- #1

Dell

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**please help urgent!**

in the following question,

E=65 GPa

V=0.3

find the new length of the arc BD??

i have found the stresses

xx=-56Mpa

yy=0

xy=-28Mpa

using hookes law i can find the strains

xx=-8.615e-5

yy=2.58e-4

0.5*xy==-1.12e-3

but how do i calculate the change in the arc using this? i would know how to solve this if i had some kind of angular strain- i need to use a polar system not Cartesian. is there any way to do this?

also how do i know the new angle DAB? i know that the XY axis' new angle is 90.06417, and the n,t system (axes tilted 45 degrees to XY) is also 90.06417 but how do i find DAB,? generally is there any way of knowing how the axis is strained, for example, has the X axis dropped 0.06417 degrees, or the Y axis opened up 0.06417 degrees, or a bit each??

in this specific case can i say that since there is no yy strain the x-axis stays at the same angle?

DA*=DA(1+tt)=4.999569cm

AB*=5.0012923cm

can i do this:

using the transformation equations, i know

ε

_{nn}= (ε

_{xx}+ ε

_{yy})/2 + (ε

_{xx}- ε

_{yy})/2*cos(2ϴ) + ε

_{xx}sin(2ϴ)

since i have already found xx, yy, xy, instead of looking for a specific ε

_{nn}can i take the whole eqaution and say

ΔL=[tex]\int[/tex]ε

_{nn}dL {dL=r*dϴ}

=[tex]\int[/tex]ε

_{nn}*r*dϴ with my integral going from 0 to pi/4

is this a possibility?

the correct answer is meant to be 2.2167e-5m

how do i know whhat my lims are for integratin, i thought maybe pi/2 -> 3pi/4 but can't get it

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