[{"data":1,"prerenderedAt":60},["ShallowReactive",2],{"q-110180-arch_structure-33":3},{"question":4,"neighbors":25,"sameNumber":44,"prev":33,"next":36},{"id":5,"classKey":6,"session":7,"year":8,"subject":9,"number":10,"groupStem":11,"ownStem":12,"stem":12,"options":13,"answer":16,"answerKind":18,"answerS":11,"answerNote":11,"images":19,"explanation":21,"withheld":11,"deepChars":22,"freq":23,"indexable":24},"arch-110180-801-0102-033","architect","110180",110,"建築結構",33,null,"有一簡支梁承受均布載重如圖所示，若梁自重不計，下列何者所得之最大正彎矩值與此梁相同？",{"A":14,"B":15,"C":14,"D":14},"","（P ≠ 0）（梁加深）",[17],"B","single",[20],"\u002Fimages\u002Farch-110180-801-0102-033.png","本題考點：靜定梁的彎矩只由載重、跨度與支承條件決定，與斷面大小無關；改變支承條件（懸臂端載重、增設中間支承、兩端固定）則會改變彎矩分布。\n【正解理由】題目的原梁是簡支梁承受全跨均布載重 w，取跨中斷面的自由體：支承反力 wL\u002F2 乘以半跨 L\u002F2，減去半跨載重 wL\u002F2 乘以其力臂 L\u002F4，得最大正彎矩 wL²\u002F8。這個計算只用到平衡方程式，完全沒有用到梁的斷面性質。選項 (B) 的梁支承、跨度與均布載重都與原梁相同，只把梁加深；簡支梁是靜定結構，加深只會改變斷面模數與剛度，使應力與撓度變小，最大正彎矩仍為 wL²\u002F8；題目又說明梁自重不計，加深也不會增加載重。故選 B。\n【逐項排除】\n(A) 不符。依題圖所示，此梁兩端外伸，懸臂端各有集中載重（P ≠ 0）。懸臂端載重在支承處產生負彎矩，並使支承間的彎矩圖整體往負方向平移，跨中的最大正彎矩因此小於 wL²\u002F8，與原梁不同。\n(B) 符合。支承條件、跨度、載重皆不變，靜定梁的彎矩與斷面深淺無關，最大正彎矩仍為 wL²\u002F8。\n(C) 不符。依題圖所示，此梁在跨中增設一個滾支承，成為兩跨連續梁（靜不定）。中間支承向上頂住梁，使中間支承處產生負彎矩，跨內的正彎矩大幅降低，與原簡支梁不同。\n(D) 不符。依題圖所示，此梁兩端固定（靜不定）。固定端限制轉角而產生負彎矩，跨中正彎矩等於簡支梁的自由彎矩扣除端部負彎矩的影響，因此小於 wL²\u002F8。\n【演算步驟】\n原簡支梁跨中彎矩：M = (wL\u002F2)(L\u002F2) − (wL\u002F2)(L\u002F4)\n以 w = 1 kN\u002Fm、L = 1 m 代入：M = (1 × 1 \u002F 2 kN)(1 \u002F 2 m) − (1 × 1 \u002F 2 kN)(1 \u002F 4 m) = 0.125 kN-m\n即 M = 1\u002F8 × wL² = 0.125 wL²\n【記憶點】靜定梁「彎矩看支承與載重，應力與撓度才看斷面」；加深梁只降應力與撓度，不改彎矩。",569,1,true,[26,29,32,35,38,41],{"number":27,"session":7,"stem":28},30,"無梁版系統在我國較少應用於上部結構，大多僅應用在地下室結構，下列敘述何者錯誤？",{"number":30,"session":7,"stem":31},31,"原有一剛構架進行耐震補強，在兩側增設圖示之桿件，其中 A、D 為固端，B、C 為鉸接…",{"number":33,"session":7,"stem":34},32,"圖示桁架結構在 F、E 點受力分別為 P1 = 10 kN 及 P2 = 15 kN…",{"number":36,"session":7,"stem":37},34,"圖中構架 ABCD 之 A 點固端彎矩為何？ 3m 2 kN 4m 10 kN-m …",{"number":39,"session":7,"stem":40},35,"下圖的結構中，關於支承 A、B 點之反力的敘述何者錯誤？ 60°",{"number":42,"session":7,"stem":43},36,"圖示結構 A、C 為鉸端，B 為鉸接，則 A 點處水平反力為何？ 60 kN 9m …",[45,48,51,54,57],{"number":10,"session":46,"stem":47},"114180","下圖為一偏心斜撐構架（Eccentrically Braced Frame）之示意圖…",{"number":10,"session":49,"stem":50},"113190","下列鋼結構斜撐構架中，地震時何種耐震性能最差？圖(a) 圖(b) 圖(c) 圖(d)",{"number":10,"session":52,"stem":53},"112190","關於鋼梁桿件的鋼板「局部挫屈」，下列敘述何者錯誤？",{"number":10,"session":55,"stem":56},"111180","關於矩形斷面鋼筋混凝土簡支梁的設計與分析，下列敘述何者錯誤？",{"number":10,"session":58,"stem":59},"109180","桁架結構之受力如下圖，則 B 點的反力為何？ P P 5m A B 5m 5m 5m",1791863205096]