[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-112190-arch_structure-22":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-112190-801-0102-022","architect","112190",112,"建築結構",22,null,"對一個寬度為 b 深度為 h 的矩形斷面梁的斷面模數（S）及塑性斷面模數（Z），下列敘述何者錯誤？",{"A":14,"B":15,"C":16,"D":17},"S=bh2\u002F6","S 乘上降伏應力為降伏彎矩","Z=bh2\u002F3","Z 乘上降伏應力為全斷面達塑性時之彎矩",[19],"C","single",[],"本題考點：矩形斷面的彈性斷面模數 S 與塑性斷面模數 Z 怎麼推、各自對應哪一個彎矩（降伏彎矩 My 與塑性彎矩 Mp），以及兩者的比值。\n【正解理由】彈性階段的應力沿深度呈直線分布，中性軸在斷面中央，最外纖維應力最大；S 定義為慣性矩除以中性軸到最外纖維的距離，矩形斷面 I = bh³\u002F12、距離 h\u002F2，相除得 S = bh²\u002F6。全斷面塑性化時，中性軸兩側各有 b × h\u002F2 的面積全部達降伏應力，一拉一壓形成力偶，各半邊合力作用在該半邊的形心、距中性軸 h\u002F4，所以 Z = 2 × (b·h\u002F2) × (h\u002F4) = bh²\u002F4，不是 bh²\u002F3。選項 (C) 的係數寫錯，是本題要找的錯誤敘述，故選 C。\n【逐項排除】\n(A) 正確。S = I ÷ (h\u002F2) = (bh³\u002F12) ÷ (h\u002F2) = bh²\u002F6，這是矩形斷面彈性斷面模數的標準結果，題幹的 bh2\u002F6 即 bh²\u002F6。\n(B) 正確。彈性公式 σ = M\u002FS，最外纖維應力剛好等於降伏應力時的彎矩就是降伏彎矩，即 My = S × 降伏應力；此時只有最外緣一條纖維降伏，內部仍是彈性。\n(C) 錯誤，本題答案。矩形斷面的塑性斷面模數是 Z = bh²\u002F4。bh²\u002F3 這個係數是把塑性狀態的合力（每半邊 b·h\u002F2 全部達降伏應力）配上彈性三角形應力塊的力臂（合力距中性軸 h\u002F3）混算出來的：塑性狀態的應力塊是矩形，力臂應取半邊形心 h\u002F4。改成 Z = bh²\u002F4 才對。\n(D) 正確。Z 乘降伏應力就是塑性彎矩 Mp，代表整個斷面從上到下全部達降伏、形成塑性鉸時能承受的彎矩，這也是《建築技術規則建築構造編》第 244 條所說「彎矩強度可達塑性彎矩」的那個彎矩。\n【記憶點】矩形斷面：S = bh²\u002F6 對應降伏彎矩，Z = bh²\u002F4 對應塑性彎矩，兩者相除得形狀因子 1.5。",820,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},19,"下圖中之圖(i)為一棟兩跨的單層鋼筋混凝土造建築物的結構示意圖。該建築物在遭受恐怖攻…",{"number":31,"session":7,"stem":32},20,"關於承重牆結構系統特性，下列敘述何者正確？",{"number":34,"session":7,"stem":35},21,"關於隔震系統，下列敘述何者錯誤？",{"number":37,"session":7,"stem":38},23,"如下圖所示之四種桁架結構，各桿件之軸向剛度（AE）值皆相等。若溫度改變時，何者最有可…",{"number":40,"session":7,"stem":41},24,"桁架於 E 點受力 P，DF 軸力為何？ B D F H A C E G G P",{"number":43,"session":7,"stem":44},25,"下圖所示結構中，支承 A 與 B 的反力大小為何？ 100 kN 45 kN C 4…",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","桁架結構如下圖，a~d 桿件中何者軸拉力最大？ 1.5 m 3m 3m 1.5 m …",{"number":10,"session":50,"stem":51},"113190","下列那種牆設計對於建築物耐震時水平強度的提升效果最好？圖中以網點圖樣填滿的部分為牆體…",{"number":10,"session":53,"stem":54},"111180","有關建築物耐風設計規範的要求，下列敘述何者錯誤？",{"number":10,"session":56,"stem":57},"110180","以下關於材料力學中常用物理量之單位，何者錯誤？",{"number":10,"session":59,"stem":60},"109180","關於鋼筋混凝土預鑄工法之敘述，下列何者最不適當？",1791863200034]