作者thefirst (陳金鋒 #52 )
看板Grad-ProbAsk
標題Re: [理工] [材力]Strain and Material Relations
時間Sat Mar 27 16:33:34 2010
※ 引述《a1133333 (阿傑)》之銘言：
: A 2-in.-diameter and 4-in.-long solid cylinder is subjected to hydrostatic
: loading with σx=σy=σz=-7.2ksi.Use E=30*10^6psi and υ=1/3. Calculate
: (a)the change in length of the cylinder and (b)the change in volume of the
: cylinder.
: 幫幫我 謝謝
賺個P幣
由廣義虎克定律
εx = [σx-ν(σy+σz)] / E = -81.6μ
εy = [σy-ν(σx+σz)] / E = -81.6μ
εz = [σz-ν(σx+σy)] / E = -81.6μ
(a)
△L = εx × L = -81.6μ × 4 = -0.0003264 in (負表長度縮短)
(b)
△V = (εx+εy+εz) × V
= (-81.6μ-81.6μ-81.6μ) ×π×4
= -0.003076247526 (in^3) (負表體積減少)
△V另一算法
△V = εv × V = [ (1-2ν)(3σ) / E ] × V
= -244.8μ × 4π
= -0.003076247526 (in^3)
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推 a1133333:答案是-0.348*10^-3in和-0.482*10^-3in^3 03/27 21:59
推 a1133333:請問εx怎麼會是-81.6μ帶入數據後好像不是這樣 是我錯嗎 03/27 22:05
→ thefirst:我ν帶0.33 若ν帶1/3 算出來是80μ 03/28 15:33
推 a1133333:3我一開始也像你這樣算 但跟答案不一樣 所以答案是錯的? 03/28 18:32
→ thefirst:應該吧 = =" 03/28 19:09
推 qoodeva:原po用的是体積應變近似的方法算 03/28 22:59
→ qoodeva:體積應變=(1+Ex)(1+Ey)(1+Ez)-1近似於三個方向的應變合 03/28 23:01
→ qoodeva:Ex+Ey+Ez算出來是近似值 如果一直計算錯誤請檢查自己按 03/28 23:01
→ qoodeva:計算機的步驟有無錯誤 ... 03/28 23:02