課程名稱︰材料力學 課程性質︰必修 課程教師︰鄭榮和 開課學院：工學院 開課系所︰機械系 考試日期（年月日）︰100/4/20 考試時限（分鐘）：50分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : <<需畫圖說明或 Free Body Diagram 而未畫者，扣該題1/5分數>> (20% will be deducted from the designated score od that problem if you fail to draw free-body diagram.) 1.A closees-end pressure vessel shown below is fabricated from fiber-reinforced,in which the fibers carry all of the pressure induced stresses while the plastic seals the cylinder and transfer the pressure loading to fibers.Suppose that the fibers can carry tensile stresses in the "fiber" direction only,determine the relations of fibers stress σ veru shoop stress φ and longitudinal stress ψ of the vessel.Also determine an optimal value of α such that all of the fibers carry the same magnitude of stress.(60%) __________________________________ φ ▕ ＼ ╳ ╳ ／ ▏ ↑ ▕ ╳ ╳ ╳ α ▏ ∣ ▕ ／ ╳ ╳ ＼ ▏ ∣ ▕ ／ ／ ╳ ＼ ▏ ——→ ψ ————————————————— ﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏ ︴ ╳ ╳ ╳ ╳ ╳ ︴ ︴ ╳ ╳ ╳ ╳ ╳ ╳ ︴ ╳ ╳ ╳ ╳ ╳ ╳ ╳︴ ︴ ╳ ╳ ╳ ╳ ╳ ╳ ︴ ︴ ╳ ╳σ↖↗╳ ╳ ╳︴ ︴ ╳ ╳ ——— ╳ ╳ ︴ ︴ ↖︴ ︴↗σ ╳︴ ︴ ╳ ↙︴ ︴↘ ╳ ︴ ╳ ╳ α︴ ︴ ╳ ╳︴ ︴ ╳ ╳ ——— ╳ ╳ ︴ ︴ ╳ ╳↙↘α╳ ╳ ╳︴ ︴ ╳ ╳ ╳ ╳ ╳ ╳ ︴ ︴ ╳ ╳ ╳ ╳ ╳ ╳︴ ﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌ 2.when a 45 degrees strain gage rosette is cemented to a pressure vessel with (ε-gage) being parallel to the longitudinal direction(x-axis),the following data is obtianed:εa= 1000*10^-6 ,εc=4250*10^-6.Determine from a Mohr circle, (1)εb,(2)the maximum in=plane(x-y plane)shear strain,(3)the(absolute)maximum shear strain,(4)and show the properly oriented(with respect th x-axis)strain element for above three cases.(40%) ———————————————— ▏ ∣Y 。 ▏ ▏ ＿＿ 45 ╱╳ ▏ ▏ ∣∥∣ ╱╱╱ ▏ ▏ ∣∥∣ ╳╱ 。 ▏ ▏ ▕ ＿＿ 45 ▏ ▏ ▕▁▁▁∣▁ ▏ ▏ ＿＿∣ X ▏ ————————————————— --

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