[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-107180-arch_structure-12":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-107180-801-0102-012","architect","107180",107,"建築結構",12,null,"圖示桿件在中央 b 點及自由端 a 點分別承受 2P 及 P 之軸力作用，若 a 點垂直向下之伸長量為 δ=KPL\u002F(EA)，試問 K 值為何？",{"A":14,"B":15,"C":16,"D":17},"3\u002F5","1","2","2.5",[19],"D","single",[22],"\u002Fimages\u002Farch-107180-801-0102-012.png","本題考點：分段變斷面軸力桿的伸長量，δ = NL\u002F(EA) 分段計算再相加，關鍵在於每一段的軸力要由自由體圖求出，不能直接用外力。\n【正解理由】依題圖所示，桿件上端 c 固定，cb 段長 L、軸向剛度 2EA；ba 段長 L、軸向剛度 EA；b 點受向下 2P、自由端 a 點受向下 P。由 a 端往上取自由體：ba 段內只承受下方的 P，軸力為 P（張力）；cb 段承受其下方全部的外力 2P + P = 3P（張力）。各段伸長量：δ_cb = 3P × L\u002F(2EA) = 1.5 PL\u002F(EA)，δ_ba = P × L\u002F(EA) = 1 PL\u002F(EA)。a 點的總位移是兩段伸長量之和 δ = 2.5 PL\u002F(EA)，對照 δ = KPL\u002F(EA)，K = 2.5，故選 D。\n【逐項排除】\n(A) 3\u002F5：比正確值 2.5 小得多。兩段都受張力、伸長量必須相加，a 點位移不會小於 ba 段自身的伸長量 PL\u002F(EA)，K 值不可能小於 1。\n(B) 1：這只是 ba 段的伸長量 P × L\u002F(EA)，漏掉了 cb 段的伸長。a 點跟著 b 點一起往下移，cb 段伸長 1.5 PL\u002F(EA) 也要加進去。\n(C) 2：比正確值 2.5 小；cb 段的軸力是 3P、剛度是 2EA，伸長量 1.5 PL\u002F(EA)，加上 ba 段的 PL\u002F(EA) 才是 2.5，數值不符。\n(D) 2.5：cb 段 1.5 PL\u002F(EA) 加 ba 段 PL\u002F(EA)，符合題目所問。\n【演算步驟】\n1. 公式：軸力桿伸長量 δ = N × L\u002F(E × A)，分段計算後相加。\n2. ba 段軸力：N_ba = P（kN，張力）。\n3. cb 段軸力：N_cb = 2P + P = 3P（kN，張力）。\n4. cb 段伸長：δ_cb = 3P × L\u002F(2EA) = (3\u002F2) PL\u002F(EA)（m）。\n5. ba 段伸長：δ_ba = P × L\u002F(EA) = (1\u002F1) PL\u002F(EA)（m）。\n6. a 點位移：δ = (3\u002F2 + 1\u002F1) PL\u002F(EA) = 2.5 PL\u002F(EA)（m），K = 2.5。\n【記憶點】分段軸力桿：每段軸力 = 該段以下（自由端側）所有外力之和，伸長量 NL\u002F(EA) 逐段相加。",602,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},9,"如圖所示之 AB 及 BC 桿件，桿件之彈性係數 E 均相同，AB 及 BC 之斷面…",{"number":32,"session":7,"stem":33},10,"如下圖所示之桁架，關於 A、B、C 三桿件的受力敘述，何者正確？",{"number":35,"session":7,"stem":36},11,"有一座五跨度之連續梁，建構之各梁斷面與材料均相同。就以下四種不同之均布載重作用下，何…",{"number":38,"session":7,"stem":39},13,"鋼筋混凝土斷面寬度 b=30 cm，有效深度 d=50 cm，拉力筋之 As=22.…",{"number":41,"session":7,"stem":42},14,"承上題，該梁斷面的彎矩計算強度（Mn）約為多少 tf-m？",{"number":44,"session":7,"stem":45},15,"結構材料之承載效率可利用強度除以比重來評估，則在建築結構常用之鋼鐵、混凝土及木材中，…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","如圖所示之甲乙兩支梁承受相同垂直均布靜載重，若兩梁皆為鋼筋混凝土構造，斷面(1)、(…",{"number":10,"session":51,"stem":52},"113190","非結構物耐震考量，下列敘述何者錯誤？",{"number":10,"session":54,"stem":55},"112190","如下圖所示，一構件斜面之中心點受一水平力 P=1000 N 作用，此斜面與水平方向之…",{"number":10,"session":57,"stem":58},"111180","在結構系統的規劃上，下列敘述何者錯誤？",{"number":10,"session":60,"stem":61},"110180","圖示之鋼筋混凝土韌性構架，有關主筋搭接之敘述，下列何者正確？ D A B C",1791863209290]