Dell
Nov16-09, 01:56 AM
can anyone see where i have gone wrong? i am talking about question 4.17 below
http://lh5.ggpht.com/_H4Iz7SmBrbk/SwEB0MVvMyI/AAAAAAAAB_Q/Uy80NKhkTOI/Capture.JPG
what i did was define \epsilon1 \epsilon2 and \epsilon3
\epsilonx=\epsilon1
\epsilony=\epsilon3
2\epsilonxy=2\epsilon2-\epsilon1-\epsilon3
\sigmax=\frac{E}{(1+\nu)(1-2\nu)}*[(1-\nu)\epsilon1+\nu\epsilon3]
\sigmay=\frac{E}{(1+\nu)(1-2\nu)}*[(1-\nu)\epsilon3+\nu\epsilon1]
\sigmaxy=G*2*\epsilonxy=\frac{E}{2(1+\nu)}(2\epsil on2-\epsilon1-\epsilon3)
---\frac{E}{2(1+\nu)}=A---
now to find the principal stresses
\sigma=\frac{\sigmax + \sigmay}{2} +- \sqrt{\frac{\sigmax - \sigmay}{2}}^2+\sigmaxy^2
after plugging all the sigma's in i get
=A*(\epsilon1+\epsilon3)/(1-2\nu) +- \sqrt{A^2*(\epsilon1-\epsilon3)^2+(A*((2\epsilon2-\epsilon1-\epsilon3))^2}
which is all perfect except for that in the answer the denominator for the first part is : 2(1-\nu) and i get 2(1+\nu )(1-2\nu) every time, is my algebra off somewhere, am i using the wrong method or could they have a mistake in the answer??
http://lh5.ggpht.com/_H4Iz7SmBrbk/SwEB0MVvMyI/AAAAAAAAB_Q/Uy80NKhkTOI/Capture.JPG
what i did was define \epsilon1 \epsilon2 and \epsilon3
\epsilonx=\epsilon1
\epsilony=\epsilon3
2\epsilonxy=2\epsilon2-\epsilon1-\epsilon3
\sigmax=\frac{E}{(1+\nu)(1-2\nu)}*[(1-\nu)\epsilon1+\nu\epsilon3]
\sigmay=\frac{E}{(1+\nu)(1-2\nu)}*[(1-\nu)\epsilon3+\nu\epsilon1]
\sigmaxy=G*2*\epsilonxy=\frac{E}{2(1+\nu)}(2\epsil on2-\epsilon1-\epsilon3)
---\frac{E}{2(1+\nu)}=A---
now to find the principal stresses
\sigma=\frac{\sigmax + \sigmay}{2} +- \sqrt{\frac{\sigmax - \sigmay}{2}}^2+\sigmaxy^2
after plugging all the sigma's in i get
=A*(\epsilon1+\epsilon3)/(1-2\nu) +- \sqrt{A^2*(\epsilon1-\epsilon3)^2+(A*((2\epsilon2-\epsilon1-\epsilon3))^2}
which is all perfect except for that in the answer the denominator for the first part is : 2(1-\nu) and i get 2(1+\nu )(1-2\nu) every time, is my algebra off somewhere, am i using the wrong method or could they have a mistake in the answer??