[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-107180-arch_structure-13":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-107180-801-0102-013","architect","107180",107,"建築結構",13,null,"鋼筋混凝土斷面寬度 b=30 cm，有效深度 d=50 cm，拉力筋之 As=22.5 cm2，fc'=210 kgf\u002Fcm2， fy=4200 kgf\u002Fcm2，當梁斷面達到其彎矩計算強度（Mn）時，中性軸距受壓面之距離約為多少公分？",{"A":14,"B":15,"C":16,"D":17},"15","18","21","24",[19],"C","single",[],"本題考點：鋼筋混凝土單筋矩形梁的極限強度分析——以等值矩形應力塊（Whitney 應力塊）由力平衡 C = T 求應力塊深度 a，再以 c = a\u002Fβ₁ 換算中性軸深度。\n【正解理由】梁達彎矩計算強度 Mn 時，假設拉力筋已降伏，拉力 T = As·fy；壓力區以 0.85fc' 的均勻應力作用於深度 a 的矩形塊，壓力 C = 0.85fc'·a·b。由 C = T 得 a = As·fy\u002F(0.85fc'·b) = 94500\u002F5355 = 17.65 cm。fc' = 210 kgf\u002Fcm² 屬一般強度混凝土，β₁ 取 0.85，故中性軸深度 c = a\u002Fβ₁ = 17.65\u002F0.85 = 20.76 cm。中性軸位置偏淺，以應變相容回算，拉力筋應變明顯大於其降伏應變，「拉力筋已降伏」的假設成立。20.76 cm 最接近 21 cm，故選 C。\n【逐項排除】\n(A) 15：比計算值 20.76 cm 小，連應力塊深度 a = 17.65 cm 都不到；中性軸深度 c 必大於 a（c = a\u002Fβ₁），正確值約 21 cm。\n(B) 18：接近應力塊深度 a 的 17.65 cm，但 a 只是等值矩形應力塊的深度，不是中性軸位置；須再除以 β₁ 才是中性軸深度，正確值約 21 cm。\n(C) 21：c = 17.65\u002F0.85 = 20.76 cm，約 21 cm，符合題目所問，為正解。\n(D) 24：比計算值 20.76 cm 大，中性軸偏深會使壓力區面積過大、C 大於 T，不滿足力平衡，正確值約 21 cm。\n【演算步驟】\n拉力：T = As·fy = 22.5 cm² × 4200 kgf\u002Fcm² = 94500 kgf\n壓力區係數：0.85fc'·b = 0.85 × 210 kgf\u002Fcm² × 30 cm = 5355 kgf\u002Fcm\n應力塊深度：a = T \u002F (0.85fc'·b) = 94500 kgf \u002F 5355 kgf\u002Fcm = 17.65 cm\n中性軸深度：c = a \u002F β₁ = 17.65 cm \u002F 0.85 = 20.76 cm，最接近 21 cm\n【記憶點】先由 C = T 求 a，再除以 β₁ 才是中性軸 c；a 與 c 是兩個不同的深度。",564,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},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":31,"session":7,"stem":32},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":34,"session":7,"stem":35},12,"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…",{"number":37,"session":7,"stem":38},14,"承上題，該梁斷面的彎矩計算強度（Mn）約為多少 tf-m？",{"number":40,"session":7,"stem":41},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":43,"session":7,"stem":44},16,"鋼製桿件其彈性係數 E = 200 GPa，長度 L = 3 m，斷面積 A= 30…",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","下列有關結構穩定性與靜定性之敘述，何者錯誤？",{"number":10,"session":50,"stem":51},"113190","下列關於建築物所使用被動消能元件之敘述，何者錯誤？",{"number":10,"session":53,"stem":54},"112190","下列有關「固定拱」、「雙鉸拱」和「三鉸拱」的敘述，何者錯誤？",{"number":10,"session":56,"stem":57},"111180","柱 1、柱 2、柱 3 之長度、材料、斷面均同，其最小挫屈載重分別為 P1、P2、P…",{"number":10,"session":59,"stem":60},"110180","鋼筋混凝土結構在耐震設計時，係依據鋼筋應力為 1.25 fy 所求得之彎矩強度以計算…",1791863209293]