[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-107180-arch_structure-14":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-107180-801-0102-014","architect","107180",107,"建築結構",14,null,"承上題，該梁斷面的彎矩計算強度（Mn）約為多少 tf-m？",{"A":14,"B":15,"C":16,"D":17},"30","39","48","57",[19],"B","single",[],"本題考點：鋼筋混凝土單筋矩形梁的彎矩計算強度 Mn = As·fy·(d − a\u002F2)，即拉力筋拉力乘以拉壓合力間的內力臂，並注意 kgf-cm 與 tf-m 的單位換算。\n【正解理由】承上題條件，b = 30 cm、d = 50 cm、As = 22.5 cm²、fc' = 210 kgf\u002Fcm²、fy = 4200 kgf\u002Fcm²，且拉力筋降伏。由力平衡得應力塊深度 a = 17.65 cm，壓力合力作用於應力塊中心，距受壓面 a\u002F2；拉力合力作用於鋼筋形心，距受壓面 d。兩者間的內力臂為 d − a\u002F2 = 41.18 cm。Mn = T × 內力臂 = 94500 kgf × 41.18 cm = 3891510 kgf-cm；kgf 換成 tf、cm 換成 m，換算係數為 100000，得 38.92 tf-m，約 39 tf-m，故選 B。\n【逐項排除】\n(A) 30：明顯小於計算值 38.92 tf-m，與 Mn = As·fy·(d − a\u002F2) 的結果不符；正確為約 39 tf-m。\n(B) 39：Mn = 94500 kgf × 41.18 cm 換算為 38.92 tf-m，約 39 tf-m，符合題目所問，為正解。\n(C) 48：超過「拉力 × 有效深度」的上限 47.25 tf-m（內力臂不可能大於 d = 50 cm），數值偏大；正確為約 39 tf-m。\n(D) 57：遠大於計算值 38.92 tf-m，同樣超過內力臂取 d 時的上限 47.25 tf-m，不可能成立；正確為約 39 tf-m。\n【演算步驟】\n拉力：T = As·fy = 22.5 cm² × 4200 kgf\u002Fcm² = 94500 kgf\n應力塊深度：a = 94500 kgf \u002F (0.85 × 210 kgf\u002Fcm² × 30 cm) = 94500 kgf \u002F 5355 kgf\u002Fcm = 17.65 cm\n內力臂：d − a\u002F2 = 50 cm − 17.65 cm \u002F 2 = 41.18 cm\n彎矩計算強度：Mn = 94500 kgf × 41.18 cm = 3891510 kgf-cm\n單位換算：kgf-cm 換為 tf-m 的換算係數 = 1000 × 100 = 100000，Mn = 3891510 kgf-cm \u002F 100000 = 38.92 tf-m，最接近 39 tf-m\n【記憶點】Mn = As·fy·(d − a\u002F2)，內力臂是 d − a\u002F2，不是 d − c；kgf-cm 除以 100000 才是 tf-m。",603,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},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":31,"session":7,"stem":32},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":34,"session":7,"stem":35},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":37,"session":7,"stem":38},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":40,"session":7,"stem":41},16,"鋼製桿件其彈性係數 E = 200 GPa，長度 L = 3 m，斷面積 A= 30…",{"number":43,"session":7,"stem":44},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？",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","圖示之梁構造中 C 為鉸接，不考慮自重影響，在 B 出現微小垂直沉陷時，下列敘述何者…",{"number":10,"session":50,"stem":51},"113190","一般建築結構耐震設計時，下列敘述何者錯誤？",{"number":10,"session":53,"stem":54},"112190","下列有關纜索結構系統的敘述，何者正確？",{"number":10,"session":56,"stem":57},"111180","關於木質構造，下列敘述何者錯誤？",{"number":10,"session":59,"stem":60},"110180","下列有關鋼柱挫屈強度 Pcr 之敘述，何者錯誤？",1791863209297]