[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-111180-arch_structure-9":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-111180-801-0102-009","architect","111180",111,"建築結構",9,null,"有一長度為 L，直徑為 d 之圓桿，彈性模數為 E，波松比（Poisson’s ratio）為 v，受到軸向拉力 P，下列敘述何者正確？",{"A":14,"B":15,"C":16,"D":17},"剪力彈性模數 G = E\u002F(1+2v)","直徑的變化量為 2vPd\u002FEA","體積改變量為(π\u002F4d2LP(1-2v))\u002FAE","體積減少",[19],"C","single",[],"本題考點：圓桿受軸向拉力時的材料力學基本關係，包括剪力彈性模數 G 與 E、ν 的換算、波松效應造成的橫向（直徑）變化，以及體積應變與 1−2ν 的關係。題目中的波松比記作 v，以下寫成 ν。\n【正解理由】先建立縱向應變：軸向拉力 P 作用在斷面積 A 上，軸向應力為 P\u002FA，縱向應變 ε = P\u002F(AE)。波松效應使橫向應變為 −νε，也就是桿件拉長的同時變細。小變形下，體積應變等於三個方向應變之和：ε + (−νε) + (−νε) = ε(1−2ν)。原體積 V = (π\u002F4)d²L，所以體積改變量 ΔV = V·ε(1−2ν) = (π\u002F4)d²L·P(1−2ν)\u002F(AE)，與選項 (C) 的式子完全一致。故選 C。\n【逐項排除】\n(A) 錯誤。均質等向性線彈性材料的三個彈性常數關係為 G = E\u002F[2(1+ν)]，分母是 2 乘上 (1+ν)，不是 (1+2ν)。選項把係數 2 放錯位置，改成 G = E\u002F[2(1+ν)] 才對。\n(B) 錯誤。直徑變化量 = 橫向應變 × 直徑 = νε·d = νPd\u002F(EA)，選項多乘了一個 2；而且受拉時直徑是縮小，變化量應帶負號或註明為減少。改成「直徑減少 νPd\u002F(EA)」才對。\n(C) 正確。如正解理由所推，ΔV = (π\u002F4)d²L·P(1−2ν)\u002F(AE)，即原體積乘上體積應變 ε(1−2ν)，與選項所列式子相同。\n(D) 錯誤。體積應變為 ε(1−2ν)，受拉時 ε 為正，而一般材料的波松比使 1−2ν 不為負，因此受拉桿的體積是增加（至多不變），不會減少。縱向伸長的效果大於兩個橫向收縮的合計，選項方向相反，應改為「體積增加」。\n【記憶點】受拉體積應變 = ε(1−2ν)，G = E\u002F[2(1+ν)]，直徑變化 = νεd 且是縮小。",554,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},6,"關於薄膜、纜索、與拱結構系統之敘述，下列何者錯誤？",{"number":31,"session":7,"stem":32},7,"下圖為一鋼結構的梁柱接頭所使用鋼材之拉力試驗結果，於 C 點發生材料斷裂，下列敘述何…",{"number":34,"session":7,"stem":35},8,"有關一般混凝土材料的敘述，下列何者正確？",{"number":37,"session":7,"stem":38},10,"有關材料性質，下列敘述何者正確？",{"number":40,"session":7,"stem":41},11,"下列何者不屬於形抗結構？",{"number":43,"session":7,"stem":44},12,"在結構系統的規劃上，下列敘述何者錯誤？",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","某等跨距構架活載重 w 全部負載、間隔負載如圖(a)、圖(b)所示，若活載重大於靜載…",{"number":10,"session":50,"stem":51},"113190","依「建築物耐震設計規範」，下列有關地震加速度反應譜之敘述何者正確？",{"number":10,"session":53,"stem":54},"112190","一個微小的矩型六面體受到純剪力作用，下列敘述何者正確？",{"number":10,"session":56,"stem":57},"110180","下圖結構的穩定與可定性質為何？ L L L L",{"number":10,"session":59,"stem":60},"109180","如圖所示，鋼筋混凝土剪力牆因開口而形成短梁，如圖中圈選處。若此結構承受來自左方的水平…",1791863201912]