"A":14,"B":15,"C":16,"D":17},"2D\u002F3L","3L\u002F2D","3D\u002FL","6L\u002FD",[19],"D","single",[22],"\u002Fimages\u002Farch-107180-801-0102-026.png","本題考點：偏心受壓（軸力加彎矩）的組合應力，求斷面恰好全斷面受壓、拉應力為零的臨界條件，即軸壓應力 N\u002FA 等於撓曲應力 M\u002FS。\n【正解理由】依題圖所示，柱為底部固定的懸臂柱，高 L，頂端受軸壓力 N 與水平側力 V；斷面寬 B、深 D，深度 D 與側力 V 的方向一致，所以彎曲是繞著以 B 為寬的軸發生。柱底彎矩最大 M = V × L。矩形斷面積 A = B × D，斷面模數 S = B × D²\u002F6。軸壓應力 σ_a = N\u002F(BD)；撓曲應力 σ_b = M\u002FS = 6VL\u002F(BD²)，受拉側的拉應力等於 σ_b。題圖中柱底應力分布一側為 0、另一側為 σ_c，表示受拉側的撓曲拉應力剛好被軸壓應力抵銷。令 N\u002F(BD) = 6VL\u002F(BD²)，B 兩邊消去、D 消去一次，得 N = 6VL\u002FD，所以 N\u002FV = 6L\u002FD，故選 D。\n【逐項排除】\n(A) 2D\u002F3L：D 在分子、L 在分母，表示柱越高所需軸力越小，與「柱越高、柱底彎矩 VL 越大，越需要更大軸力抵銷拉應力」的方向相反；正確應為 L 在分子、D 在分母，係數 6。\n(B) 3L\u002F2D：L 在分子、D 在分母的形式正確，但係數小於正確值 6，所需軸力被低估，柱底仍會出現拉應力；應改為 6L\u002FD。\n(C) 3D\u002FL：與 (A) 同樣把 D 與 L 的位置顛倒，隨柱高增加比值反而變小，方向錯誤；正確為 6L\u002FD。\n(D) 6L\u002FD：由 N\u002F(BD) = 6VL\u002F(BD²) 解得，符合題目所問。\n【演算步驟】\n1. 柱底彎矩：M = V × L（kN × m = kN·m）。\n2. 斷面性質：A = B × D（m²），S = B × D²\u002F6（m³）。\n3. 軸壓應力：σ_a = N\u002FA = N\u002F(BD)（kN\u002Fm²）。\n4. 撓曲應力：σ_b = M\u002FS = VL\u002F(BD²\u002F6) = 6VL\u002F(BD²)（kN\u002Fm²）。\n5. 臨界條件：σ_a = σ_b → N\u002F(BD) = 6VL\u002F(BD²) → N = 6VL\u002FD（kN）。\n6. 比值：N\u002FV = (L\u002FD) ÷ (1\u002F6) = 6L\u002FD（無因次）。\n【記憶點】全斷面受壓的臨界條件是 N\u002FA = M\u002FS；矩形斷面 S = BD²\u002F6，等價於偏心距 M\u002FN 不超過 D\u002F6（斷面核心）。",554,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},23,"有關圓頂殼（dome shell）結構的敘述，下列何者正確？",{"number":32,"session":7,"stem":33},24,"下列有關傾角變位法之敘述，何者錯誤？",{"number":35,"session":7,"stem":36},25,"下列敘述何者正確？",{"number":38,"session":7,"stem":39},27,"如下圖所示之鋼結構接合部位設計方式（鋼梁翼板未銲接，腹板以螺栓固定），下列敘述何者正…",{"number":41,"session":7,"stem":42},28,"結構材料若具有高延展性，可對整體結構產生之正面效應，下列何者正確？",{"number":44,"session":7,"stem":45},29,"下列單位中，何者不適合用於混凝土抗壓強度 f'c？",[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 …",1791863209395]