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
已知條件: P=30psi t=0.01in D=2in
E=30×10^6 ν=0.3 F=100lb
求周向應力:σh，縱向應力: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 (主應變)
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
※以上請問Prob.1-5:
(1)如果將兩端封壁面拿掉，不一樣在那?
(2)如果其中一個軸向負荷改變，則要如何計算之?
煩請版友們，幫忙解題，萬分感謝^^!!
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