作者g96117XX (Jane)
看板NTHU-MSE11
标题[问题] 材料力学
时间Tue Apr 15 22:20:19 2008
Prob.1-3
A thin-walled tube, capped on the ends, is slowly loaded by internal pressure.
During elastic deformation, what happens to the length of the tube, assuming
end effects are negligible?
Prob.1-5
Consider a steel tube, such as the one in Prob.1-3, whose diameter is 2in.
and wall thickness is 0.010in. If it is loaded axially by 100lb in tension
and exposed to an internal pressure of 30 psi, determine the magnitude of
each principal strain (elastic deformations are to be assumed).
解Prob.1-5
已知条件: P=30psi t=0.01in D=2in
E=30×10^6 ν=0.3 F=100lb
求周向应力:σh，纵向应力:σl
σh = σy = (p˙r)/t = (30×1)/0.01 = 3000psi
σl = σx = (p˙r)/(2t) + F/A = 1500 + (100×4)/(π×2^2)=1531.83psi
由Generalized Hook's Law 求 εx，εy (主应变)
εx = (1/E)σx － (ν/E)σy
εx = [1/(30×10^6)] × 1531.83 － [0.3/(30×10^6)] × 3000= 2.106×10^-5
εy = [－(ν/E)σx] + [(1/E)σy]
εy = [－0.3/(30×10^6)] × 1531.83 + [1/(30×10^6)] ×3000 = 8.468×10^-5
※以上请问Prob.1-5:
(1)如果将两端封壁面拿掉，不一样在那?
(2)如果其中一个轴向负荷改变，则要如何计算之?
烦请版友们，帮忙解题，万分感谢^^!!
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