课程名称︰材料力学 课程性质︰必修 课程教师︰郑荣和 开课学院：工学院 开课系所︰机械系 考试日期（年月日）︰100/4/20 考试时限（分钟）：50分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : <<需画图说明或 Free Body Diagram 而未画者，扣该题1/5分数>> (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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