[{"data":1,"prerenderedAt":60},["ShallowReactive",2],{"q-107180-arch_structure-4":3},{"question":4,"neighbors":26,"sameNumber":44,"prev":33,"next":36},{"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-107180-801-0102-004","architect","107180",107,"建築結構",4,null,"承上題，則梁中央之撓度為原來的幾倍？",{"A":14,"B":15,"C":16,"D":17},"2\u002F3","1","8\u002F5","2",[19],"C","single",[],"本題考點：簡支梁在均布載重與跨中集中載重下的跨中最大撓度公式，並在總載重相同（P = wL）、其他條件（L、E、I）不變時比較兩者的倍數。\n【正解理由】簡支梁受均布載重 w 時，跨中撓度 δ₁ = 5wL⁴\u002F(384EI)；改為跨中集中外力 P 時，跨中撓度 δ₂ = PL³\u002F(48EI)。代入 P = wL 得 δ₂ = wL⁴\u002F(48EI)。兩者相比 δ₂\u002Fδ₁ = (1\u002F48)\u002F(5\u002F384) = 384\u002F240 = 1.6，即 8\u002F5 倍，故選 C。\n【逐項排除】\n(A) 2\u002F3：倍數小於 1，表示集中載重的撓度反而較小，方向錯誤；集中在跨中的載重使梁中段彎矩較大，撓度也較大，正確倍數為 8\u002F5。\n(B) 1：表示兩種載重形式的撓度相同；但均布載重與跨中集中載重的彎矩分布不同，撓度係數一個是 5\u002F384、一個是 1\u002F48，兩者不相等，正確倍數為 8\u002F5。\n(C) 8\u002F5：正確。集中載重撓度係數 1\u002F48 除以均布載重撓度係數 5\u002F384，得 1.6，即 8\u002F5。\n(D) 2：2 是上一題跨中「彎矩」的倍數，彎矩比 (1\u002F4)\u002F(1\u002F8) = 2；本題問的是撓度，撓度取決於彎矩沿全跨的分布，不等於跨中彎矩比，正確倍數為 8\u002F5。\n【演算步驟】\n① 均布載重跨中撓度：δ₁ = 5wL⁴\u002F(384EI)，w 單位 kN\u002Fm、L 單位 m、E 單位 kN\u002Fm²、I 單位 m⁴，δ₁ 單位 m。\n② 集中載重跨中撓度：δ₂ = PL³\u002F(48EI)，P 單位 kN；代入 P = wL（kN），δ₂ = wL⁴\u002F(48EI)（m）。\n③ 倍數：δ₂\u002Fδ₁ = [wL⁴\u002F(48EI)]\u002F[5wL⁴\u002F(384EI)] = (1\u002F48)\u002F(5\u002F384) = 384\u002F240 = 1.6 = 8\u002F5（無因次）。\n【記憶點】簡支梁總載重相同時，跨中集中載重的跨中撓度是均布載重的 8\u002F5 倍，與彎矩的 2 倍不同。",595,1,true,[27,29,32,35,38,41],{"number":24,"session":7,"stem":28},"下列何者為面積慣性矩（I）之單位？",{"number":30,"session":7,"stem":31},2,"圖示各結構物之彎矩圖中，何者錯誤？",{"number":33,"session":7,"stem":34},3,"一簡支梁跨距長 L，受到均勻分布載重 w 之作用。若其他條件不變，載重改為梁中央受集…",{"number":36,"session":7,"stem":37},5,"下列四個具相同長度及斷面之梁承受相同集中力作用，則集中力作用處之撓度其大小順序為何？",{"number":39,"session":7,"stem":40},6,"一懸臂梁如圖所示，其斷面所承受之最大彎矩為 β•WL2，試問 β 值為何？",{"number":42,"session":7,"stem":43},7,"依建築物耐震設計規範進行設計地震力之靜力分析時，有意外扭矩之規定，此規定主要係考慮下…",[45,48,51,54,57],{"number":10,"session":46,"stem":47},"114180","一長度為 2 m 圓棒，直徑為 30 mm，彈性模數為 70 GPa，波松比（Poi…",{"number":10,"session":49,"stem":50},"113190","下列材料性質之敘述何者正確？",{"number":10,"session":52,"stem":53},"112190","有關材料性質，下列敘述何者正確？",{"number":10,"session":55,"stem":56},"111180","關於結構設計時之靜載重 D 與活載重 L，下列敘述何者錯誤？",{"number":10,"session":58,"stem":59},"110180","建築物設計風力之計算與所在地點之基本設計風速有關，依地況分成：地況 A：大城市市中心…",1791863209213]