[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-107180-arch_structure-16":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-107180-801-0102-016","architect","107180",107,"建築結構",16,null,"鋼製桿件其彈性係數 E = 200 GPa，長度 L = 3 m，斷面積 A= 300 mm2，受拉力 P = 120 kN 作用，桿件之伸長量 δ 為多少 mm？",{"A":14,"B":15,"C":16,"D":17},"2","4","6","8",[19],"C","single",[],"本題考點：軸力桿件的彈性伸長量公式 δ = PL\u002F(AE)（虎克定律），重點在於把 kN、m、mm²、GPa 統一成一致的單位再代入。\n【正解理由】桿件受軸拉力時，應力 σ = P\u002FA，應變 ε = σ\u002FE，伸長量 δ = ε·L，合併得 δ = PL\u002F(AE)。將單位統一為 N 與 mm：P = 120 kN = 120000 N，L = 3 m = 3000 mm，A = 300 mm²，E = 200 GPa = 200000 N\u002Fmm²（1 GPa = 1000 N\u002Fmm²）。代入得 δ = 120000 × 3000 \u002F (300 × 200000) = 360000000 \u002F 60000000 = 6 mm，故選 C。\n【逐項排除】\n(A) 2：小於 δ = PL\u002F(AE) 的計算結果，與正確值不符；正確伸長量為 6 mm。\n(B) 4：小於正確值，不符 δ = PL\u002F(AE) 的計算結果；正確伸長量為 6 mm。\n(C) 6：δ = 120000 N × 3000 mm \u002F (300 mm² × 200000 N\u002Fmm²) = 6 mm，符合題目所問，為正解。\n(D) 8：大於正確值，不符計算結果；正確伸長量為 6 mm。\n【演算步驟】\n單位統一：P = 120 kN = 120 × 1000 = 120000 N；L = 3 m = 3 × 1000 = 3000 mm；E = 200 GPa = 200 × 1000 = 200000 N\u002Fmm²\n公式：δ = PL \u002F (AE)\n分子：P·L = 120000 N × 3000 mm = 360000000 N·mm\n分母：A·E = 300 mm² × 200000 N\u002Fmm² = 60000000 N\n伸長量：δ = 360000000 N·mm \u002F 60000000 N = 6 mm\n【記憶點】δ = PL\u002F(AE)，先把 kN→N、m→mm、GPa→N\u002Fmm² 換齊再代入。",528,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},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":31,"session":7,"stem":32},14,"承上題，該梁斷面的彎矩計算強度（Mn）約為多少 tf-m？",{"number":34,"session":7,"stem":35},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，…",{"number":37,"session":7,"stem":38},17,"一高樓結構採具剪力牆之二元系統，其平面如圖所示。樓層之剛心最有可能在何處？",{"number":40,"session":7,"stem":41},18,"關於拱結構之敘述，下列何者正確？",{"number":43,"session":7,"stem":44},19,"關於薄膜結構之基本力學原理，下列敘述何者錯誤？",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","圖中所示一正三角形桁架，求可施加之最大負載 P，使得無任何桿件受力超過 3 kN 之…",{"number":10,"session":50,"stem":51},"113190","一剛架結構受外力作用如圖所示，下列何種梁上塑性鉸產生時，不會形成不穩定結構？",{"number":10,"session":53,"stem":54},"112190","下列何種設計策略會增長建物基本振動週期？",{"number":10,"session":56,"stem":57},"111180","關於柱子的挫屈（buckling）破壞與臨界負載（critical load）之敘述…",{"number":10,"session":59,"stem":60},"110180","建築物耐震設計規範的鋼骨造結構系統中，常採用偏心斜撐結構系統。此系統的主要消能機制一…",1791863209317]