[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-106180-arch_structure-24":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-106180-801-0102-024","architect","106180",106,"建築結構",24,null,"下圖桿件之自由端 a 點受 2P 力作用，a 點垂直向下伸長量為 δ av = ，則 K 值為： AE",{"A":14,"B":15,"C":16,"D":17},"4\u002F3 b","1","2\u002F3 4AE 2L","1\u002F3 a 2P",[19],"B","single",[22],"\u002Fimages\u002Farch-106180-801-0102-024.png","本題考點：軸力桿件的伸長量公式 δ = PL\u002F(AE)，代入題圖標示的軸力、桿長與軸向剛度後，對照題目給的 δav = KPL\u002F(AE) 求 K。\n【正解理由】依題圖，桿件上端 b 固定、下端 a 自由，a 點受向下 2P，桿長 2L，軸向剛度標為 4AE。桿件全長只有一段、軸力處處等於 2P（張力）。伸長量 δ = （軸力 × 桿長）\u002F（軸向剛度） = (2P × 2L)\u002F(4AE) = PL\u002FAE。對照 δav = KPL\u002F(AE)，得 K = 1，故選 B。\n【逐項排除】\n(A) 4\u002F3：代入題圖的軸力 2P、長度 2L、剛度 4AE，係數為 (2 × 2)\u002F4 = 1，4\u002F3 大於 1，代表伸長量被高估，與正確值不符。\n(B) 1：正解。δ = (2P)(2L)\u002F(4AE) = PL\u002FAE。\n(C) 2\u002F3：小於正確值 1，伸長量被低估；本題桿件只有一段、斷面與軸力全長一致，不需要分段疊加，結果應為 1。\n(D) 1\u002F3：同樣小於正確值 1，與 (2 × 2)\u002F4 = 1 不符。\n【演算步驟】\n① 公式：δ = NL\u002F(EA)，N 為軸力。\n② 軸力：N = 2P（力，張力）。\n③ 代入：δ = (2P × 2L)\u002F(4AE) = (2 × 2\u002F4) × PL\u002F(AE) = 1 × PL\u002F(AE)（長度）。\n④ 對照 δav = KPL\u002F(AE) → K = 1。\n【記憶點】伸長量 = 軸力 × 長度 ÷ 軸向剛度；力加倍、長度加倍、剛度四倍，三者剛好抵銷。",459,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},21,"下圖結構原為不穩定，擬於各節點間增加兩根桿件進行改善，則下列選項何者仍為不穩定結構？",{"number":32,"session":7,"stem":33},22,"型鋼會因製造過程產生殘餘應力（residual stress），下列敘述何者錯誤？",{"number":35,"session":7,"stem":36},23,"如圖所示桁架，桿件 ED 的內力為何？",{"number":38,"session":7,"stem":39},25,"有一矩形梁斷面，梁寬 30 cm，梁高 60 cm。已知材料之彈性係數為 20,00…",{"number":41,"session":7,"stem":42},26,"下圖簡支梁之跨度為 L。已知材料之彈性係數為 E，梁斷面之慣性矩為 I。今於跨度中央…",{"number":44,"session":7,"stem":45},27,"下圖之懸臂梁，端點 B 承受一集中載重 P，則 B 點之垂直位移為： PL2",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","下圖框架之 A 點彎矩為何？ D 1 1 1 1",{"number":10,"session":51,"stem":52},"113190","在靜態條件下，擋土牆可能之破壞型式不包括下列何者？",{"number":10,"session":54,"stem":55},"112190","桁架於 E 點受力 P，DF 軸力為何？ B D F H A C E G G P",{"number":10,"session":57,"stem":58},"111180","如圖所示桿件受軸向外力作用，F1 = 100 kN，F2 = 500 kN，則 A、…",{"number":10,"session":60,"stem":61},"110180","建築結構之樓地版設計活載重，依據規範下列何種用途類別的單位面積活載重最高？",1791863212001]