# 45 degree strain-stress rosette

1. Nov 16, 2009

### Dell

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 [Broken]

what i did was define $$\epsilon$$1 $$\epsilon$$2 and $$\epsilon$$3
$$\epsilon$$x=$$\epsilon$$1
$$\epsilon$$y=$$\epsilon$$3
2$$\epsilon$$xy=2$$\epsilon$$2-$$\epsilon$$1-$$\epsilon$$3

$$\sigma$$x=$$\frac{E}{(1+\nu)(1-2\nu)}$$*[(1-$$\nu$$)$$\epsilon$$1+$$\nu$$$$\epsilon$$3]

$$\sigma$$y=$$\frac{E}{(1+\nu)(1-2\nu)}$$*[(1-$$\nu$$)$$\epsilon$$3+$$\nu$$$$\epsilon$$1]

$$\sigma$$xy=G*2*$$\epsilon$$xy=$$\frac{E}{2(1+\nu)}$$(2$$\epsilon$$2-$$\epsilon$$1-$$\epsilon$$3)

---$$\frac{E}{2(1+\nu)}$$=A---

now to find the principal stresses

$$\sigma$$=$$\frac{\sigmax + \sigmay}{2}$$ +- $$\sqrt{\frac{\sigmax - \sigmay}{2}}^2+$$\sigma$$xy^2$$

after plugging all the sigma's in i get

=A*($$\epsilon$$1+$$\epsilon$$3)/(1-2$$\nu$$) +- $$\sqrt{A^2*(\epsilon1-\epsilon3)^2+(A*((2$$\epsilon$$2-$$\epsilon$$1-$$\epsilon$$3))^2}$$

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??

Last edited by a moderator: May 4, 2017
2. Nov 16, 2009

### Dell

sorry about the LATEX work, i see it now, looks terrible, i will try to fix it